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+ + + + + + + + + + + + + Lecture 7: Bayesian Vector Autoregressions + + + + + + + + + + + + + + + +

+
+ +
+

Lecture 7: Bayesian Vector Autoregressions

+ +
+
+
+by Tomasz Woźniak +
+
+
+ +
+
+

+

\[ \]

+

Vector Autoregressions

+

Three Useful Distributions

+

Bayesian Estimation

+

Minnesota and Dummy Observations Prior

+

Bayesian Estimation for Hierarchical Prior

+

Bayesian Forecasting using VARs

+

US Data Analysis Using R Package bsvarSIGNs

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+
+

+

+
+
+

Materials

+

\[ \]

+

Lecture Slides as a Website

+

A Dedicated Reading Woźniak (2016, AERev)

+

Quarto document template for your own Australian data forecasting

+

GitHub repo to reproduce the slides and results

+

A Kahoot! Quiz

+

Tasks

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+
+

Vector Autoregressions

+
+
+

Vector Autoregressions

+
    +
  • go-to models for forecasting
  • +
+
+
    +
  • simple: linear and Gaussian
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  • extendible: featuring many variations in specification +
      +
    • non-normality
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    • heteroskedasticity
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    • time-varying parameters
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    • Bayesian
    • +
  • +
  • interpretable +
      +
    • Granger causality
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    • spillovers
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    • networks
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    • structural
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  • +
  • Proposed by Sims (1980)
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+
+ +
+
+

VAR(p) Model

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Model equations.

+

\[\begin{align*} +y_t &= \mathbf{A}_1 y_{t-1} + \dots + \mathbf{A}_p y_{t-p} + \boldsymbol\mu_0 + \epsilon_t\\ +\epsilon_t|Y_{t-1} &\sim iidN\left(\mathbf{0}_N,\mathbf\Sigma\right) +\end{align*}\] for \(t=1,\dots,T\)

+
+ +

Notation.

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    +
  • \(y_t\) is an \(N\times 1\) vector of observations at time \(t\)
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  • \(\mathbf{A}_i\) - \(N\times N\) matrix of autoregressive slope parameters
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  • \(\boldsymbol\mu_0\) - \(N\times 1\) vector of constant terms
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  • \(\epsilon_t\) - \(N\times 1\) vector of error terms - a multivariate white noise process
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  • \(Y_{t-1}\) - information set collecting observations on} \(y\) up to time \(t-1\)
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  • \(\mathbf\Sigma\) - \(N\times N\) covariance matrix of the error term
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+
+ +
+
+

A Bivariate VAR(2) Model

+

Let the number of variable \(N=2\) and the lag order \(p=2\).

+

Then, the model equation is:

+\[\begin{align*} +\begin{bmatrix} y_{1.t} \\ y_{2.t} \end{bmatrix} +&= \begin{bmatrix} \mathbf{A}_{1.11} & \mathbf{A}_{1.12} \\ \mathbf{A}_{1.21} & \mathbf{A}_{1.22} \end{bmatrix} \begin{bmatrix} y_{1.t-1} \\ y_{2.t-1} \end{bmatrix} ++ \begin{bmatrix} \mathbf{A}_{2.11} & \mathbf{A}_{2.12} \\ \mathbf{A}_{2.21} & \mathbf{A}_{2.22} \end{bmatrix} \begin{bmatrix} y_{1.t-2} \\ y_{2.t-2} \end{bmatrix} + \begin{bmatrix} \boldsymbol\mu_{0.1} \\ \boldsymbol\mu_{0.2} \end{bmatrix} + \begin{bmatrix} \epsilon_{1.t} \\ \epsilon_{2.t} \end{bmatrix}\\[2ex] +\begin{bmatrix} \epsilon_{1.t} \\ \epsilon_{2.t} \end{bmatrix} &\Big|Y_{t-1} \sim iid N_2\left( \begin{bmatrix} 0\\ 0\end{bmatrix}, \begin{bmatrix}\boldsymbol\sigma_1^2 & \boldsymbol\sigma_{12} \\ \boldsymbol\sigma_{12} & \boldsymbol\sigma_2^2\end{bmatrix} \right) +\end{align*}\] +
+

Task:

+

Perform the matrix multiplications and write out the equations for \(y_{1.t}\) and \(y_{2.t}\).

+ +
+
+
+

Three Useful Distributions

+
+
+

Matrix-Variate Normal Distribution

+

A \(K\times N\) matrix \(\mathbf{A}\) is said to follow a matrix-variate normal distribution: \[ \mathbf{A} \sim MN_{K\times N}\left( M, Q, P \right), \] where

+
    +
  • \(M\) - a \(K\times N\) matrix of the mean
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  • \(Q\) - a \(N\times N\) row-specific covariance matrix
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  • \(P\) - a \(K\times K\) column-specific covariance matrix
  • +
+

if \(\text{vec}(\mathbf{A})\) is multivariate normal: \[ \text{vec}(\mathbf{A}) \sim N_{KN}\left( \text{vec}(M), Q\otimes P \right) \]

+

Density function.

+\[\begin{align*} +MN_{K\times N}\left( M, Q, P \right) &\propto \exp\left\{ -\frac{1}{2}\text{tr}\left[ Q^{-1}(\mathbf{A}-M)'P^{-1}(\mathbf{A}-M) \right] \right\} +\end{align*}\] +
    +
  • \(\text{tr}()\) is a trace of a matrix - a sum of diagonal elements
  • +
+ +
+
+

Inverse Wishart Distribution

+

An \(N\times N\) square symmetric and positive definite matrix \(\mathbf\Sigma\) follows an inverse Wishart distribution: \[ \mathbf\Sigma \sim IW_{N}\left( S, \nu \right) \] where

+
    +
  • \(S\) is \(N\times N\) positive definite symmetric matrix called the scale matrix
  • +
  • \(\nu \geq N\) denotes degrees of freedom, if its density is given by:
  • +
+

Density function.

+\[\begin{align*} +IW_{N}\left( S, \nu \right) \propto \text{det}(\mathbf\Sigma)^{-\frac{\nu+N+1}{2}}\exp\left\{ -\frac{1}{2}\text{tr}\left[ \mathbf\Sigma^{-1} S \right] \right\} +\end{align*}\] + +
+
+

Normal-Inverse Wishart Distribution

+\[\begin{align*} +\mathbf{A}|\mathbf\Sigma &\sim MN_{K\times N}\left( M, \mathbf\Sigma, P \right)\\ +\mathbf\Sigma &\sim IW_{N}\left( S, \nu \right) +\end{align*}\] +

then the joint distribution of \((\mathbf{A},\mathbf\Sigma)\) is normal-inverse Wishart \[ +p(\mathbf{A},\mathbf\Sigma) = NIW_{K\times N}\left( M,P,S,\nu\right) +\]

+

Density function.

+\[\begin{align*} +NIW_{K\times N}\left( M,P,S,\nu\right) \propto &\text{det}(\mathbf{\Sigma})^{-(\nu+N+K+1)/2}\exp\left\{ -\frac{1}{2}\text{tr}\left[ \mathbf{\Sigma}^{-1} S \right] \right\}\\ +&\times\exp\left\{ -\frac{1}{2}\text{tr}\left[ \mathbf{\Sigma}^{-1} (\mathbf{A}-M)'P^{-1}(\mathbf{A}-M) \right] \right\} +\end{align*}\] + +
+
+

Example: Error Term Distribution

+

The model assumptions state: \[\begin{align*} +\epsilon_t|Y_{t-1} &\sim iidN_N\left(\mathbf{0}_N,\mathbf\Sigma\right) +\end{align*}\]

+

Collect error term vectors in a \(T\times N\) matrix: \[\underset{(T\times N)}{E}= \begin{bmatrix}\epsilon_1 & \epsilon_2 & \dots & \epsilon_{T}\end{bmatrix}'\]

+

Error term matrix is matrix-variate distributed: \[\begin{align*} +E|X &\sim MN_{T\times N}\left(\mathbf{0}_{T\times N},\mathbf\Sigma, I_T\right) +\end{align*}\]

+
+ +

Tasks: what is

+
    +
  • the covariance of \(\text{vec}(E)\)
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  • the distribution of the first equation error terms \(\begin{bmatrix}\epsilon_{1.1} &\dots&\epsilon_{1.T}\end{bmatrix}'\)
  • +
+
+ +
+
+

Example: Univariate Inverse Wishart Distribution

+

The inverse Wishart density function is proportional to: \[\begin{align*} +\text{det}(\mathbf\Sigma)^{-\frac{\nu+N+1}{2}}\exp\left\{ -\frac{1}{2}\text{tr}\left[ \mathbf\Sigma^{-1} S \right] \right\} +\end{align*}\]

+

Consider a case where:

+
    +
  • \(N=1\)
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  • the matrix \(\mathbf\Sigma\) is replaced by a scalar \(\boldsymbol\sigma^2\)
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+
+ +

Task:

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    +
  • write out the kernel of the density function for \(\boldsymbol\sigma^2\)
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  • the kernel of what density it represents?
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+
+ +
+
+

Bayesian Estimation

+
+
+

The model in Matrix Notation

+

VAR(p) model.

+\[\begin{align*} +y_t &= \mathbf{A}_1 y_{t-1} + \dots + \mathbf{A}_p y_{t-p} + \boldsymbol\mu_0 + \epsilon_t\\ +\epsilon_t|Y_{t-1} &\sim iidN_N\left(\mathbf{0}_N,\mathbf\Sigma\right) +\end{align*}\] +

Matrix notation.

+\[\begin{align*} +Y &= X\mathbf{A} + E\\ +E|X &\sim MN_{T\times N}\left(\mathbf{0}_{T\times N},\mathbf\Sigma, I_T\right) +\end{align*}\] +
+

\[ +\underset{(K\times N)}{\mathbf{A}}=\begin{bmatrix} \mathbf{A}_1'\\ \vdots \\ \mathbf{A}_p' \\ \boldsymbol\mu_0' \end{bmatrix} \quad +\underset{(T\times N)}{Y}= \begin{bmatrix}y_1' \\ y_2'\\ \vdots \\ y_T'\end{bmatrix} \quad +\underset{(K\times1)}{x_t}=\begin{bmatrix} y_{t-1}\\ \vdots \\ y_{t-p}\\ 1 \end{bmatrix}\quad +\underset{(T\times K)}{X}= \begin{bmatrix}x_1' \\ x_2' \\ \vdots \\ x_{T}'\end{bmatrix} \quad +\underset{(T\times N)}{E}= \begin{bmatrix}\epsilon_1' \\ \epsilon_2' \\ \vdots \\ \epsilon_{T}'\end{bmatrix} +\] where \(K=pN+1\)

+
+ +
+
+

The model as Predictive Density

+

VAR model.

+\[\begin{align*} +Y &= X\mathbf{A} +E\\ +E|X &\sim MN_{T\times N}\left(\mathbf{0}_{T\times N},\mathbf\Sigma, I_T\right) +\end{align*}\] +

Predictive density.

+\[\begin{align*} +Y|X,\mathbf{A}, \mathbf{\Sigma} &\sim MN_{T\times N}\left(X\mathbf{A},\mathbf{\Sigma},I_T\right) +\end{align*}\] + +
+
+

Likelihood Function

+

Predictive density.

+\[\begin{align*} +Y|X,\mathbf{A}, \mathbf{\Sigma} &\sim MN_{T\times N}\left(X\mathbf{A},\mathbf{\Sigma},I_T\right) +\end{align*}\] +

Likelihood function.

+\[\begin{align*} +L\left(\mathbf{A},\mathbf{\Sigma}|Y,X\right)&\propto\text{det}(\mathbf{\Sigma})^{-\frac{T}{2}}\exp\left\{-\frac{1}{2}\text{tr}\left[\mathbf{\Sigma}^{-1}(Y-X\mathbf{A})'(Y-X\mathbf{A})\right]\right\} +\end{align*}\] + +
+
+

Likelihood Function as NIW

+

Define the MLE: \(\widehat{A}=(X'X)^{-1}X'Y\)

+

Perform simple transformation of the likelihood

+\[\begin{align*} +L\left(\mathbf{A},\mathbf{\Sigma}|Y,X\right)&\propto\text{det}(\mathbf{\Sigma})^{-\frac{T}{2}}\exp\left\{-\frac{1}{2}\text{tr}\left[\mathbf{\Sigma}^{-1}(Y-X\mathbf{A})'(Y-X\mathbf{A})\right]\right\}\\ +&=\text{det}(\mathbf{\Sigma})^{-\frac{T}{2}}\\ +&\quad\times\exp\left\{ -\frac{1}{2}\text{tr}\left[\mathbf{\Sigma}^{-1}(\mathbf{A}-\widehat{A})'X'X(\mathbf{A}-\widehat{A}) \right] \right\}\\ +&\quad\times \exp\left\{ -\frac{1}{2}\text{tr}\left[ \mathbf{\Sigma}^{-1}(Y-X\widehat{A})'(Y-X\widehat{A}) \right] \right\} +\end{align*}\] +

Under the likelihood, \((\mathbf{A},\mathbf{\Sigma})\) are normal-inverse Wishart distributed:

+\[\begin{align*} +L\left( \mathbf{A},\mathbf{\Sigma}|Y,X \right) &= NIW_{K\times N}\left(\widehat{A},(X'X)^{-1},(Y-X\widehat{A})'(Y-X\widehat{A}), T-N-K-1 \right) +\end{align*}\] + +
+
+

Prior Distribution

+

Construction.

+

A natural-conjugate prior leads to joint posterior distribution for \((\mathbf{A},\mathbf{\Sigma})\) of the same form \[\begin{align*} +p\left( \mathbf{A}, \mathbf{\Sigma} \right) &= p\left( \mathbf{A}| \mathbf{\Sigma} \right)p\left( \mathbf{\Sigma} \right)\\ +\mathbf{A}|\mathbf{\Sigma} &\sim MN_{K\times N}\left( \underline{A},\mathbf{\Sigma},\underline{V} \right)\\ +\mathbf{\Sigma} &\sim IW_N\left( \underline{S}, \underline{\nu} \right) +\end{align*}\]

+

Kernel.

+\[\begin{align*} +p\left( \mathbf{A},\mathbf{\Sigma} \right) +&\propto \text{det}(\mathbf{\Sigma})^{-\frac{N+K+\underline{\nu}+1}{2}}\\ +&\quad\times\exp\left\{ -\frac{1}{2}\text{tr}\left[ \mathbf{\Sigma}^{-1}(\mathbf{A}-\underline{A})'\underline{V}^{-1}(\mathbf{A}-\underline{A}) \right] \right\}\\ +&\quad\times \exp\left\{ -\frac{1}{2}\text{tr}\left[ \mathbf{\Sigma}^{-1}\underline{S} \right] \right\} +\end{align*}\] + +
+
+

Posterior Distribution

+

Bayes Rule.

+\[\begin{align*} +p\left( \mathbf{A}, \mathbf{\Sigma}|Y,X \right) &\propto L(\mathbf{A},\mathbf{\Sigma}|Y,X)p\left( \mathbf{A}, \mathbf{\Sigma} \right)\\ +&= L(\mathbf{A},\mathbf{\Sigma}|Y,X)p\left( \mathbf{A}| \mathbf{\Sigma} \right)p\left( \mathbf{\Sigma} \right) +\end{align*}\] +

Kernel.

+\[\begin{align*} +p\left( \mathbf{A},\mathbf{\Sigma} |Y,X\right) +&\propto \text{det}(\mathbf{\Sigma})^{-\frac{T}{2}}\exp\left\{-\frac{1}{2}\text{tr}\left[\mathbf{\Sigma}^{-1}(Y-X\mathbf{A})'(Y-X\mathbf{A})\right]\right\}\\ +& \quad\times\text{det}(\mathbf{\Sigma})^{-\frac{N+K+\underline{\nu}+1}{2}}\exp\left\{ -\frac{1}{2}\text{tr}\left[ \mathbf{\Sigma}^{-1}\underline{S} \right] \right\}\\ +&\quad\times\exp\left\{ -\frac{1}{2}\text{tr}\left[ \mathbf{\Sigma}^{-1}(\mathbf{A}-\underline{A})'\underline{V}^{-1}(\mathbf{A}-\underline{A}) \right] \right\} +\end{align*}\] + +
+
+

Joint Posterior Distribution

+

Conditional and marginal.

+\[\begin{align*} +p\left( \mathbf{A}, \mathbf{\Sigma}|Y,X \right) &= p(\mathbf{A}|Y,X,\mathbf{\Sigma})p\left( \mathbf{\Sigma}|Y,X \right)\\[2ex] +p(\mathbf{A}|Y,X,\mathbf{\Sigma}) &= MN_{K\times N}\left( \overline{A},\mathbf{\Sigma},\overline{V} \right)\\ +p(\mathbf{\Sigma}|Y,X) &= IW_N\left( \overline{S}, \overline{\nu} \right) +\end{align*}\] +

Posterior parameters.

+\[\begin{align*} +\overline{V}&= \left( X'X + \underline{V}^{-1}\right)^{-1} \\ +\overline{A}&= \overline{V}\left( X'Y + \underline{V}^{-1}\underline{A} \right)\\ +\overline{\nu}&= T+\underline{\nu}\\ +\overline{S}&= \underline{S}+Y'Y + \underline{A}'\underline{V}^{-1}\underline{A} - \overline{A}'\overline{V}^{-1}\overline{A} +\end{align*}\] + +
+
+

Posterior Mean of \(\mathbf{A}\)

+

Posterior mean of matrix \(\mathbf{A}\) is: \[\begin{align*} +\overline{A} &= \overline{V}\left( X'Y + \underline{V}^{-1}\underline{A} \right)\\[2ex] +&= \overline{V}\left( X'X\widehat{A} + \underline{V}^{-1}\underline{A} \right)\\[2ex] +&= \overline{V} X'X\widehat{A} + \overline{V}\underline{V}^{-1}\underline{A} +\end{align*}\] a linear combination of the MLE \(\widehat{A}\) and the prior mean \(\underline{A}\)

+

Note that: \[ +\overline{V} X'X + \overline{V}\underline{V}^{-1} = \overline{V} ( X'X + \underline{V}^{-1}) = I_K +\]

+

Play with the posterior in an interactive graph

+ +
+
+

Marginal Data Density

+

According to Bayes Rule, the kernel of the posterior is normalised by the Marginal Data Density \(p(data)\):

+

\[ +p\left( \mathbf{A}, \mathbf{\Sigma}| data \right) = \frac{L(\mathbf{A},\mathbf{\Sigma}| data)p\left( \mathbf{A}, \mathbf{\Sigma} \right)}{p(data)} +\]

+

For Bayesian VARs the posterior is known \[ +p\left( \mathbf{A}, \mathbf{\Sigma}| data \right) = MNIW\left(\overline{A},\overline{V}, \overline{S}, \overline{\nu} \right) +\]

+

and so is the analytical formula for the MDD: \[p(data)\]

+

This can be used to our advantage!

+ +
+
+

Minnesota and Dummy Observations Prior

+
+
+

Minnesota Prior

+

Sims, Litterman, Doan (1984) proposed an interpretable way of setting the hyper-parameters on the NIW prior \(\underline{A}\), \(\underline{V}\), \(\underline{S}\), and \(\underline{\nu}\) for macroeconomic data.

+
+

\[ \] The prior reflects the following stylised facts about macro time series:

+
    +
  • the data are unit-root non-stationary
  • +
  • the effect of more lagged variables should be smaller and smaller
  • +
  • the effect of other variables lags should be less than that of own lags
  • +
+ +
+
+
+

Minnesota Prior

+

Inverse-Wishart prior.

+\[\begin{align*} +\mathbf{\Sigma} &\sim IW_N\left( \underline{S}, \underline{\nu} \right) +\end{align*}\] +

Set

+\[\begin{align*} +\underline{S} &= \begin{bmatrix} +\psi_1 &0 &\dots & 0 \\ +0 & \psi_2 &\dots & 0\\ +\vdots &\vdots&\ddots& \vdots\\ +0&0&\dots&\psi_N +\end{bmatrix}\\[2ex] +\underline{\nu}&= N+2 +\end{align*}\] +

Hyper-parameters.

+

\(\psi =(\psi_1, \dots, \psi_N)\) have to be chosen (or estimated)

+ +
+
+

Minnesota Prior

+

Matrix-Variate Normal prior.

+\[\begin{align*} +\mathbf{A}|\mathbf{\Sigma} &\sim MN_{K\times N}\left( \underline{A},\mathbf{\Sigma},\underline{V} \right) +\end{align*}\] +

Set \[\begin{align*} +\underline{A} &= \begin{bmatrix} I_N \\ \mathbf{0}_{((p-1)N +1)\times N}\end{bmatrix}& +\underline{V}_{ij} &= \left\{\begin{array} (\lambda ^ 2 / (\psi_k l^2) &\text{ for }i=j,\text{ and } i\neq pN+1 \\ +\lambda^2 &\text{ for }i=j,\text{ and } i= pN+1 \\ +0&\text{ for } i\neq j +\end{array}\right. +\end{align*}\]

+

for \(\quad l = 1+\text{floor}((i-1)/N) \quad\text{and }\quad k = i - (l-1)N\)

+

Hyper-parameters.

+

\(\lambda^2\) has to be chosen (or estimated)

+ +
+
+

Dummy Observations Prior

+

Idea.

+
    +
  1. Generate artificial data matrices with \(T_d\) rows \(Y^*\) and \(X^*\)
  2. +
  3. Append them to the original data matrices \(Y\) and \(X\) respectively.
  4. +
+
+ +

Implied prior distribution.

+

Use Bayes Rule to derive the joint prior of \((\mathbf{A},\mathbf\Sigma)\) given \(Y^*\) and \(X^*\).

+

It is given by the MNIW distribution:

+

\[\begin{align*} +p\left( \mathbf{A}, \mathbf{\Sigma}|Y^*,X^* \right) &= MNIV_{K\times N}\left( \underline{A}^*,\underline{V}^*, \underline{S}^*, \underline{\nu}^* \right) +\end{align*}\] \[\begin{align*} +\underline{V}^*&= \left( X^{*\prime}X^* + \underline{V}^{-1}\right)^{-1} & \underline{A}^*&= \underline{V}^*\left( X^{*\prime}Y^* + \underline{V}^{-1}\underline{A} \right)\\ +\underline{\nu}^*&= T_d+\underline{\nu} & \underline{S}^*&= \underline{S}+Y^{*\prime}Y^* + \underline{A}'\underline{V}^{-1}\underline{A} - \underline{A}^{*\prime}\underline{V}^{*-1}\underline{A}^* +\end{align*}\]

+
+ +
+
+

Dummy Observations Prior

+

Let a \(p\times N\) matrix \(Y_0\) denote the initial observations, that is, the first \(p\) observations of the available time series.

+

Let an \(N\)-vector \(\bar{Y}_0\) denote its columns’ means.

+
+ +

Sum-of-coefficients prior.

+

Generate additional \(N\) rows by \[ +Y^+ = \text{diag}\left(\frac{\bar{Y}_0}{\mu}\right) \quad\text{ and }\quad X^+ = \begin{bmatrix}\mathbf{0}_N & Y^+ & \dots & Y^+ \end{bmatrix} +\]

+
    +
  • \(\mu\) is a hyper-parameter to be chosen (or estimated)
  • +
  • if \(\mu \rightarrow 0\) the prior implies the presence of a unit root in each equation and rules out cointegration
  • +
  • if \(\mu \rightarrow\infty\) the prior becomes uninformative
  • +
+
+ +
+
+

Dummy Observations Prior

+

Dummy-initial-observation prior.

+

Generate an additional row by \[ +Y^{++} = \frac{\bar{Y}_0'}{\delta} \quad\text{ and }\quad X^{++} = \begin{bmatrix}\frac{1}{\delta} & Y^{++} & \dots & Y^{++} \end{bmatrix} +\]

+
    +
  • hyper-parameter \(\delta\) is to be chosen (or estimated)
  • +
  • if \(\delta \rightarrow 0\) all the variables of the VAR are forced to be at their unconditional mean, or the system is characterized by the presence of an unspecified number of unit roots without drift (cointegration)
  • +
  • if \(\delta \rightarrow\infty\) the prior becomes uninformative
  • +
+
+ +

Combining dummy observations.

+

\[ +Y^* = \begin{bmatrix}Y^+ \\ Y^{++} \end{bmatrix}\quad\text{ and }\quad +X^* = \begin{bmatrix}X^+ \\ X^{++} \end{bmatrix} +\]

+
+ +
+
+

Dummy Observations Prior

+

Task.

+

Suppose that:

+
    +
  • \(\bar{Y}_0 = \begin{bmatrix}1&2\end{bmatrix}'\)
  • +
  • \(\mu = 0.5\)
  • +
  • \(\delta = 3\)
  • +
  • \(p = 1\)
  • +
+

Write out the matrices \(Y^*\) and \(X^*\) of dimensions \(2\times 3\) and \(3\times 3\) respectively.

+ +
+
+

Bayesian Estimation for Hierarchical Prior

+
+
+

Bayesian Estimation for Hierarchical Prior

+

Hyper-parameters \(\psi\), \(\lambda\), \(\mu\) and \(\delta\) can be fixed to values chosen by the econometrician.

+

Hierarcical prior.

+

A better idea is to assume priors for these hyper-parameters and estimate them as in Giannone, Lenza, Primiceri (2015).

+

Extend the existing prior to: \[\begin{align*} +p\left( \mathbf{A}, \mathbf{\Sigma}|Y^*,X^*,\psi,\lambda,\mu,\delta \right) &= MNIV_{K\times N}\left( \underline{A}^*,\underline{V}^*, \underline{S}^*, \underline{\nu}^* \right) +\end{align*}\] And specify: \[\begin{align*} +\psi_n &\sim IG\left(0.02^2, 0.02^2\right)\\ +\lambda &\sim G\left(0.2,2\right)\\ +\mu &\sim G\left(1,2\right)\\ +\delta &\sim G\left(1,2\right) +\end{align*}\]

+ +
+
+

Bayesian Estimation for Hierarchical Prior

+

Giannone, Lenza, Primiceri (2015) propose the following estimation procedure:

+

Step 1: Estimate \((\psi,\lambda,\mu,\delta)\) using a random-walk Metropolis-Hastings sampler

+
    +
  • Sample these hyper-parameters marginally on \((\mathbf{A},\mathbf\Sigma)\)
  • +
  • extend the conditioning of Marginal Data Density: \[ p(data|\psi,\lambda,\mu,\delta)\]
  • +
  • apply Bayes Rule to obtain the kernel of the posterior:
  • +
+

\[ p(\psi,\lambda,\mu,\delta|data) \propto p(\psi,\lambda,\mu,\delta)p(data|\psi,\lambda,\mu,\delta)\] - Use an \((N+3)\)-variate Student-t distribution as the candidate generating density

+ +
+
+

Bayesian Estimation for Hierarchical Prior

+

Step 2: For each draw of \((\psi,\lambda,\mu,\delta)\) sample the corresponding draw of \((\mathbf{A},\mathbf{\Sigma})\)

+

Use the MNIW posterior derived for the implied prior:

+\[\begin{align*} +p\left( \mathbf{A}, \mathbf{\Sigma}|Y,X, Y^*,X^* \right) &= MNIW_{K\times N}\left( \overline{A}^*,\overline{V}^*,\overline{S}^*, \overline{\nu}^* \right)\\[2ex] +\overline{V}^*&= \left( X'X + \underline{V}^{*-1}\right)^{-1} \\ +\overline{A}^*&= \overline{V}^*\left( X'Y + \underline{V}^{*-1}\underline{A}^* \right)\\ +\overline{\nu}^*&= T+\underline{\nu}^*\\ +\overline{S}^*&= \underline{S}^*+Y'Y + \underline{A}^{*\prime}\underline{V}^{*-1}\underline{A}^* - \overline{A}^{*\prime}\overline{V}^{*-1}\overline{A}^* +\end{align*}\] +

R implementation.

+

Package BVAR by Kuschnig, Vashold (2021) implements this algorithm.

+ +
+
+

Bayesian Forecasting using VARs

+
+
+

The objective of economic forecasting

+ +

\(\left.\right.\)

+

… is to use the available data to provide a statistical characterisation of the unknown future values of quantities of interest.

+

\(\left.\right.\)

+

The full statistical characterisation of the unknown future values of random variables is given by their predictive density.

+

\(\left.\right.\)

+

Simplified outcomes in a form of statistics summarising the predictive densities are usually used in decision-making processes.

+

\(\left.\right.\)

+

Summary statistics are also communicated to general audiences.

+
+
+

One-Period Ahead Predictive Density

+ +

VAR(p) model.

+

\[\begin{align*} +y_t &= \mathbf{A}_1 y_{t-1} + \dots + \mathbf{A}_p y_{t-p} + \boldsymbol\mu_0 + \epsilon_t\\[2ex] +\epsilon_t|Y_{t-1} &\sim iidN_N\left(\mathbf{0}_N,\mathbf\Sigma\right)\\ +& +\end{align*}\]

+

One-Period Ahead Conditional Predictive Density

+

… is implied by the model formulation: \[\begin{align*} +y_{t+h}|Y_{t+h-1},\mathbf{A},\mathbf\Sigma &\sim N_N\left(\mathbf{A}_1 y_{t+h-1} + \dots + \mathbf{A}_p y_{t+h-p} + \boldsymbol\mu_0,\mathbf\Sigma\right) +\end{align*}\]

+
+
+

One-Period Ahead Predictive Density

+ +

\(\left.\right.\)

+

Bayesian forecasting takes into account the uncertainty w.r.t. parameter estimation by integrating it out from the predictive density.

+

\[\begin{align*} +&\\ +p(y_{T+1}|Y,X) &= \int p(y_{T+1}|Y_{T},\mathbf{A},\mathbf\Sigma) p(\mathbf{A},\mathbf\Sigma|Y,X) d(\mathbf{A},\mathbf\Sigma)\\ & +\end{align*}\]

+
    +
  • \(p(y_{T+1}|Y,X)\) - predictive density
  • +
  • \(p(y_{T+1}|Y_{t},\mathbf{A},\mathbf\Sigma)\) - one-period-ahead conditional predictive density
  • +
  • \(p(\mathbf{A},\mathbf\Sigma|Y,X)\) - marginal posterior distribution
  • +
+
+
+

Sampling from One-Period Ahead Predictive Density

+ +

\(\left.\right.\)

+

Step 1: Sample from the posterior

+

… and obtain \(S\) draws \(\left\{ \mathbf{A}^{(s)},\mathbf\Sigma^{(s)} \right\}_{s=1}^{S}\)

+

\(\left.\right.\)

+

Step 2: Sample from the predictive density

+

In order to obtain draws from \(p(y_{T+1}|Y,X)\), for each of the \(S\) draws of \((\mathbf{A},\mathbf\Sigma)\) sample the corresponding draw of \(y_{T+1}\):

+

Sample \(y_{T+1}^{(s)}\) from \[ +N_N\left(\mathbf{A}_1^{(s)} y_{T} + \dots + \mathbf{A}_p^{(s)} y_{T-p+1} + \boldsymbol\mu_0^{(s)},\mathbf\Sigma^{(s)}\right) +\] and obtain \(\left\{y_{T+1}^{(s)}\right\}_{s=1}^{S}\)

+
+
+

\(h\)-Period Ahead Predictive Density

+ +

\(\left.\right.\)

+

This procedure can be generalised to any forecasting horizon.

+

This is an illustration for \(h=2\).

+

\[\begin{align*} +&\\ +p(y_{T+2},y_{T+1}|Y,X) +&= \int p(y_{T+2},y_{T+1}|Y_{T},\mathbf{A},\mathbf\Sigma) p(\mathbf{A},\mathbf\Sigma|Y,X) d(\mathbf{A},\mathbf\Sigma)\\[1ex] +&= \int p(y_{T+2}|y_{T+1},Y_{T},\mathbf{A},\mathbf\Sigma)p(y_{T+1}|Y_{T},\mathbf{A},\mathbf\Sigma) p(\mathbf{A},\mathbf\Sigma|Y,X) d(\mathbf{A},\mathbf\Sigma)\\ & +\end{align*}\]

+
+
+

\(h\)-Period Ahead Predictive Density

+ +

\(\left.\right.\)

+

Step 1: Sample from the posterior

+

… and obtain \(S\) draws \(\left\{ \mathbf{A}^{(s)},\mathbf\Sigma^{(s)} \right\}_{s=1}^{S}\)

+

Step 2: Sample from 1-period ahead predictive density

+

For each of the \(S\) draws, sample \(y_{T+1}^{(s)}\) from \[ +N_N\left(\mathbf{A}_1^{(s)} y_{T} + \dots + \mathbf{A}_p^{(s)} y_{T-p+1} + \boldsymbol\mu_0^{(s)},\mathbf\Sigma^{(s)}\right) +\]

+

Step 3: Sample from 2-period ahead predictive density

+

For each of the \(S\) draws, sample \(y_{T+2}^{(s)}\) from \[ +N_N\left(\mathbf{A}_1^{(s)} y_{T+1}^{(s)} + \mathbf{A}_2 y_{T} + \dots + \mathbf{A}_p^{(s)} y_{T-p+2} + \boldsymbol\mu_0^{(s)},\mathbf\Sigma^{(s)}\right) +\]

+

and obtain \(\left\{y_{T+2}^{(s)},y_{T+1}^{(s)}\right\}_{s=1}^{S}\)

+
+
+

The Bayesian VARs Quiz

+

\[ \]

+

GO TO THE GAME

+ +
+
+

US Data Analysis Using R Package BVAR

+
+
+

Data preparation

+ +
+
+
set.seed(42)
+library(BVAR)
+
+# data
+x = fred_qd[, c("GDPC1", 
+                "GDPCTPI", 
+                "FEDFUNDS")]
+x = fred_transform(
+  x, 
+  codes = c(4, 4, 1)
+)
+
+plot.ts(
+  x, 
+  main = "",
+  col = "#F500BD",
+  lwd = 4,
+  cex.axis = 2,
+  cex.lab = 2
+)
+
+
+
+
+

+
+
+
+
+
+
+
+

Prior setup

+ +
+
# priors
+mn      = bv_minnesota(
+  lambda = bv_lambda(mode = 0.2, sd = 0.4, min = 0.0001, max = 5),
+  alpha = bv_alpha(mode = 2), 
+  psi <- bv_psi(scale = 0.004, shape = 0.004, mode = "auto", min = "auto", max = "auto"),
+  var = 1e07
+)
+
+soc     = bv_soc(mode = 1, sd = 1, min = 1e-04, max = 50)
+sur     = bv_sur(mode = 1, sd = 1, min = 1e-04, max = 50)
+
+priors  = bv_priors(hyper = "auto", mn = mn, soc = soc, sur = sur)
+
+# MH setup
+mh      = bv_metropolis(
+  scale_hess = c(0.05, 0.0001, 0.0001),
+  adjust_acc = TRUE, 
+  acc_lower = 0.25, 
+  acc_upper = 0.45
+)
+
+
+
+

Estimation

+ +
+
# estimation
+p     = 5
+run   = bvar(
+  x, 
+  lags = p, 
+  n_draw = 3e4,
+  n_burn = 1e4,
+  n_thin = 1,
+  priors = priors, 
+  mh = mh, 
+  verbose = TRUE # with progress bar
+)
+
+
Optimisation concluded.
+Posterior marginal likelihood: 1450.246
+Hyperparameters: lambda = 1.89602; soc = 0.19593; sur = 0.61619
+
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+Finished MCMC after 7.89 secs.
+
+
+
+
+

Forecasting

+ +
+
# forecasting 
+predict(run) <- predict(
+  run, 
+  horizon = 20, 
+  conf_bands = seq(from = 0.05, to = 0.4, by = 0.01)
+)
+plot(
+  predict(run), 
+  area = TRUE, 
+  t_back = 32,
+  vars = c("GDPC1")
+)
+
+ +
+

Forecasting

+
+
+
+

+
+
+
+
+

Forecasting

+ + +
+
+

Forecasting

+ + +
+
+

Forecasting

+ +
+
Y.h   = aperm(run$fcast$fcast, c(2,3,1))
+h     = dim(Y.h)[1]
+
+limits.1    = range(Y.h[,1,])
+point.f     = apply(Y.h[,1,],1,mean)
+interval.f  = apply(Y.h[,1,],1,HDInterval::hdi,credMass=0.90)
+
+x           = seq(from=limits.1[1], to=limits.1[2], length.out=100)
+z           = matrix(NA,h,99)
+for (i in 1:h){
+  z[i,]     = hist(Y.h[i,1,], breaks=x, plot=FALSE)$density
+}
+x           = hist(Y.h[i,1,], breaks=x, plot=FALSE)$mids
+yy          = 1:h
+z           = t(z)
+
+library(plot3D)
+theta = 180
+phi   = 15.5
+f4    = persp3D(x=x, y=yy, z=z, phi=phi, theta=theta, xlab="\nrgdp[t+h|t]", ylab="h", zlab="\npredictive densities of rgdp", shade=NA, border=NA, ticktype="detailed", nticks=3,cex.lab=1, col=NA,plot=FALSE)
+perspbox (x=x, y=yy, z=z, bty="f", col.axis="black", phi=phi, theta=theta, xlab="\nrgdp[t+h|t]", ylab="h", zlab="\npredictive densities of rgdp", ticktype="detailed", nticks=3,cex.lab=1, col = NULL, plot = TRUE)
+polygon3D(x=c(interval.f[1,],interval.f[2,h:1]), y=c(1:h,h:1), z=rep(0,2*h), col = "#F500BD", NAcol = "white", border = NA, add = TRUE, plot = TRUE)
+for (i in 1:h){
+  f4.l = trans3d(x=x, y=yy[i], z=z[,i], pmat=f4)
+  lines(f4.l, lwd=0.5, col="black")
+}
+f4.l1 = trans3d(x=point.f, y=yy, z=0, pmat=f4)
+lines(f4.l1, lwd=2, col="black")
+
+ +
+

Forecasting

+
+
+
+

+
+
+
+
+

MCMC convergence for hyper-parameters

+ +
+
plot.ts(run$hyper, main = "", col = "#F500BD", xlab = "s", cex.lab = 2, cex.axis = 1.3)
+ +
+
+
+

MCMC convergence for \(\mathbf\Sigma_{\cdot1}\)

+ +
+
plot.ts(run$sigma[,1,], main = "", col = "#F500BD", xlab = "s", cex.lab = 2, cex.axis = 1.3)
+ +
+
+
+

MCMC convergence for \(\boldsymbol\mu_0\)

+ +
+
plot.ts(run$beta[,1,], main = "", col = "#F500BD", xlab = "s", cex.lab = 2, cex.axis = 1.3)
+ +
+
+
+

Posterior means for \(\mathbf{A}\)

+ +
+
mean_A  = t(apply(run$beta, 2:3, mean))
+rownames(mean_A) = colnames(x)
+colnames(mean_A) = c("mu0",paste0("A",1:p %x% rep(1,3)))
+knitr::kable(mean_A, caption = "Posterior estimates for autoregressive parameters", digits = 2)
+
+ + ++++++++++++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Posterior estimates for autoregressive parameters
mu0A1A1A1A2A2A2A3A3A3A4A4A4A5A5A5
0.011.01-0.100.000.050.080.00-0.020.020.00-0.020.000.00-0.020.000.00
0.000.001.380.000.01-0.130.000.00-0.100.000.00-0.080.000.00-0.060.00
-0.0311.4011.351.21-3.672.72-0.49-3.98-8.600.36-2.39-3.73-0.12-1.36-1.76-0.03
+
+
+
+
+

Posterior means for \(\mathbf\Sigma\)

+ +
+
mean_S  = t(apply(run$sigma, 2:3, mean))
+mean_S  = cbind(mean_S, cov2cor(mean_S))
+rownames(mean_S) = colnames(x)
+colnames(mean_S) = c(rep("cov",3),rep("cor",3))
+knitr::kable(mean_S, caption = "Posterior estimates for covariance", digits = 5)
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Posterior estimates for covariance
covcovcovcorcorcor
0.000150.000010.001991.000000.098140.21109
0.000010.000020.000330.098141.000000.09753
0.001990.000330.607620.211090.097531.00000
+
+
+
+
+

Posterior means for hyper-parameters

+ +
+
mean_h  = rbind(apply(run$hyper, 2, mean), apply(run$hyper, 2, sd))
+rownames(mean_h) = c("E[hyper|data]", "sd[hyper|data]")
+knitr::kable(mean_h, caption = "Posterior estimates for hyper-parameters", digits = 3)
+
+ + + + + + + + + + + + + + + + + + + + + + + + +
Posterior estimates for hyper-parameters
lambdasocsur
E[hyper|data]1.9550.3140.947
sd[hyper|data]0.3020.1800.495
+
+
+
+
+

Australian Data Forecasting

+ +

\[ \]

+

DOWNLOAD THE SCRIPT

+ +
+
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/index.html b/index.html new file mode 100644 index 0000000..8232d48 --- /dev/null +++ b/index.html @@ -0,0 +1,2230 @@ + + + + + + + + + + + + + + Lecture 7: Bayesian Vector Autoregressions + + + + + + + + + + + + + + + +
+
+ +
+

Lecture 7: Bayesian Vector Autoregressions

+ +
+
+
+by Tomasz Woźniak +
+
+
+ +
+
+

+

\[ \]

+

Vector Autoregressions

+

Three Useful Distributions

+

Bayesian Estimation

+

Minnesota and Dummy Observations Prior

+

Bayesian Estimation for Hierarchical Prior

+

Bayesian Forecasting using VARs

+

US Data Analysis Using R Package bsvarSIGNs

+
+
+

+

+
+
+

Materials

+

\[ \]

+

Lecture Slides as a Website

+

A Dedicated Reading Woźniak (2016, AERev)

+

Quarto document template for your own Australian data forecasting

+

GitHub repo to reproduce the slides and results

+

A Kahoot! Quiz

+

Tasks

+
+
+

Vector Autoregressions

+
+
+

Vector Autoregressions

+
    +
  • go-to models for forecasting
  • +
+
+
    +
  • simple: linear and Gaussian
  • +
  • extendible: featuring many variations in specification +
      +
    • non-normality
    • +
    • heteroskedasticity
    • +
    • time-varying parameters
    • +
    • Bayesian
    • +
  • +
  • interpretable +
      +
    • Granger causality
    • +
    • spillovers
    • +
    • networks
    • +
    • structural
    • +
  • +
  • Proposed by Sims (1980)
  • +
+
+ +
+
+

VAR(p) Model

+

Model equations.

