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scalorPotential.cpp
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#include "scalorPotential.h"
#include <iomanip>
ScalorPotentialState::ScalorPotentialState()
{
value = 0;
firstSpatialDerivative.setZero(3,1);
secondSpatialDerivative.setZero(3,3);
thirdSpatialDerivative.setZero(5,3);
firstSpatialDerivative_SourceHeadingDerivative.clear();
secondSpatialDerivative_SourceHeadingDerivative.clear();
firstSpatialDerivative_SourcePositionDerivative.clear();
secondSpatialDerivative_SourcePositionDerivative.clear();
}
ScalorPotentialCalibrationJacobians::ScalorPotentialCalibrationJacobians()
{
firstSpatialDerivative.setZero(3,1); ///< Field, the gradient of the potential.
firstSpatialDerivative_A_CoeffDerivative.setZero(0,0); ///< How the field changes with the A coefficients
firstSpatialDerivative_B_CoeffDerivative.setZero(0,0); ///< How the field changes with the B coefficients
firstSpatialDerivative_SourcePositionDerivative.setZero(3,3); ///< Field spatial gradient
firstSpatialDerivative_SourceHeadingDerivative.setZero(3,3); ///< How the field changes with the source heading
firstSpatialDerivative_secondSourceHeadingDerivative.setZero(9,3); ///< the second deritive of field with heading (d(BX)dz; d(BY/dz; d(BZ)/dz)
firstSpatialDerivative_dA_dHeading.setZero(0,0);
firstSpatialDerivative_dB_dHeading.setZero(0,0);
firstSpatialDerivative_dA_dPosition.setZero(0,0);
firstSpatialDerivative_dB_dPosition.setZero(0,0);
}
ScalorPotential::srcCoeff::srcCoeff():
order(0),
coeff(0)
{
return;
}
ScalorPotential::srcCoeff::srcCoeff(double value, unsigned int order):
order(order),
coeff(value)
{
return;
}
ScalorPotential::srcStruct::srcStruct():
A_Coeff(std::vector<srcCoeff>(0)),
B_Coeff(std::vector<srcCoeff>(0)),
srcPosition(0,0,0),
srcDirection(0,0,1)
{
return;
}
unsigned int ScalorPotential::srcStruct::getMaxOrder_A_Coeff() const
{
unsigned int maxCoeffOrder = 0;
for( unsigned int i=0; i<A_Coeff.size(); i++ )
maxCoeffOrder = std::max(maxCoeffOrder,A_Coeff[i].order );
return maxCoeffOrder;
}
unsigned int ScalorPotential::srcStruct::getMaxOrder_B_Coeff() const
{
unsigned int maxCoeffOrder = 0;
for( unsigned int i=0; i<B_Coeff.size(); i++ )
maxCoeffOrder = std::max(maxCoeffOrder,B_Coeff[i].order );
return maxCoeffOrder;
}
ScalorPotential::ScalorPotential():
srcList(std::vector<srcStruct>(0))
{
return;
}
///
/// \brief the constructor from a coil list.
/// \param coilList The list of coils and their respective sources.
/// \param dc_field_offset The dc offset field, if any.
///
ScalorPotential::ScalorPotential(const std::vector<srcStruct>& srcList_ ):
srcList(srcList_)
{
int numA = 0;
int numB = 0;
int numP = srcList.size()*3;
int numZ = srcList.size()*3;
for( unsigned int i=0; i<srcList.size(); i++ )
{
numA += srcList[i].A_Coeff.size();
numB += srcList[i].B_Coeff.size();
}
numCalParameters = numA + numB + numP + numZ;
}
// This function returns the field, gradient, gradientJacobian, and field/gradient current jacobain. It is more efficient than requesting them seporately
ScalorPotentialState ScalorPotential::getState(const Eigen::Vector3d& position, int sourceNumber ) const
{
ScalorPotentialState returnState;
if( sourceNumber > 0 && sourceNumber < (int)srcList.size() )
{
srcFieldGradient(position,srcList[sourceNumber],returnState);
}else if( sourceNumber == -1 )
{
for( unsigned int src = 0; src < srcList.size(); src++ )
{
srcFieldGradient(position, srcList[src], returnState );
}
}
return returnState;
}
// These two functions convert a vector packing of the gradient to a matrix packing and vice versa.
Eigen::Matrix3d ScalorPotential::remapSecondDerivativeVec(const Vector5d& gradVector )
{
Eigen::Matrix3d gradientMatrix;
// repack vector gradient into matrix gradient
gradientMatrix.leftCols<1>() = gradVector.topRows<3>();
gradientMatrix.block<2,1>(1,1) = gradVector.bottomRows<2>();
gradientMatrix(0,1) = gradientMatrix(1,0);
gradientMatrix(0,2) = gradientMatrix(2,0);
gradientMatrix(1,2) = gradientMatrix(2,1);
gradientMatrix(2,2) = -1.0*(gradientMatrix(0,0)+gradientMatrix(1,1));
return gradientMatrix;
}
Vector5d ScalorPotential::remapSecondDerivativeMat( const Eigen::Matrix3d& gradMatrix)
{
Vector5d gradVec;
gradVec.topRows<3>() = gradMatrix.leftCols<1>();
gradVec(3) = gradMatrix(1,1);
gradVec(4) = gradMatrix(2,1);
return gradVec;
}
///@brief returns the number of sources for the given coil
unsigned int ScalorPotential::getNumberOfSources( ) const
{
return srcList.size();
}
ScalorPotential::srcStruct ScalorPotential::getSourceStruct(unsigned int sourceNumber) const
{
if( sourceNumber < getNumberOfSources() )
return srcList[sourceNumber];
else
return srcStruct();
}
void ScalorPotential::setSourceStruct(unsigned int sourceNumber, const srcStruct& newSrc)
{
assert(('ScalorPotential::setSourceStruct: newSrc must have a direction of length greator than zero', newSrc.srcDirection.norm() != 0 ));
if( sourceNumber < getNumberOfSources() )
srcList[sourceNumber] = newSrc;
else
{
while( sourceNumber !=0 && srcList.size()< sourceNumber-1)
{
srcList.push_back(srcStruct());
}
srcList.push_back(newSrc);
srcList.back().srcDirection.normalize();
}
int numA = 0;
int numB = 0;
int numP = srcList.size()*3;
int numZ = srcList.size()*3;
for( int i=0; i<srcList.size(); i++ )
{
numA += srcList[i].A_Coeff.size();
numB += srcList[i].B_Coeff.size();
}
numCalParameters = numA + numB + numP + numZ;
}
void ScalorPotential::removeSourceStruct(unsigned int sourceNumber)
{
if( sourceNumber < getNumberOfSources() )
{
std::vector<srcStruct>::iterator it = srcList.begin();
for( unsigned int i=0;i=sourceNumber; i++ ) it++;
srcList.erase(it);
}
int numA = 0;
int numB = 0;
int numP = srcList.size()*3;
int numZ = srcList.size()*3;
for( int i=0; i<srcList.size(); i++ )
{
numA += srcList[i].A_Coeff.size();
numB += srcList[i].B_Coeff.size();
}
numCalParameters = numA + numB + numP + numZ;
}
double ScalorPotential::getValue( const Eigen::Vector3d& position, int sourceNumber ) const
{
// field Coefficients
double value = 0;
int srcStart = sourceNumber;
int srcEnd = sourceNumber+1;
if(sourceNumber == -1 )
{
srcStart = 0;
srcEnd = srcList.size();
} else if( sourceNumber >= srcList.size() )
return 0;
for( int srcNum=srcStart; srcNum<srcEnd; srcNum++ )
{
Eigen::Vector3d p( position - srcList[srcNum].srcPosition );
double pMag = p.norm();
if( pMag > 0 )
{
p /= pMag;
}
Eigen::Vector3d z( srcList[srcNum].srcDirection );
if( z.norm() == 0 )
z(3) = 1;
z.normalize();
// define Cosine Theta
double cTh = p.dot(z);
std::vector<srcCoeff>::const_iterator coeffIT;
for( coeffIT = srcList[srcNum].A_Coeff.begin();
coeffIT !=srcList[srcNum].A_Coeff.end();
coeffIT ++ )
{
double n = coeffIT->order;
double Pn = LegandrePolynomial(cTh, n, 0); // Legandre Polynomial at cos(theta)
value += coeffIT->coeff * std::pow(pMag,n)*Pn;
}