+

\[\begin{align*} +y_t &= \mathbf{A}_1 y_{t-1} + \dots + \mathbf{A}_p y_{t-p} + \boldsymbol\mu_0 + \epsilon_t\\ +\epsilon_t|Y_{t-1} &\sim iidN\left(\mathbf{0}_N,\mathbf\Sigma\right) +\end{align*}\] for \(t=1,\dots,T\)

+
+ +

Notation.

+
    +
  • \(y_t\) is an \(N\times 1\) vector of observations at time \(t\)
  • +
  • \(\mathbf{A}_i\) - \(N\times N\) matrix of autoregressive slope parameters
  • +
  • \(\boldsymbol\mu_0\) - \(N\times 1\) vector of constant terms
  • +
  • \(\epsilon_t\) - \(N\times 1\) vector of error terms - a multivariate white noise process
  • +
  • \(Y_{t-1}\) - information set collecting observations on} \(y\) up to time \(t-1\)
  • +
  • \(\mathbf\Sigma\) - \(N\times N\) covariance matrix of the error term
  • +
+
+ +
+
+

A Bivariate VAR(2) Model

+

Let the number of variable \(N=2\) and the lag order \(p=2\).

+

Then, the model equation is:

+\[\begin{align*} +\begin{bmatrix} y_{1.t} \\ y_{2.t} \end{bmatrix} +&= \begin{bmatrix} \mathbf{A}_{1.11} & \mathbf{A}_{1.12} \\ \mathbf{A}_{1.21} & \mathbf{A}_{1.22} \end{bmatrix} \begin{bmatrix} y_{1.t-1} \\ y_{2.t-1} \end{bmatrix} ++ \begin{bmatrix} \mathbf{A}_{2.11} & \mathbf{A}_{2.12} \\ \mathbf{A}_{2.21} & \mathbf{A}_{2.22} \end{bmatrix} \begin{bmatrix} y_{1.t-2} \\ y_{2.t-2} \end{bmatrix} + \begin{bmatrix} \boldsymbol\mu_{0.1} \\ \boldsymbol\mu_{0.2} \end{bmatrix} + \begin{bmatrix} \epsilon_{1.t} \\ \epsilon_{2.t} \end{bmatrix}\\[2ex] +\begin{bmatrix} \epsilon_{1.t} \\ \epsilon_{2.t} \end{bmatrix} &\Big|Y_{t-1} \sim iid N_2\left( \begin{bmatrix} 0\\ 0\end{bmatrix}, \begin{bmatrix}\boldsymbol\sigma_1^2 & \boldsymbol\sigma_{12} \\ \boldsymbol\sigma_{12} & \boldsymbol\sigma_2^2\end{bmatrix} \right) +\end{align*}\] +
+

Task:

+

Perform the matrix multiplications and write out the equations for \(y_{1.t}\) and \(y_{2.t}\).

+ +
+
+
+

Three Useful Distributions

+
+
+

Matrix-Variate Normal Distribution

+

A \(K\times N\) matrix \(\mathbf{A}\) is said to follow a matrix-variate normal distribution: \[ \mathbf{A} \sim MN_{K\times N}\left( M, Q, P \right), \] where

+
    +
  • \(M\) - a \(K\times N\) matrix of the mean
  • +
  • \(Q\) - a \(N\times N\) row-specific covariance matrix
  • +
  • \(P\) - a \(K\times K\) column-specific covariance matrix
  • +
+

if \(\text{vec}(\mathbf{A})\) is multivariate normal: \[ \text{vec}(\mathbf{A}) \sim N_{KN}\left( \text{vec}(M), Q\otimes P \right) \]

+

Density function.

+\[\begin{align*} +MN_{K\times N}\left( M, Q, P \right) &\propto \exp\left\{ -\frac{1}{2}\text{tr}\left[ Q^{-1}(\mathbf{A}-M)'P^{-1}(\mathbf{A}-M) \right] \right\} +\end{align*}\] +
    +
  • \(\text{tr}()\) is a trace of a matrix - a sum of diagonal elements
  • +
+ +
+
+

Inverse Wishart Distribution

+

An \(N\times N\) square symmetric and positive definite matrix \(\mathbf\Sigma\) follows an inverse Wishart distribution: \[ \mathbf\Sigma \sim IW_{N}\left( S, \nu \right) \] where

+
    +
  • \(S\) is \(N\times N\) positive definite symmetric matrix called the scale matrix
  • +
  • \(\nu \geq N\) denotes degrees of freedom, if its density is given by:
  • +
+

Density function.

+\[\begin{align*} +IW_{N}\left( S, \nu \right) \propto \text{det}(\mathbf\Sigma)^{-\frac{\nu+N+1}{2}}\exp\left\{ -\frac{1}{2}\text{tr}\left[ \mathbf\Sigma^{-1} S \right] \right\} +\end{align*}\] + +
+
+

Normal-Inverse Wishart Distribution

+\[\begin{align*} +\mathbf{A}|\mathbf\Sigma &\sim MN_{K\times N}\left( M, \mathbf\Sigma, P \right)\\ +\mathbf\Sigma &\sim IW_{N}\left( S, \nu \right) +\end{align*}\] +

then the joint distribution of \((\mathbf{A},\mathbf\Sigma)\) is normal-inverse Wishart \[ +p(\mathbf{A},\mathbf\Sigma) = NIW_{K\times N}\left( M,P,S,\nu\right) +\]

+

Density function.

+\[\begin{align*} +NIW_{K\times N}\left( M,P,S,\nu\right) \propto &\text{det}(\mathbf{\Sigma})^{-(\nu+N+K+1)/2}\exp\left\{ -\frac{1}{2}\text{tr}\left[ \mathbf{\Sigma}^{-1} S \right] \right\}\\ +&\times\exp\left\{ -\frac{1}{2}\text{tr}\left[ \mathbf{\Sigma}^{-1} (\mathbf{A}-M)'P^{-1}(\mathbf{A}-M) \right] \right\} +\end{align*}\] + +
+
+

Example: Error Term Distribution

+

The model assumptions state: \[\begin{align*} +\epsilon_t|Y_{t-1} &\sim iidN_N\left(\mathbf{0}_N,\mathbf\Sigma\right) +\end{align*}\]

+

Collect error term vectors in a \(T\times N\) matrix: \[\underset{(T\times N)}{E}= \begin{bmatrix}\epsilon_1 & \epsilon_2 & \dots & \epsilon_{T}\end{bmatrix}'\]

+

Error term matrix is matrix-variate distributed: \[\begin{align*} +E|X &\sim MN_{T\times N}\left(\mathbf{0}_{T\times N},\mathbf\Sigma, I_T\right) +\end{align*}\]

+
+ +

Tasks: what is

+
    +
  • the covariance of \(\text{vec}(E)\)
  • +
  • the distribution of the first equation error terms \(\begin{bmatrix}\epsilon_{1.1} &\dots&\epsilon_{1.T}\end{bmatrix}'\)
  • +
+
+ +
+
+

Example: Univariate Inverse Wishart Distribution

+

The inverse Wishart density function is proportional to: \[\begin{align*} +\text{det}(\mathbf\Sigma)^{-\frac{\nu+N+1}{2}}\exp\left\{ -\frac{1}{2}\text{tr}\left[ \mathbf\Sigma^{-1} S \right] \right\} +\end{align*}\]

+

Consider a case where:

+
    +
  • \(N=1\)
  • +
  • the matrix \(\mathbf\Sigma\) is replaced by a scalar \(\boldsymbol\sigma^2\)
  • +
+
+ +

Task:

+
    +
  • write out the kernel of the density function for \(\boldsymbol\sigma^2\)
  • +
  • the kernel of what density it represents?
  • +
+
+ +
+
+

Bayesian Estimation

+
+
+

The model in Matrix Notation

+

VAR(p) model.

+\[\begin{align*} +y_t &= \mathbf{A}_1 y_{t-1} + \dots + \mathbf{A}_p y_{t-p} + \boldsymbol\mu_0 + \epsilon_t\\ +\epsilon_t|Y_{t-1} &\sim iidN_N\left(\mathbf{0}_N,\mathbf\Sigma\right) +\end{align*}\] +

Matrix notation.

+\[\begin{align*} +Y &= X\mathbf{A} + E\\ +E|X &\sim MN_{T\times N}\left(\mathbf{0}_{T\times N},\mathbf\Sigma, I_T\right) +\end{align*}\] +
+

\[ +\underset{(K\times N)}{\mathbf{A}}=\begin{bmatrix} \mathbf{A}_1'\\ \vdots \\ \mathbf{A}_p' \\ \boldsymbol\mu_0' \end{bmatrix} \quad +\underset{(T\times N)}{Y}= \begin{bmatrix}y_1' \\ y_2'\\ \vdots \\ y_T'\end{bmatrix} \quad +\underset{(K\times1)}{x_t}=\begin{bmatrix} y_{t-1}\\ \vdots \\ y_{t-p}\\ 1 \end{bmatrix}\quad +\underset{(T\times K)}{X}= \begin{bmatrix}x_1' \\ x_2' \\ \vdots \\ x_{T}'\end{bmatrix} \quad +\underset{(T\times N)}{E}= \begin{bmatrix}\epsilon_1' \\ \epsilon_2' \\ \vdots \\ \epsilon_{T}'\end{bmatrix} +\] where \(K=pN+1\)

+
+ +
+
+

The model as Predictive Density

+

VAR model.

+\[\begin{align*} +Y &= X\mathbf{A} +E\\ +E|X &\sim MN_{T\times N}\left(\mathbf{0}_{T\times N},\mathbf\Sigma, I_T\right) +\end{align*}\] +

Predictive density.

+\[\begin{align*} +Y|X,\mathbf{A}, \mathbf{\Sigma} &\sim MN_{T\times N}\left(X\mathbf{A},\mathbf{\Sigma},I_T\right) +\end{align*}\] + +
+
+

Likelihood Function

+

Predictive density.

+\[\begin{align*} +Y|X,\mathbf{A}, \mathbf{\Sigma} &\sim MN_{T\times N}\left(X\mathbf{A},\mathbf{\Sigma},I_T\right) +\end{align*}\] +

Likelihood function.

+\[\begin{align*} +L\left(\mathbf{A},\mathbf{\Sigma}|Y,X\right)&\propto\text{det}(\mathbf{\Sigma})^{-\frac{T}{2}}\exp\left\{-\frac{1}{2}\text{tr}\left[\mathbf{\Sigma}^{-1}(Y-X\mathbf{A})'(Y-X\mathbf{A})\right]\right\} +\end{align*}\] + +
+
+

Likelihood Function as NIW

+

Define the MLE: \(\widehat{A}=(X'X)^{-1}X'Y\)

+

Perform simple transformation of the likelihood

+\[\begin{align*} +L\left(\mathbf{A},\mathbf{\Sigma}|Y,X\right)&\propto\text{det}(\mathbf{\Sigma})^{-\frac{T}{2}}\exp\left\{-\frac{1}{2}\text{tr}\left[\mathbf{\Sigma}^{-1}(Y-X\mathbf{A})'(Y-X\mathbf{A})\right]\right\}\\ +&=\text{det}(\mathbf{\Sigma})^{-\frac{T}{2}}\\ +&\quad\times\exp\left\{ -\frac{1}{2}\text{tr}\left[\mathbf{\Sigma}^{-1}(\mathbf{A}-\widehat{A})'X'X(\mathbf{A}-\widehat{A}) \right] \right\}\\ +&\quad\times \exp\left\{ -\frac{1}{2}\text{tr}\left[ \mathbf{\Sigma}^{-1}(Y-X\widehat{A})'(Y-X\widehat{A}) \right] \right\} +\end{align*}\] +

Under the likelihood, \((\mathbf{A},\mathbf{\Sigma})\) are normal-inverse Wishart distributed:

+\[\begin{align*} +L\left( \mathbf{A},\mathbf{\Sigma}|Y,X \right) &= NIW_{K\times N}\left(\widehat{A},(X'X)^{-1},(Y-X\widehat{A})'(Y-X\widehat{A}), T-N-K-1 \right) +\end{align*}\] + +
+
+

Prior Distribution

+

Construction.

+

A natural-conjugate prior leads to joint posterior distribution for \((\mathbf{A},\mathbf{\Sigma})\) of the same form \[\begin{align*} +p\left( \mathbf{A}, \mathbf{\Sigma} \right) &= p\left( \mathbf{A}| \mathbf{\Sigma} \right)p\left( \mathbf{\Sigma} \right)\\ +\mathbf{A}|\mathbf{\Sigma} &\sim MN_{K\times N}\left( \underline{A},\mathbf{\Sigma},\underline{V} \right)\\ +\mathbf{\Sigma} &\sim IW_N\left( \underline{S}, \underline{\nu} \right) +\end{align*}\]

+

Kernel.

+\[\begin{align*} +p\left( \mathbf{A},\mathbf{\Sigma} \right) +&\propto \text{det}(\mathbf{\Sigma})^{-\frac{N+K+\underline{\nu}+1}{2}}\\ +&\quad\times\exp\left\{ -\frac{1}{2}\text{tr}\left[ \mathbf{\Sigma}^{-1}(\mathbf{A}-\underline{A})'\underline{V}^{-1}(\mathbf{A}-\underline{A}) \right] \right\}\\ +&\quad\times \exp\left\{ -\frac{1}{2}\text{tr}\left[ \mathbf{\Sigma}^{-1}\underline{S} \right] \right\} +\end{align*}\] + +
+
+

Posterior Distribution

+

Bayes Rule.

+\[\begin{align*} +p\left( \mathbf{A}, \mathbf{\Sigma}|Y,X \right) &\propto L(\mathbf{A},\mathbf{\Sigma}|Y,X)p\left( \mathbf{A}, \mathbf{\Sigma} \right)\\ +&= L(\mathbf{A},\mathbf{\Sigma}|Y,X)p\left( \mathbf{A}| \mathbf{\Sigma} \right)p\left( \mathbf{\Sigma} \right) +\end{align*}\] +

Kernel.

+\[\begin{align*} +p\left( \mathbf{A},\mathbf{\Sigma} |Y,X\right) +&\propto \text{det}(\mathbf{\Sigma})^{-\frac{T}{2}}\exp\left\{-\frac{1}{2}\text{tr}\left[\mathbf{\Sigma}^{-1}(Y-X\mathbf{A})'(Y-X\mathbf{A})\right]\right\}\\ +& \quad\times\text{det}(\mathbf{\Sigma})^{-\frac{N+K+\underline{\nu}+1}{2}}\exp\left\{ -\frac{1}{2}\text{tr}\left[ \mathbf{\Sigma}^{-1}\underline{S} \right] \right\}\\ +&\quad\times\exp\left\{ -\frac{1}{2}\text{tr}\left[ \mathbf{\Sigma}^{-1}(\mathbf{A}-\underline{A})'\underline{V}^{-1}(\mathbf{A}-\underline{A}) \right] \right\} +\end{align*}\] + +
+
+

Joint Posterior Distribution

+

Conditional and marginal.

+\[\begin{align*} +p\left( \mathbf{A}, \mathbf{\Sigma}|Y,X \right) &= p(\mathbf{A}|Y,X,\mathbf{\Sigma})p\left( \mathbf{\Sigma}|Y,X \right)\\[2ex] +p(\mathbf{A}|Y,X,\mathbf{\Sigma}) &= MN_{K\times N}\left( \overline{A},\mathbf{\Sigma},\overline{V} \right)\\ +p(\mathbf{\Sigma}|Y,X) &= IW_N\left( \overline{S}, \overline{\nu} \right) +\end{align*}\] +

Posterior parameters.

+\[\begin{align*} +\overline{V}&= \left( X'X + \underline{V}^{-1}\right)^{-1} \\ +\overline{A}&= \overline{V}\left( X'Y + \underline{V}^{-1}\underline{A} \right)\\ +\overline{\nu}&= T+\underline{\nu}\\ +\overline{S}&= \underline{S}+Y'Y + \underline{A}'\underline{V}^{-1}\underline{A} - \overline{A}'\overline{V}^{-1}\overline{A} +\end{align*}\] + +
+
+

Posterior Mean of \(\mathbf{A}\)

+

Posterior mean of matrix \(\mathbf{A}\) is: \[\begin{align*} +\overline{A} &= \overline{V}\left( X'Y + \underline{V}^{-1}\underline{A} \right)\\[2ex] +&= \overline{V}\left( X'X\widehat{A} + \underline{V}^{-1}\underline{A} \right)\\[2ex] +&= \overline{V} X'X\widehat{A} + \overline{V}\underline{V}^{-1}\underline{A} +\end{align*}\] a linear combination of the MLE \(\widehat{A}\) and the prior mean \(\underline{A}\)

+

Note that: \[ +\overline{V} X'X + \overline{V}\underline{V}^{-1} = \overline{V} ( X'X + \underline{V}^{-1}) = I_K +\]

+

Play with the posterior in an interactive graph

+ +
+
+

Marginal Data Density

+

According to Bayes Rule, the kernel of the posterior is normalised by the Marginal Data Density \(p(data)\):

+

\[ +p\left( \mathbf{A}, \mathbf{\Sigma}| data \right) = \frac{L(\mathbf{A},\mathbf{\Sigma}| data)p\left( \mathbf{A}, \mathbf{\Sigma} \right)}{p(data)} +\]

+

For Bayesian VARs the posterior is known \[ +p\left( \mathbf{A}, \mathbf{\Sigma}| data \right) = MNIW\left(\overline{A},\overline{V}, \overline{S}, \overline{\nu} \right) +\]

+

and so is the analytical formula for the MDD: \[p(data)\]

+

This can be used to our advantage!

+ +
+
+

Minnesota and Dummy Observations Prior

+
+
+

Minnesota Prior

+

Sims, Litterman, Doan (1984) proposed an interpretable way of setting the hyper-parameters on the NIW prior \(\underline{A}\), \(\underline{V}\), \(\underline{S}\), and \(\underline{\nu}\) for macroeconomic data.

+
+

\[ \] The prior reflects the following stylised facts about macro time series:

+
    +
  • the data are unit-root non-stationary
  • +
  • the effect of more lagged variables should be smaller and smaller
  • +
  • the effect of other variables lags should be less than that of own lags
  • +
+ +
+
+
+

Minnesota Prior

+

Inverse-Wishart prior.

+\[\begin{align*} +\mathbf{\Sigma} &\sim IW_N\left( \underline{S}, \underline{\nu} \right) +\end{align*}\] +

Set

+\[\begin{align*} +\underline{S} &= \begin{bmatrix} +\psi_1 &0 &\dots & 0 \\ +0 & \psi_2 &\dots & 0\\ +\vdots &\vdots&\ddots& \vdots\\ +0&0&\dots&\psi_N +\end{bmatrix}\\[2ex] +\underline{\nu}&= N+2 +\end{align*}\] +

Hyper-parameters.

+

\(\psi =(\psi_1, \dots, \psi_N)\) have to be chosen (or estimated)

+ +
+
+

Minnesota Prior

+

Matrix-Variate Normal prior.

+\[\begin{align*} +\mathbf{A}|\mathbf{\Sigma} &\sim MN_{K\times N}\left( \underline{A},\mathbf{\Sigma},\underline{V} \right) +\end{align*}\] +

Set \[\begin{align*} +\underline{A} &= \begin{bmatrix} I_N \\ \mathbf{0}_{((p-1)N +1)\times N}\end{bmatrix}& +\underline{V}_{ij} &= \left\{\begin{array} (\lambda ^ 2 / (\psi_k l^2) &\text{ for }i=j,\text{ and } i\neq pN+1 \\ +\lambda^2 &\text{ for }i=j,\text{ and } i= pN+1 \\ +0&\text{ for } i\neq j +\end{array}\right. +\end{align*}\]

+

for \(\quad l = 1+\text{floor}((i-1)/N) \quad\text{and }\quad k = i - (l-1)N\)

+

Hyper-parameters.

+

\(\lambda^2\) has to be chosen (or estimated)

+ +
+
+

Dummy Observations Prior

+

Idea.

+
    +
  1. Generate artificial data matrices with \(T_d\) rows \(Y^*\) and \(X^*\)
  2. +
  3. Append them to the original data matrices \(Y\) and \(X\) respectively.
  4. +
+
+ +

Implied prior distribution.

+

Use Bayes Rule to derive the joint prior of \((\mathbf{A},\mathbf\Sigma)\) given \(Y^*\) and \(X^*\).

+

It is given by the MNIW distribution:

+

\[\begin{align*} +p\left( \mathbf{A}, \mathbf{\Sigma}|Y^*,X^* \right) &= MNIV_{K\times N}\left( \underline{A}^*,\underline{V}^*, \underline{S}^*, \underline{\nu}^* \right) +\end{align*}\] \[\begin{align*} +\underline{V}^*&= \left( X^{*\prime}X^* + \underline{V}^{-1}\right)^{-1} & \underline{A}^*&= \underline{V}^*\left( X^{*\prime}Y^* + \underline{V}^{-1}\underline{A} \right)\\ +\underline{\nu}^*&= T_d+\underline{\nu} & \underline{S}^*&= \underline{S}+Y^{*\prime}Y^* + \underline{A}'\underline{V}^{-1}\underline{A} - \underline{A}^{*\prime}\underline{V}^{*-1}\underline{A}^* +\end{align*}\]

+
+ +
+
+

Dummy Observations Prior

+

Let a \(p\times N\) matrix \(Y_0\) denote the initial observations, that is, the first \(p\) observations of the available time series.

+

Let an \(N\)-vector \(\bar{Y}_0\) denote its columns’ means.

+
+ +

Sum-of-coefficients prior.

+

Generate additional \(N\) rows by \[ +Y^+ = \text{diag}\left(\frac{\bar{Y}_0}{\mu}\right) \quad\text{ and }\quad X^+ = \begin{bmatrix}\mathbf{0}_N & Y^+ & \dots & Y^+ \end{bmatrix} +\]

+
    +
  • \(\mu\) is a hyper-parameter to be chosen (or estimated)
  • +
  • if \(\mu \rightarrow 0\) the prior implies the presence of a unit root in each equation and rules out cointegration
  • +
  • if \(\mu \rightarrow\infty\) the prior becomes uninformative
  • +
+
+ +
+
+

Dummy Observations Prior

+

Dummy-initial-observation prior.

+

Generate an additional row by \[ +Y^{++} = \frac{\bar{Y}_0'}{\delta} \quad\text{ and }\quad X^{++} = \begin{bmatrix}\frac{1}{\delta} & Y^{++} & \dots & Y^{++} \end{bmatrix} +\]

+
    +
  • hyper-parameter \(\delta\) is to be chosen (or estimated)
  • +
  • if \(\delta \rightarrow 0\) all the variables of the VAR are forced to be at their unconditional mean, or the system is characterized by the presence of an unspecified number of unit roots without drift (cointegration)
  • +
  • if \(\delta \rightarrow\infty\) the prior becomes uninformative
  • +
+
+ +

Combining dummy observations.

+

\[ +Y^* = \begin{bmatrix}Y^+ \\ Y^{++} \end{bmatrix}\quad\text{ and }\quad +X^* = \begin{bmatrix}X^+ \\ X^{++} \end{bmatrix} +\]

+
+ +
+
+

Dummy Observations Prior

+

Task.

+

Suppose that:

+
    +
  • \(\bar{Y}_0 = \begin{bmatrix}1&2\end{bmatrix}'\)
  • +
  • \(\mu = 0.5\)
  • +
  • \(\delta = 3\)
  • +
  • \(p = 1\)
  • +
+

Write out the matrices \(Y^*\) and \(X^*\) of dimensions \(2\times 3\) and \(3\times 3\) respectively.

+ +
+
+

Bayesian Estimation for Hierarchical Prior

+
+
+

Bayesian Estimation for Hierarchical Prior

+

Hyper-parameters \(\psi\), \(\lambda\), \(\mu\) and \(\delta\) can be fixed to values chosen by the econometrician.

+

Hierarcical prior.

+

A better idea is to assume priors for these hyper-parameters and estimate them as in Giannone, Lenza, Primiceri (2015).

+

Extend the existing prior to: \[\begin{align*} +p\left( \mathbf{A}, \mathbf{\Sigma}|Y^*,X^*,\psi,\lambda,\mu,\delta \right) &= MNIV_{K\times N}\left( \underline{A}^*,\underline{V}^*, \underline{S}^*, \underline{\nu}^* \right) +\end{align*}\] And specify: \[\begin{align*} +\psi_n &\sim IG\left(0.02^2, 0.02^2\right)\\ +\lambda &\sim G\left(0.2,2\right)\\ +\mu &\sim G\left(1,2\right)\\ +\delta &\sim G\left(1,2\right) +\end{align*}\]

+ +
+
+

Bayesian Estimation for Hierarchical Prior

+

Giannone, Lenza, Primiceri (2015) propose the following estimation procedure:

+

Step 1: Estimate \((\psi,\lambda,\mu,\delta)\) using a random-walk Metropolis-Hastings sampler

+
    +
  • Sample these hyper-parameters marginally on \((\mathbf{A},\mathbf\Sigma)\)
  • +
  • extend the conditioning of Marginal Data Density: \[ p(data|\psi,\lambda,\mu,\delta)\]
  • +
  • apply Bayes Rule to obtain the kernel of the posterior:
  • +
+

\[ p(\psi,\lambda,\mu,\delta|data) \propto p(\psi,\lambda,\mu,\delta)p(data|\psi,\lambda,\mu,\delta)\] - Use an \((N+3)\)-variate Student-t distribution as the candidate generating density

+ +
+
+

Bayesian Estimation for Hierarchical Prior

+

Step 2: For each draw of \((\psi,\lambda,\mu,\delta)\) sample the corresponding draw of \((\mathbf{A},\mathbf{\Sigma})\)

+

Use the MNIW posterior derived for the implied prior:

+\[\begin{align*} +p\left( \mathbf{A}, \mathbf{\Sigma}|Y,X, Y^*,X^* \right) &= MNIW_{K\times N}\left( \overline{A}^*,\overline{V}^*,\overline{S}^*, \overline{\nu}^* \right)\\[2ex] +\overline{V}^*&= \left( X'X + \underline{V}^{*-1}\right)^{-1} \\ +\overline{A}^*&= \overline{V}^*\left( X'Y + \underline{V}^{*-1}\underline{A}^* \right)\\ +\overline{\nu}^*&= T+\underline{\nu}^*\\ +\overline{S}^*&= \underline{S}^*+Y'Y + \underline{A}^{*\prime}\underline{V}^{*-1}\underline{A}^* - \overline{A}^{*\prime}\overline{V}^{*-1}\overline{A}^* +\end{align*}\] +

R implementation.

+

Package BVAR by Kuschnig, Vashold (2021) implements this algorithm.

+ +
+
+

Bayesian Forecasting using VARs

+
+
+

The objective of economic forecasting

+ +

\(\left.\right.\)

+

… is to use the available data to provide a statistical characterisation of the unknown future values of quantities of interest.

+

\(\left.\right.\)

+

The full statistical characterisation of the unknown future values of random variables is given by their predictive density.

+

\(\left.\right.\)

+

Simplified outcomes in a form of statistics summarising the predictive densities are usually used in decision-making processes.

+

\(\left.\right.\)

+

Summary statistics are also communicated to general audiences.

+
+
+

One-Period Ahead Predictive Density

+ +

VAR(p) model.

+

\[\begin{align*} +y_t &= \mathbf{A}_1 y_{t-1} + \dots + \mathbf{A}_p y_{t-p} + \boldsymbol\mu_0 + \epsilon_t\\[2ex] +\epsilon_t|Y_{t-1} &\sim iidN_N\left(\mathbf{0}_N,\mathbf\Sigma\right)\\ +& +\end{align*}\]

+

One-Period Ahead Conditional Predictive Density

+

… is implied by the model formulation: \[\begin{align*} +y_{t+h}|Y_{t+h-1},\mathbf{A},\mathbf\Sigma &\sim N_N\left(\mathbf{A}_1 y_{t+h-1} + \dots + \mathbf{A}_p y_{t+h-p} + \boldsymbol\mu_0,\mathbf\Sigma\right) +\end{align*}\]

+
+
+

One-Period Ahead Predictive Density

+ +

\(\left.\right.\)

+

Bayesian forecasting takes into account the uncertainty w.r.t. parameter estimation by integrating it out from the predictive density.

+

\[\begin{align*} +&\\ +p(y_{T+1}|Y,X) &= \int p(y_{T+1}|Y_{T},\mathbf{A},\mathbf\Sigma) p(\mathbf{A},\mathbf\Sigma|Y,X) d(\mathbf{A},\mathbf\Sigma)\\ & +\end{align*}\]

+
    +
  • \(p(y_{T+1}|Y,X)\) - predictive density
  • +
  • \(p(y_{T+1}|Y_{t},\mathbf{A},\mathbf\Sigma)\) - one-period-ahead conditional predictive density
  • +
  • \(p(\mathbf{A},\mathbf\Sigma|Y,X)\) - marginal posterior distribution
  • +
+
+
+

Sampling from One-Period Ahead Predictive Density

+ +

\(\left.\right.\)

+

Step 1: Sample from the posterior

+

… and obtain \(S\) draws \(\left\{ \mathbf{A}^{(s)},\mathbf\Sigma^{(s)} \right\}_{s=1}^{S}\)

+

\(\left.\right.\)

+

Step 2: Sample from the predictive density

+

In order to obtain draws from \(p(y_{T+1}|Y,X)\), for each of the \(S\) draws of \((\mathbf{A},\mathbf\Sigma)\) sample the corresponding draw of \(y_{T+1}\):

+

Sample \(y_{T+1}^{(s)}\) from \[ +N_N\left(\mathbf{A}_1^{(s)} y_{T} + \dots + \mathbf{A}_p^{(s)} y_{T-p+1} + \boldsymbol\mu_0^{(s)},\mathbf\Sigma^{(s)}\right) +\] and obtain \(\left\{y_{T+1}^{(s)}\right\}_{s=1}^{S}\)

+
+
+

\(h\)-Period Ahead Predictive Density

+ +

\(\left.\right.\)

+

This procedure can be generalised to any forecasting horizon.

+

This is an illustration for \(h=2\).

+

\[\begin{align*} +&\\ +p(y_{T+2},y_{T+1}|Y,X) +&= \int p(y_{T+2},y_{T+1}|Y_{T},\mathbf{A},\mathbf\Sigma) p(\mathbf{A},\mathbf\Sigma|Y,X) d(\mathbf{A},\mathbf\Sigma)\\[1ex] +&= \int p(y_{T+2}|y_{T+1},Y_{T},\mathbf{A},\mathbf\Sigma)p(y_{T+1}|Y_{T},\mathbf{A},\mathbf\Sigma) p(\mathbf{A},\mathbf\Sigma|Y,X) d(\mathbf{A},\mathbf\Sigma)\\ & +\end{align*}\]

+
+
+

\(h\)-Period Ahead Predictive Density

+ +

\(\left.\right.\)

+

Step 1: Sample from the posterior

+

… and obtain \(S\) draws \(\left\{ \mathbf{A}^{(s)},\mathbf\Sigma^{(s)} \right\}_{s=1}^{S}\)

+

Step 2: Sample from 1-period ahead predictive density

+

For each of the \(S\) draws, sample \(y_{T+1}^{(s)}\) from \[ +N_N\left(\mathbf{A}_1^{(s)} y_{T} + \dots + \mathbf{A}_p^{(s)} y_{T-p+1} + \boldsymbol\mu_0^{(s)},\mathbf\Sigma^{(s)}\right) +\]

+

Step 3: Sample from 2-period ahead predictive density

+

For each of the \(S\) draws, sample \(y_{T+2}^{(s)}\) from \[ +N_N\left(\mathbf{A}_1^{(s)} y_{T+1}^{(s)} + \mathbf{A}_2 y_{T} + \dots + \mathbf{A}_p^{(s)} y_{T-p+2} + \boldsymbol\mu_0^{(s)},\mathbf\Sigma^{(s)}\right) +\]

+

and obtain \(\left\{y_{T+2}^{(s)},y_{T+1}^{(s)}\right\}_{s=1}^{S}\)

+
+
+

The Bayesian VARs Quiz

+

\[ \]

+

GO TO THE GAME

+ +
+
+

US Data Analysis Using R Package BVAR

+
+
+

Data preparation

+ +
+
+
set.seed(42)
+library(BVAR)
+
+# data
+x = fred_qd[, c("GDPC1", 
+                "GDPCTPI", 
+                "FEDFUNDS")]
+x = fred_transform(
+  x, 
+  codes = c(4, 4, 1)
+)
+
+plot.ts(
+  x, 
+  main = "",
+  col = "#F500BD",
+  lwd = 4,
+  cex.axis = 2,
+  cex.lab = 2
+)
+
+
+
+
+

+
+
+
+
+
+
+
+

Prior setup

+ +
+
# priors
+mn      = bv_minnesota(
+  lambda = bv_lambda(mode = 0.2, sd = 0.4, min = 0.0001, max = 5),
+  alpha = bv_alpha(mode = 2), 
+  psi <- bv_psi(scale = 0.004, shape = 0.004, mode = "auto", min = "auto", max = "auto"),
+  var = 1e07
+)
+
+soc     = bv_soc(mode = 1, sd = 1, min = 1e-04, max = 50)
+sur     = bv_sur(mode = 1, sd = 1, min = 1e-04, max = 50)
+
+priors  = bv_priors(hyper = "auto", mn = mn, soc = soc, sur = sur)
+
+# MH setup
+mh      = bv_metropolis(
+  scale_hess = c(0.05, 0.0001, 0.0001),
+  adjust_acc = TRUE, 
+  acc_lower = 0.25, 
+  acc_upper = 0.45
+)
+
+
+
+

Estimation

+ +
+
# estimation
+p     = 5
+run   = bvar(
+  x, 
+  lags = p, 
+  n_draw = 3e4,
+  n_burn = 1e4,
+  n_thin = 1,
+  priors = priors, 
+  mh = mh, 
+  verbose = TRUE # with progress bar
+)
+
+
Optimisation concluded.
+Posterior marginal likelihood: 1450.246
+Hyperparameters: lambda = 1.89602; soc = 0.19593; sur = 0.61619
+
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+Finished MCMC after 7.89 secs.
+
+
+
+
+

Forecasting

+ +
+
# forecasting 
+predict(run) <- predict(
+  run, 
+  horizon = 20, 
+  conf_bands = seq(from = 0.05, to = 0.4, by = 0.01)
+)
+plot(
+  predict(run), 
+  area = TRUE, 
+  t_back = 32,
+  vars = c("GDPC1")
+)
+
+ +
+

Forecasting

+
+
+
+

+
+
+
+
+

Forecasting

+ + +
+
+

Forecasting

+ + +
+
+

Forecasting

+ +
+
Y.h   = aperm(run$fcast$fcast, c(2,3,1))
+h     = dim(Y.h)[1]
+
+limits.1    = range(Y.h[,1,])
+point.f     = apply(Y.h[,1,],1,mean)
+interval.f  = apply(Y.h[,1,],1,HDInterval::hdi,credMass=0.90)
+
+x           = seq(from=limits.1[1], to=limits.1[2], length.out=100)
+z           = matrix(NA,h,99)
+for (i in 1:h){
+  z[i,]     = hist(Y.h[i,1,], breaks=x, plot=FALSE)$density
+}
+x           = hist(Y.h[i,1,], breaks=x, plot=FALSE)$mids
+yy          = 1:h
+z           = t(z)
+
+library(plot3D)
+theta = 180
+phi   = 15.5
+f4    = persp3D(x=x, y=yy, z=z, phi=phi, theta=theta, xlab="\nrgdp[t+h|t]", ylab="h", zlab="\npredictive densities of rgdp", shade=NA, border=NA, ticktype="detailed", nticks=3,cex.lab=1, col=NA,plot=FALSE)
+perspbox (x=x, y=yy, z=z, bty="f", col.axis="black", phi=phi, theta=theta, xlab="\nrgdp[t+h|t]", ylab="h", zlab="\npredictive densities of rgdp", ticktype="detailed", nticks=3,cex.lab=1, col = NULL, plot = TRUE)
+polygon3D(x=c(interval.f[1,],interval.f[2,h:1]), y=c(1:h,h:1), z=rep(0,2*h), col = "#F500BD", NAcol = "white", border = NA, add = TRUE, plot = TRUE)
+for (i in 1:h){
+  f4.l = trans3d(x=x, y=yy[i], z=z[,i], pmat=f4)
+  lines(f4.l, lwd=0.5, col="black")
+}
+f4.l1 = trans3d(x=point.f, y=yy, z=0, pmat=f4)
+lines(f4.l1, lwd=2, col="black")
+
+ +
+

Forecasting

+
+
+
+

+
+
+
+
+

MCMC convergence for hyper-parameters

+ +
+
plot.ts(run$hyper, main = "", col = "#F500BD", xlab = "s", cex.lab = 2, cex.axis = 1.3)
+ +
+
+
+

MCMC convergence for \(\mathbf\Sigma_{\cdot1}\)

+ +
+
plot.ts(run$sigma[,1,], main = "", col = "#F500BD", xlab = "s", cex.lab = 2, cex.axis = 1.3)
+ +
+
+
+

MCMC convergence for \(\boldsymbol\mu_0\)

+ +
+
plot.ts(run$beta[,1,], main = "", col = "#F500BD", xlab = "s", cex.lab = 2, cex.axis = 1.3)
+ +
+
+
+

Posterior means for \(\mathbf{A}\)

+ +
+
mean_A  = t(apply(run$beta, 2:3, mean))
+rownames(mean_A) = colnames(x)
+colnames(mean_A) = c("mu0",paste0("A",1:p %x% rep(1,3)))
+knitr::kable(mean_A, caption = "Posterior estimates for autoregressive parameters", digits = 2)
+
+ + ++++++++++++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Posterior estimates for autoregressive parameters
mu0A1A1A1A2A2A2A3A3A3A4A4A4A5A5A5
0.011.01-0.100.000.050.080.00-0.020.020.00-0.020.000.00-0.020.000.00
0.000.001.380.000.01-0.130.000.00-0.100.000.00-0.080.000.00-0.060.00
-0.0311.4011.351.21-3.672.72-0.49-3.98-8.600.36-2.39-3.73-0.12-1.36-1.76-0.03
+
+
+
+
+

Posterior means for \(\mathbf\Sigma\)

+ +
+
mean_S  = t(apply(run$sigma, 2:3, mean))
+mean_S  = cbind(mean_S, cov2cor(mean_S))
+rownames(mean_S) = colnames(x)
+colnames(mean_S) = c(rep("cov",3),rep("cor",3))
+knitr::kable(mean_S, caption = "Posterior estimates for covariance", digits = 5)
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Posterior estimates for covariance
covcovcovcorcorcor
0.000150.000010.001991.000000.098140.21109
0.000010.000020.000330.098141.000000.09753
0.001990.000330.607620.211090.097531.00000
+
+
+
+
+

Posterior means for hyper-parameters

+ +
+
mean_h  = rbind(apply(run$hyper, 2, mean), apply(run$hyper, 2, sd))
+rownames(mean_h) = c("E[hyper|data]", "sd[hyper|data]")
+knitr::kable(mean_h, caption = "Posterior estimates for hyper-parameters", digits = 3)
+
+ + + + + + + + + + + + + + + + + + + + + + + + +
Posterior estimates for hyper-parameters
lambdasocsur
E[hyper|data]1.9550.3140.947
sd[hyper|data]0.3020.1800.495
+
+
+
+
+

Australian Data Forecasting

+ +

\[ \]