if( pMag > 0 )
{
for( coeffIT = srcList[srcNum].B_Coeff.begin();
coeffIT !=srcList[srcNum].B_Coeff.end();
coeffIT ++ )
{
double n = coeffIT->order;
double Pn = LegandrePolynomial(cTh, n, 0); // Legandre Polynomial at cos(theta)
value += coeffIT->coeff * 1.0/std::pow(pMag,n+1.0)*Pn;
}
}
}
return value;
}
Eigen::Vector3d ScalorPotential::getGradient( const Eigen::Vector3d& position, int sourceNumber ) const
{
Eigen::Vector3d field(0,0,0);
int srcStart = sourceNumber;
int srcEnd = sourceNumber+1;
if(sourceNumber == -1 )
{
srcStart = 0;
srcEnd = srcList.size();
}else if( sourceNumber >= srcList.size() )
return Eigen::Vector3d::Zero();
for( int srcNum=srcStart; srcNum<srcEnd; srcNum++ )
{
Eigen::Vector3d p( position - srcList[srcNum].srcPosition );
double pMag = p.norm();
if( pMag > 0 )
{
p /= pMag;
}
Eigen::Vector3d z( srcList[srcNum].srcDirection );
if( z.norm() == 0 )
z(3) = 1;
z.normalize();
// define Cosine Theta
double cTh = p.dot(z);
// field Coefficients
double field_r_mult=0;
double field_z_mult=0;
std::vector<srcCoeff>::const_iterator coeffIT;
for( coeffIT = srcList[srcNum].A_Coeff.begin();
coeffIT !=srcList[srcNum].A_Coeff.end();
coeffIT ++ )
{
double n = coeffIT->order;
double Pn = LegandrePolynomial(cTh, n, 0); // Legandre Polynomial at cos(theta)
double Pn_1 = LegandrePolynomial(cTh, n, 1); // First Derivative of Legandre Polynomial at cos(theta)
if( n==0 )
continue;
double c1 = 0;
double c2 = 0;
double tmp = coeffIT->coeff;
if( n > 1 )
tmp *= pow(pMag,n-1);
c2 += tmp;
tmp *= n;
c1 += tmp;
// field terms
field_r_mult += c2*cTh*Pn_1-c1*Pn;
field_z_mult -= c2*Pn_1;
}
if( pMag > 0 )
{
for( coeffIT = srcList[srcNum].B_Coeff.begin();
coeffIT !=srcList[srcNum].B_Coeff.end();
coeffIT ++ )
{
double n = coeffIT->order;
double Pn = LegandrePolynomial(cTh, n, 0); // Legandre Polynomial at cos(theta)
double Pn_1 = LegandrePolynomial(cTh, n, 1); // First Derivative of Legandre Polynomial at cos(theta)
double c1 = 0;
double c2 = 0;
double tmp = coeffIT->coeff/pow(pMag,n+2);
c2 += tmp;
tmp *= (n+1);
c1 += -1.0*tmp;
// field terms
field_r_mult += c2*cTh*Pn_1-c1*Pn;
field_z_mult -= c2*Pn_1;
}
}
field+= field_r_mult*p + field_z_mult*z;
}
// calculate field
return field;
}
// This fuction returns the field and gradient (stacked) assuming a current of 1 at the position specified in the work space
void ScalorPotential::srcFieldGradient(const Eigen::Vector3d& position, const srcStruct& src, ScalorPotentialState& currentState )
{
Eigen::Vector3d p( position - src.srcPosition );
double pMag = p.norm();
double pMagSq = pMag*pMag;
if( pMag > 0 )
{
p /= pMag;
}
Eigen::Vector3d z( src.srcDirection );
if( z.norm() == 0 )
z(3) = 1;
z.normalize();
Eigen::Matrix3d pzt_zpt( p*z.transpose()+z*p.transpose() );
Eigen::Matrix3d ppt( p*p.transpose() );// = p*p.transpose(); // p*p'
Eigen::Matrix3d zzt(z *z.transpose() );// = src.srcDirection *src.srcDirection.transpose(); // z*z'
Eigen::Matrix3d rzt = p*z.transpose();
Eigen::Matrix3d zrt = z*p.transpose();
// some constant vectors and matricies
Eigen::Vector3d X(1,0,0);
Eigen::Vector3d Y(0,1,0);
Eigen::Matrix3d I(Eigen::Matrix3d::Identity());
// define Cosine Theta
double cTh = p.dot(z);
double cThsq = cTh*cTh;
// field Coefficients
double field_r_mult=0;