+

DOWNLOAD THE SCRIPT

+ +
+
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/index.qmd b/index.qmd new file mode 100644 index 0000000..9fa5e39 --- /dev/null +++ b/index.qmd @@ -0,0 +1,1217 @@ +--- +title: "Lecture 7: Bayesian Vector Autoregressions" +author: "by Tomasz Woźniak" +email: "tomasz.wozniak@unimelb.edu.au" +title-slide-attributes: + data-background-color: "#F500BD" +number-sections: false +format: + revealjs: + theme: [simple, theme.scss] + slide-number: c + transition: concave + smaller: true + multiplex: true +execute: + echo: true +--- + +## {background-color="#F500BD"} + +$$ $$ + +### Vector Autoregressions + +### Three Useful Distributions + +### Bayesian Estimation + +### Minnesota and Dummy Observations Prior + +### Bayesian Estimation for Hierarchical Prior + +### Bayesian Forecasting using VARs + +### US Data Analysis Using R Package bsvarSIGNs + + + + + +## {background-color="#001D31"} + +![](bsvarSIGNs.png){.absolute top=30 right=275 width="500"} + + + +## Materials {background-color="#F500BD"} + +$$ $$ + +### Lecture Slides [as a Website](https://bayesian-econometrics-2023.github.io/be23-lecture7/) + +### A Dedicated Reading [Woźniak (2016, AERev)]( https://doi.org/10.1111/1467-8462.12179) + +### **Quarto** [document template](https://github.com/Bayesian-Econometrics-2023/be23-lecture7/blob/main/be23-AUdata.qmd) for your own Australian data forecasting + +### GitHub [repo](https://github.com/Bayesian-Econometrics-2023/be23-lecture7) to reproduce the slides and results + +### A [Kahoot!](https://kahoot.it/) Quiz + +### Tasks + + +## Vector Autoregressions {background-color="#F500BD"} + +## Vector Autoregressions + +- go-to models for forecasting + +::: incremental +- simple: *linear and Gaussian* +- extendible: *featuring many variations in specification* + - non-normality + - heteroskedasticity + - time-varying parameters + - Bayesian +- interpretable + - Granger causality + - spillovers + - networks + - structural +- Proposed by [Sims (1980)](https://doi.org/10.2307/1912017) +::: + +::: footer +[Bayesian VARs](https://bayesian-econometrics-2023.github.io/be23-lecture7/) +::: + +## VAR(p) Model + +### Model equations. + +\begin{align*} +y_t &= \mathbf{A}_1 y_{t-1} + \dots + \mathbf{A}_p y_{t-p} + \boldsymbol\mu_0 + \epsilon_t\\ +\epsilon_t|Y_{t-1} &\sim iidN\left(\mathbf{0}_N,\mathbf\Sigma\right) +\end{align*} for $t=1,\dots,T$ + +::: fragment +### Notation. + +- $y_t$ is an $N\times 1$ vector of observations at time $t$ +- $\mathbf{A}_i$ - $N\times N$ matrix of autoregressive slope parameters +- $\boldsymbol\mu_0$ - $N\times 1$ vector of constant terms +- $\epsilon_t$ - $N\times 1$ vector of error terms - a multivariate white noise process +- $Y_{t-1}$ - information set collecting observations on} $y$ up to time $t-1$ +- $\mathbf\Sigma$ - $N\times N$ covariance matrix of the error term +::: + +::: footer +[Bayesian VARs](https://bayesian-econometrics-2023.github.io/be23-lecture7/) +::: + +## A Bivariate VAR(2) Model + +Let the number of variable $N=2$ and the lag order $p=2$. + +Then, the model equation is: + +```{=tex} +\begin{align*} +\begin{bmatrix} y_{1.t} \\ y_{2.t} \end{bmatrix} +&= \begin{bmatrix} \mathbf{A}_{1.11} & \mathbf{A}_{1.12} \\ \mathbf{A}_{1.21} & \mathbf{A}_{1.22} \end{bmatrix} \begin{bmatrix} y_{1.t-1} \\ y_{2.t-1} \end{bmatrix} ++ \begin{bmatrix} \mathbf{A}_{2.11} & \mathbf{A}_{2.12} \\ \mathbf{A}_{2.21} & \mathbf{A}_{2.22} \end{bmatrix} \begin{bmatrix} y_{1.t-2} \\ y_{2.t-2} \end{bmatrix} + \begin{bmatrix} \boldsymbol\mu_{0.1} \\ \boldsymbol\mu_{0.2} \end{bmatrix} + \begin{bmatrix} \epsilon_{1.t} \\ \epsilon_{2.t} \end{bmatrix}\\[2ex] +\begin{bmatrix} \epsilon_{1.t} \\ \epsilon_{2.t} \end{bmatrix} &\Big|Y_{t-1} \sim iid N_2\left( \begin{bmatrix} 0\\ 0\end{bmatrix}, \begin{bmatrix}\boldsymbol\sigma_1^2 & \boldsymbol\sigma_{12} \\ \boldsymbol\sigma_{12} & \boldsymbol\sigma_2^2\end{bmatrix} \right) +\end{align*} +``` +. . . + +### Task: + +Perform the matrix multiplications and write out the equations for $y_{1.t}$ and $y_{2.t}$. + +::: footer +[Bayesian VARs](https://bayesian-econometrics-2023.github.io/be23-lecture7/) +::: + +## Three Useful Distributions {background-color="#F500BD"} + +## Matrix-Variate Normal Distribution + +A $K\times N$ matrix $\mathbf{A}$ is said to follow a *matrix-variate normal* distribution: $$ \mathbf{A} \sim MN_{K\times N}\left( M, Q, P \right), $$ where + +- $M$ - a $K\times N$ matrix of the mean +- $Q$ - a $N\times N$ row-specific covariance matrix +- $P$ - a $K\times K$ column-specific covariance matrix + +if $\text{vec}(\mathbf{A})$ is multivariate normal: $$ \text{vec}(\mathbf{A}) \sim N_{KN}\left( \text{vec}(M), Q\otimes P \right) $$ + +### Density function. + +```{=tex} +\begin{align*} +MN_{K\times N}\left( M, Q, P \right) &\propto \exp\left\{ -\frac{1}{2}\text{tr}\left[ Q^{-1}(\mathbf{A}-M)'P^{-1}(\mathbf{A}-M) \right] \right\} +\end{align*} +``` +- $\text{tr}()$ is a trace of a matrix - a sum of diagonal elements + +::: footer +[Bayesian VARs](https://bayesian-econometrics-2023.github.io/be23-lecture7/) +::: + +## Inverse Wishart Distribution + +An $N\times N$ square symmetric and positive definite matrix $\mathbf\Sigma$ follows an *inverse Wishart* distribution: $$ \mathbf\Sigma \sim IW_{N}\left( S, \nu \right) $$ where + +- $S$ is $N\times N$ positive definite symmetric matrix called the scale matrix +- $\nu \geq N$ denotes degrees of freedom, if its density is given by: + +### Density function. + +```{=tex} +\begin{align*} +IW_{N}\left( S, \nu \right) \propto \text{det}(\mathbf\Sigma)^{-\frac{\nu+N+1}{2}}\exp\left\{ -\frac{1}{2}\text{tr}\left[ \mathbf\Sigma^{-1} S \right] \right\} +\end{align*} +``` +::: footer +[Bayesian VARs](https://bayesian-econometrics-2023.github.io/be23-lecture7/) +::: + +## Normal-Inverse Wishart Distribution + +```{=tex} +\begin{align*} +\mathbf{A}|\mathbf\Sigma &\sim MN_{K\times N}\left( M, \mathbf\Sigma, P \right)\\ +\mathbf\Sigma &\sim IW_{N}\left( S, \nu \right) +\end{align*} +``` +then the joint distribution of $(\mathbf{A},\mathbf\Sigma)$ is *normal-inverse Wishart* $$ +p(\mathbf{A},\mathbf\Sigma) = NIW_{K\times N}\left( M,P,S,\nu\right) +$$ + +### Density function. + +```{=tex} +\begin{align*} +NIW_{K\times N}\left( M,P,S,\nu\right) \propto &\text{det}(\mathbf{\Sigma})^{-(\nu+N+K+1)/2}\exp\left\{ -\frac{1}{2}\text{tr}\left[ \mathbf{\Sigma}^{-1} S \right] \right\}\\ +&\times\exp\left\{ -\frac{1}{2}\text{tr}\left[ \mathbf{\Sigma}^{-1} (\mathbf{A}-M)'P^{-1}(\mathbf{A}-M) \right] \right\} +\end{align*} +``` +::: footer +[Bayesian VARs](https://bayesian-econometrics-2023.github.io/be23-lecture7/) +::: + +## Example: Error Term Distribution + +The model assumptions state: \begin{align*} +\epsilon_t|Y_{t-1} &\sim iidN_N\left(\mathbf{0}_N,\mathbf\Sigma\right) +\end{align*} + +Collect error term vectors in a $T\times N$ matrix: $$\underset{(T\times N)}{E}= \begin{bmatrix}\epsilon_1 & \epsilon_2 & \dots & \epsilon_{T}\end{bmatrix}'$$ + +Error term matrix is matrix-variate distributed: \begin{align*} +E|X &\sim MN_{T\times N}\left(\mathbf{0}_{T\times N},\mathbf\Sigma, I_T\right) +\end{align*} + +::: {.fragment .fade-in} +### Tasks: what is + +- the covariance of $\text{vec}(E)$ +- the distribution of the first equation error terms $\begin{bmatrix}\epsilon_{1.1} &\dots&\epsilon_{1.T}\end{bmatrix}'$ +::: + +::: footer +[Bayesian VARs](https://bayesian-econometrics-2023.github.io/be23-lecture7/) +::: + +## Example: Univariate *Inverse Wishart* Distribution + +The *inverse Wishart* density function is proportional to: \begin{align*} +\text{det}(\mathbf\Sigma)^{-\frac{\nu+N+1}{2}}\exp\left\{ -\frac{1}{2}\text{tr}\left[ \mathbf\Sigma^{-1} S \right] \right\} +\end{align*} + +Consider a case where: + +- $N=1$ +- the matrix $\mathbf\Sigma$ is replaced by a scalar $\boldsymbol\sigma^2$ + +::: {.fragment .fade-in} +### Task: + +- write out the kernel of the density function for $\boldsymbol\sigma^2$ +- the kernel of what density it represents? +::: + +::: footer +[Bayesian VARs](https://bayesian-econometrics-2023.github.io/be23-lecture7/) +::: + +## Bayesian Estimation {background-color="#F500BD"} + +## The model in Matrix Notation + +### VAR(p) model. + +```{=tex} +\begin{align*} +y_t &= \mathbf{A}_1 y_{t-1} + \dots + \mathbf{A}_p y_{t-p} + \boldsymbol\mu_0 + \epsilon_t\\ +\epsilon_t|Y_{t-1} &\sim iidN_N\left(\mathbf{0}_N,\mathbf\Sigma\right) +\end{align*} +``` +### Matrix notation. + +```{=tex} +\begin{align*} +Y &= X\mathbf{A} + E\\ +E|X &\sim MN_{T\times N}\left(\mathbf{0}_{T\times N},\mathbf\Sigma, I_T\right) +\end{align*} +``` +::: {.fragment .fade-out} +$$ +\underset{(K\times N)}{\mathbf{A}}=\begin{bmatrix} \mathbf{A}_1'\\ \vdots \\ \mathbf{A}_p' \\ \boldsymbol\mu_0' \end{bmatrix} \quad +\underset{(T\times N)}{Y}= \begin{bmatrix}y_1' \\ y_2'\\ \vdots \\ y_T'\end{bmatrix} \quad +\underset{(K\times1)}{x_t}=\begin{bmatrix} y_{t-1}\\ \vdots \\ y_{t-p}\\ 1 \end{bmatrix}\quad +\underset{(T\times K)}{X}= \begin{bmatrix}x_1' \\ x_2' \\ \vdots \\ x_{T}'\end{bmatrix} \quad +\underset{(T\times N)}{E}= \begin{bmatrix}\epsilon_1' \\ \epsilon_2' \\ \vdots \\ \epsilon_{T}'\end{bmatrix} +$$ where $K=pN+1$ +::: + +::: footer +[Bayesian VARs](https://bayesian-econometrics-2023.github.io/be23-lecture7/) +::: + +## The model as Predictive Density + +### VAR model. + +```{=tex} +\begin{align*} +Y &= X\mathbf{A} +E\\ +E|X &\sim MN_{T\times N}\left(\mathbf{0}_{T\times N},\mathbf\Sigma, I_T\right) +\end{align*} +``` +### Predictive density. + +```{=tex} +\begin{align*} +Y|X,\mathbf{A}, \mathbf{\Sigma} &\sim MN_{T\times N}\left(X\mathbf{A},\mathbf{\Sigma},I_T\right) +\end{align*} +``` +::: footer +[Bayesian VARs](https://bayesian-econometrics-2023.github.io/be23-lecture7/) +::: + +## Likelihood Function + +### Predictive density. + +```{=tex} +\begin{align*} +Y|X,\mathbf{A}, \mathbf{\Sigma} &\sim MN_{T\times N}\left(X\mathbf{A},\mathbf{\Sigma},I_T\right) +\end{align*} +``` +### Likelihood function. + +```{=tex} +\begin{align*} +L\left(\mathbf{A},\mathbf{\Sigma}|Y,X\right)&\propto\text{det}(\mathbf{\Sigma})^{-\frac{T}{2}}\exp\left\{-\frac{1}{2}\text{tr}\left[\mathbf{\Sigma}^{-1}(Y-X\mathbf{A})'(Y-X\mathbf{A})\right]\right\} +\end{align*} +``` +::: footer +[Bayesian VARs](https://bayesian-econometrics-2023.github.io/be23-lecture7/) +::: + +## Likelihood Function as NIW + +Define the MLE: $\widehat{A}=(X'X)^{-1}X'Y$ + +Perform simple transformation of the likelihood + +```{=tex} +\begin{align*} +L\left(\mathbf{A},\mathbf{\Sigma}|Y,X\right)&\propto\text{det}(\mathbf{\Sigma})^{-\frac{T}{2}}\exp\left\{-\frac{1}{2}\text{tr}\left[\mathbf{\Sigma}^{-1}(Y-X\mathbf{A})'(Y-X\mathbf{A})\right]\right\}\\ +&=\text{det}(\mathbf{\Sigma})^{-\frac{T}{2}}\\ +&\quad\times\exp\left\{ -\frac{1}{2}\text{tr}\left[\mathbf{\Sigma}^{-1}(\mathbf{A}-\widehat{A})'X'X(\mathbf{A}-\widehat{A}) \right] \right\}\\ +&\quad\times \exp\left\{ -\frac{1}{2}\text{tr}\left[ \mathbf{\Sigma}^{-1}(Y-X\widehat{A})'(Y-X\widehat{A}) \right] \right\} +\end{align*} +``` +Under the likelihood, $(\mathbf{A},\mathbf{\Sigma})$ are *normal-inverse Wishart* distributed: + +```{=tex} +\begin{align*} +L\left( \mathbf{A},\mathbf{\Sigma}|Y,X \right) &= NIW_{K\times N}\left(\widehat{A},(X'X)^{-1},(Y-X\widehat{A})'(Y-X\widehat{A}), T-N-K-1 \right) +\end{align*} +``` +::: footer +[Bayesian VARs](https://bayesian-econometrics-2023.github.io/be23-lecture7/) +::: + +## Prior Distribution + +### Construction. + +A natural-conjugate prior leads to joint posterior distribution for $(\mathbf{A},\mathbf{\Sigma})$ of the same form \begin{align*} +p\left( \mathbf{A}, \mathbf{\Sigma} \right) &= p\left( \mathbf{A}| \mathbf{\Sigma} \right)p\left( \mathbf{\Sigma} \right)\\ +\mathbf{A}|\mathbf{\Sigma} &\sim MN_{K\times N}\left( \underline{A},\mathbf{\Sigma},\underline{V} \right)\\ +\mathbf{\Sigma} &\sim IW_N\left( \underline{S}, \underline{\nu} \right) +\end{align*} + +### Kernel. + +```{=tex} +\begin{align*} +p\left( \mathbf{A},\mathbf{\Sigma} \right) +&\propto \text{det}(\mathbf{\Sigma})^{-\frac{N+K+\underline{\nu}+1}{2}}\\ +&\quad\times\exp\left\{ -\frac{1}{2}\text{tr}\left[ \mathbf{\Sigma}^{-1}(\mathbf{A}-\underline{A})'\underline{V}^{-1}(\mathbf{A}-\underline{A}) \right] \right\}\\ +&\quad\times \exp\left\{ -\frac{1}{2}\text{tr}\left[ \mathbf{\Sigma}^{-1}\underline{S} \right] \right\} +\end{align*} +``` +::: footer +[Bayesian VARs](https://bayesian-econometrics-2023.github.io/be23-lecture7/) +::: + +## Posterior Distribution + +### Bayes Rule. + +```{=tex} +\begin{align*} +p\left( \mathbf{A}, \mathbf{\Sigma}|Y,X \right) &\propto L(\mathbf{A},\mathbf{\Sigma}|Y,X)p\left( \mathbf{A}, \mathbf{\Sigma} \right)\\ +&= L(\mathbf{A},\mathbf{\Sigma}|Y,X)p\left( \mathbf{A}| \mathbf{\Sigma} \right)p\left( \mathbf{\Sigma} \right) +\end{align*} +``` +### Kernel. + +```{=tex} +\begin{align*} +p\left( \mathbf{A},\mathbf{\Sigma} |Y,X\right) +&\propto \text{det}(\mathbf{\Sigma})^{-\frac{T}{2}}\exp\left\{-\frac{1}{2}\text{tr}\left[\mathbf{\Sigma}^{-1}(Y-X\mathbf{A})'(Y-X\mathbf{A})\right]\right\}\\ +& \quad\times\text{det}(\mathbf{\Sigma})^{-\frac{N+K+\underline{\nu}+1}{2}}\exp\left\{ -\frac{1}{2}\text{tr}\left[ \mathbf{\Sigma}^{-1}\underline{S} \right] \right\}\\ +&\quad\times\exp\left\{ -\frac{1}{2}\text{tr}\left[ \mathbf{\Sigma}^{-1}(\mathbf{A}-\underline{A})'\underline{V}^{-1}(\mathbf{A}-\underline{A}) \right] \right\} +\end{align*} +``` +::: footer +[Bayesian VARs](https://bayesian-econometrics-2023.github.io/be23-lecture7/) +::: + +## Joint Posterior Distribution + +### Conditional and marginal. + +```{=tex} +\begin{align*} +p\left( \mathbf{A}, \mathbf{\Sigma}|Y,X \right) &= p(\mathbf{A}|Y,X,\mathbf{\Sigma})p\left( \mathbf{\Sigma}|Y,X \right)\\[2ex] +p(\mathbf{A}|Y,X,\mathbf{\Sigma}) &= MN_{K\times N}\left( \overline{A},\mathbf{\Sigma},\overline{V} \right)\\ +p(\mathbf{\Sigma}|Y,X) &= IW_N\left( \overline{S}, \overline{\nu} \right) +\end{align*} +``` +### Posterior parameters. + +```{=tex} +\begin{align*} +\overline{V}&= \left( X'X + \underline{V}^{-1}\right)^{-1} \\ +\overline{A}&= \overline{V}\left( X'Y + \underline{V}^{-1}\underline{A} \right)\\ +\overline{\nu}&= T+\underline{\nu}\\ +\overline{S}&= \underline{S}+Y'Y + \underline{A}'\underline{V}^{-1}\underline{A} - \overline{A}'\overline{V}^{-1}\overline{A} +\end{align*} +``` +::: footer +[Bayesian VARs](https://bayesian-econometrics-2023.github.io/be23-lecture7/) +::: + +## Posterior Mean of $\mathbf{A}$ + +Posterior mean of matrix $\mathbf{A}$ is: \begin{align*} +\overline{A} &= \overline{V}\left( X'Y + \underline{V}^{-1}\underline{A} \right)\\[2ex] +&= \overline{V}\left( X'X\widehat{A} + \underline{V}^{-1}\underline{A} \right)\\[2ex] +&= \overline{V} X'X\widehat{A} + \overline{V}\underline{V}^{-1}\underline{A} +\end{align*} a linear combination of the MLE $\widehat{A}$ and the prior mean $\underline{A}$ + +Note that: $$ +\overline{V} X'X + \overline{V}\underline{V}^{-1} = \overline{V} ( X'X + \underline{V}^{-1}) = I_K +$$ + +[Play with the posterior in an interactive graph](https://rpsychologist.com/d3/bayes/){preview-link="true"} + +::: footer +[Bayesian VARs](https://bayesian-econometrics-2023.github.io/be23-lecture7/) +::: + +## Marginal Data Density + +According to *Bayes Rule*, the kernel of the posterior is normalised by the *Marginal Data Density* $p(data)$: + +$$ +p\left( \mathbf{A}, \mathbf{\Sigma}| data \right) = \frac{L(\mathbf{A},\mathbf{\Sigma}| data)p\left( \mathbf{A}, \mathbf{\Sigma} \right)}{p(data)} +$$ + +For *Bayesian VARs* the posterior is known $$ +p\left( \mathbf{A}, \mathbf{\Sigma}| data \right) = MNIW\left(\overline{A},\overline{V}, \overline{S}, \overline{\nu} \right) +$$ + +and so is the analytical formula for the *MDD*: $$p(data)$$ + +This can be used to our advantage! + +::: footer +[Bayesian VARs](https://bayesian-econometrics-2023.github.io/be23-lecture7/) +::: + +## Minnesota and Dummy Observations Prior {background-color="#F500BD"} + +## Minnesota Prior + +[Sims, Litterman, Doan (1984)](https://doi.org/10.1080/07474938408800053) proposed an interpretable way of setting the hyper-parameters on the NIW prior $\underline{A}$, $\underline{V}$, $\underline{S}$, and $\underline{\nu}$ for macroeconomic data. + +. . . + +$$ $$ The prior reflects the following stylised facts about macro time series: + +- the data are unit-root non-stationary +- the effect of more lagged variables should be smaller and smaller +- the effect of other variables lags should be less than that of own lags + +::: footer +[Bayesian VARs](https://bayesian-econometrics-2023.github.io/be23-lecture7/) +::: + +## Minnesota Prior + +### Inverse-Wishart prior. + +```{=tex} +\begin{align*} +\mathbf{\Sigma} &\sim IW_N\left( \underline{S}, \underline{\nu} \right) +\end{align*} +``` +Set + +```{=tex} +\begin{align*} +\underline{S} &= \begin{bmatrix} +\psi_1 &0 &\dots & 0 \\ +0 & \psi_2 &\dots & 0\\ +\vdots &\vdots&\ddots& \vdots\\ +0&0&\dots&\psi_N +\end{bmatrix}\\[2ex] +\underline{\nu}&= N+2 +\end{align*} +``` +### Hyper-parameters. + +$\psi =(\psi_1, \dots, \psi_N)$ have to be chosen (or estimated) + +::: footer +[Bayesian VARs](https://bayesian-econometrics-2023.github.io/be23-lecture7/) +::: + +## Minnesota Prior + +### Matrix-Variate Normal prior. + +```{=tex} +\begin{align*} +\mathbf{A}|\mathbf{\Sigma} &\sim MN_{K\times N}\left( \underline{A},\mathbf{\Sigma},\underline{V} \right) +\end{align*} +``` +Set \begin{align*} +\underline{A} &= \begin{bmatrix} I_N \\ \mathbf{0}_{((p-1)N +1)\times N}\end{bmatrix}& +\underline{V}_{ij} &= \left\{\begin{array} (\lambda ^ 2 / (\psi_k l^2) &\text{ for }i=j,\text{ and } i\neq pN+1 \\ +\lambda^2 &\text{ for }i=j,\text{ and } i= pN+1 \\ +0&\text{ for } i\neq j +\end{array}\right. +\end{align*} + +for $\quad l = 1+\text{floor}((i-1)/N) \quad\text{and }\quad k = i - (l-1)N$ + +### Hyper-parameters. + +$\lambda^2$ has to be chosen (or estimated) + +::: footer +[Bayesian VARs](https://bayesian-econometrics-2023.github.io/be23-lecture7/) +::: + +## Dummy Observations Prior + +### Idea. + +1. Generate artificial data matrices with $T_d$ rows $Y^*$ and $X^*$ +2. Append them to the original data matrices $Y$ and $X$ respectively. + +::: fragment +### Implied prior distribution. + +Use Bayes Rule to derive the joint prior of $(\mathbf{A},\mathbf\Sigma)$ given $Y^*$ and $X^*$. + +It is given by the MNIW distribution: + +\begin{align*} +p\left( \mathbf{A}, \mathbf{\Sigma}|Y^*,X^* \right) &= MNIV_{K\times N}\left( \underline{A}^*,\underline{V}^*, \underline{S}^*, \underline{\nu}^* \right) +\end{align*} \begin{align*} +\underline{V}^*&= \left( X^{*\prime}X^* + \underline{V}^{-1}\right)^{-1} & \underline{A}^*&= \underline{V}^*\left( X^{*\prime}Y^* + \underline{V}^{-1}\underline{A} \right)\\ +\underline{\nu}^*&= T_d+\underline{\nu} & \underline{S}^*&= \underline{S}+Y^{*\prime}Y^* + \underline{A}'\underline{V}^{-1}\underline{A} - \underline{A}^{*\prime}\underline{V}^{*-1}\underline{A}^* +\end{align*} +::: + +::: footer +[Bayesian VARs](https://bayesian-econometrics-2023.github.io/be23-lecture7/) +::: + +## Dummy Observations Prior + +Let a $p\times N$ matrix $Y_0$ denote the initial observations, that is, the first $p$ observations of the available time series. + +Let an $N$-vector $\bar{Y}_0$ denote its columns' means. + +::: fragment +### Sum-of-coefficients prior. + +Generate additional $N$ rows by $$ +Y^+ = \text{diag}\left(\frac{\bar{Y}_0}{\mu}\right) \quad\text{ and }\quad X^+ = \begin{bmatrix}\mathbf{0}_N & Y^+ & \dots & Y^+ \end{bmatrix} +$$ + +- $\mu$ is a hyper-parameter to be chosen (or estimated) +- if $\mu \rightarrow 0$ the prior implies the presence of a unit root in each equation and rules out cointegration +- if $\mu \rightarrow\infty$ the prior becomes uninformative +::: + +::: footer +[Bayesian VARs](https://bayesian-econometrics-2023.github.io/be23-lecture7/) +::: + +## Dummy Observations Prior + +### Dummy-initial-observation prior. + +Generate an additional row by $$ +Y^{++} = \frac{\bar{Y}_0'}{\delta} \quad\text{ and }\quad X^{++} = \begin{bmatrix}\frac{1}{\delta} & Y^{++} & \dots & Y^{++} \end{bmatrix} +$$ + +- hyper-parameter $\delta$ is to be chosen (or estimated) +- if $\delta \rightarrow 0$ all the variables of the VAR are forced to be at their unconditional mean, or the system is characterized by the presence of an unspecified number of unit roots without drift (cointegration) +- if $\delta \rightarrow\infty$ the prior becomes uninformative + +::: fragment +### Combining dummy observations. + +$$ +Y^* = \begin{bmatrix}Y^+ \\ Y^{++} \end{bmatrix}\quad\text{ and }\quad +X^* = \begin{bmatrix}X^+ \\ X^{++} \end{bmatrix} +$$ +::: + +::: footer +[Bayesian VARs](https://bayesian-econometrics-2023.github.io/be23-lecture7/) +::: + + + +## Dummy Observations Prior + +### Task. + +Suppose that: + +- $\bar{Y}_0 = \begin{bmatrix}1&2\end{bmatrix}'$ +- $\mu = 0.5$ +- $\delta = 3$ +- $p = 1$ + +Write out the matrices $Y^*$ and $X^*$ of dimensions $2\times 3$ and $3\times 3$ respectively. + + +::: footer +[Bayesian VARs](https://bayesian-econometrics-2023.github.io/be23-lecture7/) +::: + + + + + + + + + + + + + + + + +## Bayesian Estimation for Hierarchical Prior {background-color="#F500BD"} + +## Bayesian Estimation for Hierarchical Prior + +Hyper-parameters $\psi$, $\lambda$, $\mu$ and $\delta$ can be fixed to values chosen by the econometrician. + +### Hierarcical prior. + +A better idea is to assume priors for these hyper-parameters and estimate them as in [Giannone, Lenza, Primiceri (2015)](https://doi.org/10.1162/REST_a_00483). + +Extend the existing prior to: \begin{align*} +p\left( \mathbf{A}, \mathbf{\Sigma}|Y^*,X^*,\psi,\lambda,\mu,\delta \right) &= MNIV_{K\times N}\left( \underline{A}^*,\underline{V}^*, \underline{S}^*, \underline{\nu}^* \right) +\end{align*} And specify: \begin{align*} +\psi_n &\sim IG\left(0.02^2, 0.02^2\right)\\ +\lambda &\sim G\left(0.2,2\right)\\ +\mu &\sim G\left(1,2\right)\\ +\delta &\sim G\left(1,2\right) +\end{align*} + +::: footer +[Bayesian VARs](https://bayesian-econometrics-2023.github.io/be23-lecture7/) +::: + +## Bayesian Estimation for Hierarchical Prior + +[Giannone, Lenza, Primiceri (2015)](https://doi.org/10.1162/REST_a_00483) propose the following estimation procedure: + +#### Step 1: Estimate $(\psi,\lambda,\mu,\delta)$ using a random-walk Metropolis-Hastings sampler + +- Sample these hyper-parameters marginally on $(\mathbf{A},\mathbf\Sigma)$ +- extend the conditioning of *Marginal Data Density*: $$ p(data|\psi,\lambda,\mu,\delta)$$ +- apply Bayes Rule to obtain the kernel of the posterior: + +$$ p(\psi,\lambda,\mu,\delta|data) \propto p(\psi,\lambda,\mu,\delta)p(data|\psi,\lambda,\mu,\delta)$$ - Use an $(N+3)$-variate Student-t distribution as the candidate generating density + +::: footer +[Bayesian VARs](https://bayesian-econometrics-2023.github.io/be23-lecture7/) +::: + +## Bayesian Estimation for Hierarchical Prior + +#### Step 2: For each draw of $(\psi,\lambda,\mu,\delta)$ sample the corresponding draw of $(\mathbf{A},\mathbf{\Sigma})$ + +Use the MNIW posterior derived for the implied prior: + +```{=tex} +\begin{align*} +p\left( \mathbf{A}, \mathbf{\Sigma}|Y,X, Y^*,X^* \right) &= MNIW_{K\times N}\left( \overline{A}^*,\overline{V}^*,\overline{S}^*, \overline{\nu}^* \right)\\[2ex] +\overline{V}^*&= \left( X'X + \underline{V}^{*-1}\right)^{-1} \\ +\overline{A}^*&= \overline{V}^*\left( X'Y + \underline{V}^{*-1}\underline{A}^* \right)\\ +\overline{\nu}^*&= T+\underline{\nu}^*\\ +\overline{S}^*&= \underline{S}^*+Y'Y + \underline{A}^{*\prime}\underline{V}^{*-1}\underline{A}^* - \overline{A}^{*\prime}\overline{V}^{*-1}\overline{A}^* +\end{align*} +``` +### R implementation. + +Package [**BVAR**](https://cran.r-project.org/web/packages/BVAR/index.html) by [Kuschnig, Vashold (2021)](https://doi.org/10.1162%2FREST_a_00483) implements this algorithm. + +::: footer +[Bayesian VARs](https://bayesian-econometrics-2023.github.io/be23-lecture7/) +::: + + + + + + +## Bayesian Forecasting using VARs {background-color="#F500BD"} + + + +## The objective of economic forecasting + +::: footer +[Bayesian VARs](https://bayesian-econometrics-2023.github.io/be23-lecture7/) +::: + +$\left.\right.$ + +... is to use the available data to provide a statistical characterisation of the unknown future values of quantities of interest. + +$\left.\right.$ + +The full statistical characterisation of the unknown future values of random variables is given by their *predictive density*. + +$\left.\right.$ + +Simplified outcomes in a form of statistics summarising the predictive densities are usually used in decision-making processes. + +$\left.\right.$ + +Summary statistics are also communicated to general audiences. + + +## One-Period Ahead Predictive Density + +::: footer +[Bayesian VARs](https://bayesian-econometrics-2023.github.io/be23-lecture7/) +::: + +### VAR(p) model. +\begin{align*} +y_t &= \mathbf{A}_1 y_{t-1} + \dots + \mathbf{A}_p y_{t-p} + \boldsymbol\mu_0 + \epsilon_t\\[2ex] +\epsilon_t|Y_{t-1} &\sim iidN_N\left(\mathbf{0}_N,\mathbf\Sigma\right)\\ +& +\end{align*} + +### One-Period Ahead Conditional Predictive Density + +... is implied by the model formulation: +\begin{align*} +y_{t+h}|Y_{t+h-1},\mathbf{A},\mathbf\Sigma &\sim N_N\left(\mathbf{A}_1 y_{t+h-1} + \dots + \mathbf{A}_p y_{t+h-p} + \boldsymbol\mu_0,\mathbf\Sigma\right) +\end{align*} + + +## One-Period Ahead Predictive Density + +::: footer +[Bayesian VARs](https://bayesian-econometrics-2023.github.io/be23-lecture7/) +::: + +$\left.\right.$ + +Bayesian forecasting takes into account the uncertainty w.r.t. parameter estimation by integrating it out from the predictive density. + + +\begin{align*} +&\\ +p(y_{T+1}|Y,X) &= \int p(y_{T+1}|Y_{T},\mathbf{A},\mathbf\Sigma) p(\mathbf{A},\mathbf\Sigma|Y,X) d(\mathbf{A},\mathbf\Sigma)\\ & +\end{align*} + +- $p(y_{T+1}|Y,X)$ - predictive density +- $p(y_{T+1}|Y_{t},\mathbf{A},\mathbf\Sigma)$ - one-period-ahead conditional predictive density +- $p(\mathbf{A},\mathbf\Sigma|Y,X)$ - marginal posterior distribution + + +## Sampling from One-Period Ahead Predictive Density + +::: footer +[Bayesian VARs](https://bayesian-econometrics-2023.github.io/be23-lecture7/) +::: + +$\left.\right.$ + +#### Step 1: Sample from the posterior + +... and obtain $S$ draws $\left\{ \mathbf{A}^{(s)},\mathbf\Sigma^{(s)} \right\}_{s=1}^{S}$ + +$\left.\right.$ + +#### Step 2: Sample from the predictive density + +In order to obtain draws from $p(y_{T+1}|Y,X)$, for each of the $S$ draws of $(\mathbf{A},\mathbf\Sigma)$ sample the corresponding draw of $y_{T+1}$: + +Sample $y_{T+1}^{(s)}$ from +$$ +N_N\left(\mathbf{A}_1^{(s)} y_{T} + \dots + \mathbf{A}_p^{(s)} y_{T-p+1} + \boldsymbol\mu_0^{(s)},\mathbf\Sigma^{(s)}\right) +$$ +and obtain $\left\{y_{T+1}^{(s)}\right\}_{s=1}^{S}$ + + +## $h$-Period Ahead Predictive Density + +::: footer +[Bayesian VARs](https://bayesian-econometrics-2023.github.io/be23-lecture7/) +::: + +$\left.\right.$ + +This procedure can be generalised to any forecasting horizon. + +This is an illustration for $h=2$. + +\begin{align*} +&\\ +p(y_{T+2},y_{T+1}|Y,X) +&= \int p(y_{T+2},y_{T+1}|Y_{T},\mathbf{A},\mathbf\Sigma) p(\mathbf{A},\mathbf\Sigma|Y,X) d(\mathbf{A},\mathbf\Sigma)\\[1ex] +&= \int p(y_{T+2}|y_{T+1},Y_{T},\mathbf{A},\mathbf\Sigma)p(y_{T+1}|Y_{T},\mathbf{A},\mathbf\Sigma) p(\mathbf{A},\mathbf\Sigma|Y,X) d(\mathbf{A},\mathbf\Sigma)\\ & +\end{align*} + + +## $h$-Period Ahead Predictive Density + +::: footer +[Bayesian VARs](https://bayesian-econometrics-2023.github.io/be23-lecture7/) +::: + +$\left.\right.$ + +#### Step 1: Sample from the posterior + +... and obtain $S$ draws $\left\{ \mathbf{A}^{(s)},\mathbf\Sigma^{(s)} \right\}_{s=1}^{S}$ + +#### Step 2: Sample from 1-period ahead predictive density + +For each of the $S$ draws, sample $y_{T+1}^{(s)}$ from +$$ +N_N\left(\mathbf{A}_1^{(s)} y_{T} + \dots + \mathbf{A}_p^{(s)} y_{T-p+1} + \boldsymbol\mu_0^{(s)},\mathbf\Sigma^{(s)}\right) +$$ + +#### Step 3: Sample from 2-period ahead predictive density + +For each of the $S$ draws, sample $y_{T+2}^{(s)}$ from +$$ +N_N\left(\mathbf{A}_1^{(s)} y_{T+1}^{(s)} + \mathbf{A}_2 y_{T} + \dots + \mathbf{A}_p^{(s)} y_{T-p+2} + \boldsymbol\mu_0^{(s)},\mathbf\Sigma^{(s)}\right) +$$ + +and obtain $\left\{y_{T+2}^{(s)},y_{T+1}^{(s)}\right\}_{s=1}^{S}$ + + + + + +## The Bayesian VARs Quiz + +$$ $$ + +[GO TO THE GAME](https://kahoot.it) + + +::: footer +[Bayesian VARs](https://bayesian-econometrics-2023.github.io/be23-lecture7/) +::: + + + + + + + + + + + +## US Data Analysis Using R Package BVAR {background-color="#F500BD"} + +## Data preparation + +::: footer +[Bayesian VARs](https://bayesian-econometrics-2023.github.io/be23-lecture7/) +::: + +```{r} +#| label: us-data +#| warning: false +#| fig-align: "center" +#| fig-height: 11 +#| output-location: column +#| cache: true + +set.seed(42) +library(BVAR) + +# data +x = fred_qd[, c("GDPC1", + "GDPCTPI", + "FEDFUNDS")] +x = fred_transform( + x, + codes = c(4, 4, 1) +) + +plot.ts( + x, + main = "", + col = "#F500BD", + lwd = 4, + cex.axis = 2, + cex.lab = 2 +) +``` + + + + +## Prior setup + +::: footer +[Bayesian VARs](https://bayesian-econometrics-2023.github.io/be23-lecture7/) +::: + +```{r} +#| label: priors +#| warning: false +#| cache: true + +# priors +mn = bv_minnesota( + lambda = bv_lambda(mode = 0.2, sd = 0.4, min = 0.0001, max = 5), + alpha = bv_alpha(mode = 2), + psi <- bv_psi(scale = 0.004, shape = 0.004, mode = "auto", min = "auto", max = "auto"), + var = 1e07 +) + +soc = bv_soc(mode = 1, sd = 1, min = 1e-04, max = 50) +sur = bv_sur(mode = 1, sd = 1, min = 1e-04, max = 50) + +priors = bv_priors(hyper = "auto", mn = mn, soc = soc, sur = sur) + +# MH setup +mh = bv_metropolis( + scale_hess = c(0.05, 0.0001, 0.0001), + adjust_acc = TRUE, + acc_lower = 0.25, + acc_upper = 0.45 +) +``` + + +## Estimation + +::: footer +[Bayesian VARs](https://bayesian-econometrics-2023.github.io/be23-lecture7/) +::: + +```{r} +#| label: estimation +#| cache: true + +# estimation +p = 5 +run = bvar( + x, + lags = p, + n_draw = 3e4, + n_burn = 1e4, + n_thin = 1, + priors = priors, + mh = mh, + verbose = TRUE # with progress bar +) + +``` + + + +## Forecasting + +::: footer +[Bayesian VARs](https://bayesian-econometrics-2023.github.io/be23-lecture7/) +::: + +```{r} +#| label: forecasting +#| warning: false +#| fig-align: "center" +#| out.width: "100%" +#| output-location: slide +#| cache: true + +# forecasting +predict(run) <- predict( + run, + horizon = 20, + conf_bands = seq(from = 0.05, to = 0.4, by = 0.01) +) +plot( + predict(run), + area = TRUE, + t_back = 32, + vars = c("GDPC1") +) +``` + + + +## Forecasting + +::: footer +[Bayesian VARs](https://bayesian-econometrics-2023.github.io/be23-lecture7/) +::: + +```{r} +#| label: forecasting-gdpdef +#| echo: false +#| warning: false +#| fig-align: "center" +#| out.width: "100%" +#| output-location: slide +#| cache: true + +plot( + predict(run), + area = TRUE, + t_back = 32, + vars = c("GDPCTPI") +) +``` + + +## Forecasting + +::: footer +[Bayesian VARs](https://bayesian-econometrics-2023.github.io/be23-lecture7/) +::: + +```{r} +#| label: forecasting-ffr +#| echo: false +#| warning: false +#| fig-align: "center" +#| out.width: "100%" +#| output-location: slide +#| cache: true + +plot( + predict(run), + area = TRUE, + t_back = 32, + vars = c("FEDFUNDS") +) +``` + + + +## Forecasting + +::: footer +[Bayesian VARs](https://bayesian-econometrics-2023.github.io/be23-lecture7/) +::: + +```{r} +#| label: 3D-gdp +#| warning: false +#| fig-align: "center" +#| out.width: "100%" +#| output-location: slide +#| cache: true + +Y.h = aperm(run$fcast$fcast, c(2,3,1)) +h = dim(Y.h)[1] + +limits.1 = range(Y.h[,1,]) +point.f = apply(Y.h[,1,],1,mean) +interval.f = apply(Y.h[,1,],1,HDInterval::hdi,credMass=0.90) + +x = seq(from=limits.1[1], to=limits.1[2], length.out=100) +z = matrix(NA,h,99) +for (i in 1:h){ + z[i,] = hist(Y.h[i,1,], breaks=x, plot=FALSE)$density +} +x = hist(Y.h[i,1,], breaks=x, plot=FALSE)$mids +yy = 1:h +z = t(z) + +library(plot3D) +theta = 180 +phi = 15.5 +f4 = persp3D(x=x, y=yy, z=z, phi=phi, theta=theta, xlab="\nrgdp[t+h|t]", ylab="h", zlab="\npredictive densities of rgdp", shade=NA, border=NA, ticktype="detailed", nticks=3,cex.lab=1, col=NA,plot=FALSE) +perspbox (x=x, y=yy, z=z, bty="f", col.axis="black", phi=phi, theta=theta, xlab="\nrgdp[t+h|t]", ylab="h", zlab="\npredictive densities of rgdp", ticktype="detailed", nticks=3,cex.lab=1, col = NULL, plot = TRUE) +polygon3D(x=c(interval.f[1,],interval.f[2,h:1]), y=c(1:h,h:1), z=rep(0,2*h), col = "#F500BD", NAcol = "white", border = NA, add = TRUE, plot = TRUE) +for (i in 1:h){ + f4.l = trans3d(x=x, y=yy[i], z=z[,i], pmat=f4) + lines(f4.l, lwd=0.5, col="black") +} +f4.l1 = trans3d(x=point.f, y=yy, z=0, pmat=f4) +lines(f4.l1, lwd=2, col="black") +``` + + + + +## MCMC convergence for hyper-parameters + +::: footer +[Bayesian VARs](https://bayesian-econometrics-2023.github.io/be23-lecture7/) +::: + +```{r} +#| label: mcmc +#| warning: false +#| fig-align: "center" +#| out.width: "100%" +#| cache: true + +plot.ts(run$hyper, main = "", col = "#F500BD", xlab = "s", cex.lab = 2, cex.axis = 1.3) +``` + +## MCMC convergence for $\mathbf\Sigma_{\cdot1}$ + +::: footer +[Bayesian VARs](https://bayesian-econometrics-2023.github.io/be23-lecture7/) +::: + +```{r} +#| label: mcmc-si +#| warning: false +#| fig-align: "center" +#| out.width: "100%" +#| cache: true + +plot.ts(run$sigma[,1,], main = "", col = "#F500BD", xlab = "s", cex.lab = 2, cex.axis = 1.3) +``` + +## MCMC convergence for $\boldsymbol\mu_0$ + +::: footer +[Bayesian VARs](https://bayesian-econometrics-2023.github.io/be23-lecture7/) +::: + +```{r} +#| label: mcmc-mu +#| warning: false +#| fig-align: "center" +#| out.width: "100%" +#| cache: true + +plot.ts(run$beta[,1,], main = "", col = "#F500BD", xlab = "s", cex.lab = 2, cex.axis = 1.3) +``` + +## Posterior means for $\mathbf{A}$ + +::: footer +[Bayesian VARs](https://bayesian-econometrics-2023.github.io/be23-lecture7/) +::: + +```{r} +#| label: mean-a +#| warning: false +#| out.width: "100%" +#| cache: true + +mean_A = t(apply(run$beta, 2:3, mean)) +rownames(mean_A) = colnames(x) +colnames(mean_A) = c("mu0",paste0("A",1:p %x% rep(1,3))) +knitr::kable(mean_A, caption = "Posterior estimates for autoregressive parameters", digits = 2) +``` + + +## Posterior means for $\mathbf\Sigma$ + +::: footer +[Bayesian VARs](https://bayesian-econometrics-2023.github.io/be23-lecture7/) +::: + +```{r} +#| label: mean-s +#| warning: false +#| out.width: "100%" +#| cache: true + +mean_S = t(apply(run$sigma, 2:3, mean)) +mean_S = cbind(mean_S, cov2cor(mean_S)) +rownames(mean_S) = colnames(x) +colnames(mean_S) = c(rep("cov",3),rep("cor",3)) +knitr::kable(mean_S, caption = "Posterior estimates for covariance", digits = 5) +``` + +## Posterior means for hyper-parameters + +::: footer +[Bayesian VARs](https://bayesian-econometrics-2023.github.io/be23-lecture7/) +::: + +```{r} +#| label: mean-h +#| warning: false +#| out.width: "100%" +#| cache: true + +mean_h = rbind(apply(run$hyper, 2, mean), apply(run$hyper, 2, sd)) +rownames(mean_h) = c("E[hyper|data]", "sd[hyper|data]") +knitr::kable(mean_h, caption = "Posterior estimates for hyper-parameters", digits = 3) +``` + + +## Australian Data Forecasting + +::: footer +[Bayesian VARs](https://bayesian-econometrics-2023.github.io/be23-lecture7/) +::: + +$$ $$ + +[DOWNLOAD THE SCRIPT](https://github.com/Bayesian-Econometrics-2023/be23-lecture7/blob/main/be23-AUdata.qmd) \ No newline at end of file diff --git a/index_files/figure-revealjs/3D-gdp-1.png b/index_files/figure-revealjs/3D-gdp-1.png new file mode 100644 index 0000000000000000000000000000000000000000..4cb60dd6bf3a43945d53de42510cae45e05ac764 GIT binary patch literal 143770 zcmeFZ_dnHt_&TwiG_TIg7rgmKC zSdTu<&l25Rf1^1m=>h%v;eWCnb-&!~7+JrVb*1w_q+|B6h}wy+SbIU~fz?F&{YP1k zF@AW}8`-;I{6UD{A#E~5?0L4%bLZXgxJ7D~%dmrWiXS&#rrv9wzp^6H5j}QKhJNz5PM8h76JQPIl9w;mAn4IRT>i+gC 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b/index_files/libs/quarto-html/quarto-html.min.css @@ -0,0 +1 @@ +/*# sourceMappingURL=0a6b880beb84f9b6f36107a76f82c5b1.css.map */ diff --git a/index_files/libs/quarto-html/quarto-syntax-highlighting.css b/index_files/libs/quarto-html/quarto-syntax-highlighting.css new file mode 100644 index 0000000..d9fd98f --- /dev/null +++ b/index_files/libs/quarto-html/quarto-syntax-highlighting.css @@ -0,0 +1,203 @@ +/* quarto syntax highlight colors */ +:root { + --quarto-hl-ot-color: #003B4F; + --quarto-hl-at-color: #657422; + --quarto-hl-ss-color: #20794D; + --quarto-hl-an-color: #5E5E5E; + --quarto-hl-fu-color: #4758AB; + --quarto-hl-st-color: #20794D; + --quarto-hl-cf-color: #003B4F; + --quarto-hl-op-color: #5E5E5E; + --quarto-hl-er-color: #AD0000; + --quarto-hl-bn-color: #AD0000; + --quarto-hl-al-color: #AD0000; + --quarto-hl-va-color: #111111; + --quarto-hl-bu-color: inherit; + --quarto-hl-ex-color: inherit; + --quarto-hl-pp-color: #AD0000; + --quarto-hl-in-color: #5E5E5E; + --quarto-hl-vs-color: #20794D; + --quarto-hl-wa-color: #5E5E5E; + --quarto-hl-do-color: #5E5E5E; + --quarto-hl-im-color: #00769E; + --quarto-hl-ch-color: #20794D; + --quarto-hl-dt-color: #AD0000; + --quarto-hl-fl-color: #AD0000; + --quarto-hl-co-color: #5E5E5E; + --quarto-hl-cv-color: #5E5E5E; + --quarto-hl-cn-color: #8f5902; + --quarto-hl-sc-color: #5E5E5E; + --quarto-hl-dv-color: #AD0000; + --quarto-hl-kw-color: #003B4F; +} + +/* other quarto variables */ +:root { + --quarto-font-monospace: SFMono-Regular, Menlo, Monaco, Consolas, "Liberation Mono", "Courier New", monospace; +} + +pre > code.sourceCode > span { + color: #003B4F; +} + +code span { + color: #003B4F; +} + +code.sourceCode > span { + color: #003B4F; +} + +div.sourceCode, +div.sourceCode pre.sourceCode { + color: #003B4F; +} + +code span.ot { + color: #003B4F; + font-style: inherit; +} + +code span.at { + color: #657422; + font-style: inherit; +} + +code span.ss { + color: #20794D; + font-style: inherit; +} + +code span.an { + color: #5E5E5E; + font-style: inherit; +} + +code span.fu { + color: #4758AB; + font-style: inherit; +} + +code span.st { + color: #20794D; + font-style: inherit; +} + +code span.cf { + color: #003B4F; + font-style: inherit; +} + +code span.op { + color: #5E5E5E; + font-style: inherit; +} + +code span.er { + color: #AD0000; + font-style: inherit; +} + +code span.bn { + color: #AD0000; + font-style: inherit; +} + +code span.al { + color: #AD0000; + font-style: inherit; +} + +code span.va { + color: #111111; + font-style: inherit; +} + +code span.bu { + font-style: inherit; +} + +code span.ex { + font-style: inherit; +} + +code span.pp { + color: #AD0000; + font-style: inherit; +} + +code span.in { + color: #5E5E5E; + font-style: inherit; +} + +code span.vs { + color: #20794D; + font-style: inherit; +} + +code span.wa { + color: #5E5E5E; + font-style: italic; +} + +code span.do { + color: #5E5E5E; + font-style: italic; +} + +code span.im { + color: #00769E; + font-style: inherit; +} + +code span.ch { + color: #20794D; + font-style: inherit; +} + +code span.dt { + color: #AD0000; + font-style: inherit; +} + +code span.fl { + color: #AD0000; + font-style: inherit; +} + +code span.co { + color: #5E5E5E; + font-style: inherit; +} + +code span.cv { + color: #5E5E5E; + font-style: italic; +} + +code span.cn { + color: #8f5902; + font-style: inherit; +} + +code span.sc { + color: #5E5E5E; + font-style: inherit; +} + +code span.dv { + color: #AD0000; + font-style: inherit; +} + +code span.kw { + color: #003B4F; + font-style: inherit; +} + +.prevent-inlining { + content: " !el.hasAttribute("disabled") && !el.getAttribute("aria-hidden") + ); + }; + + /** + * Remove roles and attributes from a tab and its content + * @param {Node} tab The tab + * @param {Node} content The tab content + * @param {Object} settings User settings and options + */ + var destroyTab = function (tab, content, settings) { + // Remove the generated ID + if (tab.id.slice(0, settings.idPrefix.length) === settings.idPrefix) { + tab.id = ""; + } + + // remove event listener + tab.removeEventListener("focus", focusHandler, true); + + // Remove roles + tab.removeAttribute("role"); + tab.removeAttribute("aria-controls"); + tab.removeAttribute("aria-selected"); + tab.removeAttribute("tabindex"); + tab.closest("li").removeAttribute("role"); + content.removeAttribute("role"); + content.removeAttribute("aria-labelledby"); + content.removeAttribute("hidden"); + }; + + /** + * Add the required roles and attributes to a tab and its content + * @param {Node} tab The tab + * @param {Node} content The tab content + * @param {Object} settings User settings and options + */ + var setupTab = function (tab, content, settings) { + // Give tab an ID if it doesn't already have one + if (!tab.id) { + tab.id = settings.idPrefix + content.id; + } + + // Add roles + tab.setAttribute("role", "tab"); + tab.setAttribute("aria-controls", content.id); + tab.closest("li").setAttribute("role", "presentation"); + content.setAttribute("role", "tabpanel"); + content.setAttribute("aria-labelledby", tab.id); + + // Add selected state + if (tab.matches(settings.default)) { + tab.setAttribute("aria-selected", "true"); + } else { + tab.setAttribute("aria-selected", "false"); + content.setAttribute("hidden", "hidden"); + } + + // add focus event listender + tab.addEventListener("focus", focusHandler); + }; + + /** + * Hide a tab and its content + * @param {Node} newTab The new tab that's replacing it + */ + var hide = function (newTab) { + // Variables + var tabGroup = newTab.closest('[role="tablist"]'); + if (!tabGroup) return {}; + var tab = tabGroup.querySelector('[role="tab"][aria-selected="true"]'); + if (!tab) return {}; + var content = document.querySelector(tab.hash); + + // Hide the tab + tab.setAttribute("aria-selected", "false"); + + // Hide the content + if (!content) return { previousTab: tab }; + content.setAttribute("hidden", "hidden"); + + // Return the hidden tab and content + return { + previousTab: tab, + previousContent: content, + }; + }; + + /** + * Show a tab and its content + * @param {Node} tab The tab + * @param {Node} content The tab content + */ + var show = function (tab, content) { + tab.setAttribute("aria-selected", "true"); + content.removeAttribute("hidden"); + tab.focus(); + }; + + /** + * Toggle a new tab + * @param {Node} tab The tab to show + */ + var toggle = function (tab) { + // Make sure there's a tab to toggle and it's not already active + if (!tab || tab.getAttribute("aria-selected") == "true") return; + + // Variables + var content = document.querySelector(tab.hash); + if (!content) return; + + // Hide active tab and content + var details = hide(tab); + + // Show new tab and content + show(tab, content); + + // Add event details + details.tab = tab; + details.content = content; + + // Emit a custom event + emitEvent(tab, details); + }; + + /** + * Get all of the tabs in a tablist + * @param {Node} tab A tab from the list + * @return {Object} The tabs and the index of the currently active one + */ + var getTabsMap = function (tab) { + var tabGroup = tab.closest('[role="tablist"]'); + var tabs = tabGroup ? tabGroup.querySelectorAll('[role="tab"]') : null; + if (!tabs) return; + return { + tabs: tabs, + index: Array.prototype.indexOf.call(tabs, tab), + }; + }; + + /** + * Switch the active tab based on keyboard activity + * @param {Node} tab The currently active tab + * @param {Key} key The key that was pressed + */ + var switchTabs = function (tab, key) { + // Get a map of tabs + var map = getTabsMap(tab); + if (!map) return; + var length = map.tabs.length - 1; + var index; + + // Go to previous tab + if (["ArrowUp", "ArrowLeft", "Up", "Left"].indexOf(key) > -1) { + index = map.index < 1 ? length : map.index - 1; + } + + // Go to next tab + else if (["ArrowDown", "ArrowRight", "Down", "Right"].indexOf(key) > -1) { + index = map.index === length ? 0 : map.index + 1; + } + + // Go to home + else if (key === "Home") { + index = 0; + } + + // Go to end + else if (key === "End") { + index = length; + } + + // Toggle the tab + toggle(map.tabs[index]); + }; + + /** + * Create the Constructor object + */ + var Constructor = function (selector, options) { + // + // Variables + // + + var publicAPIs = {}; + var settings, tabWrapper; + + // + // Methods + // + + publicAPIs.destroy = function () { + // Get all tabs + var tabs = tabWrapper.querySelectorAll("a"); + + // Add roles to tabs + Array.prototype.forEach.call(tabs, function (tab) { + // Get the tab content + var content = document.querySelector(tab.hash); + if (!content) return; + + // Setup the tab + destroyTab(tab, content, settings); + }); + + // Remove role from wrapper + tabWrapper.removeAttribute("role"); + + // Remove event listeners + document.documentElement.removeEventListener( + "click", + clickHandler, + true + ); + tabWrapper.removeEventListener("keydown", keyHandler, true); + + // Reset variables + settings = null; + tabWrapper = null; + }; + + /** + * Setup the DOM with the proper attributes + */ + publicAPIs.setup = function () { + // Variables + tabWrapper = document.querySelector(selector); + if (!tabWrapper) return; + var tabs = tabWrapper.querySelectorAll("a"); + + // Add role to wrapper + tabWrapper.setAttribute("role", "tablist"); + + // Add roles to tabs. provide dynanmic tab indexes if we are within reveal + var contentTabindexes = + window.document.body.classList.contains("reveal-viewport"); + var nextTabindex = 1; + Array.prototype.forEach.call(tabs, function (tab) { + if (contentTabindexes) { + tab.setAttribute("tabindex", "" + nextTabindex++); + } else { + tab.setAttribute("tabindex", "0"); + } + + // Get the tab content + var content = document.querySelector(tab.hash); + if (!content) return; + + // set tab indexes for content + if (contentTabindexes) { + getKeyboardFocusableElements(content).forEach(function (el) { + el.setAttribute("tabindex", "" + nextTabindex++); + }); + } + + // Setup the tab + setupTab(tab, content, settings); + }); + }; + + /** + * Toggle a tab based on an ID + * @param {String|Node} id The tab to toggle + */ + publicAPIs.toggle = function (id) { + // Get the tab + var tab = id; + if (typeof id === "string") { + tab = document.querySelector( + selector + ' [role="tab"][href*="' + id + '"]' + ); + } + + // Toggle the tab + toggle(tab); + }; + + /** + * Handle click events + */ + var clickHandler = function (event) { + // Only run on toggles + var tab = event.target.closest(selector + ' [role="tab"]'); + if (!tab) return; + + // Prevent link behavior + event.preventDefault(); + + // Toggle the tab + toggle(tab); + }; + + /** + * Handle keydown events + */ + var keyHandler = function (event) { + // Only run if a tab is in focus + var tab = document.activeElement; + if (!tab.matches(selector + ' [role="tab"]')) return; + + // Only run for specific keys + if (["Home", "End"].indexOf(event.key) < 0) return; + + // Switch tabs + switchTabs(tab, event.key); + }; + + /** + * Initialize the instance + */ + var init = function () { + // Merge user options with defaults + settings = extend(defaults, options || {}); + + // Setup the DOM + publicAPIs.setup(); + + // Add event listeners + document.documentElement.addEventListener("click", clickHandler, true); + tabWrapper.addEventListener("keydown", keyHandler, true); + }; + + // + // Initialize and return the Public APIs + // + + init(); + return publicAPIs; + }; + + // + // Return the Constructor + // + + return Constructor; + } +); diff --git a/index_files/libs/quarto-html/tippy.css b/index_files/libs/quarto-html/tippy.css new file mode 100644 index 0000000..e6ae635 --- /dev/null +++ b/index_files/libs/quarto-html/tippy.css @@ -0,0 +1 @@ +.tippy-box[data-animation=fade][data-state=hidden]{opacity:0}[data-tippy-root]{max-width:calc(100vw - 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e(h,{...Ot,announceStatus:fe,getStatusText:be,print:oe,focus:le,progress:ae,controls:se,location:ie,overview:ee,fragments:G,slideContent:_,slideNumber:J,onUserInput:Mt,closeOverlay:ze,updateSlidesVisibility:at,layoutSlideContents:qe,transformSlides:xe,cueAutoSlide:Et,cancelAutoSlide:Rt}),Ot}let W=U,K=[];W.initialize=e=>(Object.assign(W,new U(document.querySelector(".reveal"),e)),K.map((e=>e(W))),W.initialize()),["configure","on","off","addEventListener","removeEventListener","registerPlugin"].forEach((e=>{W[e]=(...t)=>{K.push((i=>i[e].call(null,...t)))}})),W.isReady=()=>!1,W.VERSION="4.3.1";export default W; +//# sourceMappingURL=reveal.esm.js.map diff --git a/index_files/libs/revealjs/dist/reveal.esm.js.map b/index_files/libs/revealjs/dist/reveal.esm.js.map new file mode 100644 index 0000000..286c75a --- /dev/null +++ b/index_files/libs/revealjs/dist/reveal.esm.js.map @@ -0,0 +1 @@ +{"version":3,"file":"reveal.esm.js","sources":["../js/utils/util.js","../js/utils/device.js","../node_modules/fitty/dist/fitty.module.js","../js/controllers/slidecontent.js","../js/controllers/slidenumber.js","../js/utils/color.js","../js/controllers/backgrounds.js","../js/utils/constants.js","../js/controllers/autoanimate.js","../js/controllers/fragments.js","../js/controllers/overview.js","../js/controllers/keyboard.js","../js/controllers/location.js","../js/controllers/controls.js","../js/controllers/progress.js","../js/controllers/pointer.js","../js/utils/loader.js","../js/controllers/plugins.js","../js/controllers/print.js","../js/controllers/touch.js","../js/controllers/focus.js","../js/controllers/notes.js","../js/components/playback.js","../js/config.js","../js/reveal.js","../js/index.js"],"sourcesContent":["/**\n * Extend object a with the properties of object b.\n * If there's a conflict, object b takes precedence.\n *\n * @param {object} a\n * @param {object} b\n */\nexport const extend = ( a, b ) => {\n\n\tfor( let i in b ) {\n\t\ta[ i ] = b[ i ];\n\t}\n\n\treturn a;\n\n}\n\n/**\n * querySelectorAll but returns an Array.\n */\nexport const queryAll = ( el, selector ) => {\n\n\treturn Array.from( el.querySelectorAll( selector ) );\n\n}\n\n/**\n * classList.toggle() with cross browser support\n */\nexport const toggleClass = ( el, className, value ) => {\n\tif( value ) {\n\t\tel.classList.add( className );\n\t}\n\telse {\n\t\tel.classList.remove( className );\n\t}\n}\n\n/**\n * Utility for deserializing a value.\n *\n * @param {*} value\n * @return {*}\n */\nexport const deserialize = ( value ) => {\n\n\tif( typeof value === 'string' ) {\n\t\tif( value === 'null' ) return null;\n\t\telse if( value === 'true' ) return true;\n\t\telse if( value === 'false' ) return false;\n\t\telse if( value.match( /^-?[\\d\\.]+$/ ) ) return parseFloat( value );\n\t}\n\n\treturn value;\n\n}\n\n/**\n * Measures the distance in pixels between point a\n * and point b.\n *\n * @param {object} a point with x/y properties\n * @param {object} b point with x/y properties\n *\n * @return {number}\n */\nexport const distanceBetween = ( a, b ) => {\n\n\tlet dx = a.x - b.x,\n\t\tdy = a.y - b.y;\n\n\treturn Math.sqrt( dx*dx + dy*dy );\n\n}\n\n/**\n * Applies a CSS transform to the target element.\n *\n * @param {HTMLElement} element\n * @param {string} transform\n */\nexport const transformElement = ( element, transform ) => {\n\n\telement.style.transform = transform;\n\n}\n\n/**\n * Element.matches with IE support.\n *\n * @param {HTMLElement} target The element to match\n * @param {String} selector The CSS selector to match\n * the element against\n *\n * @return {Boolean}\n */\nexport const matches = ( target, selector ) => {\n\n\tlet matchesMethod = target.matches || target.matchesSelector || target.msMatchesSelector;\n\n\treturn !!( matchesMethod && matchesMethod.call( target, selector ) );\n\n}\n\n/**\n * Find the closest parent that matches the given\n * selector.\n *\n * @param {HTMLElement} target The child element\n * @param {String} selector The CSS selector to match\n * the parents against\n *\n * @return {HTMLElement} The matched parent or null\n * if no matching parent was found\n */\nexport const closest = ( target, selector ) => {\n\n\t// Native Element.closest\n\tif( typeof target.closest === 'function' ) {\n\t\treturn target.closest( selector );\n\t}\n\n\t// Polyfill\n\twhile( target ) {\n\t\tif( matches( target, selector ) ) {\n\t\t\treturn target;\n\t\t}\n\n\t\t// Keep searching\n\t\ttarget = target.parentNode;\n\t}\n\n\treturn null;\n\n}\n\n/**\n * Handling the fullscreen functionality via the fullscreen API\n *\n * @see http://fullscreen.spec.whatwg.org/\n * @see https://developer.mozilla.org/en-US/docs/DOM/Using_fullscreen_mode\n */\nexport const enterFullscreen = element => {\n\n\telement = element || document.documentElement;\n\n\t// Check which implementation is available\n\tlet requestMethod = element.requestFullscreen ||\n\t\t\t\t\t\telement.webkitRequestFullscreen ||\n\t\t\t\t\t\telement.webkitRequestFullScreen ||\n\t\t\t\t\t\telement.mozRequestFullScreen ||\n\t\t\t\t\t\telement.msRequestFullscreen;\n\n\tif( requestMethod ) {\n\t\trequestMethod.apply( element );\n\t}\n\n}\n\n/**\n * Creates an HTML element and returns a reference to it.\n * If the element already exists the existing instance will\n * be returned.\n *\n * @param {HTMLElement} container\n * @param {string} tagname\n * @param {string} classname\n * @param {string} innerHTML\n *\n * @return {HTMLElement}\n */\nexport const createSingletonNode = ( container, tagname, classname, innerHTML='' ) => {\n\n\t// Find all nodes matching the description\n\tlet nodes = container.querySelectorAll( '.' + classname );\n\n\t// Check all matches to find one which is a direct child of\n\t// the specified container\n\tfor( let i = 0; i < nodes.length; i++ ) {\n\t\tlet testNode = nodes[i];\n\t\tif( testNode.parentNode === container ) {\n\t\t\treturn testNode;\n\t\t}\n\t}\n\n\t// If no node was found, create it now\n\tlet node = document.createElement( tagname );\n\tnode.className = classname;\n\tnode.innerHTML = innerHTML;\n\tcontainer.appendChild( node );\n\n\treturn node;\n\n}\n\n/**\n * Injects the given CSS styles into the DOM.\n *\n * @param {string} value\n */\nexport const createStyleSheet = ( value ) => {\n\n\tlet tag = document.createElement( 'style' );\n\ttag.type = 'text/css';\n\n\tif( value && value.length > 0 ) {\n\t\tif( tag.styleSheet ) {\n\t\t\ttag.styleSheet.cssText = value;\n\t\t}\n\t\telse {\n\t\t\ttag.appendChild( document.createTextNode( value ) );\n\t\t}\n\t}\n\n\tdocument.head.appendChild( tag );\n\n\treturn tag;\n\n}\n\n/**\n * Returns a key:value hash of all query params.\n */\nexport const getQueryHash = () => {\n\n\tlet query = {};\n\n\tlocation.search.replace( /[A-Z0-9]+?=([\\w\\.%-]*)/gi, a => {\n\t\tquery[ a.split( '=' ).shift() ] = a.split( '=' ).pop();\n\t} );\n\n\t// Basic deserialization\n\tfor( let i in query ) {\n\t\tlet value = query[ i ];\n\n\t\tquery[ i ] = deserialize( unescape( value ) );\n\t}\n\n\t// Do not accept new dependencies via query config to avoid\n\t// the potential of malicious script injection\n\tif( typeof query['dependencies'] !== 'undefined' ) delete query['dependencies'];\n\n\treturn query;\n\n}\n\n/**\n * Returns the remaining height within the parent of the\n * target element.\n *\n * remaining height = [ configured parent height ] - [ current parent height ]\n *\n * @param {HTMLElement} element\n * @param {number} [height]\n */\nexport const getRemainingHeight = ( element, height = 0 ) => {\n\n\tif( element ) {\n\t\tlet newHeight, oldHeight = element.style.height;\n\n\t\t// Change the .stretch element height to 0 in order find the height of all\n\t\t// the other elements\n\t\telement.style.height = '0px';\n\n\t\t// In Overview mode, the parent (.slide) height is set of 700px.\n\t\t// Restore it temporarily to its natural height.\n\t\telement.parentNode.style.height = 'auto';\n\n\t\tnewHeight = height - element.parentNode.offsetHeight;\n\n\t\t// Restore the old height, just in case\n\t\telement.style.height = oldHeight + 'px';\n\n\t\t// Clear the parent (.slide) height. .removeProperty works in IE9+\n\t\telement.parentNode.style.removeProperty('height');\n\n\t\treturn newHeight;\n\t}\n\n\treturn height;\n\n}\n\nconst fileExtensionToMimeMap = {\n\t'mp4': 'video/mp4',\n\t'm4a': 'video/mp4',\n\t'ogv': 'video/ogg',\n\t'mpeg': 'video/mpeg',\n\t'webm': 'video/webm'\n}\n\n/**\n * Guess the MIME type for common file formats.\n */\nexport const getMimeTypeFromFile = ( filename='' ) => {\n\treturn fileExtensionToMimeMap[filename.split('.').pop()]\n}","const UA = navigator.userAgent;\n\nexport const isMobile = /(iphone|ipod|ipad|android)/gi.test( UA ) ||\n\t\t\t\t\t\t( navigator.platform === 'MacIntel' && navigator.maxTouchPoints > 1 ); // iPadOS\n\nexport const isChrome = /chrome/i.test( UA ) && !/edge/i.test( UA );\n\nexport const isAndroid = /android/gi.test( UA );","/*\n * fitty v2.3.3 - Snugly resizes text to fit its parent container\n * Copyright (c) 2020 Rik Schennink (https://pqina.nl/)\n */\n'use strict';\n\nObject.defineProperty(exports, \"__esModule\", {\n value: true\n});\n\nvar _extends = Object.assign || function (target) { for (var i = 1; i < arguments.length; i++) { var source = arguments[i]; for (var key in source) { if (Object.prototype.hasOwnProperty.call(source, key)) { target[key] = source[key]; } } } return target; };\n\nexports.default = function (w) {\n\n // no window, early exit\n if (!w) return;\n\n // node list to array helper method\n var toArray = function toArray(nl) {\n return [].slice.call(nl);\n };\n\n // states\n var DrawState = {\n IDLE: 0,\n DIRTY_CONTENT: 1,\n DIRTY_LAYOUT: 2,\n DIRTY: 3\n };\n\n // all active fitty elements\n var fitties = [];\n\n // group all redraw calls till next frame, we cancel each frame request when a new one comes in. If no support for request animation frame, this is an empty function and supports for fitty stops.\n var redrawFrame = null;\n var requestRedraw = 'requestAnimationFrame' in w ? function () {\n w.cancelAnimationFrame(redrawFrame);\n redrawFrame = w.requestAnimationFrame(function () {\n return redraw(fitties.filter(function (f) {\n return f.dirty && f.active;\n }));\n });\n } : function () {};\n\n // sets all fitties to dirty so they are redrawn on the next redraw loop, then calls redraw\n var redrawAll = function redrawAll(type) {\n return function () {\n fitties.forEach(function (f) {\n return f.dirty = type;\n });\n requestRedraw();\n };\n };\n\n // redraws fitties so they nicely fit their parent container\n var redraw = function redraw(fitties) {\n\n // getting info from the DOM at this point should not trigger a reflow, let's gather as much intel as possible before triggering a reflow\n\n // check if styles of all fitties have been computed\n fitties.filter(function (f) {\n return !f.styleComputed;\n }).forEach(function (f) {\n f.styleComputed = computeStyle(f);\n });\n\n // restyle elements that require pre-styling, this triggers a reflow, please try to prevent by adding CSS rules (see docs)\n fitties.filter(shouldPreStyle).forEach(applyStyle);\n\n // we now determine which fitties should be redrawn\n var fittiesToRedraw = fitties.filter(shouldRedraw);\n\n // we calculate final styles for these fitties\n fittiesToRedraw.forEach(calculateStyles);\n\n // now we apply the calculated styles from our previous loop\n fittiesToRedraw.forEach(function (f) {\n applyStyle(f);\n markAsClean(f);\n });\n\n // now we dispatch events for all restyled fitties\n fittiesToRedraw.forEach(dispatchFitEvent);\n };\n\n var markAsClean = function markAsClean(f) {\n return f.dirty = DrawState.IDLE;\n };\n\n var calculateStyles = function calculateStyles(f) {\n\n // get available width from parent node\n f.availableWidth = f.element.parentNode.clientWidth;\n\n // the space our target element uses\n f.currentWidth = f.element.scrollWidth;\n\n // remember current font size\n f.previousFontSize = f.currentFontSize;\n\n // let's calculate the new font size\n f.currentFontSize = Math.min(Math.max(f.minSize, f.availableWidth / f.currentWidth * f.previousFontSize), f.maxSize);\n\n // if allows wrapping, only wrap when at minimum font size (otherwise would break container)\n f.whiteSpace = f.multiLine && f.currentFontSize === f.minSize ? 'normal' : 'nowrap';\n };\n\n // should always redraw if is not dirty layout, if is dirty layout, only redraw if size has changed\n var shouldRedraw = function shouldRedraw(f) {\n return f.dirty !== DrawState.DIRTY_LAYOUT || f.dirty === DrawState.DIRTY_LAYOUT && f.element.parentNode.clientWidth !== f.availableWidth;\n };\n\n // every fitty element is tested for invalid styles\n var computeStyle = function computeStyle(f) {\n\n // get style properties\n var style = w.getComputedStyle(f.element, null);\n\n // get current font size in pixels (if we already calculated it, use the calculated version)\n f.currentFontSize = parseFloat(style.getPropertyValue('font-size'));\n\n // get display type and wrap mode\n f.display = style.getPropertyValue('display');\n f.whiteSpace = style.getPropertyValue('white-space');\n };\n\n // determines if this fitty requires initial styling, can be prevented by applying correct styles through CSS\n var shouldPreStyle = function shouldPreStyle(f) {\n\n var preStyle = false;\n\n // if we already tested for prestyling we don't have to do it again\n if (f.preStyleTestCompleted) return false;\n\n // should have an inline style, if not, apply\n if (!/inline-/.test(f.display)) {\n preStyle = true;\n f.display = 'inline-block';\n }\n\n // to correctly calculate dimensions the element should have whiteSpace set to nowrap\n if (f.whiteSpace !== 'nowrap') {\n preStyle = true;\n f.whiteSpace = 'nowrap';\n }\n\n // we don't have to do this twice\n f.preStyleTestCompleted = true;\n\n return preStyle;\n };\n\n // apply styles to single fitty\n var applyStyle = function applyStyle(f) {\n f.element.style.whiteSpace = f.whiteSpace;\n f.element.style.display = f.display;\n f.element.style.fontSize = f.currentFontSize + 'px';\n };\n\n // dispatch a fit event on a fitty\n var dispatchFitEvent = function dispatchFitEvent(f) {\n f.element.dispatchEvent(new CustomEvent('fit', {\n detail: {\n oldValue: f.previousFontSize,\n newValue: f.currentFontSize,\n scaleFactor: f.currentFontSize / f.previousFontSize\n }\n }));\n };\n\n // fit method, marks the fitty as dirty and requests a redraw (this will also redraw any other fitty marked as dirty)\n var fit = function fit(f, type) {\n return function () {\n f.dirty = type;\n if (!f.active) return;\n requestRedraw();\n };\n };\n\n var init = function init(f) {\n\n // save some of the original CSS properties before we change them\n f.originalStyle = {\n whiteSpace: f.element.style.whiteSpace,\n display: f.element.style.display,\n fontSize: f.element.style.fontSize\n };\n\n // should we observe DOM mutations\n observeMutations(f);\n\n // this is a new fitty so we need to validate if it's styles are in order\n f.newbie = true;\n\n // because it's a new fitty it should also be dirty, we want it to redraw on the first loop\n f.dirty = true;\n\n // we want to be able to update this fitty\n fitties.push(f);\n };\n\n var destroy = function destroy(f) {\n return function () {\n\n // remove from fitties array\n fitties = fitties.filter(function (_) {\n return _.element !== f.element;\n });\n\n // stop observing DOM\n if (f.observeMutations) f.observer.disconnect();\n\n // reset the CSS properties we changes\n f.element.style.whiteSpace = f.originalStyle.whiteSpace;\n f.element.style.display = f.originalStyle.display;\n f.element.style.fontSize = f.originalStyle.fontSize;\n };\n };\n\n // add a new fitty, does not redraw said fitty\n var subscribe = function subscribe(f) {\n return function () {\n if (f.active) return;\n f.active = true;\n requestRedraw();\n };\n };\n\n // remove an existing fitty\n var unsubscribe = function unsubscribe(f) {\n return function () {\n return f.active = false;\n };\n };\n\n var observeMutations = function observeMutations(f) {\n\n // no observing?\n if (!f.observeMutations) return;\n\n // start observing mutations\n f.observer = new MutationObserver(fit(f, DrawState.DIRTY_CONTENT));\n\n // start observing\n f.observer.observe(f.element, f.observeMutations);\n };\n\n // default mutation observer settings\n var mutationObserverDefaultSetting = {\n subtree: true,\n childList: true,\n characterData: true\n };\n\n // default fitty options\n var defaultOptions = {\n minSize: 16,\n maxSize: 512,\n multiLine: true,\n observeMutations: 'MutationObserver' in w ? mutationObserverDefaultSetting : false\n };\n\n // array of elements in, fitty instances out\n function fittyCreate(elements, options) {\n\n // set options object\n var fittyOptions = _extends({}, defaultOptions, options);\n\n // create fitties\n var publicFitties = elements.map(function (element) {\n\n // create fitty instance\n var f = _extends({}, fittyOptions, {\n\n // internal options for this fitty\n element: element,\n active: true\n });\n\n // initialise this fitty\n init(f);\n\n // expose API\n return {\n element: element,\n fit: fit(f, DrawState.DIRTY),\n unfreeze: subscribe(f),\n freeze: unsubscribe(f),\n unsubscribe: destroy(f)\n };\n });\n\n // call redraw on newly initiated fitties\n requestRedraw();\n\n // expose fitties\n return publicFitties;\n }\n\n // fitty creation function\n function fitty(target) {\n var options = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : {};\n\n\n // if target is a string\n return typeof target === 'string' ?\n\n // treat it as a querySelector\n fittyCreate(toArray(document.querySelectorAll(target)), options) :\n\n // create single fitty\n fittyCreate([target], options)[0];\n }\n\n // handles viewport changes, redraws all fitties, but only does so after a timeout\n var resizeDebounce = null;\n var onWindowResized = function onWindowResized() {\n w.clearTimeout(resizeDebounce);\n resizeDebounce = w.setTimeout(redrawAll(DrawState.DIRTY_LAYOUT), fitty.observeWindowDelay);\n };\n\n // define observe window property, so when we set it to true or false events are automatically added and removed\n var events = ['resize', 'orientationchange'];\n Object.defineProperty(fitty, 'observeWindow', {\n set: function set(enabled) {\n var method = (enabled ? 'add' : 'remove') + 'EventListener';\n events.forEach(function (e) {\n w[method](e, onWindowResized);\n });\n }\n });\n\n // fitty global properties (by setting observeWindow to true the events above get added)\n fitty.observeWindow = true;\n fitty.observeWindowDelay = 100;\n\n // public fit all method, will force redraw no matter what\n fitty.fitAll = redrawAll(DrawState.DIRTY);\n\n // export our fitty function, we don't want to keep it to our selves\n return fitty;\n}(typeof window === 'undefined' ? null : window);","import { extend, queryAll, closest, getMimeTypeFromFile } from '../utils/util.js'\nimport { isMobile } from '../utils/device.js'\n\nimport fitty from 'fitty';\n\n/**\n * Handles loading, unloading and playback of slide\n * content such as images, videos and iframes.\n */\nexport default class SlideContent {\n\n\tconstructor( Reveal ) {\n\n\t\tthis.Reveal = Reveal;\n\n\t\tthis.startEmbeddedIframe = this.startEmbeddedIframe.bind( this );\n\n\t}\n\n\t/**\n\t * Should the given element be preloaded?\n\t * Decides based on local element attributes and global config.\n\t *\n\t * @param {HTMLElement} element\n\t */\n\tshouldPreload( element ) {\n\n\t\t// Prefer an explicit global preload setting\n\t\tlet preload = this.Reveal.getConfig().preloadIframes;\n\n\t\t// If no global setting is available, fall back on the element's\n\t\t// own preload setting\n\t\tif( typeof preload !== 'boolean' ) {\n\t\t\tpreload = element.hasAttribute( 'data-preload' );\n\t\t}\n\n\t\treturn preload;\n\t}\n\n\t/**\n\t * Called when the given slide is within the configured view\n\t * distance. Shows the slide element and loads any content\n\t * that is set to load lazily (data-src).\n\t *\n\t * @param {HTMLElement} slide Slide to show\n\t */\n\tload( slide, options = {} ) {\n\n\t\t// Show the slide element\n\t\tslide.style.display = this.Reveal.getConfig().display;\n\n\t\t// Media elements with data-src attributes\n\t\tqueryAll( slide, 'img[data-src], video[data-src], audio[data-src], iframe[data-src]' ).forEach( element => {\n\t\t\tif( element.tagName !