double field_z_mult=0;
// gradient Coefficients
double grad_I_mult=0;
double grad_rr_mult=0;
double grad_zz_mult=0;
double grad_rzzr_mult=0;
// field change with source heading
double dBdz_grz_rrt_mult = 0;
double dBdz_zzt_mult = 0;
double dBdz_zrt_mult = 0;
double dBdz_I_mult = 0 ;
// gradient Jacobian Coefficients
double gradJacob_zmmz_mult = 0;
double gradJacob_rmmr_mult = 0;
double gradJacob_zrrz_zm_mult = 0;
double gradJacob_zrrz_rm_mult = 0;
double gradJacob_I_zm_mult = 0;
double gradJacob_I_rm_mult = 0;
double gradJacob_zz_zm_mult = 0;
double gradJacob_zz_rm_mult = 0;
double gradJacob_rr_zm_mult = 0;
double gradJacob_rr_rm_mult = 0;
// gradZhatDerJacob
double gradZJacob_I_rm_mult = 0;
double gradZJacob_I_zm_mult = 0;
double gradZJacob_rr_rm_mult = 0;
double gradZJacob_rr_zm_mult = 0;
double gradZJacob_zz_rm_mult = 0;
double gradZJacob_zz_zm_mult = 0;
double gradZJacob_rz_rm_mult = 0;
double gradZJacob_rz_zm_mult = 0;
double gradZJacob_zr_zm_mult = 0;
double gradZJacob_zr_rm_mult = 0;
double gradZJacob_mrrm_mult = 0;
double gradZJacob_mz_mult = 0;
double gradZJacob_zm_mult = 0;
std::vector<srcCoeff>::const_iterator coeffIT;
for( coeffIT = src.A_Coeff.begin();
coeffIT !=src.A_Coeff.end();
coeffIT ++ )
{
double n = coeffIT->order;
double Pn = LegandrePolynomial(cTh, n, 0); // Legandre Polynomial at cos(theta)
double Pn_1 = LegandrePolynomial(cTh, n, 1); // First Derivative of Legandre Polynomial at cos(theta)
double Pn_2 = LegandrePolynomial(cTh, n, 2); // Second Derivative of Legandre Polynomial at cos(theta)
double Pn_3 = LegandrePolynomial(cTh, n, 3); // Third Derivative of Legandre Polynomial at cos(theta)
currentState.value += coeffIT->coeff * std::pow(pMag,n)*Pn;
if( n==0 )
continue;
double c1 = 0;
double c2 = 0;
double c3 = 0;
double c4 = 0;
double tmp = coeffIT->coeff;
if( n > 1 )
tmp *= pow(pMag,n-1);
c2 += tmp;
tmp *= n;
c1 += tmp;
if( n > 1)
{
tmp *= n-1;
c3 += tmp;
if( n > 2)
{
tmp *= n-1;
c4 += tmp;
}
}
// field terms
field_r_mult += c2*cTh*Pn_1-c1*Pn;
field_z_mult -= c2*Pn_1;
// how field changes with source direction
dBdz_grz_rrt_mult += Pn_1*(c1-c2) - cTh*Pn_2*c2;
dBdz_zzt_mult += c2*(Pn_1+cTh*Pn_2);
dBdz_zrt_mult += -1.0*c2*Pn_2;
dBdz_I_mult += -1.0*c2*Pn_1;
// field gradient
if( n > 1 )
{
grad_I_mult += (c2*cTh*Pn_1-c1*Pn);
grad_rr_mult += ((c1-c3)*Pn + (2.0*c1-3.0*c2)*cTh*Pn_1 - c2*cThsq*Pn_2);
grad_zz_mult -= c2*Pn_2;
grad_rzzr_mult += ((c2-c1)*Pn_1+c2*cTh*Pn_2);
}
// how field gradient changes with position
if( n > 2 )
{
gradJacob_zmmz_mult += (c2-c1)*Pn_1+c2*cTh*Pn_2;
gradJacob_rmmr_mult += (c1-c3)*Pn + (2*c1 - 3*c2)*cTh*Pn_1 - c2*cThsq*Pn_2;
gradJacob_zrrz_zm_mult += (2.0*c2-c1)*Pn_2+c2*cTh*Pn_3;
gradJacob_zrrz_rm_mult += (3.0*c1-3.0*c2-c3)*Pn_1 + (2.0*c1-5.0*c2)*cTh*Pn_2 - c2*cThsq*Pn_3;
gradJacob_I_rm_mult += (c1-c3)*Pn+(2.0*c1-3.0*c2)*cTh*Pn_1-c2*cThsq*Pn_2;
gradJacob_I_zm_mult += (c2-c1)*Pn_1+c2*cTh*Pn_2;
gradJacob_zz_zm_mult += -c2*Pn_3;
gradJacob_zz_rm_mult += (2.0*c2-c1)*Pn_2+c2*cTh*Pn_3;
gradJacob_rr_zm_mult += (3.0*c1-3.0*c2-c3)*Pn_1+(2.0*c1-5.0*c2)*cTh*Pn_2-c2*cThsq*Pn_3;
gradJacob_rr_rm_mult += (4.0*c3-3.0*c1-c4)*Pn+(15.0*c2-12.0*c1+3.0*c3)*cTh*Pn_1+(9.0*c2-3.0*c1)*cThsq*Pn_2+c2*cTh*cThsq*Pn_3;
}
// how field gradient changes with source direction
if( n > 1 )
{
gradZJacob_I_rm_mult += (c2 - c1)*Pn_1 + (c2*cTh)*Pn_2;
gradZJacob_I_zm_mult += (-c2)*Pn_2;
gradZJacob_rr_rm_mult += (3*c1 - 3*c2 - c3)*Pn_1 + (2*c1*cTh - 5*c2*cTh)*Pn_2 + (-c2*cThsq)*Pn_3;
gradZJacob_rr_zm_mult += (2*c2 - c1)*Pn_2 + (c2*cTh)*Pn_3;
gradZJacob_zz_rm_mult += (c1 - c2)*Pn_1 + (c1*cTh - 3*c2*cTh)*Pn_2 + (-c2*cThsq)*Pn_3;
gradZJacob_zz_zm_mult += (2*c2)*Pn_2 + (c2*cTh)*Pn_3;
gradZJacob_rz_rm_mult += (3*c2*cTh - 3*c1*cTh + c3*cTh)*Pn_1 + (5*c2*cThsq - 2*c1*cThsq)*Pn_2 + (c2*cTh*cThsq)*Pn_3;
gradZJacob_rz_zm_mult += (c1 - c2)*Pn_1 + (c1*cTh - 3*c2*cTh)*Pn_2 + (-c2*cThsq)*Pn_3;
gradZJacob_zr_rm_mult += (2*c2 - c1)*Pn_2 + (c2*cTh)*Pn_3;
gradZJacob_zr_zm_mult += (-c2)*Pn_3;
gradZJacob_mrrm_mult += (c2 - c1)*Pn_1 + (c2*cTh)*Pn_2;
gradZJacob_mz_mult += (c1*cTh - c2*cTh)*Pn_1 + (-c2*cThsq)*Pn_2;
gradZJacob_zm_mult += (-c2)*Pn_2;
}
}
if( pMag > 0 )
{
for( coeffIT = src.B_Coeff.begin();
coeffIT !=src.B_Coeff.end();
coeffIT ++ )
{
double n = coeffIT->order;
double Pn = LegandrePolynomial(cTh, n, 0); // Legandre Polynomial at cos(theta)
double Pn_1 = LegandrePolynomial(cTh, n, 1); // First Derivative of Legandre Polynomial at cos(theta)
double Pn_2 = LegandrePolynomial(cTh, n, 2); // Second Derivative of Legandre Polynomial at cos(theta)
double Pn_3 = LegandrePolynomial(cTh, n, 3); // Third Derivative of Legandre Polynomial at cos(theta)
currentState.value += coeffIT->coeff * 1.0/std::pow(pMag,n+1.0)*Pn;
double c1 = 0;
double c2 = 0;
double c3 = 0;
double c4 = 0;
double tmp = coeffIT->coeff/pow(pMag,n+2);
c2 += tmp;
tmp *= (n+1);
c1 += -1.0*tmp;
tmp *= n+2;
c3 += tmp;
tmp *= n+2;
c4 += -1.0*tmp;
// field terms
field_r_mult += c2*cTh*Pn_1-c1*Pn;
field_z_mult -= c2*Pn_1;
// how field changes with source direction
dBdz_grz_rrt_mult += Pn_1*(c1-c2) - cTh*Pn_2*c2;
dBdz_zzt_mult += c2*(Pn_1+cTh*Pn_2);
dBdz_zrt_mult += -1.0*c2*Pn_2;
dBdz_I_mult += -1.0*c2*Pn_1;
// field spatial gradient
grad_I_mult += (c2*cTh*Pn_1-c1*Pn);
grad_rr_mult += ((c1-c3)*Pn + (2.0*c1-3.0*c2)*cTh*Pn_1 - c2*cThsq*Pn_2);
grad_zz_mult -= c2*Pn_2;
grad_rzzr_mult += ((c2-c1)*Pn_1+c2*cTh*Pn_2);
// how the field spatial gradient changes with position
gradJacob_zmmz_mult += (c2-c1)*Pn_1+c2*cTh*Pn_2;
gradJacob_rmmr_mult += (c1-c3)*Pn + (2*c1 - 3*c2)*cTh*Pn_1 - c2*cThsq*Pn_2;
gradJacob_zrrz_zm_mult += (2.0*c2-c1)*Pn_2+c2*cTh*Pn_3;
gradJacob_zrrz_rm_mult += (3.0*c1-3.0*c2-c3)*Pn_1 + (2.0*c1-5.0*c2)*cTh*Pn_2 - c2*cThsq*Pn_3;
gradJacob_I_rm_mult += (c1-c3)*Pn+(2.0*c1-3.0*c2)*cTh*Pn_1-c2*cThsq*Pn_2;
gradJacob_I_zm_mult += (c2-c1)*Pn_1+c2*cTh*Pn_2;
gradJacob_zz_zm_mult += -c2*Pn_3;
gradJacob_zz_rm_mult += (2.0*c2-c1)*Pn_2+c2*cTh*Pn_3;
gradJacob_rr_zm_mult += (3.0*c1-3.0*c2-c3)*Pn_1+(2.0*c1-5.0*c2)*cTh*Pn_2-c2*cThsq*Pn_3;
gradJacob_rr_rm_mult += (4.0*c3-3.0*c1-c4)*Pn+(15.0*c2-12.0*c1+3.0*c3)*cTh*Pn_1+(9.0*c2-3.0*c1)*cThsq*Pn_2+c2*cTh*cThsq*Pn_3;
// how the field spatial gradient changes with source direction
gradZJacob_I_rm_mult += (c2 - c1)*Pn_1 + (c2*cTh)*Pn_2;
gradZJacob_I_zm_mult += (-c2)*Pn_2;
gradZJacob_rr_rm_mult += (3*c1 - 3*c2 - c3)*Pn_1 + (2*c1*cTh - 5*c2*cTh)*Pn_2 + (-c2*cThsq)*Pn_3;
gradZJacob_rr_zm_mult += (2*c2 - c1)*Pn_2 + (c2*cTh)*Pn_3;