== 'IFRAME' || this.shouldPreload( element ) ) {\n\t\t\t\telement.setAttribute( 'src', element.getAttribute( 'data-src' ) );\n\t\t\t\telement.setAttribute( 'data-lazy-loaded', '' );\n\t\t\t\telement.removeAttribute( 'data-src' );\n\t\t\t}\n\t\t} );\n\n\t\t// Media elements with children\n\t\tqueryAll( slide, 'video, audio' ).forEach( media => {\n\t\t\tlet sources = 0;\n\n\t\t\tqueryAll( media, 'source[data-src]' ).forEach( source => {\n\t\t\t\tsource.setAttribute( 'src', source.getAttribute( 'data-src' ) );\n\t\t\t\tsource.removeAttribute( 'data-src' );\n\t\t\t\tsource.setAttribute( 'data-lazy-loaded', '' );\n\t\t\t\tsources += 1;\n\t\t\t} );\n\n\t\t\t// Enable inline video playback in mobile Safari\n\t\t\tif( isMobile && media.tagName === 'VIDEO' ) {\n\t\t\t\tmedia.setAttribute( 'playsinline', '' );\n\t\t\t}\n\n\t\t\t// If we rewrote sources for this video/audio element, we need\n\t\t\t// to manually tell it to load from its new origin\n\t\t\tif( sources > 0 ) {\n\t\t\t\tmedia.load();\n\t\t\t}\n\t\t} );\n\n\n\t\t// Show the corresponding background element\n\t\tlet background = slide.slideBackgroundElement;\n\t\tif( background ) {\n\t\t\tbackground.style.display = 'block';\n\n\t\t\tlet backgroundContent = slide.slideBackgroundContentElement;\n\t\t\tlet backgroundIframe = slide.getAttribute( 'data-background-iframe' );\n\n\t\t\t// If the background contains media, load it\n\t\t\tif( background.hasAttribute( 'data-loaded' ) === false ) {\n\t\t\t\tbackground.setAttribute( 'data-loaded', 'true' );\n\n\t\t\t\tlet backgroundImage = slide.getAttribute( 'data-background-image' ),\n\t\t\t\t\tbackgroundVideo = slide.getAttribute( 'data-background-video' ),\n\t\t\t\t\tbackgroundVideoLoop = slide.hasAttribute( 'data-background-video-loop' ),\n\t\t\t\t\tbackgroundVideoMuted = slide.hasAttribute( 'data-background-video-muted' );\n\n\t\t\t\t// Images\n\t\t\t\tif( backgroundImage ) {\n\t\t\t\t\t// base64\n\t\t\t\t\tif( /^data:/.test( backgroundImage.trim() ) ) {\n\t\t\t\t\t\tbackgroundContent.style.backgroundImage = `url(${backgroundImage.trim()})`;\n\t\t\t\t\t}\n\t\t\t\t\t// URL(s)\n\t\t\t\t\telse {\n\t\t\t\t\t\tbackgroundContent.style.backgroundImage = backgroundImage.split( ',' ).map( background => {\n\t\t\t\t\t\t\treturn `url(${encodeURI(background.trim())})`;\n\t\t\t\t\t\t}).join( ',' );\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t\t// Videos\n\t\t\t\telse if ( backgroundVideo && !this.Reveal.isSpeakerNotes() ) {\n\t\t\t\t\tlet video = document.createElement( 'video' );\n\n\t\t\t\t\tif( backgroundVideoLoop ) {\n\t\t\t\t\t\tvideo.setAttribute( 'loop', '' );\n\t\t\t\t\t}\n\n\t\t\t\t\tif( backgroundVideoMuted ) {\n\t\t\t\t\t\tvideo.muted = true;\n\t\t\t\t\t}\n\n\t\t\t\t\t// Enable inline playback in mobile Safari\n\t\t\t\t\t//\n\t\t\t\t\t// Mute is required for video to play when using\n\t\t\t\t\t// swipe gestures to navigate since they don't\n\t\t\t\t\t// count as direct user actions :'(\n\t\t\t\t\tif( isMobile ) {\n\t\t\t\t\t\tvideo.muted = true;\n\t\t\t\t\t\tvideo.setAttribute( 'playsinline', '' );\n\t\t\t\t\t}\n\n\t\t\t\t\t// Support comma separated lists of video sources\n\t\t\t\t\tbackgroundVideo.split( ',' ).forEach( source => {\n\t\t\t\t\t\tlet type = getMimeTypeFromFile( source );\n\t\t\t\t\t\tif( type ) {\n\t\t\t\t\t\t\tvideo.innerHTML += ``;\n\t\t\t\t\t\t}\n\t\t\t\t\t\telse {\n\t\t\t\t\t\t\tvideo.innerHTML += ``;\n\t\t\t\t\t\t}\n\t\t\t\t\t} );\n\n\t\t\t\t\tbackgroundContent.appendChild( video );\n\t\t\t\t}\n\t\t\t\t// Iframes\n\t\t\t\telse if( backgroundIframe && options.excludeIframes !== true ) {\n\t\t\t\t\tlet iframe = document.createElement( 'iframe' );\n\t\t\t\t\tiframe.setAttribute( 'allowfullscreen', '' );\n\t\t\t\t\tiframe.setAttribute( 'mozallowfullscreen', '' );\n\t\t\t\t\tiframe.setAttribute( 'webkitallowfullscreen', '' );\n\t\t\t\t\tiframe.setAttribute( 'allow', 'autoplay' );\n\n\t\t\t\t\tiframe.setAttribute( 'data-src', backgroundIframe );\n\n\t\t\t\t\tiframe.style.width = '100%';\n\t\t\t\t\tiframe.style.height = '100%';\n\t\t\t\t\tiframe.style.maxHeight = '100%';\n\t\t\t\t\tiframe.style.maxWidth = '100%';\n\n\t\t\t\t\tbackgroundContent.appendChild( iframe );\n\t\t\t\t}\n\t\t\t}\n\n\t\t\t// Start loading preloadable iframes\n\t\t\tlet backgroundIframeElement = backgroundContent.querySelector( 'iframe[data-src]' );\n\t\t\tif( backgroundIframeElement ) {\n\n\t\t\t\t// Check if this iframe is eligible to be preloaded\n\t\t\t\tif( this.shouldPreload( background ) && !/autoplay=(1|true|yes)/gi.test( backgroundIframe ) ) {\n\t\t\t\t\tif( backgroundIframeElement.getAttribute( 'src' ) !== backgroundIframe ) {\n\t\t\t\t\t\tbackgroundIframeElement.setAttribute( 'src', backgroundIframe );\n\t\t\t\t\t}\n\t\t\t\t}\n\n\t\t\t}\n\n\t\t}\n\n\t\tthis.layout( slide );\n\n\t}\n\n\t/**\n\t * Applies JS-dependent layout helpers for the given slide,\n\t * if there are any.\n\t */\n\tlayout( slide ) {\n\n\t\t// Autosize text with the r-fit-text class based on the\n\t\t// size of its container. This needs to happen after the\n\t\t// slide is visible in order to measure the text.\n\t\tArray.from( slide.querySelectorAll( '.r-fit-text' ) ).forEach( element => {\n\t\t\tfitty( element, {\n\t\t\t\tminSize: 24,\n\t\t\t\tmaxSize: this.Reveal.getConfig().height * 0.8,\n\t\t\t\tobserveMutations: false,\n\t\t\t\tobserveWindow: false\n\t\t\t} );\n\t\t} );\n\n\t}\n\n\t/**\n\t * Unloads and hides the given slide. This is called when the\n\t * slide is moved outside of the configured view distance.\n\t *\n\t * @param {HTMLElement} slide\n\t */\n\tunload( slide ) {\n\n\t\t// Hide the slide element\n\t\tslide.style.display = 'none';\n\n\t\t// Hide the corresponding background element\n\t\tlet background = this.Reveal.getSlideBackground( slide );\n\t\tif( background ) {\n\t\t\tbackground.style.display = 'none';\n\n\t\t\t// Unload any background iframes\n\t\t\tqueryAll( background, 'iframe[src]' ).forEach( element => {\n\t\t\t\telement.removeAttribute( 'src' );\n\t\t\t} );\n\t\t}\n\n\t\t// Reset lazy-loaded media elements with src attributes\n\t\tqueryAll( slide, 'video[data-lazy-loaded][src], audio[data-lazy-loaded][src], iframe[data-lazy-loaded][src]' ).forEach( element => {\n\t\t\telement.setAttribute( 'data-src', element.getAttribute( 'src' ) );\n\t\t\telement.removeAttribute( 'src' );\n\t\t} );\n\n\t\t// Reset lazy-loaded media elements with children\n\t\tqueryAll( slide, 'video[data-lazy-loaded] source[src], audio source[src]' ).forEach( source => {\n\t\t\tsource.setAttribute( 'data-src', source.getAttribute( 'src' ) );\n\t\t\tsource.removeAttribute( 'src' );\n\t\t} );\n\n\t}\n\n\t/**\n\t * Enforces origin-specific format rules for embedded media.\n\t */\n\tformatEmbeddedContent() {\n\n\t\tlet _appendParamToIframeSource = ( sourceAttribute, sourceURL, param ) => {\n\t\t\tqueryAll( this.Reveal.getSlidesElement(), 'iframe['+ sourceAttribute +'*=\"'+ sourceURL +'\"]' ).forEach( el => {\n\t\t\t\tlet src = el.getAttribute( sourceAttribute );\n\t\t\t\tif( src && src.indexOf( param ) === -1 ) {\n\t\t\t\t\tel.setAttribute( sourceAttribute, src + ( !/\\?/.test( src ) ? '?' : '&' ) + param );\n\t\t\t\t}\n\t\t\t});\n\t\t};\n\n\t\t// YouTube frames must include \"?enablejsapi=1\"\n\t\t_appendParamToIframeSource( 'src', 'youtube.com/embed/', 'enablejsapi=1' );\n\t\t_appendParamToIframeSource( 'data-src', 'youtube.com/embed/', 'enablejsapi=1' );\n\n\t\t// Vimeo frames must include \"?api=1\"\n\t\t_appendParamToIframeSource( 'src', 'player.vimeo.com/', 'api=1' );\n\t\t_appendParamToIframeSource( 'data-src', 'player.vimeo.com/', 'api=1' );\n\n\t}\n\n\t/**\n\t * Start playback of any embedded content inside of\n\t * the given element.\n\t *\n\t * @param {HTMLElement} element\n\t */\n\tstartEmbeddedContent( element ) {\n\n\t\tif( element && !this.Reveal.isSpeakerNotes() ) {\n\n\t\t\t// Restart GIFs\n\t\t\tqueryAll( element, 'img[src$=\".gif\"]' ).forEach( el => {\n\t\t\t\t// Setting the same unchanged source like this was confirmed\n\t\t\t\t// to work in Chrome, FF & Safari\n\t\t\t\tel.setAttribute( 'src', el.getAttribute( 'src' ) );\n\t\t\t} );\n\n\t\t\t// HTML5 media elements\n\t\t\tqueryAll( element, 'video, audio' ).forEach( el => {\n\t\t\t\tif( closest( el, '.fragment' ) && !closest( el, '.fragment.visible' ) ) {\n\t\t\t\t\treturn;\n\t\t\t\t}\n\n\t\t\t\t// Prefer an explicit global autoplay setting\n\t\t\t\tlet autoplay = this.Reveal.getConfig().autoPlayMedia;\n\n\t\t\t\t// If no global setting is available, fall back on the element's\n\t\t\t\t// own autoplay setting\n\t\t\t\tif( typeof autoplay !== 'boolean' ) {\n\t\t\t\t\tautoplay = el.hasAttribute( 'data-autoplay' ) || !!closest( el, '.slide-background' );\n\t\t\t\t}\n\n\t\t\t\tif( autoplay && typeof el.play === 'function' ) {\n\n\t\t\t\t\t// If the media is ready, start playback\n\t\t\t\t\tif( el.readyState > 1 ) {\n\t\t\t\t\t\tthis.startEmbeddedMedia( { target: el } );\n\t\t\t\t\t}\n\t\t\t\t\t// Mobile devices never fire a loaded event so instead\n\t\t\t\t\t// of waiting, we initiate playback\n\t\t\t\t\telse if( isMobile ) {\n\t\t\t\t\t\tlet promise = el.play();\n\n\t\t\t\t\t\t// If autoplay does not work, ensure that the controls are visible so\n\t\t\t\t\t\t// that the viewer can start the media on their own\n\t\t\t\t\t\tif( promise && typeof promise.catch === 'function' && el.controls === false ) {\n\t\t\t\t\t\t\tpromise.catch( () => {\n\t\t\t\t\t\t\t\tel.controls = true;\n\n\t\t\t\t\t\t\t\t// Once the video does start playing, hide the controls again\n\t\t\t\t\t\t\t\tel.addEventListener( 'play', () => {\n\t\t\t\t\t\t\t\t\tel.controls = false;\n\t\t\t\t\t\t\t\t} );\n\t\t\t\t\t\t\t} );\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\t\t// If the media isn't loaded, wait before playing\n\t\t\t\t\telse {\n\t\t\t\t\t\tel.removeEventListener( 'loadeddata', this.startEmbeddedMedia ); // remove first to avoid dupes\n\t\t\t\t\t\tel.addEventListener( 'loadeddata', this.startEmbeddedMedia );\n\t\t\t\t\t}\n\n\t\t\t\t}\n\t\t\t} );\n\n\t\t\t// Normal iframes\n\t\t\tqueryAll( element, 'iframe[src]' ).forEach( el => {\n\t\t\t\tif( closest( el, '.fragment' ) && !closest( el, '.fragment.visible' ) ) {\n\t\t\t\t\treturn;\n\t\t\t\t}\n\n\t\t\t\tthis.startEmbeddedIframe( { target: el } );\n\t\t\t} );\n\n\t\t\t// Lazy loading iframes\n\t\t\tqueryAll( element, 'iframe[data-src]' ).forEach( el => {\n\t\t\t\tif( closest( el, '.fragment' ) && !closest( el, '.fragment.visible' ) ) {\n\t\t\t\t\treturn;\n\t\t\t\t}\n\n\t\t\t\tif( el.getAttribute( 'src' ) !== el.getAttribute( 'data-src' ) ) {\n\t\t\t\t\tel.removeEventListener( 'load', this.startEmbeddedIframe ); // remove first to avoid dupes\n\t\t\t\t\tel.addEventListener( 'load', this.startEmbeddedIframe );\n\t\t\t\t\tel.setAttribute( 'src', el.getAttribute( 'data-src' ) );\n\t\t\t\t}\n\t\t\t} );\n\n\t\t}\n\n\t}\n\n\t/**\n\t * Starts playing an embedded video/audio element after\n\t * it has finished loading.\n\t *\n\t * @param {object} event\n\t */\n\tstartEmbeddedMedia( event ) {\n\n\t\tlet isAttachedToDOM = !!closest( event.target, 'html' ),\n\t\t\tisVisible \t\t= !!closest( event.target, '.present' );\n\n\t\tif( isAttachedToDOM && isVisible ) {\n\t\t\tevent.target.currentTime = 0;\n\t\t\tevent.target.play();\n\t\t}\n\n\t\tevent.target.removeEventListener( 'loadeddata', this.startEmbeddedMedia );\n\n\t}\n\n\t/**\n\t * \"Starts\" the content of an embedded iframe using the\n\t * postMessage API.\n\t *\n\t * @param {object} event\n\t */\n\tstartEmbeddedIframe( event ) {\n\n\t\tlet iframe = event.target;\n\n\t\tif( iframe && iframe.contentWindow ) {\n\n\t\t\tlet isAttachedToDOM = !!closest( event.target, 'html' ),\n\t\t\t\tisVisible \t\t= !!closest( event.target, '.present' );\n\n\t\t\tif( isAttachedToDOM && isVisible ) {\n\n\t\t\t\t// Prefer an explicit global autoplay setting\n\t\t\t\tlet autoplay = this.Reveal.getConfig().autoPlayMedia;\n\n\t\t\t\t// If no global setting is available, fall back on the element's\n\t\t\t\t// own autoplay setting\n\t\t\t\tif( typeof autoplay !== 'boolean' ) {\n\t\t\t\t\tautoplay = iframe.hasAttribute( 'data-autoplay' ) || !!closest( iframe, '.slide-background' );\n\t\t\t\t}\n\n\t\t\t\t// YouTube postMessage API\n\t\t\t\tif( /youtube\\.com\\/embed\\//.test( iframe.getAttribute( 'src' ) ) && autoplay ) {\n\t\t\t\t\tiframe.contentWindow.postMessage( '{\"event\":\"command\",\"func\":\"playVideo\",\"args\":\"\"}', '*' );\n\t\t\t\t}\n\t\t\t\t// Vimeo postMessage API\n\t\t\t\telse if( /player\\.vimeo\\.com\\//.test( iframe.getAttribute( 'src' ) ) && autoplay ) {\n\t\t\t\t\tiframe.contentWindow.postMessage( '{\"method\":\"play\"}', '*' );\n\t\t\t\t}\n\t\t\t\t// Generic postMessage API\n\t\t\t\telse {\n\t\t\t\t\tiframe.contentWindow.postMessage( 'slide:start', '*' );\n\t\t\t\t}\n\n\t\t\t}\n\n\t\t}\n\n\t}\n\n\t/**\n\t * Stop playback of any embedded content inside of\n\t * the targeted slide.\n\t *\n\t * @param {HTMLElement} element\n\t */\n\tstopEmbeddedContent( element, options = {} ) {\n\n\t\toptions = extend( {\n\t\t\t// Defaults\n\t\t\tunloadIframes: true\n\t\t}, options );\n\n\t\tif( element && element.parentNode ) {\n\t\t\t// HTML5 media elements\n\t\t\tqueryAll( element, 'video, audio' ).forEach( el => {\n\t\t\t\tif( !el.hasAttribute( 'data-ignore' ) && typeof el.pause === 'function' ) {\n\t\t\t\t\tel.setAttribute('data-paused-by-reveal', '');\n\t\t\t\t\tel.pause();\n\t\t\t\t}\n\t\t\t} );\n\n\t\t\t// Generic postMessage API for non-lazy loaded iframes\n\t\t\tqueryAll( element, 'iframe' ).forEach( el => {\n\t\t\t\tif( el.contentWindow ) el.contentWindow.postMessage( 'slide:stop', '*' );\n\t\t\t\tel.removeEventListener( 'load', this.startEmbeddedIframe );\n\t\t\t});\n\n\t\t\t// YouTube postMessage API\n\t\t\tqueryAll( element, 'iframe[src*=\"youtube.com/embed/\"]' ).forEach( el => {\n\t\t\t\tif( !el.hasAttribute( 'data-ignore' ) && el.contentWindow && typeof el.contentWindow.postMessage === 'function' ) {\n\t\t\t\t\tel.contentWindow.postMessage( '{\"event\":\"command\",\"func\":\"pauseVideo\",\"args\":\"\"}', '*' );\n\t\t\t\t}\n\t\t\t});\n\n\t\t\t// Vimeo postMessage API\n\t\t\tqueryAll( element, 'iframe[src*=\"player.vimeo.com/\"]' ).forEach( el => {\n\t\t\t\tif( !el.hasAttribute( 'data-ignore' ) && el.contentWindow && typeof el.contentWindow.postMessage === 'function' ) {\n\t\t\t\t\tel.contentWindow.postMessage( '{\"method\":\"pause\"}', '*' );\n\t\t\t\t}\n\t\t\t});\n\n\t\t\tif( options.unloadIframes === true ) {\n\t\t\t\t// Unload lazy-loaded iframes\n\t\t\t\tqueryAll( element, 'iframe[data-src]' ).forEach( el => {\n\t\t\t\t\t// Only removing the src doesn't actually unload the frame\n\t\t\t\t\t// in all browsers (Firefox) so we set it to blank first\n\t\t\t\t\tel.setAttribute( 'src', 'about:blank' );\n\t\t\t\t\tel.removeAttribute( 'src' );\n\t\t\t\t} );\n\t\t\t}\n\t\t}\n\n\t}\n\n}\n","/**\n * Handles the display of reveal.js' optional slide number.\n */\nexport default class SlideNumber {\n\n\tconstructor( Reveal ) {\n\n\t\tthis.Reveal = Reveal;\n\n\t}\n\n\trender() {\n\n\t\tthis.element = document.createElement( 'div' );\n\t\tthis.element.className = 'slide-number';\n\t\tthis.Reveal.getRevealElement().appendChild( this.element );\n\n\t}\n\n\t/**\n\t * Called when the reveal.js config is updated.\n\t */\n\tconfigure( config, oldConfig ) {\n\n\t\tlet slideNumberDisplay = 'none';\n\t\tif( config.slideNumber && !this.Reveal.isPrintingPDF() ) {\n\t\t\tif( config.showSlideNumber === 'all' ) {\n\t\t\t\tslideNumberDisplay = 'block';\n\t\t\t}\n\t\t\telse if( config.showSlideNumber === 'speaker' && this.Reveal.isSpeakerNotes() ) {\n\t\t\t\tslideNumberDisplay = 'block';\n\t\t\t}\n\t\t}\n\n\t\tthis.element.style.display = slideNumberDisplay;\n\n\t}\n\n\t/**\n\t * Updates the slide number to match the current slide.\n\t */\n\tupdate() {\n\n\t\t// Update slide number if enabled\n\t\tif( this.Reveal.getConfig().slideNumber && this.element ) {\n\t\t\tthis.element.innerHTML = this.getSlideNumber();\n\t\t}\n\n\t}\n\n\t/**\n\t * Returns the HTML string corresponding to the current slide\n\t * number, including formatting.\n\t */\n\tgetSlideNumber( slide = this.Reveal.getCurrentSlide() ) {\n\n\t\tlet config = this.Reveal.getConfig();\n\t\tlet value;\n\t\tlet format = 'h.v';\n\n\t\tif ( typeof config.slideNumber === 'function' ) {\n\t\t\tvalue = config.slideNumber( slide );\n\t\t} else {\n\t\t\t// Check if a custom number format is available\n\t\t\tif( typeof config.slideNumber === 'string' ) {\n\t\t\t\tformat = config.slideNumber;\n\t\t\t}\n\n\t\t\t// If there are ONLY vertical slides in this deck, always use\n\t\t\t// a flattened slide number\n\t\t\tif( !/c/.test( format ) && this.Reveal.getHorizontalSlides().length === 1 ) {\n\t\t\t\tformat = 'c';\n\t\t\t}\n\n\t\t\t// Offset the current slide number by 1 to make it 1-indexed\n\t\t\tlet horizontalOffset = slide && slide.dataset.visibility === 'uncounted' ? 0 : 1;\n\n\t\t\tvalue = [];\n\t\t\tswitch( format ) {\n\t\t\t\tcase 'c':\n\t\t\t\t\tvalue.push( this.Reveal.getSlidePastCount( slide ) + horizontalOffset );\n\t\t\t\t\tbreak;\n\t\t\t\tcase 'c/t':\n\t\t\t\t\tvalue.push( this.Reveal.getSlidePastCount( slide ) + horizontalOffset, '/', this.Reveal.getTotalSlides() );\n\t\t\t\t\tbreak;\n\t\t\t\tdefault:\n\t\t\t\t\tlet indices = this.Reveal.getIndices( slide );\n\t\t\t\t\tvalue.push( indices.h + horizontalOffset );\n\t\t\t\t\tlet sep = format === 'h/v' ? '/' : '.';\n\t\t\t\t\tif( this.Reveal.isVerticalSlide( slide ) ) value.push( sep, indices.v + 1 );\n\t\t\t}\n\t\t}\n\n\t\tlet url = '#' + this.Reveal.location.getHash( slide );\n\t\treturn this.formatNumber( value[0], value[1], value[2], url );\n\n\t}\n\n\t/**\n\t * Applies HTML formatting to a slide number before it's\n\t * written to the DOM.\n\t *\n\t * @param {number} a Current slide\n\t * @param {string} delimiter Character to separate slide numbers\n\t * @param {(number|*)} b Total slides\n\t * @param {HTMLElement} [url='#'+locationHash()] The url to link to\n\t * @return {string} HTML string fragment\n\t */\n\tformatNumber( a, delimiter, b, url = '#' + this.Reveal.location.getHash() ) {\n\n\t\tif( typeof b === 'number' && !isNaN( b ) ) {\n\t\t\treturn `\n\t\t\t\t\t${a}\n\t\t\t\t\t${delimiter}\n\t\t\t\t\t${b}\n\t\t\t\t\t`;\n\t\t}\n\t\telse {\n\t\t\treturn `\n\t\t\t\t\t${a}\n\t\t\t\t\t`;\n\t\t}\n\n\t}\n\n\tdestroy() {\n\n\t\tthis.element.remove();\n\n\t}\n\n}","/**\n * Converts various color input formats to an {r:0,g:0,b:0} object.\n *\n * @param {string} color The string representation of a color\n * @example\n * colorToRgb('#000');\n * @example\n * colorToRgb('#000000');\n * @example\n * colorToRgb('rgb(0,0,0)');\n * @example\n * colorToRgb('rgba(0,0,0)');\n *\n * @return {{r: number, g: number, b: number, [a]: number}|null}\n */\nexport const colorToRgb = ( color ) => {\n\n\tlet hex3 = color.match( /^#([0-9a-f]{3})$/i );\n\tif( hex3 && hex3[1] ) {\n\t\thex3 = hex3[1];\n\t\treturn {\n\t\t\tr: parseInt( hex3.charAt( 0 ), 16 ) * 0x11,\n\t\t\tg: parseInt( hex3.charAt( 1 ), 16 ) * 0x11,\n\t\t\tb: parseInt( hex3.charAt( 2 ), 16 ) * 0x11\n\t\t};\n\t}\n\n\tlet hex6 = color.match( /^#([0-9a-f]{6})$/i );\n\tif( hex6 && hex6[1] ) {\n\t\thex6 = hex6[1];\n\t\treturn {\n\t\t\tr: parseInt( hex6.slice( 0, 2 ), 16 ),\n\t\t\tg: parseInt( hex6.slice( 2, 4 ), 16 ),\n\t\t\tb: parseInt( hex6.slice( 4, 6 ), 16 )\n\t\t};\n\t}\n\n\tlet rgb = color.match( /^rgb\\s*\\(\\s*(\\d+)\\s*,\\s*(\\d+)\\s*,\\s*(\\d+)\\s*\\)$/i );\n\tif( rgb ) {\n\t\treturn {\n\t\t\tr: parseInt( rgb[1], 10 ),\n\t\t\tg: parseInt( rgb[2], 10 ),\n\t\t\tb: parseInt( rgb[3], 10 )\n\t\t};\n\t}\n\n\tlet rgba = color.match( /^rgba\\s*\\(\\s*(\\d+)\\s*,\\s*(\\d+)\\s*,\\s*(\\d+)\\s*\\,\\s*([\\d]+|[\\d]*.[\\d]+)\\s*\\)$/i );\n\tif( rgba ) {\n\t\treturn {\n\t\t\tr: parseInt( rgba[1], 10 ),\n\t\t\tg: parseInt( rgba[2], 10 ),\n\t\t\tb: parseInt( rgba[3], 10 ),\n\t\t\ta: parseFloat( rgba[4] )\n\t\t};\n\t}\n\n\treturn null;\n\n}\n\n/**\n * Calculates brightness on a scale of 0-255.\n *\n * @param {string} color See colorToRgb for supported formats.\n * @see {@link colorToRgb}\n */\nexport const colorBrightness = ( color ) => {\n\n\tif( typeof color === 'string' ) color = colorToRgb( color );\n\n\tif( color ) {\n\t\treturn ( color.r * 299 + color.g * 587 + color.b * 114 ) / 1000;\n\t}\n\n\treturn null;\n\n}","import { queryAll } from '../utils/util.js'\nimport { colorToRgb, colorBrightness } from '../utils/color.js'\n\n/**\n * Creates and updates slide backgrounds.\n */\nexport default class Backgrounds {\n\n\tconstructor( Reveal ) {\n\n\t\tthis.Reveal = Reveal;\n\n\t}\n\n\trender() {\n\n\t\tthis.element = document.createElement( 'div' );\n\t\tthis.element.className = 'backgrounds';\n\t\tthis.Reveal.getRevealElement().appendChild( this.element );\n\n\t}\n\n\t/**\n\t * Creates the slide background elements and appends them\n\t * to the background container. One element is created per\n\t * slide no matter if the given slide has visible background.\n\t */\n\tcreate() {\n\n\t\t// Clear prior backgrounds\n\t\tthis.element.innerHTML = '';\n\t\tthis.element.classList.add( 'no-transition' );\n\n\t\t// Iterate over all horizontal slides\n\t\tthis.Reveal.getHorizontalSlides().forEach( slideh => {\n\n\t\t\tlet backgroundStack = this.createBackground( slideh, this.element );\n\n\t\t\t// Iterate over all vertical slides\n\t\t\tqueryAll( slideh, 'section' ).forEach( slidev => {\n\n\t\t\t\tthis.createBackground( slidev, backgroundStack );\n\n\t\t\t\tbackgroundStack.classList.add( 'stack' );\n\n\t\t\t} );\n\n\t\t} );\n\n\t\t// Add parallax background if specified\n\t\tif( this.Reveal.getConfig().parallaxBackgroundImage ) {\n\n\t\t\tthis.element.style.backgroundImage = 'url(\"' + this.Reveal.getConfig().parallaxBackgroundImage + '\")';\n\t\t\tthis.element.style.backgroundSize = this.Reveal.getConfig().parallaxBackgroundSize;\n\t\t\tthis.element.style.backgroundRepeat = this.Reveal.getConfig().parallaxBackgroundRepeat;\n\t\t\tthis.element.style.backgroundPosition = this.Reveal.getConfig().parallaxBackgroundPosition;\n\n\t\t\t// Make sure the below properties are set on the element - these properties are\n\t\t\t// needed for proper transitions to be set on the element via CSS. To remove\n\t\t\t// annoying background slide-in effect when the presentation starts, apply\n\t\t\t// these properties after short time delay\n\t\t\tsetTimeout( () => {\n\t\t\t\tthis.Reveal.getRevealElement().classList.add( 'has-parallax-background' );\n\t\t\t}, 1 );\n\n\t\t}\n\t\telse {\n\n\t\t\tthis.element.style.backgroundImage = '';\n\t\t\tthis.Reveal.getRevealElement().classList.remove( 'has-parallax-background' );\n\n\t\t}\n\n\t}\n\n\t/**\n\t * Creates a background for the given slide.\n\t *\n\t * @param {HTMLElement} slide\n\t * @param {HTMLElement} container The element that the background\n\t * should be appended to\n\t * @return {HTMLElement} New background div\n\t */\n\tcreateBackground( slide, container ) {\n\n\t\t// Main slide background element\n\t\tlet element = document.createElement( 'div' );\n\t\telement.className = 'slide-background ' + slide.className.replace( /present|past|future/, '' );\n\n\t\t// Inner background element that wraps images/videos/iframes\n\t\tlet contentElement = document.createElement( 'div' );\n\t\tcontentElement.className = 'slide-background-content';\n\n\t\telement.appendChild( contentElement );\n\t\tcontainer.appendChild( element );\n\n\t\tslide.slideBackgroundElement = element;\n\t\tslide.slideBackgroundContentElement = contentElement;\n\n\t\t// Syncs the background to reflect all current background settings\n\t\tthis.sync( slide );\n\n\t\treturn element;\n\n\t}\n\n\t/**\n\t * Renders all of the visual properties of a slide background\n\t * based on the various background attributes.\n\t *\n\t * @param {HTMLElement} slide\n\t */\n\tsync( slide ) {\n\n\t\tconst element = slide.slideBackgroundElement,\n\t\t\tcontentElement = slide.slideBackgroundContentElement;\n\n\t\tconst data = {\n\t\t\tbackground: slide.getAttribute( 'data-background' ),\n\t\t\tbackgroundSize: slide.getAttribute( 'data-background-size' ),\n\t\t\tbackgroundImage: slide.getAttribute( 'data-background-image' ),\n\t\t\tbackgroundVideo: slide.getAttribute( 'data-background-video' ),\n\t\t\tbackgroundIframe: slide.getAttribute( 'data-background-iframe' ),\n\t\t\tbackgroundColor: slide.getAttribute( 'data-background-color' ),\n\t\t\tbackgroundRepeat: slide.getAttribute( 'data-background-repeat' ),\n\t\t\tbackgroundPosition: slide.getAttribute( 'data-background-position' ),\n\t\t\tbackgroundTransition: slide.getAttribute( 'data-background-transition' ),\n\t\t\tbackgroundOpacity: slide.getAttribute( 'data-background-opacity' ),\n\t\t};\n\n\t\tconst dataPreload = slide.hasAttribute( 'data-preload' );\n\n\t\t// Reset the prior background state in case this is not the\n\t\t// initial sync\n\t\tslide.classList.remove( 'has-dark-background' );\n\t\tslide.classList.remove( 'has-light-background' );\n\n\t\telement.removeAttribute( 'data-loaded' );\n\t\telement.removeAttribute( 'data-background-hash' );\n\t\telement.removeAttribute( 'data-background-size' );\n\t\telement.removeAttribute( 'data-background-transition' );\n\t\telement.style.backgroundColor = '';\n\n\t\tcontentElement.style.backgroundSize = '';\n\t\tcontentElement.style.backgroundRepeat = '';\n\t\tcontentElement.style.backgroundPosition = '';\n\t\tcontentElement.style.backgroundImage = '';\n\t\tcontentElement.style.opacity = '';\n\t\tcontentElement.innerHTML = '';\n\n\t\tif( data.background ) {\n\t\t\t// Auto-wrap image urls in url(...)\n\t\t\tif( /^(http|file|\\/\\/)/gi.test( data.background ) || /\\.(svg|png|jpg|jpeg|gif|bmp)([?#\\s]|$)/gi.test( data.background ) ) {\n\t\t\t\tslide.setAttribute( 'data-background-image', data.background );\n\t\t\t}\n\t\t\telse {\n\t\t\t\telement.style.background = data.background;\n\t\t\t}\n\t\t}\n\n\t\t// Create a hash for this combination of background settings.\n\t\t// This is used to determine when two slide backgrounds are\n\t\t// the same.\n\t\tif( data.background || data.backgroundColor || data.backgroundImage || data.backgroundVideo || data.backgroundIframe ) {\n\t\t\telement.setAttribute( 'data-background-hash', data.background +\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tdata.backgroundSize +\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tdata.backgroundImage +\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tdata.backgroundVideo +\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tdata.backgroundIframe +\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tdata.backgroundColor +\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tdata.backgroundRepeat +\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tdata.backgroundPosition +\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tdata.backgroundTransition +\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tdata.backgroundOpacity );\n\t\t}\n\n\t\t// Additional and optional background properties\n\t\tif( data.backgroundSize ) element.setAttribute( 'data-background-size', data.backgroundSize );\n\t\tif( data.backgroundColor ) element.style.backgroundColor = data.backgroundColor;\n\t\tif( data.backgroundTransition ) element.setAttribute( 'data-background-transition', data.backgroundTransition );\n\n\t\tif( dataPreload ) element.setAttribute( 'data-preload', '' );\n\n\t\t// Background image options are set on the content wrapper\n\t\tif( data.backgroundSize ) contentElement.style.backgroundSize = data.backgroundSize;\n\t\tif( data.backgroundRepeat ) contentElement.style.backgroundRepeat = data.backgroundRepeat;\n\t\tif( data.backgroundPosition ) contentElement.style.backgroundPosition = data.backgroundPosition;\n\t\tif( data.backgroundOpacity ) contentElement.style.opacity = data.backgroundOpacity;\n\n\t\t// If this slide has a background color, we add a class that\n\t\t// signals if it is light or dark. If the slide has no background\n\t\t// color, no class will be added\n\t\tlet contrastColor = data.backgroundColor;\n\n\t\t// If no bg color was found, or it cannot be converted by colorToRgb, check the computed background\n\t\tif( !contrastColor || !colorToRgb( contrastColor ) ) {\n\t\t\tlet computedBackgroundStyle = window.getComputedStyle( element );\n\t\t\tif( computedBackgroundStyle && computedBackgroundStyle.backgroundColor ) {\n\t\t\t\tcontrastColor = computedBackgroundStyle.backgroundColor;\n\t\t\t}\n\t\t}\n\n\t\tif( contrastColor ) {\n\t\t\tconst rgb = colorToRgb( contrastColor );\n\n\t\t\t// Ignore fully transparent backgrounds. Some browsers return\n\t\t\t// rgba(0,0,0,0) when reading the computed background color of\n\t\t\t// an element with no background\n\t\t\tif( rgb && rgb.a !== 0 ) {\n\t\t\t\tif( colorBrightness( contrastColor ) < 128 ) {\n\t\t\t\t\tslide.classList.add( 'has-dark-background' );\n\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\tslide.classList.add( 'has-light-background' );\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\n\t}\n\n\t/**\n\t * Updates the background elements to reflect the current\n\t * slide.\n\t *\n\t * @param {boolean} includeAll If true, the backgrounds of\n\t * all vertical slides (not just the present) will be updated.\n\t */\n\tupdate( includeAll = false ) {\n\n\t\tlet currentSlide = this.Reveal.getCurrentSlide();\n\t\tlet indices = this.Reveal.getIndices();\n\n\t\tlet currentBackground = null;\n\n\t\t// Reverse past/future classes when in RTL mode\n\t\tlet horizontalPast = this.Reveal.getConfig().rtl ? 'future' : 'past',\n\t\t\thorizontalFuture = this.Reveal.getConfig().rtl ? 'past' : 'future';\n\n\t\t// Update the classes of all backgrounds to match the\n\t\t// states of their slides (past/present/future)\n\t\tArray.from( this.element.childNodes ).forEach( ( backgroundh, h ) => {\n\n\t\t\tbackgroundh.classList.remove( 'past', 'present', 'future' );\n\n\t\t\tif( h < indices.h ) {\n\t\t\t\tbackgroundh.classList.add( horizontalPast );\n\t\t\t}\n\t\t\telse if ( h > indices.h ) {\n\t\t\t\tbackgroundh.classList.add( horizontalFuture );\n\t\t\t}\n\t\t\telse {\n\t\t\t\tbackgroundh.classList.add( 'present' );\n\n\t\t\t\t// Store a reference to the current background element\n\t\t\t\tcurrentBackground = backgroundh;\n\t\t\t}\n\n\t\t\tif( includeAll || h === indices.h ) {\n\t\t\t\tqueryAll( backgroundh, '.slide-background' ).forEach( ( backgroundv, v ) => {\n\n\t\t\t\t\tbackgroundv.classList.remove( 'past', 'present', 'future' );\n\n\t\t\t\t\tif( v < indices.v ) {\n\t\t\t\t\t\tbackgroundv.classList.add( 'past' );\n\t\t\t\t\t}\n\t\t\t\t\telse if ( v > indices.v ) {\n\t\t\t\t\t\tbackgroundv.classList.add( 'future' );\n\t\t\t\t\t}\n\t\t\t\t\telse {\n\t\t\t\t\t\tbackgroundv.classList.add( 'present' );\n\n\t\t\t\t\t\t// Only if this is the present horizontal and vertical slide\n\t\t\t\t\t\tif( h === indices.h ) currentBackground = backgroundv;\n\t\t\t\t\t}\n\n\t\t\t\t} );\n\t\t\t}\n\n\t\t} );\n\n\t\t// Stop content inside of previous backgrounds\n\t\tif( this.previousBackground ) {\n\n\t\t\tthis.Reveal.slideContent.stopEmbeddedContent( this.previousBackground, { unloadIframes: !this.Reveal.slideContent.shouldPreload( this.previousBackground ) } );\n\n\t\t}\n\n\t\t// Start content in the current background\n\t\tif( currentBackground ) {\n\n\t\t\tthis.Reveal.slideContent.startEmbeddedContent( currentBackground );\n\n\t\t\tlet currentBackgroundContent = currentBackground.querySelector( '.slide-background-content' );\n\t\t\tif( currentBackgroundContent ) {\n\n\t\t\t\tlet backgroundImageURL = currentBackgroundContent.style.backgroundImage || '';\n\n\t\t\t\t// Restart GIFs (doesn't work in Firefox)\n\t\t\t\tif( /\\.gif/i.test( backgroundImageURL ) ) {\n\t\t\t\t\tcurrentBackgroundContent.style.backgroundImage = '';\n\t\t\t\t\twindow.getComputedStyle( currentBackgroundContent ).opacity;\n\t\t\t\t\tcurrentBackgroundContent.style.backgroundImage = backgroundImageURL;\n\t\t\t\t}\n\n\t\t\t}\n\n\t\t\t// Don't transition between identical backgrounds. This\n\t\t\t// prevents unwanted flicker.\n\t\t\tlet previousBackgroundHash = this.previousBackground ? this.previousBackground.getAttribute( 'data-background-hash' ) : null;\n\t\t\tlet currentBackgroundHash = currentBackground.getAttribute( 'data-background-hash' );\n\t\t\tif( currentBackgroundHash && currentBackgroundHash === previousBackgroundHash && currentBackground !== this.previousBackground ) {\n\t\t\t\tthis.element.classList.add( 'no-transition' );\n\t\t\t}\n\n\t\t\tthis.previousBackground = currentBackground;\n\n\t\t}\n\n\t\t// If there's a background brightness flag for this slide,\n\t\t// bubble it to the .reveal container\n\t\tif( currentSlide ) {\n\t\t\t[ 'has-light-background', 'has-dark-background' ].forEach( classToBubble => {\n\t\t\t\tif( currentSlide.classList.contains( classToBubble ) ) {\n\t\t\t\t\tthis.Reveal.getRevealElement().classList.add( classToBubble );\n\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\tthis.Reveal.getRevealElement().classList.remove( classToBubble );\n\t\t\t\t}\n\t\t\t}, this );\n\t\t}\n\n\t\t// Allow the first background to apply without transition\n\t\tsetTimeout( () => {\n\t\t\tthis.element.classList.remove( 'no-transition' );\n\t\t}, 1 );\n\n\t}\n\n\t/**\n\t * Updates the position of the parallax background based\n\t * on the current slide index.