gradZJacob_zz_rm_mult += (c1 - c2)*Pn_1 + (c1*cTh - 3*c2*cTh)*Pn_2 + (-c2*cThsq)*Pn_3;
gradZJacob_zz_zm_mult += (2*c2)*Pn_2 + (c2*cTh)*Pn_3;
gradZJacob_rz_rm_mult += (3*c2*cTh - 3*c1*cTh + c3*cTh)*Pn_1 + (5*c2*cThsq - 2*c1*cThsq)*Pn_2 + (c2*cTh*cThsq)*Pn_3;
gradZJacob_rz_zm_mult += (c1 - c2)*Pn_1 + (c1*cTh - 3*c2*cTh)*Pn_2 + (-c2*cThsq)*Pn_3;
gradZJacob_zr_rm_mult += (2*c2 - c1)*Pn_2 + (c2*cTh)*Pn_3;
gradZJacob_zr_zm_mult += (-c2)*Pn_3;
gradZJacob_mrrm_mult += (c2 - c1)*Pn_1 + (c2*cTh)*Pn_2;
gradZJacob_mz_mult += (c1*cTh - c2*cTh)*Pn_1 + (-c2*cThsq)*Pn_2;
gradZJacob_zm_mult += (-c2)*Pn_2;
// // The second zHat deritive
// zSqJacob_I_rm_mult += (-c2)*Pn_2;
// zSqJacob_I_zm_mult += c2*Pn_1 + (c2*cTh)*Pn_2;
// zSqJacob_rr_rm_mult += (2*c2 - c1)*Pn_2 + (c2*cTh)*Pn_3;
// zSqJacob_rr_zm_mult += (c1 - c2)*Pn_1 + (c1*cTh - 3*c2*cTh)*Pn_2 + (-c2*cThsq)*Pn_3;
// zSqJacob_zz_rm_mult += c2*Pn_2 + (c2*cTh)*Pn_3;
// zSqJacob_zz_zm_mult += (-2*c2)*Pn_1 + (-4*c2*cTh)*Pn_2 + (-c2*cThsq)*Pn_3;
// zSqJacob_rz_rm_mult += (c1*cTh - 2*c2*cTh)*Pn_2 + (-c2*cThsq)*Pn_3;
// zSqJacob_rz_zm_mult += (2*c2*cTh - 2*c1*cTh)*Pn_1 + (4*c2*cThsq - c1*cThsq)*Pn_2 + (c2*cThsq*cTh)*Pn_3;
// zSqJacob_zr_rm_mult += (-c2)*Pn_3;
// zSqJacob_zr_zm_mult += (2*c2)*Pn_2 + (c2*cTh)*Pn_3;
// zSqJacob_mr_mult += (-c2)*Pn_2;
// zSqJacob_rm_mult += (c1*cTh - c2*cTh)*Pn_1 + (-c2*cThsq)*Pn_2;
// zSqJacob_mz_mult += (c2*cTh)*Pn_2;
// zSqJacob_zm_mult += c2*Pn_1 + (c2*cTh)*Pn_2;
}
}
// calculate field
currentState.firstSpatialDerivative += field_r_mult*p + field_z_mult*z;
// claculate field spatial gradient
Eigen::Matrix3d GradMat = (grad_I_mult/pMag)*I
+(grad_rr_mult/pMag)*(ppt)
+(grad_zz_mult/pMag)*(zzt)
+(grad_rzzr_mult/pMag)*(pzt_zpt);
currentState.secondSpatialDerivative +=GradMat;
currentState.firstSpatialDerivative_SourcePositionDerivative.push_back(-GradMat);
// calculate how field changes with source direction
currentState.firstSpatialDerivative_SourceHeadingDerivative.push_back( dBdz_grz_rrt_mult*(cTh*rzt-ppt)
+ dBdz_zzt_mult*zzt
+ dBdz_zrt_mult*zrt
+ dBdz_I_mult *I );
// initialze terms for 3rd Derivatives
Eigen::Matrix3d rmt = p*X.transpose();
Eigen::Matrix3d mrt = X*p.transpose();
Eigen::Matrix3d rm_mr = rmt + mrt;
Eigen::Matrix3d mzt = X*z.transpose();
Eigen::Matrix3d zmt = z*X.transpose();
Eigen::Matrix3d zm_mz = zmt+mzt;
double r_dot_m = p(0);
double z_dot_m = z(0);
Eigen::Matrix<double,5,3> gradientSpatialDer;
Eigen::Matrix<double,5,3> gradientHeadingDer;
Eigen::Matrix<double,9,3> fieldHedingSecDer; fieldHedingSecDer.setZero(9,3);
// calculate how the field spatial Derivative changes with position (first 3 rows)
gradientSpatialDer.topRows<3>() = zm_mz*(gradJacob_zmmz_mult/pMagSq)
+rm_mr*(gradJacob_rmmr_mult/pMagSq)
+pzt_zpt*((gradJacob_zrrz_zm_mult*z_dot_m+gradJacob_zrrz_rm_mult*r_dot_m)/pMagSq)
+I*((gradJacob_I_zm_mult*z_dot_m+gradJacob_I_rm_mult*r_dot_m)/pMagSq)
+zzt*((gradJacob_zz_rm_mult*r_dot_m + gradJacob_zz_zm_mult*z_dot_m)/pMagSq)
+ppt*((gradJacob_rr_rm_mult*r_dot_m + gradJacob_rr_zm_mult*z_dot_m)/pMagSq);
// calculate how the field spatial Derivative changes with source direction (first 3 rows)
gradientHeadingDer.topRows<3>() = I*((gradZJacob_I_rm_mult*r_dot_m+gradZJacob_I_zm_mult*z_dot_m)/pMag)
+ppt*((gradZJacob_rr_rm_mult*r_dot_m+gradZJacob_rr_zm_mult*z_dot_m)/pMag)
+zzt*((gradZJacob_zz_rm_mult*r_dot_m+gradZJacob_zz_zm_mult*z_dot_m)/pMag)
+rzt*((gradZJacob_rz_rm_mult*r_dot_m+gradZJacob_rz_zm_mult*z_dot_m)/pMag)
+zrt*((gradZJacob_zr_rm_mult*r_dot_m+gradZJacob_zr_zm_mult*z_dot_m)/pMag)
+(rm_mr)*((gradZJacob_mrrm_mult)/pMag)
+zmt*((gradZJacob_zm_mult)/pMag)
+mzt*((gradZJacob_mz_mult)/pMag);
// fieldHedingSecDer.topRows<3>() = I*((zSqJacob_I_rm_mult*r_dot_m+zSqJacob_I_zm_mult*z_dot_m))
// +ppt*((zSqJacob_rr_rm_mult*r_dot_m+zSqJacob_rr_zm_mult*z_dot_m))
// +zzt*((zSqJacob_zz_rm_mult*r_dot_m+zSqJacob_zz_zm_mult*z_dot_m))
// +rzt*((zSqJacob_rz_rm_mult*r_dot_m+zSqJacob_rz_zm_mult*z_dot_m))
// +zrt*((zSqJacob_zr_rm_mult*r_dot_m+zSqJacob_zr_zm_mult*z_dot_m))
// +mrt*(zSqJacob_mr_mult) + rmt*(zSqJacob_rm_mult)
// +zmt*((zSqJacob_zm_mult))
// +mzt*((zSqJacob_mz_mult));
// Y Component Time
rmt = p*Y.transpose();
mrt = Y*p.transpose();
rm_mr = rmt+mrt;
mzt = Y*z.transpose();
zmt = z*Y.transpose();
zm_mz = zmt+mzt;
r_dot_m = p(1);
z_dot_m = z(1);
// calculate how the field spatial Derivative changes with position (last 2 rows)
gradientSpatialDer.bottomRows<2>() = zm_mz.bottomRows<2>()*(gradJacob_zmmz_mult/pMagSq)
+rm_mr.bottomRows<2>()*(gradJacob_rmmr_mult/pMagSq)
+pzt_zpt.bottomRows<2>()*((gradJacob_zrrz_zm_mult*z_dot_m+gradJacob_zrrz_rm_mult*r_dot_m)/pMagSq)
+I.bottomRows<2>()*((gradJacob_I_zm_mult*z_dot_m+gradJacob_I_rm_mult*r_dot_m)/pMagSq)
+zzt.bottomRows<2>()*((gradJacob_zz_rm_mult*r_dot_m + gradJacob_zz_zm_mult*z_dot_m)/pMagSq)
+ppt.bottomRows<2>()*((gradJacob_rr_rm_mult*r_dot_m + gradJacob_rr_zm_mult*z_dot_m)/pMagSq);
// calculate how the field spatial Derivative changes with source direction (last 2 rows)
gradientHeadingDer.bottomRows<2>() = I.bottomRows<2>()*((gradZJacob_I_rm_mult* r_dot_m+gradZJacob_I_zm_mult* z_dot_m)/pMag)
+ppt.bottomRows<2>()*((gradZJacob_rr_rm_mult*r_dot_m+gradZJacob_rr_zm_mult*z_dot_m)/pMag)
+zzt.bottomRows<2>()*((gradZJacob_zz_rm_mult*r_dot_m+gradZJacob_zz_zm_mult*z_dot_m)/pMag)
+rzt.bottomRows<2>()*((gradZJacob_rz_rm_mult*r_dot_m+gradZJacob_rz_zm_mult*z_dot_m)/pMag)
+zrt.bottomRows<2>()*((gradZJacob_zr_rm_mult*r_dot_m+gradZJacob_zr_zm_mult*z_dot_m)/pMag)
+(rm_mr).bottomRows<2>()*((gradZJacob_mrrm_mult)/pMag)
+zmt.bottomRows<2>()*((gradZJacob_zm_mult)/pMag)
+mzt.bottomRows<2>()*((gradZJacob_mz_mult)/pMag);
// fieldHedingSecDer.block<3,3>(3,0) = I*((zSqJacob_I_rm_mult*r_dot_m+zSqJacob_I_zm_mult*z_dot_m))
// +ppt*((zSqJacob_rr_rm_mult*r_dot_m+zSqJacob_rr_zm_mult*z_dot_m))
// +zzt*((zSqJacob_zz_rm_mult*r_dot_m+zSqJacob_zz_zm_mult*z_dot_m))
// +rzt*((zSqJacob_rz_rm_mult*r_dot_m+zSqJacob_rz_zm_mult*z_dot_m))
// +zrt*((zSqJacob_zr_rm_mult*r_dot_m+zSqJacob_zr_zm_mult*z_dot_m))
// +mrt*(zSqJacob_mr_mult) + rmt*(zSqJacob_rm_mult)
// +zmt*((zSqJacob_zm_mult))
// +mzt*((zSqJacob_mz_mult));
// Eigen::Vector3d Z(0,0,1);
// rmt = p*Z.transpose();
// mrt = Z*p.transpose();
// zmt = z*Z.transpose();
// mzt = Z*z.transpose();
// r_dot_m = p(2);
// z_dot_m = z(2);
// fieldHedingSecDer.bottomRows<3>() = I*((zSqJacob_I_rm_mult*r_dot_m+zSqJacob_I_zm_mult*z_dot_m))
// +ppt*((zSqJacob_rr_rm_mult*r_dot_m+zSqJacob_rr_zm_mult*z_dot_m))
// +zzt*((zSqJacob_zz_rm_mult*r_dot_m+zSqJacob_zz_zm_mult*z_dot_m))