\n\t */\n\tupdateParallax() {\n\n\t\tlet indices = this.Reveal.getIndices();\n\n\t\tif( this.Reveal.getConfig().parallaxBackgroundImage ) {\n\n\t\t\tlet horizontalSlides = this.Reveal.getHorizontalSlides(),\n\t\t\t\tverticalSlides = this.Reveal.getVerticalSlides();\n\n\t\t\tlet backgroundSize = this.element.style.backgroundSize.split( ' ' ),\n\t\t\t\tbackgroundWidth, backgroundHeight;\n\n\t\t\tif( backgroundSize.length === 1 ) {\n\t\t\t\tbackgroundWidth = backgroundHeight = parseInt( backgroundSize[0], 10 );\n\t\t\t}\n\t\t\telse {\n\t\t\t\tbackgroundWidth = parseInt( backgroundSize[0], 10 );\n\t\t\t\tbackgroundHeight = parseInt( backgroundSize[1], 10 );\n\t\t\t}\n\n\t\t\tlet slideWidth = this.element.offsetWidth,\n\t\t\t\thorizontalSlideCount = horizontalSlides.length,\n\t\t\t\thorizontalOffsetMultiplier,\n\t\t\t\thorizontalOffset;\n\n\t\t\tif( typeof this.Reveal.getConfig().parallaxBackgroundHorizontal === 'number' ) {\n\t\t\t\thorizontalOffsetMultiplier = this.Reveal.getConfig().parallaxBackgroundHorizontal;\n\t\t\t}\n\t\t\telse {\n\t\t\t\thorizontalOffsetMultiplier = horizontalSlideCount > 1 ? ( backgroundWidth - slideWidth ) / ( horizontalSlideCount-1 ) : 0;\n\t\t\t}\n\n\t\t\thorizontalOffset = horizontalOffsetMultiplier * indices.h * -1;\n\n\t\t\tlet slideHeight = this.element.offsetHeight,\n\t\t\t\tverticalSlideCount = verticalSlides.length,\n\t\t\t\tverticalOffsetMultiplier,\n\t\t\t\tverticalOffset;\n\n\t\t\tif( typeof this.Reveal.getConfig().parallaxBackgroundVertical === 'number' ) {\n\t\t\t\tverticalOffsetMultiplier = this.Reveal.getConfig().parallaxBackgroundVertical;\n\t\t\t}\n\t\t\telse {\n\t\t\t\tverticalOffsetMultiplier = ( backgroundHeight - slideHeight ) / ( verticalSlideCount-1 );\n\t\t\t}\n\n\t\t\tverticalOffset = verticalSlideCount > 0 ? verticalOffsetMultiplier * indices.v : 0;\n\n\t\t\tthis.element.style.backgroundPosition = horizontalOffset + 'px ' + -verticalOffset + 'px';\n\n\t\t}\n\n\t}\n\n\tdestroy() {\n\n\t\tthis.element.remove();\n\n\t}\n\n}\n","\nexport const SLIDES_SELECTOR = '.slides section';\nexport const HORIZONTAL_SLIDES_SELECTOR = '.slides>section';\nexport const VERTICAL_SLIDES_SELECTOR = '.slides>section.present>section';\n\n// Methods that may not be invoked via the postMessage API\nexport const POST_MESSAGE_METHOD_BLACKLIST = /registerPlugin|registerKeyboardShortcut|addKeyBinding|addEventListener/;\n\n// Regex for retrieving the fragment style from a class attribute\nexport const FRAGMENT_STYLE_REGEX = /fade-(down|up|right|left|out|in-then-out|in-then-semi-out)|semi-fade-out|current-visible|shrink|grow/;","import { queryAll, extend, createStyleSheet, matches, closest } from '../utils/util.js'\nimport { FRAGMENT_STYLE_REGEX } from '../utils/constants.js'\n\n// Counter used to generate unique IDs for auto-animated elements\nlet autoAnimateCounter = 0;\n\n/**\n * Automatically animates matching elements across\n * slides with the [data-auto-animate] attribute.\n */\nexport default class AutoAnimate {\n\n\tconstructor( Reveal ) {\n\n\t\tthis.Reveal = Reveal;\n\n\t}\n\n\t/**\n\t * Runs an auto-animation between the given slides.\n\t *\n\t * @param {HTMLElement} fromSlide\n\t * @param {HTMLElement} toSlide\n\t */\n\trun( fromSlide, toSlide ) {\n\n\t\t// Clean up after prior animations\n\t\tthis.reset();\n\n\t\tlet allSlides = this.Reveal.getSlides();\n\t\tlet toSlideIndex = allSlides.indexOf( toSlide );\n\t\tlet fromSlideIndex = allSlides.indexOf( fromSlide );\n\n\t\t// Ensure that both slides are auto-animate targets with the same data-auto-animate-id value\n\t\t// (including null if absent on both) and that data-auto-animate-restart isn't set on the\n\t\t// physically latter slide (independent of slide direction)\n\t\tif( fromSlide.hasAttribute( 'data-auto-animate' ) && toSlide.hasAttribute( 'data-auto-animate' )\n\t\t\t\t&& fromSlide.getAttribute( 'data-auto-animate-id' ) === toSlide.getAttribute( 'data-auto-animate-id' ) \n\t\t\t\t&& !( toSlideIndex > fromSlideIndex ? toSlide : fromSlide ).hasAttribute( 'data-auto-animate-restart' ) ) {\n\n\t\t\t// Create a new auto-animate sheet\n\t\t\tthis.autoAnimateStyleSheet = this.autoAnimateStyleSheet || createStyleSheet();\n\n\t\t\tlet animationOptions = this.getAutoAnimateOptions( toSlide );\n\n\t\t\t// Set our starting state\n\t\t\tfromSlide.dataset.autoAnimate = 'pending';\n\t\t\ttoSlide.dataset.autoAnimate = 'pending';\n\n\t\t\t// Flag the navigation direction, needed for fragment buildup\n\t\t\tanimationOptions.slideDirection = toSlideIndex > fromSlideIndex ? 'forward' : 'backward';\n\n\t\t\t// Inject our auto-animate styles for this transition\n\t\t\tlet css = this.getAutoAnimatableElements( fromSlide, toSlide ).map( elements => {\n\t\t\t\treturn this.autoAnimateElements( elements.from, elements.to, elements.options || {}, animationOptions, autoAnimateCounter++ );\n\t\t\t} );\n\n\t\t\t// Animate unmatched elements, if enabled\n\t\t\tif( toSlide.dataset.autoAnimateUnmatched !== 'false' && this.Reveal.getConfig().autoAnimateUnmatched === true ) {\n\n\t\t\t\t// Our default timings for unmatched elements\n\t\t\t\tlet defaultUnmatchedDuration = animationOptions.duration * 0.8,\n\t\t\t\t\tdefaultUnmatchedDelay = animationOptions.duration * 0.2;\n\n\t\t\t\tthis.getUnmatchedAutoAnimateElements( toSlide ).forEach( unmatchedElement => {\n\n\t\t\t\t\tlet unmatchedOptions = this.getAutoAnimateOptions( unmatchedElement, animationOptions );\n\t\t\t\t\tlet id = 'unmatched';\n\n\t\t\t\t\t// If there is a duration or delay set specifically for this\n\t\t\t\t\t// element our unmatched elements should adhere to those\n\t\t\t\t\tif( unmatchedOptions.duration !== animationOptions.duration || unmatchedOptions.delay !== animationOptions.delay ) {\n\t\t\t\t\t\tid = 'unmatched-' + autoAnimateCounter++;\n\t\t\t\t\t\tcss.push( `[data-auto-animate=\"running\"] [data-auto-animate-target=\"${id}\"] { transition: opacity ${unmatchedOptions.duration}s ease ${unmatchedOptions.delay}s; }` );\n\t\t\t\t\t}\n\n\t\t\t\t\tunmatchedElement.dataset.autoAnimateTarget = id;\n\n\t\t\t\t}, this );\n\n\t\t\t\t// Our default transition for unmatched elements\n\t\t\t\tcss.push( `[data-auto-animate=\"running\"] [data-auto-animate-target=\"unmatched\"] { transition: opacity ${defaultUnmatchedDuration}s ease ${defaultUnmatchedDelay}s; }` );\n\n\t\t\t}\n\n\t\t\t// Setting the whole chunk of CSS at once is the most\n\t\t\t// efficient way to do this. Using sheet.insertRule\n\t\t\t// is multiple factors slower.\n\t\t\tthis.autoAnimateStyleSheet.innerHTML = css.join( '' );\n\n\t\t\t// Start the animation next cycle\n\t\t\trequestAnimationFrame( () => {\n\t\t\t\tif( this.autoAnimateStyleSheet ) {\n\t\t\t\t\t// This forces our newly injected styles to be applied in Firefox\n\t\t\t\t\tgetComputedStyle( this.autoAnimateStyleSheet ).fontWeight;\n\n\t\t\t\t\ttoSlide.dataset.autoAnimate = 'running';\n\t\t\t\t}\n\t\t\t} );\n\n\t\t\tthis.Reveal.dispatchEvent({\n\t\t\t\ttype: 'autoanimate',\n\t\t\t\tdata: {\n\t\t\t\t\tfromSlide,\n\t\t\t\t\ttoSlide,\n\t\t\t\t\tsheet: this.autoAnimateStyleSheet\n\t\t\t\t}\n\t\t\t});\n\n\t\t}\n\n\t}\n\n\t/**\n\t * Rolls back all changes that we've made to the DOM so\n\t * that as part of animating.\n\t */\n\treset() {\n\n\t\t// Reset slides\n\t\tqueryAll( this.Reveal.getRevealElement(), '[data-auto-animate]:not([data-auto-animate=\"\"])' ).forEach( element => {\n\t\t\telement.dataset.autoAnimate = '';\n\t\t} );\n\n\t\t// Reset elements\n\t\tqueryAll( this.Reveal.getRevealElement(), '[data-auto-animate-target]' ).forEach( element => {\n\t\t\tdelete element.dataset.autoAnimateTarget;\n\t\t} );\n\n\t\t// Remove the animation sheet\n\t\tif( this.autoAnimateStyleSheet && this.autoAnimateStyleSheet.parentNode ) {\n\t\t\tthis.autoAnimateStyleSheet.parentNode.removeChild( this.autoAnimateStyleSheet );\n\t\t\tthis.autoAnimateStyleSheet = null;\n\t\t}\n\n\t}\n\n\t/**\n\t * Creates a FLIP animation where the `to` element starts out\n\t * in the `from` element position and animates to its original\n\t * state.\n\t *\n\t * @param {HTMLElement} from\n\t * @param {HTMLElement} to\n\t * @param {Object} elementOptions Options for this element pair\n\t * @param {Object} animationOptions Options set at the slide level\n\t * @param {String} id Unique ID that we can use to identify this\n\t * auto-animate element in the DOM\n\t */\n\tautoAnimateElements( from, to, elementOptions, animationOptions, id ) {\n\n\t\t// 'from' elements are given a data-auto-animate-target with no value,\n\t\t// 'to' elements are are given a data-auto-animate-target with an ID\n\t\tfrom.dataset.autoAnimateTarget = '';\n\t\tto.dataset.autoAnimateTarget = id;\n\n\t\t// Each element may override any of the auto-animate options\n\t\t// like transition easing, duration and delay via data-attributes\n\t\tlet options = this.getAutoAnimateOptions( to, animationOptions );\n\n\t\t// If we're using a custom element matcher the element options\n\t\t// may contain additional transition overrides\n\t\tif( typeof elementOptions.delay !== 'undefined' ) options.delay = elementOptions.delay;\n\t\tif( typeof elementOptions.duration !== 'undefined' ) options.duration = elementOptions.duration;\n\t\tif( typeof elementOptions.easing !== 'undefined' ) options.easing = elementOptions.easing;\n\n\t\tlet fromProps = this.getAutoAnimatableProperties( 'from', from, elementOptions ),\n\t\t\ttoProps = this.getAutoAnimatableProperties( 'to', to, elementOptions );\n\n\t\t// Maintain fragment visibility for matching elements when\n\t\t// we're navigating forwards, this way the viewer won't need\n\t\t// to step through the same fragments twice\n\t\tif( to.classList.contains( 'fragment' ) ) {\n\n\t\t\t// Don't auto-animate the opacity of fragments to avoid\n\t\t\t// conflicts with fragment animations\n\t\t\tdelete toProps.styles['opacity'];\n\n\t\t\tif( from.classList.contains( 'fragment' ) ) {\n\n\t\t\t\tlet fromFragmentStyle = ( from.className.match( FRAGMENT_STYLE_REGEX ) || [''] )[0];\n\t\t\t\tlet toFragmentStyle = ( to.className.match( FRAGMENT_STYLE_REGEX ) || [''] )[0];\n\n\t\t\t\t// Only skip the fragment if the fragment animation style\n\t\t\t\t// remains unchanged\n\t\t\t\tif( fromFragmentStyle === toFragmentStyle && animationOptions.slideDirection === 'forward' ) {\n\t\t\t\t\tto.classList.add( 'visible', 'disabled' );\n\t\t\t\t}\n\n\t\t\t}\n\n\t\t}\n\n\t\t// If translation and/or scaling are enabled, css transform\n\t\t// the 'to' element so that it matches the position and size\n\t\t// of the 'from' element\n\t\tif( elementOptions.translate !== false || elementOptions.scale !== false ) {\n\n\t\t\tlet presentationScale = this.Reveal.getScale();\n\n\t\t\tlet delta = {\n\t\t\t\tx: ( fromProps.x - toProps.x ) / presentationScale,\n\t\t\t\ty: ( fromProps.y - toProps.y ) / presentationScale,\n\t\t\t\tscaleX: fromProps.width / toProps.width,\n\t\t\t\tscaleY: fromProps.height / toProps.height\n\t\t\t};\n\n\t\t\t// Limit decimal points to avoid 0.0001px blur and stutter\n\t\t\tdelta.x = Math.round( delta.x * 1000 ) / 1000;\n\t\t\tdelta.y = Math.round( delta.y * 1000 ) / 1000;\n\t\t\tdelta.scaleX = Math.round( delta.scaleX * 1000 ) / 1000;\n\t\t\tdelta.scaleX = Math.round( delta.scaleX * 1000 ) / 1000;\n\n\t\t\tlet translate = elementOptions.translate !== false && ( delta.x !== 0 || delta.y !== 0 ),\n\t\t\t\tscale = elementOptions.scale !== false && ( delta.scaleX !== 0 || delta.scaleY !== 0 );\n\n\t\t\t// No need to transform if nothing's changed\n\t\t\tif( translate || scale ) {\n\n\t\t\t\tlet transform = [];\n\n\t\t\t\tif( translate ) transform.push( `translate(${delta.x}px, ${delta.y}px)` );\n\t\t\t\tif( scale ) transform.push( `scale(${delta.scaleX}, ${delta.scaleY})` );\n\n\t\t\t\tfromProps.styles['transform'] = transform.join( ' ' );\n\t\t\t\tfromProps.styles['transform-origin'] = 'top left';\n\n\t\t\t\ttoProps.styles['transform'] = 'none';\n\n\t\t\t}\n\n\t\t}\n\n\t\t// Delete all unchanged 'to' styles\n\t\tfor( let propertyName in toProps.styles ) {\n\t\t\tconst toValue = toProps.styles[propertyName];\n\t\t\tconst fromValue = fromProps.styles[propertyName];\n\n\t\t\tif( toValue === fromValue ) {\n\t\t\t\tdelete toProps.styles[propertyName];\n\t\t\t}\n\t\t\telse {\n\t\t\t\t// If these property values were set via a custom matcher providing\n\t\t\t\t// an explicit 'from' and/or 'to' value, we always inject those values.\n\t\t\t\tif( toValue.explicitValue === true ) {\n\t\t\t\t\ttoProps.styles[propertyName] = toValue.value;\n\t\t\t\t}\n\n\t\t\t\tif( fromValue.explicitValue === true ) {\n\t\t\t\t\tfromProps.styles[propertyName] = fromValue.value;\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\n\t\tlet css = '';\n\n\t\tlet toStyleProperties = Object.keys( toProps.styles );\n\n\t\t// Only create animate this element IF at least one style\n\t\t// property has changed\n\t\tif( toStyleProperties.length > 0 ) {\n\n\t\t\t// Instantly move to the 'from' state\n\t\t\tfromProps.styles['transition'] = 'none';\n\n\t\t\t// Animate towards the 'to' state\n\t\t\ttoProps.styles['transition'] = `all ${options.duration}s ${options.easing} ${options.delay}s`;\n\t\t\ttoProps.styles['transition-property'] = toStyleProperties.join( ', ' );\n\t\t\ttoProps.styles['will-change'] = toStyleProperties.join( ', ' );\n\n\t\t\t// Build up our custom CSS. We need to override inline styles\n\t\t\t// so we need to make our styles vErY IMPORTANT!1!!\n\t\t\tlet fromCSS = Object.keys( fromProps.styles ).map( propertyName => {\n\t\t\t\treturn propertyName + ': ' + fromProps.styles[propertyName] + ' !important;';\n\t\t\t} ).join( '' );\n\n\t\t\tlet toCSS = Object.keys( toProps.styles ).map( propertyName => {\n\t\t\t\treturn propertyName + ': ' + toProps.styles[propertyName] + ' !important;';\n\t\t\t} ).join( '' );\n\n\t\t\tcss = \t'[data-auto-animate-target=\"'+ id +'\"] {'+ fromCSS +'}' +\n\t\t\t\t\t'[data-auto-animate=\"running\"] [data-auto-animate-target=\"'+ id +'\"] {'+ toCSS +'}';\n\n\t\t}\n\n\t\treturn css;\n\n\t}\n\n\t/**\n\t * Returns the auto-animate options for the given element.\n\t *\n\t * @param {HTMLElement} element Element to pick up options\n\t * from, either a slide or an animation target\n\t * @param {Object} [inheritedOptions] Optional set of existing\n\t * options\n\t */\n\tgetAutoAnimateOptions( element, inheritedOptions ) {\n\n\t\tlet options = {\n\t\t\teasing: this.Reveal.getConfig().autoAnimateEasing,\n\t\t\tduration: this.Reveal.getConfig().autoAnimateDuration,\n\t\t\tdelay: 0\n\t\t};\n\n\t\toptions = extend( options, inheritedOptions );\n\n\t\t// Inherit options from parent elements\n\t\tif( element.parentNode ) {\n\t\t\tlet autoAnimatedParent = closest( element.parentNode, '[data-auto-animate-target]' );\n\t\t\tif( autoAnimatedParent ) {\n\t\t\t\toptions = this.getAutoAnimateOptions( autoAnimatedParent, options );\n\t\t\t}\n\t\t}\n\n\t\tif( element.dataset.autoAnimateEasing ) {\n\t\t\toptions.easing = element.dataset.autoAnimateEasing;\n\t\t}\n\n\t\tif( element.dataset.autoAnimateDuration ) {\n\t\t\toptions.duration = parseFloat( element.dataset.autoAnimateDuration );\n\t\t}\n\n\t\tif( element.dataset.autoAnimateDelay ) {\n\t\t\toptions.delay = parseFloat( element.dataset.autoAnimateDelay );\n\t\t}\n\n\t\treturn options;\n\n\t}\n\n\t/**\n\t * Returns an object containing all of the properties\n\t * that can be auto-animated for the given element and\n\t * their current computed values.\n\t *\n\t * @param {String} direction 'from' or 'to'\n\t */\n\tgetAutoAnimatableProperties( direction, element, elementOptions ) {\n\n\t\tlet config = this.Reveal.getConfig();\n\n\t\tlet properties = { styles: [] };\n\n\t\t// Position and size\n\t\tif( elementOptions.translate !== false || elementOptions.scale !== false ) {\n\t\t\tlet bounds;\n\n\t\t\t// Custom auto-animate may optionally return a custom tailored\n\t\t\t// measurement function\n\t\t\tif( typeof elementOptions.measure === 'function' ) {\n\t\t\t\tbounds = elementOptions.measure( element );\n\t\t\t}\n\t\t\telse {\n\t\t\t\tif( config.center ) {\n\t\t\t\t\t// More precise, but breaks when used in combination\n\t\t\t\t\t// with zoom for scaling the deck ¯\\_(ツ)_/¯\n\t\t\t\t\tbounds = element.getBoundingClientRect();\n\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\tlet scale = this.Reveal.getScale();\n\t\t\t\t\tbounds = {\n\t\t\t\t\t\tx: element.offsetLeft * scale,\n\t\t\t\t\t\ty: element.offsetTop * scale,\n\t\t\t\t\t\twidth: element.offsetWidth * scale,\n\t\t\t\t\t\theight: element.offsetHeight * scale\n\t\t\t\t\t};\n\t\t\t\t}\n\t\t\t}\n\n\t\t\tproperties.x = bounds.x;\n\t\t\tproperties.y = bounds.y;\n\t\t\tproperties.width = bounds.width;\n\t\t\tproperties.height = bounds.height;\n\t\t}\n\n\t\tconst computedStyles = getComputedStyle( element );\n\n\t\t// CSS styles\n\t\t( elementOptions.styles || config.autoAnimateStyles ).forEach( style => {\n\t\t\tlet value;\n\n\t\t\t// `style` is either the property name directly, or an object\n\t\t\t// definition of a style property\n\t\t\tif( typeof style === 'string' ) style = { property: style };\n\n\t\t\tif( typeof style.from !== 'undefined' && direction === 'from' ) {\n\t\t\t\tvalue = { value: style.from, explicitValue: true };\n\t\t\t}\n\t\t\telse if( typeof style.to !== 'undefined' && direction === 'to' ) {\n\t\t\t\tvalue = { value: style.to, explicitValue: true };\n\t\t\t}\n\t\t\telse {\n\t\t\t\tvalue = computedStyles[style.property];\n\t\t\t}\n\n\t\t\tif( value !== '' ) {\n\t\t\t\tproperties.styles[style.property] = value;\n\t\t\t}\n\t\t} );\n\n\t\treturn properties;\n\n\t}\n\n\t/**\n\t * Get a list of all element pairs that we can animate\n\t * between the given slides.\n\t *\n\t * @param {HTMLElement} fromSlide\n\t * @param {HTMLElement} toSlide\n\t *\n\t * @return {Array} Each value is an array where [0] is\n\t * the element we're animating from and [1] is the\n\t * element we're animating to\n\t */\n\tgetAutoAnimatableElements( fromSlide, toSlide ) {\n\n\t\tlet matcher = typeof this.Reveal.getConfig().autoAnimateMatcher === 'function' ? this.Reveal.getConfig().autoAnimateMatcher : this.getAutoAnimatePairs;\n\n\t\tlet pairs = matcher.call( this, fromSlide, toSlide );\n\n\t\tlet reserved = [];\n\n\t\t// Remove duplicate pairs\n\t\treturn pairs.filter( ( pair, index ) => {\n\t\t\tif( reserved.indexOf( pair.to ) === -1 ) {\n\t\t\t\treserved.push( pair.to );\n\t\t\t\treturn true;\n\t\t\t}\n\t\t} );\n\n\t}\n\n\t/**\n\t * Identifies matching elements between slides.\n\t *\n\t * You can specify a custom matcher function by using\n\t * the `autoAnimateMatcher` config option.\n\t */\n\tgetAutoAnimatePairs( fromSlide, toSlide ) {\n\n\t\tlet pairs = [];\n\n\t\tconst codeNodes = 'pre';\n\t\tconst textNodes = 'h1, h2, h3, h4, h5, h6, p, li';\n\t\tconst mediaNodes = 'img, video, iframe';\n\n\t\t// Eplicit matches via data-id\n\t\tthis.findAutoAnimateMatches( pairs, fromSlide, toSlide, '[data-id]', node => {\n\t\t\treturn node.nodeName + ':::' + node.getAttribute( 'data-id' );\n\t\t} );\n\n\t\t// Text\n\t\tthis.findAutoAnimateMatches( pairs, fromSlide, toSlide, textNodes, node => {\n\t\t\treturn node.nodeName + ':::' + node.innerText;\n\t\t} );\n\n\t\t// Media\n\t\tthis.findAutoAnimateMatches( pairs, fromSlide, toSlide, mediaNodes, node => {\n\t\t\treturn node.nodeName + ':::' + ( node.getAttribute( 'src' ) || node.getAttribute( 'data-src' ) );\n\t\t} );\n\n\t\t// Code\n\t\tthis.findAutoAnimateMatches( pairs, fromSlide, toSlide, codeNodes, node => {\n\t\t\treturn node.nodeName + ':::' + node.innerText;\n\t\t} );\n\n\t\tpairs.forEach( pair => {\n\n\t\t\t// Disable scale transformations on text nodes, we transition\n\t\t\t// each individual text property instead\n\t\t\tif( matches( pair.from, textNodes ) ) {\n\t\t\t\tpair.options = { scale: false };\n\t\t\t}\n\t\t\t// Animate individual lines of code\n\t\t\telse if( matches( pair.from, codeNodes ) ) {\n\n\t\t\t\t// Transition the code block's width and height instead of scaling\n\t\t\t\t// to prevent its content from being squished\n\t\t\t\tpair.options = { scale: false, styles: [ 'width', 'height' ] };\n\n\t\t\t\t// Lines of code\n\t\t\t\tthis.findAutoAnimateMatches( pairs, pair.from, pair.to, '.hljs .hljs-ln-code', node => {\n\t\t\t\t\treturn node.textContent;\n\t\t\t\t}, {\n\t\t\t\t\tscale: false,\n\t\t\t\t\tstyles: [],\n\t\t\t\t\tmeasure: this.getLocalBoundingBox.bind( this )\n\t\t\t\t} );\n\n\t\t\t\t// Line numbers\n\t\t\t\tthis.findAutoAnimateMatches( pairs, pair.from, pair.to, '.hljs .hljs-ln-line[data-line-number]', node => {\n\t\t\t\t\treturn node.getAttribute( 'data-line-number' );\n\t\t\t\t}, {\n\t\t\t\t\tscale: false,\n\t\t\t\t\tstyles: [ 'width' ],\n\t\t\t\t\tmeasure: this.getLocalBoundingBox.bind( this )\n\t\t\t\t} );\n\n\t\t\t}\n\n\t\t}, this );\n\n\t\treturn pairs;\n\n\t}\n\n\t/**\n\t * Helper method which returns a bounding box based on\n\t * the given elements offset coordinates.\n\t *\n\t * @param {HTMLElement} element\n\t * @return {Object} x, y, width, height\n\t */\n\tgetLocalBoundingBox( element ) {\n\n\t\tconst presentationScale = this.Reveal.getScale();\n\n\t\treturn {\n\t\t\tx: Math.round( ( element.offsetLeft * presentationScale ) * 100 ) / 100,\n\t\t\ty: Math.round( ( element.offsetTop * presentationScale ) * 100 ) / 100,\n\t\t\twidth: Math.round( ( element.offsetWidth * presentationScale ) * 100 ) / 100,\n\t\t\theight: Math.round( ( element.offsetHeight * presentationScale ) * 100 ) / 100\n\t\t};\n\n\t}\n\n\t/**\n\t * Finds matching elements between two slides.\n\t *\n\t * @param {Array} pairs \tList of pairs to push matches to\n\t * @param {HTMLElement} fromScope Scope within the from element exists\n\t * @param {HTMLElement} toScope Scope within the to element exists\n\t * @param {String} selector CSS selector of the element to match\n\t * @param {Function} serializer A function that accepts an element and returns\n\t * a stringified ID based on its contents\n\t * @param {Object} animationOptions Optional config options for this pair\n\t */\n\tfindAutoAnimateMatches( pairs, fromScope, toScope, selector, serializer, animationOptions ) {\n\n\t\tlet fromMatches = {};\n\t\tlet toMatches = {};\n\n\t\t[].slice.call( fromScope.querySelectorAll( selector ) ).forEach( ( element, i ) => {\n\t\t\tconst key = serializer( element );\n\t\t\tif( typeof key === 'string' && key.length ) {\n\t\t\t\tfromMatches[key] = fromMatches[key] || [];\n\t\t\t\tfromMatches[key].push( element );\n\t\t\t}\n\t\t} );\n\n\t\t[].slice.call( toScope.querySelectorAll( selector ) ).forEach( ( element, i ) => {\n\t\t\tconst key = serializer( element );\n\t\t\ttoMatches[key] = toMatches[key] || [];\n\t\t\ttoMatches[key].push( element );\n\n\t\t\tlet fromElement;\n\n\t\t\t// Retrieve the 'from' element\n\t\t\tif( fromMatches[key] ) {\n\t\t\t\tconst pimaryIndex = toMatches[key].length - 1;\n\t\t\t\tconst secondaryIndex = fromMatches[key].length - 1;\n\n\t\t\t\t// If there are multiple identical from elements, retrieve\n\t\t\t\t// the one at the same index as our to-element.\n\t\t\t\tif( fromMatches[key][ pimaryIndex ] ) {\n\t\t\t\t\tfromElement = fromMatches[key][ pimaryIndex ];\n\t\t\t\t\tfromMatches[key][ pimaryIndex ] = null;\n\t\t\t\t}\n\t\t\t\t// If there are no matching from-elements at the same index,\n\t\t\t\t// use the last one.\n\t\t\t\telse if( fromMatches[key][ secondaryIndex ] ) {\n\t\t\t\t\tfromElement = fromMatches[key][ secondaryIndex ];\n\t\t\t\t\tfromMatches[key][ secondaryIndex ] = null;\n\t\t\t\t}\n\t\t\t}\n\n\t\t\t// If we've got a matching pair, push it to the list of pairs\n\t\t\tif( fromElement ) {\n\t\t\t\tpairs.push({\n\t\t\t\t\tfrom: fromElement,\n\t\t\t\t\tto: element,\n\t\t\t\t\toptions: animationOptions\n\t\t\t\t});\n\t\t\t}\n\t\t} );\n\n\t}\n\n\t/**\n\t * Returns a all elements within the given scope that should\n\t * be considered unmatched in an auto-animate transition. If\n\t * fading of unmatched elements is turned on, these elements\n\t * will fade when going between auto-animate slides.\n\t *\n\t * Note that parents of auto-animate targets are NOT considerd\n\t * unmatched since fading them would break the auto-animation.\n\t *\n\t * @param {HTMLElement} rootElement\n\t * @return {Array}\n\t */\n\tgetUnmatchedAutoAnimateElements( rootElement ) {\n\n\t\treturn [].slice.call( rootElement.children ).reduce( ( result, element ) => {\n\n\t\t\tconst containsAnimatedElements = element.querySelector( '[data-auto-animate-target]' );\n\n\t\t\t// The element is unmatched if\n\t\t\t// - It is not an auto-animate target\n\t\t\t// - It does not contain any auto-animate targets\n\t\t\tif( !element.hasAttribute( 'data-auto-animate-target' ) && !containsAnimatedElements ) {\n\t\t\t\tresult.push( element );\n\t\t\t}\n\n\t\t\tif( element.querySelector( '[data-auto-animate-target]' ) ) {\n\t\t\t\tresult = result.concat( this.getUnmatchedAutoAnimateElements( element ) );\n\t\t\t}\n\n\t\t\treturn result;\n\n\t\t}, [] );\n\n\t}\n\n}\n","import { extend, queryAll } from '../utils/util.js'\n\n/**\n * Handles sorting and navigation of slide fragments.\n * Fragments are elements within a slide that are\n * revealed/animated incrementally.\n */\nexport default class Fragments {\n\n\tconstructor( Reveal ) {\n\n\t\tthis.Reveal = Reveal;\n\n\t}\n\n\t/**\n\t * Called when the reveal.js config is updated.\n\t */\n\tconfigure( config, oldConfig ) {\n\n\t\tif( config.fragments === false ) {\n\t\t\tthis.disable();\n\t\t}\n\t\telse if( oldConfig.fragments === false ) {\n\t\t\tthis.enable();\n\t\t}\n\n\t}\n\n\t/**\n\t * If fragments are disabled in the deck, they should all be\n\t * visible rather than stepped through.\n\t */\n\tdisable() {\n\n\t\tqueryAll( this.Reveal.getSlidesElement(), '.fragment' ).forEach( element => {\n\t\t\telement.classList.add( 'visible' );\n\t\t\telement.classList.remove( 'current-fragment' );\n\t\t} );\n\n\t}\n\n\t/**\n\t * Reverse of #disable(). Only called if fragments have\n\t * previously been disabled.\n\t */\n\tenable() {\n\n\t\tqueryAll( this.Reveal.getSlidesElement(), '.fragment' ).forEach( element => {\n\t\t\telement.classList.remove( 'visible' );\n\t\t\telement.classList.remove( 'current-fragment' );\n\t\t} );\n\n\t}\n\n\t/**\n\t * Returns an object describing the available fragment\n\t * directions.\n\t *\n\t * @return {{prev: boolean, next: boolean}}\n\t */\n\tavailableRoutes() {\n\n\t\tlet currentSlide = this.Reveal.getCurrentSlide();\n\t\tif( currentSlide && this.Reveal.getConfig().fragments ) {\n\t\t\tlet fragments = currentSlide.querySelectorAll( '.fragment:not(.disabled)' );\n\t\t\tlet hiddenFragments = currentSlide.querySelectorAll( '.fragment:not(.disabled):not(.visible)' );\n\n\t\t\treturn {\n\t\t\t\tprev: fragments.length - hiddenFragments.length > 0,\n\t\t\t\tnext: !!hiddenFragments.length\n\t\t\t};\n\t\t}\n\t\telse {\n\t\t\treturn { prev: false, next: false };\n\t\t}\n\n\t}\n\n\t/**\n\t * Return a sorted fragments list, ordered by an increasing\n\t * \"data-fragment-index\" attribute.\n\t *\n\t * Fragments will be revealed in the order that they are returned by\n\t * this function, so you can use the index attributes to control the\n\t * order of fragment appearance.\n\t *\n\t * To maintain a sensible default fragment order, fragments are presumed\n\t * to be passed in document order. This function adds a \"fragment-index\"\n\t * attribute to each node if such an attribute is not already present,\n\t * and sets that attribute to an integer value which is the position of\n\t * the fragment within the fragments list.\n\t *\n\t * @param {object[]|*} fragments\n\t * @param {boolean} grouped If true the returned array will contain\n\t * nested arrays for all fragments with the same index\n\t * @return {object[]} sorted Sorted array of fragments\n\t */\n\tsort( fragments, grouped = false ) {\n\n\t\tfragments = Array.from( fragments );\n\n\t\tlet ordered = [],\n\t\t\tunordered = [],\n\t\t\tsorted = [];\n\n\t\t// Group ordered and unordered elements\n\t\tfragments.forEach( fragment => {\n\t\t\tif( fragment.hasAttribute( 'data-fragment-index' ) ) {\n\t\t\t\tlet index = parseInt( fragment.getAttribute( 'data-fragment-index' ), 10 );\n\n\t\t\t\tif( !ordered[index] ) {\n\t\t\t\t\tordered[index] = [];\n\t\t\t\t}\n\n\t\t\t\tordered[index].push( fragment );\n\t\t\t}\n\t\t\telse {\n\t\t\t\tunordered.push( [ fragment ] );\n\t\t\t}\n\t\t} );\n\n\t\t// Append fragments without explicit indices in their\n\t\t// DOM order\n\t\tordered = ordered.concat( unordered );\n\n\t\t// Manually count the index up per group to ensure there\n\t\t// are no gaps\n\t\tlet index = 0;\n\n\t\t// Push all fragments in their sorted order to an array,\n\t\t// this flattens the groups\n\t\tordered.forEach( group => {\n\t\t\tgroup.forEach( fragment => {\n\t\t\t\tsorted.push( fragment );\n\t\t\t\tfragment.setAttribute( 'data-fragment-index', index );\n\t\t\t} );\n\n\t\t\tindex ++;\n\t\t} );\n\n\t\treturn grouped === true ? ordered : sorted;\n\n\t}\n\n\t/**\n\t * Sorts and formats all of fragments in the\n\t * presentation.\n\t */\n\tsortAll() {\n\n\t\tthis.Reveal.getHorizontalSlides().forEach( horizontalSlide => {\n\n\t\t\tlet verticalSlides = queryAll( horizontalSlide, 'section' );\n\t\t\tverticalSlides.forEach( ( verticalSlide, y ) => {\n\n\t\t\t\tthis.sort( verticalSlide.querySelectorAll( '.fragment' ) );\n\n\t\t\t}, this );\n\n\t\t\tif( verticalSlides.length === 0 ) this.sort( horizontalSlide.querySelectorAll( '.fragment' ) );\n\n\t\t} );\n\n\t}\n\n\t/**\n\t * Refreshes the fragments on the current slide so that they\n\t * have the appropriate classes (.visible + .current-fragment).\n\t *\n\t * @param {number} [index] The index of the current fragment\n\t * @param {array} [fragments] Array containing all fragments\n\t * in the current slide\n\t *\n\t * @return {{shown: array, hidden: array}}\n\t */\n\tupdate( index, fragments ) {\n\n\t\tlet changedFragments = {\n\t\t\tshown: [],\n\t\t\thidden: []\n\t\t};\n\n\t\tlet currentSlide = this.Reveal.getCurrentSlide();\n\t\tif( currentSlide && this.Reveal.getConfig().fragments ) {\n\n\t\t\tfragments = fragments || this.sort( currentSlide.querySelectorAll( '.fragment' ) );\n\n\t\t\tif( fragments.length ) {\n\n\t\t\t\tlet maxIndex = 0;\n\n\t\t\t\tif( typeof index !== 'number' ) {\n\t\t\t\t\tlet currentFragment = this.sort( currentSlide.querySelectorAll( '.fragment.visible' ) ).pop();\n\t\t\t\t\tif( currentFragment ) {\n\t\t\t\t\t\tindex = parseInt( currentFragment.getAttribute( 'data-fragment-index' ) || 0, 10 );\n\t\t\t\t\t}\n\t\t\t\t}\n\n\t\t\t\tArray.from( fragments ).forEach( ( el, i ) => {\n\n\t\t\t\t\tif( el.hasAttribute( 'data-fragment-index' ) ) {\n\t\t\t\t\t\ti = parseInt( el.getAttribute( 'data-fragment-index' ), 10 );\n\t\t\t\t\t}\n\n\t\t\t\t\tmaxIndex = Math.max( maxIndex, i );\n\n\t\t\t\t\t// Visible fragments\n\t\t\t\t\tif( i <= index ) {\n\t\t\t\t\t\tlet wasVisible = el.classList.contains( 'visible' )\n\t\t\t\t\t\tel.classList.add( 'visible' );\n\t\t\t\t\t\tel.classList.remove( 'current-fragment' );\n\n\t\t\t\t\t\tif( i === index ) {\n\t\t\t\t\t\t\t// Announce the fragments one by one to the Screen Reader\n\t\t\t\t\t\t\tthis.Reveal.announceStatus( this.Reveal.getStatusText( el ) );\n\n\t\t\t\t\t\t\tel.classList.add( 'current-fragment' );\n\t\t\t\t\t\t\tthis.Reveal.slideContent.startEmbeddedContent( el );\n\t\t\t\t\t\t}\n\n\t\t\t\t\t\tif( !wasVisible ) {\n\t\t\t\t\t\t\tchangedFragments.shown.push( el )\n\t\t\t\t\t\t\tthis.Reveal.dispatchEvent({\n\t\t\t\t\t\t\t\ttarget: el,\n\t\t\t\t\t\t\t\ttype: 'visible',\n\t\t\t\t\t\t\t\tbubbles: false\n\t\t\t\t\t\t\t});\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\t\t// Hidden fragments\n\t\t\t\t\telse {\n\t\t\t\t\t\tlet wasVisible = el.classList.contains( 'visible' )\n\t\t\t\t\t\tel.classList.remove( 'visible' );\n\t\t\t\t\t\tel.classList.remove( 'current-fragment' );\n\n\t\t\t\t\t\tif( wasVisible ) {\n\t\t\t\t\t\t\tthis.Reveal.slideContent.stopEmbeddedContent( el );\n\t\t\t\t\t\t\tchangedFragments.hidden.push( el );\n\t\t\t\t\t\t\tthis.Reveal.dispatchEvent({\n\t\t\t\t\t\t\t\ttarget: el,\n\t\t\t\t\t\t\t\ttype: 'hidden',\n\t\t\t\t\t\t\t\tbubbles: false\n\t\t\t\t\t\t\t});\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\n\t\t\t\t} );\n\n\t\t\t\t// Write the current fragment index to the slide
.\n\t\t\t\t// This can be used by end users to apply styles based on\n\t\t\t\t// the current fragment index.\n\t\t\t\tindex = typeof index === 'number' ? index : -1;\n\t\t\t\tindex = Math.max( Math.min( index, maxIndex ), -1 );\n\t\t\t\tcurrentSlide.setAttribute( 'data-fragment', index );\n\n\t\t\t}\n\n\t\t}\n\n\t\treturn changedFragments;\n\n\t}\n\n\t/**\n\t * Formats the fragments on the given slide so that they have\n\t * valid indices. Call this if fragments are changed in the DOM\n\t * after reveal.js has already initialized.\n\t *\n\t * @param {HTMLElement} slide\n\t * @return {Array} a list of the HTML fragments that were synced\n\t */\n\tsync( slide = this.Reveal.getCurrentSlide() ) {\n\n\t\treturn this.sort( slide.querySelectorAll( '.fragment' ) );\n\n\t}\n\n\t/**\n\t * Navigate to the specified slide fragment.\n\t *\n\t * @param {?number} index The index of the fragment that\n\t * should be shown, -1 means all are invisible\n\t * @param {number} offset Integer offset to apply to the\n\t * fragment index\n\t *\n\t * @return {boolean} true if a change was made in any\n\t * fragments visibility as part of this call\n\t */\n\tgoto( index, offset = 0 ) {\n\n\t\tlet currentSlide = this.Reveal.getCurrentSlide();\n\t\tif( currentSlide && this.Reveal.getConfig().fragments ) {\n\n\t\t\tlet fragments = this.sort( currentSlide.querySelectorAll( '.fragment:not(.disabled)' ) );\n\t\t\tif( fragments.length ) {\n\n\t\t\t\t// If no index is specified, find the current\n\t\t\t\tif( typeof index !== 'number' ) {\n\t\t\t\t\tlet lastVisibleFragment = this.sort( currentSlide.querySelectorAll( '.fragment:not(.disabled).visible' ) ).pop();\n\n\t\t\t\t\tif( lastVisibleFragment ) {\n\t\t\t\t\t\tindex = parseInt( lastVisibleFragment.getAttribute( 'data-fragment-index' ) || 0, 10 );\n\t\t\t\t\t}\n\t\t\t\t\telse {\n\t\t\t\t\t\tindex = -1;\n\t\t\t\t\t}\n\t\t\t\t}\n\n\t\t\t\t// Apply the offset if there is one\n\t\t\t\tindex += offset;\n\n\t\t\t\tlet changedFragments = this.update( index, fragments );\n\n\t\t\t\tif( changedFragments.hidden.length ) {\n\t\t\t\t\tthis.Reveal.dispatchEvent({\n\t\t\t\t\t\ttype: 'fragmenthidden',\n\t\t\t\t\t\tdata: {\n\t\t\t\t\t\t\tfragment: changedFragments.hidden[0],\n\t\t\t\t\t\t\tfragments: changedFragments.hidden\n\t\t\t\t\t\t}\n\t\t\t\t\t});\n\t\t\t\t}\n\n\t\t\t\tif( changedFragments.shown.length ) {\n\t\t\t\t\tthis.Reveal.dispatchEvent({\n\t\t\t\t\t\ttype: 'fragmentshown',\n\t\t\t\t\t\tdata: {\n\t\t\t\t\t\t\tfragment: changedFragments.shown[0],\n\t\t\t\t\t\t\tfragments: changedFragments.shown\n\t\t\t\t\t\t}\n\t\t\t\t\t});\n\t\t\t\t}\n\n\t\t\t\tthis.Reveal.controls.update();\n\t\t\t\tthis.Reveal.progress.update();\n\n\t\t\t\tif( this.Reveal.getConfig().fragmentInURL ) {\n\t\t\t\t\tthis.Reveal.location.writeURL();\n\t\t\t\t}\n\n\t\t\t\treturn !!( changedFragments.shown.length || changedFragments.hidden.length );\n\n\t\t\t}\n\n\t\t}\n\n\t\treturn false;\n\n\t}\n\n\t/**\n\t * Navigate to the next slide fragment.\n\t *\n\t * @return {boolean} true if there was a next fragment,\n\t * false otherwise\n\t */\n\tnext() {\n\n\t\treturn this.goto( null, 1 );\n\n\t}\n\n\t/**\n\t * Navigate to the previous slide fragment.\n\t *\n\t * @return {boolean} true if there was a previous fragment,\n\t * false otherwise\n\t */\n\tprev() {\n\n\t\treturn this.goto( null, -1 );\n\n\t}\n\n}","import { SLIDES_SELECTOR } from '../utils/constants.js'\nimport { extend, queryAll, transformElement } from '../utils/util.js'\n\n/**\n * Handles all logic related to the overview mode\n * (birds-eye view of all slides).\n */\nexport default class Overview {\n\n\tconstructor( Reveal ) {\n\n\t\tthis.Reveal = Reveal;\n\n\t\tthis.active = false;\n\n\t\tthis.onSlideClicked = this.onSlideClicked.bind( this );\n\n\t}\n\n\t/**\n\t * Displays the overview of slides (quick nav) by scaling\n\t * down and arranging all slide elements.\n\t */\n\tactivate() {\n\n\t\t// Only proceed if enabled in config\n\t\tif( this.Reveal.getConfig().overview && !this.isActive() ) {\n\n\t\t\tthis.active = true;\n\n\t\t\tthis.Reveal.getRevealElement().classList.add( 'overview' );\n\n\t\t\t// Don't auto-slide while in overview mode\n\t\t\tthis.Reveal.cancelAutoSlide();\n\n\t\t\t// Move the backgrounds element into the slide container to\n\t\t\t// that the same scaling is applied\n\t\t\tthis.Reveal.getSlidesElement().appendChild( this.Reveal.getBackgroundsElement() );\n\n\t\t\t// Clicking on an overview slide navigates to it\n\t\t\tqueryAll( this.Reveal.getRevealElement(), SLIDES_SELECTOR ).forEach( slide => {\n\t\t\t\tif( !slide.classList.contains( 'stack' ) ) {\n\t\t\t\t\tslide.addEventListener( 'click', this.onSlideClicked, true );\n\t\t\t\t}\n\t\t\t} );\n\n\t\t\t// Calculate slide sizes\n\t\t\tconst margin = 70;\n\t\t\tconst slideSize = this.Reveal.getComputedSlideSize();\n\t\t\tthis.overviewSlideWidth = slideSize.width + margin;\n\t\t\tthis.overviewSlideHeight = slideSize.height + margin;\n\n\t\t\t// Reverse in RTL mode\n\t\t\tif( this.Reveal.getConfig().rtl ) {\n\t\t\t\tthis.overviewSlideWidth = -this.overviewSlideWidth;\n\t\t\t}\n\n\t\t\tthis.Reveal.updateSlidesVisibility();\n\n\t\t\tthis.layout();\n\t\t\tthis.update();\n\n\t\t\tthis.Reveal.layout();\n\n\t\t\tconst indices = this.Reveal.getIndices();\n\n\t\t\t// Notify observers of the overview showing\n\t\t\tthis.Reveal.dispatchEvent({\n\t\t\t\ttype: 'overviewshown',\n\t\t\t\tdata: {\n\t\t\t\t\t'indexh': indices.h,\n\t\t\t\t\t'indexv': indices.v,\n\t\t\t\t\t'currentSlide': this.Reveal.getCurrentSlide()\n\t\t\t\t}\n\t\t\t});\n\n\t\t}\n\n\t}\n\n\t/**\n\t * Uses CSS transforms to position all slides in a grid for\n\t * display inside of the overview mode.\n\t */\n\tlayout() {\n\n\t\t// Layout slides\n\t\tthis.Reveal.getHorizontalSlides().forEach( ( hslide, h ) => {\n\t\t\thslide.setAttribute( 'data-index-h', h );\n\t\t\ttransformElement( hslide, 'translate3d(' + ( h * this.overviewSlideWidth ) + 'px, 0, 0)' );\n\n\t\t\tif( hslide.classList.contains( 'stack' ) ) {\n\n\t\t\t\tqueryAll( hslide, 'section' ).forEach( ( vslide, v ) => {\n\t\t\t\t\tvslide.setAttribute( 'data-index-h', h );\n\t\t\t\t\tvslide.setAttribute( 'data-index-v', v );\n\n\t\t\t\t\ttransformElement( vslide, 'translate3d(0, ' + ( v * this.overviewSlideHeight ) + 'px, 0)' );\n\t\t\t\t} );\n\n\t\t\t}\n\t\t} );\n\n\t\t// Layout slide backgrounds\n\t\tArray.from( this.Reveal.getBackgroundsElement().childNodes ).forEach( ( hbackground, h ) => {\n\t\t\ttransformElement( hbackground, 'translate3d(' + ( h * this.overviewSlideWidth ) + 'px, 0, 0)' );\n\n\t\t\tqueryAll( hbackground, '.slide-background' ).forEach( ( vbackground, v ) => {\n\t\t\t\ttransformElement( vbackground, 'translate3d(0, ' + ( v * this.overviewSlideHeight ) + 'px, 0)' );\n\t\t\t} );\n\t\t} );\n\n\t}\n\n\t/**\n\t * Moves the overview viewport to the current slides.\n\t * Called each time the current slide changes.\n\t */\n\tupdate() {\n\n\t\tconst vmin = Math.min( window.innerWidth, window.innerHeight );\n\t\tconst scale = Math.max( vmin / 5, 150 ) / vmin;\n\t\tconst indices = this.Reveal.getIndices();\n\n\t\tthis.Reveal.transformSlides( {\n\t\t\toverview: [\n\t\t\t\t'scale('+ scale +')',\n\t\t\t\t'translateX('+ ( -indices.h * this.overviewSlideWidth ) +'px)',\n\t\t\t\t'translateY('+ ( -indices.v * this.overviewSlideHeight ) +'px)'\n\t\t\t].join( ' ' )\n\t\t} );\n\n\t}\n\n\t/**\n\t * Exits the slide overview and enters the currently\n\t * active slide.\n\t */\n\tdeactivate() {\n\n\t\t// Only proceed if enabled in config\n\t\tif( this.Reveal.getConfig().overview ) {\n\n\t\t\tthis.active = false;\n\n\t\t\tthis.Reveal.getRevealElement().classList.remove( 'overview' );\n\n\t\t\t// Temporarily add a class so that transitions can do different things\n\t\t\t// depending on whether they are exiting/entering overview, or just\n\t\t\t// moving from slide to slide\n\t\t\tthis.Reveal.getRevealElement().classList.add( 'overview-deactivating' );\n\n\t\t\tsetTimeout( () => {\n\t\t\t\tthis.Reveal.getRevealElement().classList.remove( 'overview-deactivating' );\n\t\t\t}, 1 );\n\n\t\t\t// Move the background element back out\n\t\t\tthis.Reveal.getRevealElement().appendChild( this.Reveal.getBackgroundsElement() );\n\n\t\t\t// Clean up changes made to slides\n\t\t\tqueryAll( this.Reveal.getRevealElement(), SLIDES_SELECTOR ).forEach( slide => {\n\t\t\t\ttransformElement( slide, '' );\n\n\t\t\t\tslide.removeEventListener( 'click', this.onSlideClicked, true );\n\t\t\t} );\n\n\t\t\t// Clean up changes made to backgrounds\n\t\t\tqueryAll( this.Reveal.getBackgroundsElement(), '.slide-background' ).forEach( background => {\n\t\t\t\ttransformElement( background, '' );\n\t\t\t} );\n\n\t\t\tthis.Reveal.transformSlides( { overview: '' } );\n\n\t\t\tconst indices = this.Reveal.getIndices();\n\n\t\t\tthis.Reveal.slide( indices.h, indices.v );\n\t\t\tthis.Reveal.layout();\n\t\t\tthis.Reveal.cueAutoSlide();\n\n\t\t\t// Notify observers of the overview hiding\n\t\t\tthis.Reveal.dispatchEvent({\n\t\t\t\ttype: 'overviewhidden',\n\t\t\t\tdata: {\n\t\t\t\t\t'indexh': indices.h,\n\t\t\t\t\t'indexv': indices.v,\n\t\t\t\t\t'currentSlide': this.Reveal.getCurrentSlide()\n\t\t\t\t}\n\t\t\t});\n\n\t\t}\n\t}\n\n\t/**\n\t * Toggles the slide overview mode on and off.\n\t *\n\t * @param {Boolean} [override] Flag which overrides the\n\t * toggle logic and forcibly sets the desired state. True means\n\t * overview is open, false means it's closed.\n\t */\n\ttoggle( override ) {\n\n\t\tif( typeof override === 'boolean' ) {\n\t\t\toverride ? this.activate() : this.deactivate();\n\t\t}\n\t\telse {\n\t\t\tthis.isActive() ? this.deactivate() : this.activate();\n\t\t}\n\n\t}\n\n\t/**\n\t * Checks if the overview is currently active.\n\t *\n\t * @return {Boolean} true if the overview is active,\n\t * false otherwise\n\t */\n\tisActive() {\n\n\t\treturn this.active;\n\n\t}\n\n\t/**\n\t * Invoked when a slide is and we're in the overview.\n\t *\n\t * @param {object} event\n\t */\n\tonSlideClicked( event ) {\n\n\t\tif( this.isActive() ) {\n\t\t\tevent.preventDefault();\n\n\t\t\tlet element = event.target;\n\n\t\t\twhile( element && !element.nodeName.match( /section/gi ) ) {\n\t\t\t\telement = element.parentNode;\n\t\t\t}\n\n\t\t\tif( element && !element.classList.contains( 'disabled' ) ) {\n\n\t\t\t\tthis.deactivate();\n\n\t\t\t\tif( element.nodeName.match( /section/gi ) ) {\n\t\t\t\t\tlet h = parseInt( element.getAttribute( 'data-index-h' ), 10 ),\n\t\t\t\t\t\tv = parseInt( element.getAttribute( 'data-index-v' ), 10 );\n\n\t\t\t\t\tthis.Reveal.slide( h, v );\n\t\t\t\t}\n\n\t\t\t}\n\t\t}\n\n\t}\n\n}","import { enterFullscreen } from '../utils/util.js'\n\n/**\n * Handles all reveal.js keyboard interactions.\n */\nexport default class Keyboard {\n\n\tconstructor( Reveal ) {\n\n\t\tthis.Reveal = Reveal;\n\n\t\t// A key:value map of keyboard keys and descriptions of\n\t\t// the actions they trigger\n\t\tthis.shortcuts = {};\n\n\t\t// Holds custom key code mappings\n\t\tthis.bindings = {};\n\n\t\tthis.onDocumentKeyDown = this.onDocumentKeyDown.bind( this );\n\t\tthis.onDocumentKeyPress = this.onDocumentKeyPress.bind( this );\n\n\t}\n\n\t/**\n\t * Called when the reveal.js config is updated.\n\t */\n\tconfigure( config, oldConfig ) {\n\n\t\tif( config.navigationMode === 'linear' ) {\n\t\t\tthis.shortcuts['→ , ↓ , SPACE , N , L , J'] = 'Next slide';\n\t\t\tthis.shortcuts['← , ↑ , P , H , K'] = 'Previous slide';\n\t\t}\n\t\telse {\n\t\t\tthis.shortcuts['N , SPACE'] = 'Next slide';\n\t\t\tthis.shortcuts['P , Shift SPACE'] = 'Previous slide';\n\t\t\tthis.shortcuts['← , H'] = 'Navigate left';\n\t\t\tthis.shortcuts['→ , L'] = 'Navigate right';\n\t\t\tthis.shortcuts['↑ , K'] = 'Navigate up';\n\t\t\tthis.shortcuts['↓ , J'] = 'Navigate down';\n\t\t}\n\n\t\tthis.shortcuts['Alt + ←/↑/→/↓'] = 'Navigate without fragments';\n\t\tthis.shortcuts['Shift + ←/↑/→/↓'] = 'Jump to first/last slide';\n\t\tthis.shortcuts['B , .'] = 'Pause';\n\t\tthis.shortcuts['F'] = 'Fullscreen';\n\t\tthis.shortcuts['ESC, O'] = 'Slide overview';\n\n\t}\n\n\t/**\n\t * Starts listening for keyboard events.\n\t */\n\tbind() {\n\n\t\tdocument.addEventListener( 'keydown', this.onDocumentKeyDown, false );\n\t\tdocument.addEventListener( 'keypress', this.onDocumentKeyPress, false );\n\n\t}\n\n\t/**\n\t * Stops listening for keyboard events.\n\t */\n\tunbind() {\n\n\t\tdocument.removeEventListener( 'keydown', this.onDocumentKeyDown, false );\n\t\tdocument.removeEventListener( 'keypress', this.onDocumentKeyPress, false );\n\n\t}\n\n\t/**\n\t * Add a custom key binding with optional description to\n\t * be added to the help screen.\n\t */\n\taddKeyBinding( binding, callback ) {\n\n\t\tif( typeof binding === 'object' && binding.keyCode ) {\n\t\t\tthis.bindings[binding.keyCode] = {\n\t\t\t\tcallback: callback,\n\t\t\t\tkey: binding.key,\n\t\t\t\tdescription: binding.description\n\t\t\t};\n\t\t}\n\t\telse {\n\t\t\tthis.bindings[binding] = {\n\t\t\t\tcallback: callback,\n\t\t\t\tkey: null,\n\t\t\t\tdescription: null\n\t\t\t};\n\t\t}\n\n\t}\n\n\t/**\n\t * Removes the specified custom key binding.\n\t */\n\tremoveKeyBinding( keyCode ) {\n\n\t\tdelete this.bindings[keyCode];\n\n\t}\n\n\t/**\n\t * Programmatically triggers a keyboard event\n\t *\n\t * @param {int} keyCode\n\t */\n\ttriggerKey( keyCode ) {\n\n\t\tthis.onDocumentKeyDown( { keyCode } );\n\n\t}\n\n\t/**\n\t * Registers a new shortcut to include in the help overlay\n\t *\n\t * @param {String} key\n\t * @param {String} value\n\t */\n\tregisterKeyboardShortcut( key, value ) {\n\n\t\tthis.shortcuts[key] = value;\n\n\t}\n\n\tgetShortcuts() {\n\n\t\treturn this.shortcuts;\n\n\t}\n\n\tgetBindings() {\n\n\t\treturn this.bindings;\n\n\t}\n\n\t/**\n\t * Handler for the document level 'keypress' event.\n\t *\n\t * @param {object} event\n\t */\n\tonDocumentKeyPress( event ) {\n\n\t\t// Check if the pressed key is question mark\n\t\tif( event.shiftKey && event.charCode === 63 ) {\n\t\t\tthis.Reveal.toggleHelp();\n\t\t}\n\n\t}\n\n\t/**\n\t * Handler for the document level 'keydown' event.\n\t *\n\t * @param {object} event\n\t */\n\tonDocumentKeyDown( event ) {\n\n\t\tlet config = this.Reveal.getConfig();\n\n\t\t// If there's a condition specified and it returns false,\n\t\t// ignore this event\n\t\tif( typeof config.keyboardCondition === 'function' && config.keyboardCondition(event) === false ) {\n\t\t\treturn true;\n\t\t}\n\n\t\t// If keyboardCondition is set, only capture keyboard events\n\t\t// for embedded decks when they are focused\n\t\tif( config.keyboardCondition === 'focused' && !this.Reveal.isFocused() ) {\n\t\t\treturn true;\n\t\t}\n\n\t\t// Shorthand\n\t\tlet keyCode = event.keyCode;\n\n\t\t// Remember if auto-sliding was paused so we can toggle it\n\t\tlet autoSlideWasPaused = !this.Reveal.isAutoSliding();\n\n\t\tthis.Reveal.onUserInput( event );\n\n\t\t// Is there a focused element that could be using the keyboard?\n\t\tlet activeElementIsCE = document.activeElement && document.activeElement.isContentEditable === true;\n\t\tlet activeElementIsInput = document.activeElement && document.activeElement.tagName && /input|textarea/i.test( document.activeElement.tagName );\n\t\tlet activeElementIsNotes = document.activeElement && document.activeElement.className && /speaker-notes/i.test( document.activeElement.className);\n\n\t\t// Whitelist certain modifiers for slide navigation shortcuts\n\t\tlet isNavigationKey = [32, 37, 38, 39, 40, 78, 80].indexOf( event.keyCode ) !== -1;\n\n\t\t// Prevent all other events when a modifier is pressed\n\t\tlet unusedModifier = \t!( isNavigationKey && event.shiftKey || event.altKey ) &&\n\t\t\t\t\t\t\t\t( event.shiftKey || event.altKey || event.ctrlKey || event.metaKey );\n\n\t\t// Disregard the event if there's a focused element or a\n\t\t// keyboard modifier key is present\n\t\tif( activeElementIsCE || activeElementIsInput || activeElementIsNotes || unusedModifier ) return;\n\n\t\t// While paused only allow resume keyboard events; 'b', 'v', '.'\n\t\tlet resumeKeyCodes = [66,86,190,191];\n\t\tlet key;\n\n\t\t// Custom key bindings for togglePause should be able to resume\n\t\tif( typeof config.keyboard === 'object' ) {\n\t\t\tfor( key in config.keyboard ) {\n\t\t\t\tif( config.keyboard[key] === 'togglePause' ) {\n\t\t\t\t\tresumeKeyCodes.push( parseInt( key, 10 ) );\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\n\t\tif( this.Reveal.isPaused() && resumeKeyCodes.indexOf( keyCode ) === -1 ) {\n\t\t\treturn false;\n\t\t}\n\n\t\t// Use linear navigation if we're configured to OR if\n\t\t// the presentation is one-dimensional\n\t\tlet useLinearMode = config.navigationMode === 'linear' || !this.Reveal.hasHorizontalSlides() || !this.Reveal.hasVerticalSlides();\n\n\t\tlet triggered = false;\n\n\t\t// 1. User defined key bindings\n\t\tif( typeof config.keyboard === 'object' ) {\n\n\t\t\tfor( key in config.keyboard ) {\n\n\t\t\t\t// Check if this binding matches the pressed key\n\t\t\t\tif( parseInt( key, 10 ) === keyCode ) {\n\n\t\t\t\t\tlet value = config.keyboard[ key ];\n\n\t\t\t\t\t// Callback function\n\t\t\t\t\tif( typeof value === 'function' ) {\n\t\t\t\t\t\tvalue.apply( null, [ event ] );\n\t\t\t\t\t}\n\t\t\t\t\t// String shortcuts to reveal.js API\n\t\t\t\t\telse if( typeof value === 'string' && typeof this.Reveal[ value ] === 'function' ) {\n\t\t\t\t\t\tthis.Reveal[ value ].call();\n\t\t\t\t\t}\n\n\t\t\t\t\ttriggered = true;\n\n\t\t\t\t}\n\n\t\t\t}\n\n\t\t}\n\n\t\t// 2. Registered custom key bindings\n\t\tif( triggered === false ) {\n\n\t\t\tfor( key in this.bindings ) {\n\n\t\t\t\t// Check if this binding matches the pressed key\n\t\t\t\tif( parseInt( key, 10 ) === keyCode ) {\n\n\t\t\t\t\tlet action = this.bindings[ key ].callback;\n\n\t\t\t\t\t// Callback function\n\t\t\t\t\tif( typeof action === 'function' ) {\n\t\t\t\t\t\taction.apply( null, [ event ] );\n\t\t\t\t\t}\n\t\t\t\t\t// String shortcuts to reveal.js API\n\t\t\t\t\telse if( typeof action === 'string' && typeof this.Reveal[ action ] === 'function' ) {\n\t\t\t\t\t\tthis.Reveal[ action ].call();\n\t\t\t\t\t}\n\n\t\t\t\t\ttriggered = true;\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\n\t\t// 3. System defined key bindings\n\t\tif( triggered === false ) {\n\n\t\t\t// Assume true and try to prove false\n\t\t\ttriggered = true;\n\n\t\t\t// P, PAGE UP\n\t\t\tif( keyCode === 80 || keyCode === 33 ) {\n\t\t\t\tthis.Reveal.prev({skipFragments: event.altKey});\n\t\t\t}\n\t\t\t// N, PAGE DOWN\n\t\t\telse if( keyCode === 78 || keyCode === 34 ) {\n\t\t\t\tthis.Reveal.next({skipFragments: event.altKey});\n\t\t\t}\n\t\t\t// H, LEFT\n\t\t\telse if( keyCode === 72 || keyCode === 37 ) {\n\t\t\t\tif( event.shiftKey ) {\n\t\t\t\t\tthis.Reveal.slide( 0 );\n\t\t\t\t}\n\t\t\t\telse if( !this.Reveal.overview.isActive() && useLinearMode ) {\n\t\t\t\t\tthis.Reveal.prev({skipFragments: event.altKey});\n\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\tthis.Reveal.left({skipFragments: event.altKey});\n\t\t\t\t}\n\t\t\t}\n\t\t\t// L, RIGHT\n\t\t\telse if( keyCode === 76 || keyCode === 39 ) {\n\t\t\t\tif( event.shiftKey ) {\n\t\t\t\t\tthis.Reveal.slide( this.Reveal.getHorizontalSlides().length - 1 );\n\t\t\t\t}\n\t\t\t\telse if( !this.Reveal.overview.isActive() && useLinearMode ) {\n\t\t\t\t\tthis.Reveal.next({skipFragments: event.altKey});\n\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\tthis.Reveal.right({skipFragments: event.altKey});\n\t\t\t\t}\n\t\t\t}\n\t\t\t// K, UP\n\t\t\telse if( keyCode === 75 || keyCode === 38 ) {\n\t\t\t\tif( event.shiftKey ) {\n\t\t\t\t\tthis.Reveal.slide( undefined, 0 );\n\t\t\t\t}\n\t\t\t\telse if( !this.Reveal.overview.isActive() && useLinearMode ) {\n\t\t\t\t\tthis.Reveal.prev({skipFragments: event.altKey});\n\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\tthis.Reveal.up({skipFragments: event.altKey});\n\t\t\t\t}\n\t\t\t}\n\t\t\t// J, DOWN\n\t\t\telse if( keyCode === 74 || keyCode === 40 ) {\n\t\t\t\tif( event.shiftKey ) {\n\t\t\t\t\tthis.Reveal.slide( undefined, Number.MAX_VALUE );\n\t\t\t\t}\n\t\t\t\telse if( !this.Reveal.overview.isActive() && useLinearMode ) {\n\t\t\t\t\tthis.Reveal.next({skipFragments: event.altKey});\n\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\tthis.Reveal.down({skipFragments: event.altKey});\n\t\t\t\t}\n\t\t\t}\n\t\t\t// HOME\n\t\t\telse if( keyCode === 36 ) {\n\t\t\t\tthis.Reveal.slide( 0 );\n\t\t\t}\n\t\t\t// END\n\t\t\telse if( keyCode === 35 ) {\n\t\t\t\tthis.Reveal.slide( this.Reveal.getHorizontalSlides().length - 1 );\n\t\t\t}\n\t\t\t// SPACE\n\t\t\telse if( keyCode === 32 ) {\n\t\t\t\tif( this.Reveal.overview.isActive() ) {\n\t\t\t\t\tthis.Reveal.overview.deactivate();\n\t\t\t\t}\n\t\t\t\tif( event.shiftKey ) {\n\t\t\t\t\tthis.Reveal.prev({skipFragments: event.altKey});\n\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\tthis.Reveal.next({skipFragments: event.altKey});\n\t\t\t\t}\n\t\t\t}\n\t\t\t// TWO-SPOT, SEMICOLON, B, V, PERIOD, LOGITECH PRESENTER TOOLS \"BLACK SCREEN\" BUTTON\n\t\t\telse if( keyCode === 58 || keyCode === 59 || keyCode === 66 || keyCode === 86 || keyCode === 190 || keyCode === 191 ) {\n\t\t\t\tthis.Reveal.togglePause();\n\t\t\t}\n\t\t\t// F\n\t\t\telse if( keyCode === 70 ) {\n\t\t\t\tenterFullscreen( config.embedded ? this.Reveal.getViewportElement() : document.documentElement );\n\t\t\t}\n\t\t\t// A\n\t\t\telse if( keyCode === 65 ) {\n\t\t\t\tif ( config.autoSlideStoppable ) {\n\t\t\t\t\tthis.Reveal.toggleAutoSlide( autoSlideWasPaused );\n\t\t\t\t}\n\t\t\t}\n\t\t\telse {\n\t\t\t\ttriggered = false;\n\t\t\t}\n\n\t\t}\n\n\t\t// If the input resulted in a triggered action we should prevent\n\t\t// the browsers default behavior\n\t\tif( triggered ) {\n\t\t\tevent.preventDefault && event.preventDefault();\n\t\t}\n\t\t// ESC or O key\n\t\telse if( keyCode === 27 || keyCode === 79 ) {\n\t\t\tif( this.Reveal.closeOverlay() === false ) {\n\t\t\t\tthis.Reveal.overview.toggle();\n\t\t\t}\n\n\t\t\tevent.preventDefault && event.preventDefault();\n\t\t}\n\n\t\t// If auto-sliding is enabled we need to cue up\n\t\t// another timeout\n\t\tthis.Reveal.cueAutoSlide();\n\n\t}\n\n}","/**\n * Reads and writes the URL based on reveal.js' current state.\n */\nexport default class Location {\n\n\t// The minimum number of milliseconds that must pass between\n\t// calls to history.replaceState\n\tMAX_REPLACE_STATE_FREQUENCY = 1000\n\n\tconstructor( Reveal ) {\n\n\t\tthis.Reveal = Reveal;\n\n\t\t// Delays updates to the URL due to a Chrome thumbnailer bug\n\t\tthis.writeURLTimeout = 0;\n\n\t\tthis.replaceStateTimestamp = 0;\n\n\t\tthis.onWindowHashChange = this.onWindowHashChange.bind( this );\n\n\t}\n\n\tbind() {\n\n\t\twindow.addEventListener( 'hashchange', this.onWindowHashChange, false );\n\n\t}\n\n\tunbind() {\n\n\t\twindow.removeEventListener( 'hashchange', this.onWindowHashChange, false );\n\n\t}\n\n\t/**\n\t * Returns the slide indices for the given hash link.\n\t *\n\t * @param {string} [hash] the hash string that we want to\n\t * find the indices for\n\t *\n\t * @returns slide indices or null\n\t */\n\tgetIndicesFromHash( hash=window.location.hash ) {\n\n\t\t// Attempt to parse the hash as either an index or name\n\t\tlet name = hash.replace( /^#\\/?/, '' );\n\t\tlet bits = name.split( '/' );\n\n\t\t// If the first bit is not fully numeric and there is a name we\n\t\t// can assume that this is a named link\n\t\tif( !/^[0-9]*$/.test( bits[0] ) && name.length ) {\n\t\t\tlet element;\n\n\t\t\tlet f;\n\n\t\t\t// Parse named links with fragments (#/named-link/2)\n\t\t\tif( /\\/[-\\d]+$/g.test( name ) ) {\n\t\t\t\tf = parseInt( name.split( '/' ).pop(), 10 );\n\t\t\t\tf = isNaN(f) ? undefined : f;\n\t\t\t\tname = name.split( '/' ).shift();\n\t\t\t}\n\n\t\t\t// Ensure the named link is a valid HTML ID attribute\n\t\t\ttry {\n\t\t\t\telement = document.getElementById( decodeURIComponent( name ) );\n\t\t\t}\n\t\t\tcatch ( error ) { }\n\n\t\t\tif( element ) {\n\t\t\t\treturn { ...this.Reveal.getIndices( element ), f };\n\t\t\t}\n\t\t}\n\t\telse {\n\t\t\tconst config = this.Reveal.getConfig();\n\t\t\tlet hashIndexBase = config.hashOneBasedIndex ? 1 : 0;\n\n\t\t\t// Read the index components of the hash\n\t\t\tlet h = ( parseInt( bits[0], 10 ) - hashIndexBase ) || 0,\n\t\t\t\tv = ( parseInt( bits[1], 10 ) - hashIndexBase ) || 0,\n\t\t\t\tf;\n\n\t\t\tif( config.fragmentInURL ) {\n\t\t\t\tf = parseInt( bits[2], 10 );\n\t\t\t\tif( isNaN( f ) ) {\n\t\t\t\t\tf = undefined;\n\t\t\t\t}\n\t\t\t}\n\n\t\t\treturn { h, v, f };\n\t\t}\n\n\t\t// The hash couldn't be parsed or no matching named link was found\n\t\treturn null\n\n\t}\n\n\t/**\n\t * Reads the current URL (hash) and navigates accordingly.\n\t */\n\treadURL() {\n\n\t\tconst currentIndices = this.Reveal.getIndices();\n\t\tconst newIndices = this.getIndicesFromHash();\n\n\t\tif( newIndices ) {\n\t\t\tif( ( newIndices.h !== currentIndices.h || newIndices.v !== currentIndices.v || newIndices.f !== undefined ) ) {\n\t\t\t\t\tthis.Reveal.slide( newIndices.h, newIndices.v, newIndices.f );\n\t\t\t}\n\t\t}\n\t\t// If no new indices are available, we're trying to navigate to\n\t\t// a slide hash that does not exist\n\t\telse {\n\t\t\tthis.Reveal.slide( currentIndices.h || 0, currentIndices.v || 0 );\n\t\t}\n\n\t}\n\n\t/**\n\t * Updates the page URL (hash) to reflect the current\n\t * state.\n\t *\n\t * @param {number} delay The time in ms to wait before\n\t * writing the hash\n\t */\n\twriteURL( delay ) {\n\n\t\tlet config = this.Reveal.getConfig();\n\t\tlet currentSlide = this.Reveal.getCurrentSlide();\n\n\t\t// Make sure there's never more than one timeout running\n\t\tclearTimeout( this.writeURLTimeout );\n\n\t\t// If a delay is specified, timeout this call\n\t\tif( typeof delay === 'number' ) {\n\t\t\tthis.writeURLTimeout = setTimeout( this.writeURL, delay );\n\t\t}\n\t\telse if( currentSlide ) {\n\n\t\t\tlet hash = this.getHash();\n\n\t\t\t// If we're configured to push to history OR the history\n\t\t\t// API is not avaialble.\n\t\t\tif( config.history ) {\n\t\t\t\twindow.location.hash = hash;\n\t\t\t}\n\t\t\t// If we're configured to reflect the current slide in the\n\t\t\t// URL without pushing to history.\n\t\t\telse if( config.hash ) {\n\t\t\t\t// If the hash is empty, don't add it to the URL\n\t\t\t\tif( hash === '/' ) {\n\t\t\t\t\tthis.debouncedReplaceState( window.location.pathname + window.location.search );\n\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\tthis.debouncedReplaceState( '#' + hash );\n\t\t\t\t}\n\t\t\t}\n\t\t\t// UPDATE: The below nuking of all hash changes breaks\n\t\t\t// anchors on pages where reveal.js is running. Removed\n\t\t\t// in 4.0. Why was it here in the first place? ¯\\_(ツ)_/¯\n\t\t\t//\n\t\t\t// If history and hash are both disabled, a hash may still\n\t\t\t// be added to the URL by clicking on a href with a hash\n\t\t\t// target. Counter this by always removing the hash.\n\t\t\t// else {\n\t\t\t// \twindow.history.replaceState( null, null, window.location.pathname + window.location.search );\n\t\t\t// }\n\n\t\t}\n\n\t}\n\n\treplaceState( url ) {\n\n\t\twindow.history.replaceState( null, null, url );\n\t\tthis.replaceStateTimestamp = Date.now();\n\n\t}\n\n\tdebouncedReplaceState( url ) {\n\n\t\tclearTimeout( this.replaceStateTimeout );\n\n\t\tif( Date.now() - this.replaceStateTimestamp > this.MAX_REPLACE_STATE_FREQUENCY ) {\n\t\t\tthis.replaceState( url );\n\t\t}\n\t\telse {\n\t\t\tthis.replaceStateTimeout = setTimeout( () => this.replaceState( url ), this.MAX_REPLACE_STATE_FREQUENCY );\n\t\t}\n\n\t}\n\n\t/**\n\t * Return a hash URL that will resolve to the given slide location.\n\t *\n\t * @param {HTMLElement} [slide=currentSlide] The slide to link to\n\t */\n\tgetHash( slide ) {\n\n\t\tlet url = '/';\n\n\t\t// Attempt to create a named link based on the slide's ID\n\t\tlet s = slide || this.Reveal.getCurrentSlide();\n\t\tlet id = s ? s.getAttribute( 'id' ) : null;\n\t\tif( id ) {\n\t\t\tid = encodeURIComponent( id );\n\t\t}\n\n\t\tlet index = this.Reveal.getIndices( slide );\n\t\tif( !this.Reveal.getConfig().fragmentInURL ) {\n\t\t\tindex.f = undefined;\n\t\t}\n\n\t\t// If the current slide has an ID, use that as a named link,\n\t\t// but we don't support named links with a fragment index\n\t\tif( typeof id === 'string' && id.length ) {\n\t\t\turl = '/' + id;\n\n\t\t\t// If there is also a fragment, append that at the end\n\t\t\t// of the named link, like: #/named-link/2\n\t\t\tif( index.f >= 0 ) url += '/' + index.f;\n\t\t}\n\t\t// Otherwise use the /h/v index\n\t\telse {\n\t\t\tlet hashIndexBase = this.Reveal.getConfig().hashOneBasedIndex ? 1 : 0;\n\t\t\tif( index.h > 0 || index.v > 0 || index.f >= 0 ) url += index.h + hashIndexBase;\n\t\t\tif( index.v > 0 || index.f >= 0 ) url += '/' + (index.v + hashIndexBase );\n\t\t\tif( index.f >= 0 ) url += '/' + index.f;\n\t\t}\n\n\t\treturn url;\n\n\t}\n\n\t/**\n\t * Handler for the window level 'hashchange' event.\n\t *\n\t * @param {object} [event]\n\t */\n\tonWindowHashChange( event ) {\n\n\t\tthis.readURL();\n\n\t}\n\n}","import { queryAll } from '../utils/util.js'\nimport { isAndroid } from '../utils/device.js'\n\n/**\n * Manages our presentation controls. This includes both\n * the built-in control arrows as well as event monitoring\n * of any elements within the presentation with either of the\n * following helper classes:\n * - .navigate-up\n * - .navigate-right\n * - .navigate-down\n * - .navigate-left\n * - .navigate-next\n * - .navigate-prev\n */\nexport default class Controls {\n\n\tconstructor( Reveal ) {\n\n\t\tthis.Reveal = Reveal;\n\n\t\tthis.onNavigateLeftClicked = this.onNavigateLeftClicked.bind( this );\n\t\tthis.onNavigateRightClicked = this.onNavigateRightClicked.bind( this );\n\t\tthis.onNavigateUpClicked = this.onNavigateUpClicked.bind( this );\n\t\tthis.onNavigateDownClicked = this.onNavigateDownClicked.bind( this );\n\t\tthis.onNavigatePrevClicked = this.onNavigatePrevClicked.bind( this );\n\t\tthis.onNavigateNextClicked = this.onNavigateNextClicked.bind( this );\n\n\t}\n\n\trender() {\n\n\t\tconst rtl = this.Reveal.getConfig().rtl;\n\t\tconst revealElement = this.Reveal.getRevealElement();\n\n\t\tthis.element = document.createElement( 'aside' );\n\t\tthis.element.className = 'controls';\n\t\tthis.element.innerHTML =\n\t\t\t`\n\t\t\t\n\t\t\t\n\t\t\t`;\n\n\t\tthis.Reveal.getRevealElement().appendChild( this.element );\n\n\t\t// There can be multiple instances of controls throughout the page\n\t\tthis.controlsLeft = queryAll( revealElement, '.navigate-left' );\n\t\tthis.controlsRight = queryAll( revealElement, '.navigate-right' );\n\t\tthis.controlsUp = queryAll( revealElement, '.navigate-up' );\n\t\tthis.controlsDown = queryAll( revealElement, '.navigate-down' );\n\t\tthis.controlsPrev = queryAll( revealElement, '.navigate-prev' );\n\t\tthis.controlsNext = queryAll( revealElement, '.navigate-next' );\n\n\t\t// The left, right and down arrows in the standard reveal.js controls\n\t\tthis.controlsRightArrow = this.element.querySelector( '.navigate-right' );\n\t\tthis.controlsLeftArrow = this.element.querySelector( '.navigate-left' );\n\t\tthis.controlsDownArrow = this.element.querySelector( '.navigate-down' );\n\n\t}\n\n\t/**\n\t * Called when the reveal.js config is updated.\n\t */\n\tconfigure( config, oldConfig ) {\n\n\t\tthis.element.style.display = config.controls ? 'block' : 'none';\n\n\t\tthis.element.setAttribute( 'data-controls-layout', config.controlsLayout );\n\t\tthis.element.setAttribute( 'data-controls-back-arrows', config.controlsBackArrows );\n\n\t}\n\n\tbind() {\n\n\t\t// Listen to both touch and click events, in case the device\n\t\t// supports both\n\t\tlet pointerEvents = [ 'touchstart', 'click' ];\n\n\t\t// Only support touch for Android, fixes double navigations in\n\t\t// stock browser\n\t\tif( isAndroid ) {\n\t\t\tpointerEvents = [ 'touchstart' ];\n\t\t}\n\n\t\tpointerEvents.forEach( eventName => {\n\t\t\tthis.controlsLeft.forEach( el => el.addEventListener( eventName, this.onNavigateLeftClicked, false ) );\n\t\t\tthis.controlsRight.forEach( el => el.addEventListener( eventName, this.onNavigateRightClicked, false ) );\n\t\t\tthis.controlsUp.forEach( el => el.addEventListener( eventName, this.onNavigateUpClicked, false ) );\n\t\t\tthis.controlsDown.forEach( el => el.addEventListener( eventName, this.onNavigateDownClicked, false ) );\n\t\t\tthis.controlsPrev.forEach( el => el.addEventListener( eventName, this.onNavigatePrevClicked, false ) );\n\t\t\tthis.controlsNext.forEach( el => el.addEventListener( eventName, this.onNavigateNextClicked, false ) );\n\t\t} );\n\n\t}\n\n\tunbind() {\n\n\t\t[ 'touchstart', 'click' ].forEach( eventName => {\n\t\t\tthis.controlsLeft.forEach( el => el.removeEventListener( eventName, this.onNavigateLeftClicked, false ) );\n\t\t\tthis.controlsRight.forEach( el => el.removeEventListener( eventName, this.onNavigateRightClicked, false ) );\n\t\t\tthis.controlsUp.forEach( el => el.removeEventListener( eventName, this.onNavigateUpClicked, false ) );\n\t\t\tthis.controlsDown.forEach( el => el.removeEventListener( eventName, this.onNavigateDownClicked, false ) );\n\t\t\tthis.controlsPrev.forEach( el => el.removeEventListener( eventName, this.onNavigatePrevClicked, false ) );\n\t\t\tthis.controlsNext.forEach( el => el.removeEventListener( eventName, this.onNavigateNextClicked, false ) );\n\t\t} );\n\n\t}\n\n\t/**\n\t * Updates the state of all control/navigation arrows.\n\t */\n\tupdate() {\n\n\t\tlet routes = this.Reveal.availableRoutes();\n\n\t\t// Remove the 'enabled' class from all directions\n\t\t[...this.controlsLeft, ...this.controlsRight, ...this.controlsUp, ...this.controlsDown, ...this.controlsPrev, ...this.controlsNext].forEach( node => {\n\t\t\tnode.classList.remove( 'enabled', 'fragmented' );\n\n\t\t\t// Set 'disabled' attribute on all directions\n\t\t\tnode.setAttribute( 'disabled', 'disabled' );\n\t\t} );\n\n\t\t// Add the 'enabled' class to the available routes; remove 'disabled' attribute to enable buttons\n\t\tif( routes.left ) this.controlsLeft.forEach( el => { el.classList.add( 'enabled' ); el.removeAttribute( 'disabled' ); } );\n\t\tif( routes.right ) this.controlsRight.forEach( el => { el.classList.add( 'enabled' ); el.removeAttribute( 'disabled' ); } );\n\t\tif( routes.up ) this.controlsUp.forEach( el => { el.classList.add( 'enabled' ); el.removeAttribute( 'disabled' ); } );\n\t\tif( routes.down ) this.controlsDown.forEach( el => { el.classList.add( 'enabled' ); el.removeAttribute( 'disabled' ); } );\n\n\t\t// Prev/next buttons\n\t\tif( routes.left || routes.up ) this.controlsPrev.forEach( el => { el.classList.add( 'enabled' ); el.removeAttribute( 'disabled' ); } );\n\t\tif( routes.right || routes.down ) this.controlsNext.forEach( el => { el.classList.add( 'enabled' ); el.removeAttribute( 'disabled' ); } );\n\n\t\t// Highlight fragment directions\n\t\tlet currentSlide = this.Reveal.getCurrentSlide();\n\t\tif( currentSlide ) {\n\n\t\t\tlet fragmentsRoutes = this.Reveal.fragments.availableRoutes();\n\n\t\t\t// Always apply fragment decorator to prev/next buttons\n\t\t\tif( fragmentsRoutes.prev ) this.controlsPrev.forEach( el => { el.classList.add( 'fragmented', 'enabled' ); el.removeAttribute( 'disabled' ); } );\n\t\t\tif( fragmentsRoutes.next ) this.controlsNext.forEach( el => { el.classList.add( 'fragmented', 'enabled' ); el.removeAttribute( 'disabled' ); } );\n\n\t\t\t// Apply fragment decorators to directional buttons based on\n\t\t\t// what slide axis they are in\n\t\t\tif( this.Reveal.isVerticalSlide( currentSlide ) ) {\n\t\t\t\tif( fragmentsRoutes.prev ) this.controlsUp.forEach( el => { el.classList.add( 'fragmented', 'enabled' ); el.removeAttribute( 'disabled' ); } );\n\t\t\t\tif( fragmentsRoutes.next ) this.controlsDown.forEach( el => { el.classList.add( 'fragmented', 'enabled' ); el.removeAttribute( 'disabled' ); } );\n\t\t\t}\n\t\t\telse {\n\t\t\t\tif( fragmentsRoutes.prev ) this.controlsLeft.forEach( el => { el.classList.add( 'fragmented', 'enabled' ); el.removeAttribute( 'disabled' ); } );\n\t\t\t\tif( fragmentsRoutes.next ) this.controlsRight.forEach( el => { el.classList.add( 'fragmented', 'enabled' ); el.removeAttribute( 'disabled' ); } );\n\t\t\t}\n\n\t\t}\n\n\t\tif( this.Reveal.getConfig().controlsTutorial ) {\n\n\t\t\tlet indices = this.Reveal.getIndices();\n\n\t\t\t// Highlight control arrows with an animation to ensure\n\t\t\t// that the viewer knows how to navigate\n\t\t\tif( !this.Reveal.hasNavigatedVertically() && routes.down ) {\n\t\t\t\tthis.controlsDownArrow.classList.add( 'highlight' );\n\t\t\t}\n\t\t\telse {\n\t\t\t\tthis.controlsDownArrow.classList.remove( 'highlight' );\n\n\t\t\t\tif( this.Reveal.getConfig().rtl ) {\n\n\t\t\t\t\tif( !this.Reveal.hasNavigatedHorizontally() && routes.left && indices.v === 0 ) {\n\t\t\t\t\t\tthis.controlsLeftArrow.classList.add( 'highlight' );\n\t\t\t\t\t}\n\t\t\t\t\telse {\n\t\t\t\t\t\tthis.controlsLeftArrow.classList.remove( 'highlight' );\n\t\t\t\t\t}\n\n\t\t\t\t} else {\n\n\t\t\t\t\tif( !this.Reveal.hasNavigatedHorizontally() && routes.right && indices.v === 0 ) {\n\t\t\t\t\t\tthis.controlsRightArrow.classList.add( 'highlight' );\n\t\t\t\t\t}\n\t\t\t\t\telse {\n\t\t\t\t\t\tthis.controlsRightArrow.classList.remove( 'highlight' );\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\t}\n\n\tdestroy() {\n\n\t\tthis.unbind();\n\t\tthis.element.remove();\n\n\t}\n\n\t/**\n\t * Event handlers for navigation control buttons.\n\t */\n\tonNavigateLeftClicked( event ) {\n\n\t\tevent.preventDefault();\n\t\tthis.Reveal.onUserInput();\n\n\t\tif( this.Reveal.getConfig().navigationMode === 'linear' ) {\n\t\t\tthis.Reveal.prev();\n\t\t}\n\t\telse {\n\t\t\tthis.Reveal.left();\n\t\t}\n\n\t}\n\n\tonNavigateRightClicked( event ) {\n\n\t\tevent.preventDefault();\n\t\tthis.Reveal.onUserInput();\n\n\t\tif( this.Reveal.getConfig().navigationMode === 'linear' ) {\n\t\t\tthis.Reveal.next();\n\t\t}\n\t\telse {\n\t\t\tthis.Reveal.right();\n\t\t}\n\n\t}\n\n\tonNavigateUpClicked( event ) {\n\n\t\tevent.preventDefault();\n\t\tthis.Reveal.onUserInput();\n\n\t\tthis.Reveal.up();\n\n\t}\n\n\tonNavigateDownClicked( event ) {\n\n\t\tevent.preventDefault();\n\t\tthis.Reveal.onUserInput();\n\n\t\tthis.Reveal.down();\n\n\t}\n\n\tonNavigatePrevClicked( event ) {\n\n\t\tevent.preventDefault();\n\t\tthis.Reveal.onUserInput();\n\n\t\tthis.Reveal.prev();\n\n\t}\n\n\tonNavigateNextClicked( event ) {\n\n\t\tevent.preventDefault();\n\t\tthis.Reveal.onUserInput();\n\n\t\tthis.Reveal.next();\n\n\t}\n\n\n}","/**\n * Creates a visual progress bar for the presentation.\n */\nexport default class Progress {\n\n\tconstructor( Reveal ) {\n\n\t\tthis.Reveal = Reveal;\n\n\t\tthis.onProgressClicked = this.onProgressClicked.bind( this );\n\n\t}\n\n\trender() {\n\n\t\tthis.element = document.createElement( 'div' );\n\t\tthis.element.className = 'progress';\n\t\tthis.Reveal.getRevealElement().appendChild( this.element );\n\n\t\tthis.bar = document.createElement( 'span' );\n\t\tthis.element.appendChild( this.bar );\n\n\t}\n\n\t/**\n\t * Called when the reveal.js config is updated.\n\t */\n\tconfigure( config, oldConfig ) {\n\n\t\tthis.element.style.display = config.progress ? 'block' : 'none';\n\n\t}\n\n\tbind() {\n\n\t\tif( this.Reveal.getConfig().progress && this.element ) {\n\t\t\tthis.element.addEventListener( 'click', this.onProgressClicked, false );\n\t\t}\n\n\t}\n\n\tunbind() {\n\n\t\tif ( this.Reveal.getConfig().progress && this.element ) {\n\t\t\tthis.element.removeEventListener( 'click', this.onProgressClicked, false );\n\t\t}\n\n\t}\n\n\t/**\n\t * Updates the progress bar to reflect the current slide.\n\t */\n\tupdate() {\n\n\t\t// Update progress if enabled\n\t\tif( this.Reveal.getConfig().progress && this.bar ) {\n\n\t\t\tlet scale = this.Reveal.getProgress();\n\n\t\t\t// Don't fill the progress bar if there's only one slide\n\t\t\tif( this.Reveal.getTotalSlides() < 2 ) {\n\t\t\t\tscale = 0;\n\t\t\t}\n\n\t\t\tthis.bar.style.transform = 'scaleX('+ scale +')';\n\n\t\t}\n\n\t}\n\n\tgetMaxWidth() {\n\n\t\treturn this.Reveal.getRevealElement().offsetWidth;\n\n\t}\n\n\t/**\n\t * Clicking on the progress bar results in a navigation to the\n\t * closest approximate horizontal slide using this equation:\n\t *\n\t * ( clickX / presentationWidth ) * numberOfSlides\n\t *\n\t * @param {object} event\n\t */\n\tonProgressClicked( event ) {\n\n\t\tthis.Reveal.onUserInput( event );\n\n\t\tevent.preventDefault();\n\n\t\tlet slides = this.Reveal.getSlides();\n\t\tlet slidesTotal = slides.length;\n\t\tlet slideIndex = Math.floor( ( event.clientX / this.getMaxWidth() ) * slidesTotal );\n\n\t\tif( this.Reveal.getConfig().rtl ) {\n\t\t\tslideIndex = slidesTotal - slideIndex;\n\t\t}\n\n\t\tlet targetIndices = this.Reveal.getIndices(slides[slideIndex]);\n\t\tthis.Reveal.slide( targetIndices.h, targetIndices.v );\n\n\t}\n\n\tdestroy() {\n\n\t\tthis.element.remove();\n\n\t}\n\n}","/**\n * Handles hiding of the pointer/cursor when inactive.\n */\nexport default class Pointer {\n\n\tconstructor( Reveal ) {\n\n\t\tthis.Reveal = Reveal;\n\n\t\t// Throttles mouse wheel navigation\n\t\tthis.lastMouseWheelStep = 0;\n\n\t\t// Is the mouse pointer currently hidden from view\n\t\tthis.cursorHidden = false;\n\n\t\t// Timeout used to determine when the cursor is inactive\n\t\tthis.cursorInactiveTimeout = 0;\n\n\t\tthis.onDocumentCursorActive = this.onDocumentCursorActive.bind( this );\n\t\tthis.onDocumentMouseScroll = this.onDocumentMouseScroll.bind( this );\n\n\t}\n\n\t/**\n\t * Called when the reveal.js config is updated.\n\t */\n\tconfigure( config, oldConfig ) {\n\n\t\tif( config.mouseWheel ) {\n\t\t\tdocument.addEventListener( 'DOMMouseScroll', this.onDocumentMouseScroll, false ); // FF\n\t\t\tdocument.addEventListener( 'mousewheel', this.onDocumentMouseScroll, false );\n\t\t}\n\t\telse {\n\t\t\tdocument.removeEventListener( 'DOMMouseScroll', this.onDocumentMouseScroll, false ); // FF\n\t\t\tdocument.removeEventListener( 'mousewheel', this.onDocumentMouseScroll, false );\n\t\t}\n\n\t\t// Auto-hide the mouse pointer when its inactive\n\t\tif( config.hideInactiveCursor ) {\n\t\t\tdocument.addEventListener( 'mousemove', this.onDocumentCursorActive, false );\n\t\t\tdocument.addEventListener( 'mousedown', this.onDocumentCursorActive, false );\n\t\t}\n\t\telse {\n\t\t\tthis.showCursor();\n\n\t\t\tdocument.removeEventListener( 'mousemove', this.onDocumentCursorActive, false );\n\t\t\tdocument.removeEventListener( 'mousedown', this.onDocumentCursorActive, false );\n\t\t}\n\n\t}\n\n\t/**\n\t * Shows the mouse pointer after it has been hidden with\n\t * #hideCursor.\n\t */\n\tshowCursor() {\n\n\t\tif( this.cursorHidden ) {\n\t\t\tthis.cursorHidden = false;\n\t\t\tthis.Reveal.getRevealElement().style.cursor = '';\n\t\t}\n\n\t}\n\n\t/**\n\t * Hides the mouse pointer when it's on top of the .reveal\n\t * container.\n\t */\n\thideCursor() {\n\n\t\tif( this.cursorHidden === false ) {\n\t\t\tthis.cursorHidden = true;\n\t\t\tthis.Reveal.getRevealElement().style.cursor = 'none';\n\t\t}\n\n\t}\n\n\tdestroy() {\n\n\t\tthis.showCursor();\n\n\t\tdocument.removeEventListener( 'DOMMouseScroll', this.onDocumentMouseScroll, false );\n\t\tdocument.removeEventListener( 'mousewheel', this.onDocumentMouseScroll, false );\n\t\tdocument.removeEventListener( 'mousemove', this.onDocumentCursorActive, false );\n\t\tdocument.removeEventListener( 'mousedown', this.onDocumentCursorActive, false );\n\n\t}\n\n\t/**\n\t * Called whenever there is mouse input at the document level\n\t * to determine if the cursor is active or not.\n\t *\n\t * @param {object} event\n\t */\n\tonDocumentCursorActive( event ) {\n\n\t\tthis.showCursor();\n\n\t\tclearTimeout( this.cursorInactiveTimeout );\n\n\t\tthis.cursorInactiveTimeout = setTimeout( this.hideCursor.bind( this ), this.Reveal.getConfig().hideCursorTime );\n\n\t}\n\n\t/**\n\t * Handles mouse wheel scrolling, throttled to avoid skipping\n\t * multiple slides.\n\t *\n\t * @param {object} event\n\t */\n\tonDocumentMouseScroll( event ) {\n\n\t\tif( Date.now() - this.lastMouseWheelStep > 1000 ) {\n\n\t\t\tthis.lastMouseWheelStep = Date.now();\n\n\t\t\tlet delta = event.detail || -event.wheelDelta;\n\t\t\tif( delta > 0 ) {\n\t\t\t\tthis.Reveal.next();\n\t\t\t}\n\t\t\telse if( delta < 0 ) {\n\t\t\t\tthis.Reveal.prev();\n\t\t\t}\n\n\t\t}\n\n\t}\n\n}","/**\n * Loads a JavaScript file from the given URL and executes it.\n *\n * @param {string} url Address of the .js file to load\n * @param {function} callback Method to invoke when the script\n * has loaded and executed\n */\nexport const loadScript = ( url, callback ) => {\n\n\tconst script = document.createElement( 'script' );\n\tscript.type = 'text/javascript';\n\tscript.async = false;\n\tscript.defer = false;\n\tscript.src = url;\n\n\tif( typeof callback === 'function' ) {\n\n\t\t// Success callback\n\t\tscript.onload = script.onreadystatechange = event => {\n\t\t\tif( event.type === 'load' || /loaded|complete/.test( script.readyState ) ) {\n\n\t\t\t\t// Kill event listeners\n\t\t\t\tscript.onload = script.onreadystatechange = script.onerror = null;\n\n\t\t\t\tcallback();\n\n\t\t\t}\n\t\t};\n\n\t\t// Error callback\n\t\tscript.onerror = err => {\n\n\t\t\t// Kill event listeners\n\t\t\tscript.onload = script.onreadystatechange = script.onerror = null;\n\n\t\t\tcallback( new Error( 'Failed loading script: ' + script.src + '\\n' + err ) );\n\n\t\t};\n\n\t}\n\n\t// Append the script at the end of \n\tconst head = document.querySelector( 'head' );\n\thead.insertBefore( script, head.lastChild );\n\n}","import { loadScript } from '../utils/loader.js'\n\n/**\n * Manages loading and registering of reveal.js plugins.\n */\nexport default class Plugins {\n\n\tconstructor( reveal ) {\n\n\t\tthis.Reveal = reveal;\n\n\t\t// Flags our current state (idle -> loading -> loaded)\n\t\tthis.state = 'idle';\n\n\t\t// An id:instance map of currently registed plugins\n\t\tthis.registeredPlugins = {};\n\n\t\tthis.asyncDependencies = [];\n\n\t}\n\n\t/**\n\t * Loads reveal.js dependencies, registers and\n\t * initializes plugins.\n\t *\n\t * Plugins are direct references to a reveal.js plugin\n\t * object that we register and initialize after any\n\t * synchronous dependencies have loaded.\n\t *\n\t * Dependencies are defined via the 'dependencies' config\n\t * option and will be loaded prior to starting reveal.js.\n\t * Some dependencies may have an 'async' flag, if so they\n\t * will load after reveal.js has been started up.\n\t */\n\tload( plugins, dependencies ) {\n\n\t\tthis.state = 'loading';\n\n\t\tplugins.forEach( this.registerPlugin.bind( this ) );\n\n\t\treturn new Promise( resolve => {\n\n\t\t\tlet scripts = [],\n\t\t\t\tscriptsToLoad = 0;\n\n\t\t\tdependencies.forEach( s => {\n\t\t\t\t// Load if there's no condition or the condition is truthy\n\t\t\t\tif( !s.condition || s.condition() ) {\n\t\t\t\t\tif( s.async ) {\n\t\t\t\t\t\tthis.asyncDependencies.push( s );\n\t\t\t\t\t}\n\t\t\t\t\telse {\n\t\t\t\t\t\tscripts.push( s );\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t} );\n\n\t\t\tif( scripts.length ) {\n\t\t\t\tscriptsToLoad = scripts.length;\n\n\t\t\t\tconst scriptLoadedCallback = (s) => {\n\t\t\t\t\tif( s && typeof s.callback === 'function' ) s.callback();\n\n\t\t\t\t\tif( --scriptsToLoad === 0 ) {\n\t\t\t\t\t\tthis.initPlugins().then( resolve );\n\t\t\t\t\t}\n\t\t\t\t};\n\n\t\t\t\t// Load synchronous scripts\n\t\t\t\tscripts.forEach( s => {\n\t\t\t\t\tif( typeof s.id === 'string' ) {\n\t\t\t\t\t\tthis.registerPlugin( s );\n\t\t\t\t\t\tscriptLoadedCallback( s );\n\t\t\t\t\t}\n\t\t\t\t\telse if( typeof s.src === 'string' ) {\n\t\t\t\t\t\tloadScript( s.src, () => scriptLoadedCallback(s) );\n\t\t\t\t\t}\n\t\t\t\t\telse {\n\t\t\t\t\t\tconsole.warn( 'Unrecognized plugin format', s );\n\t\t\t\t\t\tscriptLoadedCallback();\n\t\t\t\t\t}\n\t\t\t\t} );\n\t\t\t}\n\t\t\telse {\n\t\t\t\tthis.initPlugins().then( resolve );\n\t\t\t}\n\n\t\t} );\n\n\t}\n\n\t/**\n\t * Initializes our plugins and waits for them to be ready\n\t * before proceeding.\n\t */\n\tinitPlugins() {\n\n\t\treturn new Promise( resolve => {\n\n\t\t\tlet pluginValues = Object.values( this.registeredPlugins );\n\t\t\tlet pluginsToInitialize = pluginValues.length;\n\n\t\t\t// If there are no plugins, skip this step\n\t\t\tif( pluginsToInitialize === 0 ) {\n\t\t\t\tthis.loadAsync().then( resolve );\n\t\t\t}\n\t\t\t// ... otherwise initialize plugins\n\t\t\telse {\n\n\t\t\t\tlet initNextPlugin;\n\n\t\t\t\tlet afterPlugInitialized = () => {\n\t\t\t\t\tif( --pluginsToInitialize === 0 ) {\n\t\t\t\t\t\tthis.loadAsync().then( resolve );\n\t\t\t\t\t}\n\t\t\t\t\telse {\n\t\t\t\t\t\tinitNextPlugin();\n\t\t\t\t\t}\n\t\t\t\t};\n\n\t\t\t\tlet i = 0;\n\n\t\t\t\t// Initialize plugins serially\n\t\t\t\tinitNextPlugin = () => {\n\n\t\t\t\t\tlet plugin = pluginValues[i++];\n\n\t\t\t\t\t// If the plugin has an 'init' method, invoke it\n\t\t\t\t\tif( typeof plugin.init === 'function' ) {\n\t\t\t\t\t\tlet promise = plugin.init( this.Reveal );\n\n\t\t\t\t\t\t// If the plugin returned a Promise, wait for it\n\t\t\t\t\t\tif( promise && typeof promise.then === 'function' ) {\n\t\t\t\t\t\t\tpromise.then( afterPlugInitialized );\n\t\t\t\t\t\t}\n\t\t\t\t\t\telse {\n\t\t\t\t\t\t\tafterPlugInitialized();\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\t\telse {\n\t\t\t\t\t\tafterPlugInitialized();\n\t\t\t\t\t}\n\n\t\t\t\t}\n\n\t\t\t\tinitNextPlugin();\n\n\t\t\t}\n\n\t\t} )\n\n\t}\n\n\t/**\n\t * Loads all async reveal.js dependencies.\n\t */\n\tloadAsync() {\n\n\t\tthis.state = 'loaded';\n\n\t\tif( this.asyncDependencies.length ) {\n\t\t\tthis.asyncDependencies.forEach( s => {\n\t\t\t\tloadScript( s.src, s.callback );\n\t\t\t} );\n\t\t}\n\n\t\treturn Promise.resolve();\n\n\t}\n\n\t/**\n\t * Registers a new plugin with this reveal.js instance.\n\t *\n\t * reveal.js waits for all regisered plugins to initialize\n\t * before considering itself ready, as long as the plugin\n\t * is registered before calling `Reveal.initialize()`.\n\t */\n\tregisterPlugin( plugin ) {\n\n\t\t// Backwards compatibility to make reveal.js ~3.9.0\n\t\t// plugins work with reveal.js 4.0.0\n\t\tif( arguments.length === 2 && typeof arguments[0] === 'string' ) {\n\t\t\tplugin = arguments[1];\n\t\t\tplugin.id = arguments[0];\n\t\t}\n\t\t// Plugin can optionally be a function which we call\n\t\t// to create an instance of the plugin\n\t\telse if( typeof plugin === 'function' ) {\n\t\t\tplugin = plugin();\n\t\t}\n\n\t\tlet id = plugin.id;\n\n\t\tif( typeof id !== 'string' ) {\n\t\t\tconsole.warn( 'Unrecognized plugin format; can\\'t find plugin.id', plugin );\n\t\t}\n\t\telse if( this.registeredPlugins[id] === undefined ) {\n\t\t\tthis.registeredPlugins[id] = plugin;\n\n\t\t\t// If a plugin is registered after reveal.js is loaded,\n\t\t\t// initialize it right away\n\t\t\tif( this.state === 'loaded' && typeof plugin.init === 'function' ) {\n\t\t\t\tplugin.init( this.Reveal );\n\t\t\t}\n\t\t}\n\t\telse {\n\t\t\tconsole.warn( 'reveal.js: \"'+ id +'\" plugin has already been registered' );\n\t\t}\n\n\t}\n\n\t/**\n\t * Checks if a specific plugin has been registered.\n\t *\n\t * @param {String} id Unique plugin identifier\n\t */\n\thasPlugin( id ) {\n\n\t\treturn !!this.registeredPlugins[id];\n\n\t}\n\n\t/**\n\t * Returns the specific plugin instance, if a plugin\n\t * with the given ID has been registered.\n\t *\n\t * @param {String} id Unique plugin identifier\n\t */\n\tgetPlugin( id ) {\n\n\t\treturn this.registeredPlugins[id];\n\n\t}\n\n\tgetRegisteredPlugins() {\n\n\t\treturn this.registeredPlugins;\n\n\t}\n\n\tdestroy() {\n\n\t\tObject.values( this.registeredPlugins ).forEach( plugin => {\n\t\t\tif( typeof plugin.destroy === 'function' ) {\n\t\t\t\tplugin.destroy();\n\t\t\t}\n\t\t} );\n\n\t\tthis.registeredPlugins = {};\n\t\tthis.asyncDependencies = [];\n\n\t}\n\n}\n","import { SLIDES_SELECTOR } from '../utils/constants.js'\nimport { queryAll, createStyleSheet } from '../utils/util.js'\n\n/**\n * Setups up our presentation for printing/exporting to PDF.\n */\nexport default class Print {\n\n\tconstructor( Reveal ) {\n\n\t\tthis.Reveal = Reveal;\n\n\t}\n\n\t/**\n\t * Configures the presentation for printing to a static\n\t * PDF.\n\t */\n\tasync setupPDF() {\n\n\t\tconst config = this.Reveal.getConfig();\n\t\tconst slides = queryAll( this.Reveal.getRevealElement(), SLIDES_SELECTOR )\n\n\t\t// Compute slide numbers now, before we start duplicating slides\n\t\tconst doingSlideNumbers = config.slideNumber && /all|print/i.test( config.showSlideNumber );\n\n\t\tconst slideSize = this.Reveal.getComputedSlideSize( window.innerWidth, window.innerHeight );\n\n\t\t// Dimensions of the PDF pages\n\t\tconst pageWidth = Math.floor( slideSize.width * ( 1 + config.margin ) ),\n\t\t\tpageHeight = Math.floor( slideSize.height * ( 1 + config.margin ) );\n\n\t\t// Dimensions of slides within the pages\n\t\tconst slideWidth = slideSize.width,\n\t\t\tslideHeight = slideSize.height;\n\n\t\tawait new Promise( requestAnimationFrame );\n\n\t\t// Let the browser know what page size we want to print\n\t\tcreateStyleSheet( '@page{size:'+ pageWidth +'px '+ pageHeight +'px; margin: 0px;}' );\n\n\t\t// Limit the size of certain elements to the dimensions of the slide\n\t\tcreateStyleSheet( '.reveal section>img, .reveal section>video, .reveal section>iframe{max-width: '+ slideWidth +'px; max-height:'+ slideHeight +'px}' );\n\n\t\tdocument.documentElement.classList.add( 'print-pdf' );\n\t\tdocument.body.style.width = pageWidth + 'px';\n\t\tdocument.body.style.height = pageHeight + 'px';\n\n\t\tconst viewportElement = document.querySelector( '.reveal-viewport' );\n\t\tlet presentationBackground;\n\t\tif( viewportElement ) {\n\t\t\tconst viewportStyles = window.getComputedStyle( viewportElement );\n\t\t\tif( viewportStyles && viewportStyles.background ) {\n\t\t\t\tpresentationBackground = viewportStyles.background;\n\t\t\t}\n\t\t}\n\n\t\t// Make sure stretch elements fit on slide\n\t\tawait new Promise( requestAnimationFrame );\n\t\tthis.Reveal.layoutSlideContents( slideWidth, slideHeight );\n\n\t\t// Batch scrollHeight access to prevent layout thrashing\n\t\tawait new Promise( requestAnimationFrame );\n\n\t\tconst slideScrollHeights = slides.map( slide => slide.scrollHeight );\n\n\t\tconst pages = [];\n\t\tconst pageContainer = slides[0].parentNode;\n\n\t\t// Slide and slide background layout\n\t\tslides.forEach( function( slide, index ) {\n\n\t\t\t// Vertical stacks are not centred since their section\n\t\t\t// children will be\n\t\t\tif( slide.classList.contains( 'stack' ) === false ) {\n\t\t\t\t// Center the slide inside of the page, giving the slide some margin\n\t\t\t\tlet left = ( pageWidth - slideWidth ) / 2;\n\t\t\t\tlet top = ( pageHeight - slideHeight ) / 2;\n\n\t\t\t\tconst contentHeight = slideScrollHeights[ index ];\n\t\t\t\tlet numberOfPages = Math.max( Math.ceil( contentHeight / pageHeight ), 1 );\n\n\t\t\t\t// Adhere to configured pages per slide limit\n\t\t\t\tnumberOfPages = Math.min( numberOfPages, config.pdfMaxPagesPerSlide );\n\n\t\t\t\t// Center slides vertically\n\t\t\t\tif( numberOfPages === 1 && config.center || slide.classList.contains( 'center' ) ) {\n\t\t\t\t\ttop = Math.max( ( pageHeight - contentHeight ) / 2, 0 );\n\t\t\t\t}\n\n\t\t\t\t// Wrap the slide in a page element and hide its overflow\n\t\t\t\t// so that no page ever flows onto another\n\t\t\t\tconst page = document.createElement( 'div' );\n\t\t\t\tpages.push( page );\n\n\t\t\t\tpage.className = 'pdf-page';\n\t\t\t\tpage.style.height = ( ( pageHeight + config.pdfPageHeightOffset ) * numberOfPages ) + 'px';\n\n\t\t\t\t// Copy the presentation-wide background to each individual\n\t\t\t\t// page when printing\n\t\t\t\tif( presentationBackground ) {\n\t\t\t\t\tpage.style.background = presentationBackground;\n\t\t\t\t}\n\n\t\t\t\tpage.appendChild( slide );\n\n\t\t\t\t// Position the slide inside of the page\n\t\t\t\tslide.style.left = left + 'px';\n\t\t\t\tslide.style.top = top + 'px';\n\t\t\t\tslide.style.width = slideWidth + 'px';\n\n\t\t\t\t// Re-run the slide layout so that r-fit-text is applied based on\n\t\t\t\t// the printed slide size\n\t\t\t\tthis.Reveal.slideContent.layout( slide )\n\n\t\t\t\tif( slide.slideBackgroundElement ) {\n\t\t\t\t\tpage.insertBefore( slide.slideBackgroundElement, slide );\n\t\t\t\t}\n\n\t\t\t\t// Inject notes if `showNotes` is enabled\n\t\t\t\tif( config.showNotes ) {\n\n\t\t\t\t\t// Are there notes for this slide?\n\t\t\t\t\tconst notes = this.Reveal.getSlideNotes( slide );\n\t\t\t\t\tif( notes ) {\n\n\t\t\t\t\t\tconst notesSpacing = 8;\n\t\t\t\t\t\tconst notesLayout = typeof config.showNotes === 'string' ? config.showNotes : 'inline';\n\t\t\t\t\t\tconst notesElement = document.createElement( 'div' );\n\t\t\t\t\t\tnotesElement.classList.add( 'speaker-notes' );\n\t\t\t\t\t\tnotesElement.classList.add( 'speaker-notes-pdf' );\n\t\t\t\t\t\tnotesElement.setAttribute( 'data-layout', notesLayout );\n\t\t\t\t\t\tnotesElement.innerHTML = notes;\n\n\t\t\t\t\t\tif( notesLayout === 'separate-page' ) {\n\t\t\t\t\t\t\tpages.push( notesElement );\n\t\t\t\t\t\t}\n\t\t\t\t\t\telse {\n\t\t\t\t\t\t\tnotesElement.style.left = notesSpacing + 'px';\n\t\t\t\t\t\t\tnotesElement.style.bottom = notesSpacing + 'px';\n\t\t\t\t\t\t\tnotesElement.style.width = ( pageWidth - notesSpacing*2 ) + 'px';\n\t\t\t\t\t\t\tpage.appendChild( notesElement );\n\t\t\t\t\t\t}\n\n\t\t\t\t\t}\n\n\t\t\t\t}\n\n\t\t\t\t// Inject slide numbers if `slideNumbers` are enabled\n\t\t\t\tif( doingSlideNumbers ) {\n\t\t\t\t\tconst slideNumber = index + 1;\n\t\t\t\t\tconst numberElement = document.createElement( 'div' );\n\t\t\t\t\tnumberElement.classList.add( 'slide-number' );\n\t\t\t\t\tnumberElement.classList.add( 'slide-number-pdf' );\n\t\t\t\t\tnumberElement.innerHTML = slideNumber;\n\t\t\t\t\tpage.appendChild( numberElement );\n\t\t\t\t}\n\n\t\t\t\t// Copy page and show fragments one after another\n\t\t\t\tif( config.pdfSeparateFragments ) {\n\n\t\t\t\t\t// Each fragment 'group' is an array containing one or more\n\t\t\t\t\t// fragments. Multiple fragments that appear at the same time\n\t\t\t\t\t// are part of the same group.\n\t\t\t\t\tconst fragmentGroups = this.Reveal.fragments.sort( page.querySelectorAll( '.fragment' ), true );\n\n\t\t\t\t\tlet previousFragmentStep;\n\n\t\t\t\t\tfragmentGroups.forEach( function( fragments ) {\n\n\t\t\t\t\t\t// Remove 'current-fragment' from the previous group\n\t\t\t\t\t\tif( previousFragmentStep ) {\n\t\t\t\t\t\t\tpreviousFragmentStep.forEach( function( fragment ) {\n\t\t\t\t\t\t\t\tfragment.classList.remove( 'current-fragment' );\n\t\t\t\t\t\t\t} );\n\t\t\t\t\t\t}\n\n\t\t\t\t\t\t// Show the fragments for the current index\n\t\t\t\t\t\tfragments.forEach( function( fragment ) {\n\t\t\t\t\t\t\tfragment.classList.add( 'visible', 'current-fragment' );\n\t\t\t\t\t\t}, this );\n\n\t\t\t\t\t\t// Create a separate page for the current fragment state\n\t\t\t\t\t\tconst clonedPage = page.cloneNode( true );\n\t\t\t\t\t\tpages.push( clonedPage );\n\n\t\t\t\t\t\tpreviousFragmentStep = fragments;\n\n\t\t\t\t\t}, this );\n\n\t\t\t\t\t// Reset the first/original page so that all fragments are hidden\n\t\t\t\t\tfragmentGroups.forEach( function( fragments ) {\n\t\t\t\t\t\tfragments.forEach( function( fragment ) {\n\t\t\t\t\t\t\tfragment.classList.remove( 'visible', 'current-fragment' );\n\t\t\t\t\t\t} );\n\t\t\t\t\t} );\n\n\t\t\t\t}\n\t\t\t\t// Show all fragments\n\t\t\t\telse {\n\t\t\t\t\tqueryAll( page, '.fragment:not(.fade-out)' ).forEach( function( fragment ) {\n\t\t\t\t\t\tfragment.classList.add( 'visible' );\n\t\t\t\t\t} );\n\t\t\t\t}\n\n\t\t\t}\n\n\t\t}, this );\n\n\t\tawait new Promise( requestAnimationFrame );\n\n\t\tpages.forEach( page => pageContainer.appendChild( page ) );\n\n\t\t// Notify subscribers that the PDF layout is good to go\n\t\tthis.Reveal.dispatchEvent({ type: 'pdf-ready' });\n\n\t}\n\n\t/**\n\t * Checks if this instance is being used to print a PDF.\n\t */\n\tisPrintingPDF() {\n\n\t\treturn ( /print-pdf/gi ).test( window.location.search );\n\n\t}\n\n}\n","import { isAndroid } from '../utils/device.js'\nimport { matches } from '../utils/util.js'\n\nconst SWIPE_THRESHOLD = 40;\n\n/**\n * Controls all touch interactions and navigations for\n * a presentation.\n */\nexport default class Touch {\n\n\tconstructor( Reveal ) {\n\n\t\tthis.Reveal = Reveal;\n\n\t\t// Holds information about the currently ongoing touch interaction\n\t\tthis.touchStartX = 0;\n\t\tthis.touchStartY = 0;\n\t\tthis.touchStartCount = 0;\n\t\tthis.touchCaptured = false;\n\n\t\tthis.onPointerDown = this.onPointerDown.bind( this );\n\t\tthis.onPointerMove = this.onPointerMove.bind( this );\n\t\tthis.onPointerUp = this.onPointerUp.bind( this );\n\t\tthis.onTouchStart = this.onTouchStart.bind( this );\n\t\tthis.onTouchMove = this.onTouchMove.bind( this );\n\t\tthis.onTouchEnd = this.onTouchEnd.bind( this );\n\n\t}\n\n\t/**\n\t *\n\t */\n\tbind() {\n\n\t\tlet revealElement = this.Reveal.getRevealElement();\n\n\t\tif( 'onpointerdown' in window ) {\n\t\t\t// Use W3C pointer events\n\t\t\trevealElement.addEventListener( 'pointerdown', this.onPointerDown, false );\n\t\t\trevealElement.addEventListener( 'pointermove', this.onPointerMove, false );\n\t\t\trevealElement.addEventListener( 'pointerup', this.onPointerUp, false );\n\t\t}\n\t\telse if( window.navigator.msPointerEnabled ) {\n\t\t\t// IE 10 uses prefixed version of pointer events\n\t\t\trevealElement.addEventListener( 'MSPointerDown', this.onPointerDown, false );\n\t\t\trevealElement.addEventListener( 'MSPointerMove', this.onPointerMove, false );\n\t\t\trevealElement.addEventListener( 'MSPointerUp', this.onPointerUp, false );\n\t\t}\n\t\telse {\n\t\t\t// Fall back to touch events\n\t\t\trevealElement.addEventListener( 'touchstart', this.onTouchStart, false );\n\t\t\trevealElement.addEventListener( 'touchmove', this.onTouchMove, false );\n\t\t\trevealElement.addEventListener( 'touchend', this.onTouchEnd, false );\n\t\t}\n\n\t}\n\n\t/**\n\t *\n\t */\n\tunbind() {\n\n\t\tlet revealElement = this.Reveal.getRevealElement();\n\n\t\trevealElement.removeEventListener( 'pointerdown', this.onPointerDown, false );\n\t\trevealElement.removeEventListener( 'pointermove', this.onPointerMove, false );\n\t\trevealElement.removeEventListener( 'pointerup', this.onPointerUp, false );\n\n\t\trevealElement.removeEventListener( 'MSPointerDown', this.onPointerDown, false );\n\t\trevealElement.removeEventListener( 'MSPointerMove', this.onPointerMove, false );\n\t\trevealElement.removeEventListener( 'MSPointerUp', this.onPointerUp, false );\n\n\t\trevealElement.removeEventListener( 'touchstart', this.onTouchStart, false );\n\t\trevealElement.removeEventListener( 'touchmove', this.onTouchMove, false );\n\t\trevealElement.removeEventListener( 'touchend', this.onTouchEnd, false );\n\n\t}\n\n\t/**\n\t * Checks if the target element prevents the triggering of\n\t * swipe navigation.\n\t */\n\tisSwipePrevented( target ) {\n\n\t\t// Prevent accidental swipes when scrubbing timelines\n\t\tif( matches( target, 'video, audio' ) ) return true;\n\n\t\twhile( target && typeof target.hasAttribute === 'function' ) {\n\t\t\tif( target.hasAttribute( 'data-prevent-swipe' ) ) return true;\n\t\t\ttarget = target.parentNode;\n\t\t}\n\n\t\treturn false;\n\n\t}\n\n\t/**\n\t * Handler for the 'touchstart' event, enables support for\n\t * swipe and pinch gestures.\n\t *\n\t * @param {object} event\n\t */\n\tonTouchStart( event ) {\n\n\t\tif( this.isSwipePrevented( event.target ) ) return true;\n\n\t\tthis.touchStartX = event.touches[0].clientX;\n\t\tthis.touchStartY = event.touches[0].clientY;\n\t\tthis.touchStartCount = event.touches.length;\n\n\t}\n\n\t/**\n\t * Handler for the 'touchmove' event.\n\t *\n\t * @param {object} event\n\t */\n\tonTouchMove( event ) {\n\n\t\tif( this.isSwipePrevented( event.target ) ) return true;\n\n\t\tlet config = this.Reveal.getConfig();\n\n\t\t// Each touch should only trigger one action\n\t\tif( !this.touchCaptured ) {\n\t\t\tthis.Reveal.onUserInput( event );\n\n\t\t\tlet currentX = event.touches[0].clientX;\n\t\t\tlet currentY = event.touches[0].clientY;\n\n\t\t\t// There was only one touch point, look for a swipe\n\t\t\tif( event.touches.length === 1 && this.touchStartCount !== 2 ) {\n\n\t\t\t\tlet availableRoutes = this.Reveal.availableRoutes({ includeFragments: true });\n\n\t\t\t\tlet deltaX = currentX - this.touchStartX,\n\t\t\t\t\tdeltaY = currentY - this.touchStartY;\n\n\t\t\t\tif( deltaX > SWIPE_THRESHOLD && Math.abs( deltaX ) > Math.abs( deltaY ) ) {\n\t\t\t\t\tthis.touchCaptured = true;\n\t\t\t\t\tif( config.navigationMode === 'linear' ) {\n\t\t\t\t\t\tif( config.rtl ) {\n\t\t\t\t\t\t\tthis.Reveal.next();\n\t\t\t\t\t\t}\n\t\t\t\t\t\telse {\n\t\t\t\t\t\t\tthis.Reveal.prev();\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\t\telse {\n\t\t\t\t\t\tthis.Reveal.left();\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t\telse if( deltaX < -SWIPE_THRESHOLD && Math.abs( deltaX ) > Math.abs( deltaY ) ) {\n\t\t\t\t\tthis.touchCaptured = true;\n\t\t\t\t\tif( config.navigationMode === 'linear' ) {\n\t\t\t\t\t\tif( config.rtl ) {\n\t\t\t\t\t\t\tthis.Reveal.prev();\n\t\t\t\t\t\t}\n\t\t\t\t\t\telse {\n\t\t\t\t\t\t\tthis.Reveal.next();\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\t\telse {\n\t\t\t\t\t\tthis.Reveal.right();\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t\telse if( deltaY > SWIPE_THRESHOLD && availableRoutes.up ) {\n\t\t\t\t\tthis.touchCaptured = true;\n\t\t\t\t\tif( config.navigationMode === 'linear' ) {\n\t\t\t\t\t\tthis.Reveal.prev();\n\t\t\t\t\t}\n\t\t\t\t\telse {\n\t\t\t\t\t\tthis.Reveal.up();\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t\telse if( deltaY < -SWIPE_THRESHOLD && availableRoutes.down ) {\n\t\t\t\t\tthis.touchCaptured = true;\n\t\t\t\t\tif( config.navigationMode === 'linear' ) {\n\t\t\t\t\t\tthis.Reveal.next();\n\t\t\t\t\t}\n\t\t\t\t\telse {\n\t\t\t\t\t\tthis.Reveal.down();\n\t\t\t\t\t}\n\t\t\t\t}\n\n\t\t\t\t// If we're embedded, only block touch events if they have\n\t\t\t\t// triggered an action\n\t\t\t\tif( config.embedded ) {\n\t\t\t\t\tif( this.touchCaptured || this.Reveal.isVerticalSlide() ) {\n\t\t\t\t\t\tevent.preventDefault();\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t\t// Not embedded? Block them all to avoid needless tossing\n\t\t\t\t// around of the viewport in iOS\n\t\t\t\telse {\n\t\t\t\t\tevent.preventDefault();\n\t\t\t\t}\n\n\t\t\t}\n\t\t}\n\t\t// There's a bug with swiping on some Android devices unless\n\t\t// the default action is always prevented\n\t\telse if( isAndroid ) {\n\t\t\tevent.preventDefault();\n\t\t}\n\n\t}\n\n\t/**\n\t * Handler for the 'touchend' event.\n\t *\n\t * @param {object} event\n\t */\n\tonTouchEnd( event ) {\n\n\t\tthis.touchCaptured = false;\n\n\t}\n\n\t/**\n\t * Convert pointer down to touch start.\n\t *\n\t * @param {object} event\n\t */\n\tonPointerDown( event ) {\n\n\t\tif( event.pointerType === event.MSPOINTER_TYPE_TOUCH || event.pointerType === \"touch\" ) {\n\t\t\tevent.touches = [{ clientX: event.clientX, clientY: event.clientY }];\n\t\t\tthis.onTouchStart( event );\n\t\t}\n\n\t}\n\n\t/**\n\t * Convert pointer move to touch move.\n\t *\n\t * @param {object} event\n\t */\n\tonPointerMove( event ) {\n\n\t\tif( event.pointerType === event.MSPOINTER_TYPE_TOUCH || event.pointerType === \"touch\" ) {\n\t\t\tevent.touches = [{ clientX: event.clientX, clientY: event.clientY }];\n\t\t\tthis.onTouchMove( event );\n\t\t}\n\n\t}\n\n\t/**\n\t * Convert pointer up to touch end.\n\t *\n\t * @param {object} event\n\t */\n\tonPointerUp( event ) {\n\n\t\tif( event.pointerType === event.MSPOINTER_TYPE_TOUCH || event.pointerType === \"touch\" ) {\n\t\t\tevent.touches = [{ clientX: event.clientX, clientY: event.clientY }];\n\t\t\tthis.onTouchEnd( event );\n\t\t}\n\n\t}\n\n}","import { closest } from '../utils/util.js'\n\n/**\n * Manages focus when a presentation is embedded. This\n * helps us only capture keyboard from the presentation\n * a user is currently interacting with in a page where\n * multiple presentations are embedded.\n */\n\nconst STATE_FOCUS = 'focus';\nconst STATE_BLUR = 'blur';\n\nexport default class Focus {\n\n\tconstructor( Reveal ) {\n\n\t\tthis.Reveal = Reveal;\n\n\t\tthis.onRevealPointerDown = this.onRevealPointerDown.bind( this );\n\t\tthis.onDocumentPointerDown = this.onDocumentPointerDown.bind( this );\n\n\t}\n\n\t/**\n\t * Called when the reveal.js config is updated.\n\t */\n\tconfigure( config, oldConfig ) {\n\n\t\tif( config.embedded ) {\n\t\t\tthis.blur();\n\t\t}\n\t\telse {\n\t\t\tthis.focus();\n\t\t\tthis.unbind();\n\t\t}\n\n\t}\n\n\tbind() {\n\n\t\tif( this.Reveal.getConfig().embedded ) {\n\t\t\tthis.Reveal.getRevealElement().addEventListener( 'pointerdown', this.onRevealPointerDown, false );\n\t\t}\n\n\t}\n\n\tunbind() {\n\n\t\tthis.Reveal.getRevealElement().removeEventListener( 'pointerdown', this.onRevealPointerDown, false );\n\t\tdocument.removeEventListener( 'pointerdown', this.onDocumentPointerDown, false );\n\n\t}\n\n\tfocus() {\n\n\t\tif( this.state !== STATE_FOCUS ) {\n\t\t\tthis.Reveal.getRevealElement().classList.add( 'focused' );\n\t\t\tdocument.addEventListener( 'pointerdown', this.onDocumentPointerDown, false );\n\t\t}\n\n\t\tthis.state = STATE_FOCUS;\n\n\t}\n\n\tblur() {\n\n\t\tif( this.state !== STATE_BLUR ) {\n\t\t\tthis.Reveal.getRevealElement().classList.remove( 'focused' );\n\t\t\tdocument.removeEventListener( 'pointerdown', this.onDocumentPointerDown, false );\n\t\t}\n\n\t\tthis.state = STATE_BLUR;\n\n\t}\n\n\tisFocused() {\n\n\t\treturn this.state === STATE_FOCUS;\n\n\t}\n\n\tdestroy() {\n\n\t\tthis.Reveal.getRevealElement().classList.remove( 'focused' );\n\n\t}\n\n\tonRevealPointerDown( event ) {\n\n\t\tthis.focus();\n\n\t}\n\n\tonDocumentPointerDown( event ) {\n\n\t\tlet revealElement = closest( event.target, '.reveal' );\n\t\tif( !revealElement || revealElement !== this.Reveal.getRevealElement() ) {\n\t\t\tthis.blur();\n\t\t}\n\n\t}\n\n}","/**\n * Handles the showing and \n */\nexport default class Notes {\n\n\tconstructor( Reveal ) {\n\n\t\tthis.Reveal = Reveal;\n\n\t}\n\n\trender() {\n\n\t\tthis.element = document.createElement( 'div' );\n\t\tthis.element.className = 'speaker-notes';\n\t\tthis.element.setAttribute( 'data-prevent-swipe', '' );\n\t\tthis.element.setAttribute( 'tabindex', '0' );\n\t\tthis.Reveal.getRevealElement().appendChild( this.element );\n\n\t}\n\n\t/**\n\t * Called when the reveal.js config is updated.\n\t */\n\tconfigure( config, oldConfig ) {\n\n\t\tif( config.showNotes ) {\n\t\t\tthis.element.setAttribute( 'data-layout', typeof config.showNotes === 'string' ? config.showNotes : 'inline' );\n\t\t}\n\n\t}\n\n\t/**\n\t * Pick up notes from the current slide and display them\n\t * to the viewer.\n\t *\n\t * @see {@link config.showNotes}\n\t */\n\tupdate() {\n\n\t\tif( this.Reveal.getConfig().showNotes && this.element && this.Reveal.getCurrentSlide() && !this.Reveal.print.isPrintingPDF() ) {\n\n\t\t\tthis.element.innerHTML = this.getSlideNotes() || 'No notes on this slide.';\n\n\t\t}\n\n\t}\n\n\t/**\n\t * Updates the visibility of the speaker notes sidebar that\n\t * is used to share annotated slides. The notes sidebar is\n\t * only visible if showNotes is true and there are notes on\n\t * one or more slides in the deck.\n\t */\n\tupdateVisibility() {\n\n\t\tif( this.Reveal.getConfig().showNotes && this.hasNotes() && !this.Reveal.print.isPrintingPDF() ) {\n\t\t\tthis.Reveal.getRevealElement().classList.add( 'show-notes' );\n\t\t}\n\t\telse {\n\t\t\tthis.Reveal.getRevealElement().classList.remove( 'show-notes' );\n\t\t}\n\n\t}\n\n\t/**\n\t * Checks if there are speaker notes for ANY slide in the\n\t * presentation.\n\t */\n\thasNotes() {\n\n\t\treturn this.Reveal.getSlidesElement().querySelectorAll( '[data-notes], aside.notes' ).length > 0;\n\n\t}\n\n\t/**\n\t * Checks if this presentation is running inside of the\n\t * speaker notes window.\n\t *\n\t * @return {boolean}\n\t */\n\tisSpeakerNotesWindow() {\n\n\t\treturn !!window.location.search.match( /receiver/gi );\n\n\t}\n\n\t/**\n\t * Retrieves the speaker notes from a slide. Notes can be\n\t * defined in two ways:\n\t * 1. As a data-notes attribute on the slide
\n\t * 2. As an

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