// +rzt*((zSqJacob_rz_rm_mult*r_dot_m+zSqJacob_rz_zm_mult*z_dot_m))
// +zrt*((zSqJacob_zr_rm_mult*r_dot_m+zSqJacob_zr_zm_mult*z_dot_m))
// +mrt*(zSqJacob_mr_mult) + rmt*(zSqJacob_rm_mult)
// +zmt*((zSqJacob_zm_mult))
// +mzt*((zSqJacob_mz_mult));
currentState.thirdSpatialDerivative += gradientSpatialDer;
currentState.secondSpatialDerivative_SourcePositionDerivative.push_back(gradientSpatialDer);
currentState.secondSpatialDerivative_SourceHeadingDerivative.push_back(-gradientHeadingDer);
// currentState.firstSpatialDerivative_secondSourceHeadingDerivative.push_back(fieldHedingSecDer);
return ;
}
// This fuction returns the field coeffient Derivatives and direction Derivatives assuming a current of 1 at the position specified in the work space
ScalorPotentialCalibrationJacobians ScalorPotential::srcCalibrationInformation(const Eigen::Vector3d& position, unsigned int srcNum ) const
{
assert( srcNum < srcList.size() );
ScalorPotentialCalibrationJacobians currentStateJacob;
// Use forward function to get data for B, dBdps, and dBdzs
ScalorPotentialState currentState;
srcFieldGradient(position, srcList[srcNum], currentState );
currentStateJacob.firstSpatialDerivative = currentState.firstSpatialDerivative;
currentStateJacob.firstSpatialDerivative_SourcePositionDerivative = currentState.firstSpatialDerivative_SourcePositionDerivative.front();
currentStateJacob.firstSpatialDerivative_SourceHeadingDerivative = currentState.firstSpatialDerivative_SourceHeadingDerivative.front();
currentStateJacob.secondSpatialDerivative_SourceHeadingDerivative = currentState.secondSpatialDerivative_SourceHeadingDerivative.front();
currentStateJacob.secondSpatialDerivative_SourcePositionDerivative = currentState.secondSpatialDerivative_SourcePositionDerivative.front();
// Zero out other coefficients
currentStateJacob.firstSpatialDerivative_A_CoeffDerivative.setZero(3,srcList[srcNum].A_Coeff.size());
currentStateJacob.firstSpatialDerivative_B_CoeffDerivative.setZero(3,srcList[srcNum].B_Coeff.size());
currentStateJacob.firstSpatialDerivative_dA_dHeading.setZero(9,srcList[srcNum].A_Coeff.size());
currentStateJacob.firstSpatialDerivative_dB_dHeading.setZero(9,srcList[srcNum].B_Coeff.size());
currentStateJacob.firstSpatialDerivative_dA_dPosition.setZero(9,srcList[srcNum].A_Coeff.size());
currentStateJacob.firstSpatialDerivative_dB_dPosition.setZero(9,srcList[srcNum].B_Coeff.size());
Eigen::Vector3d p(position - srcList[srcNum].srcPosition);
Eigen::Vector3d z(srcList[srcNum].srcDirection.normalized());
double pMag = p.norm();
if( pMag > 0 )
{
p/=pMag;
}
// define Cosine Theta
double cTh = p.dot(z);
double cThsq = cTh*cTh;
Eigen::Matrix3d pzt_zpt( p*z.transpose()+z*p.transpose() );
Eigen::Matrix3d ppt( p*p.transpose() );// = p*p.transpose(); // p*p'
Eigen::Matrix3d zzt(z *z.transpose() );// = src.srcDirection *src.srcDirection.transpose(); // z*z'
Eigen::Matrix3d rzt = p*z.transpose();
Eigen::Matrix3d zrt = z*p.transpose();
// some constant vectors and matricies
Eigen::Matrix3d I(Eigen::Matrix3d::Identity());
std::vector<srcCoeff>::const_iterator coeffIT;
int colNum = 0;
// The second zHat deritive
double zSqJacob_I_rm_mult = 0;
double zSqJacob_I_zm_mult = 0;
double zSqJacob_rr_rm_mult = 0;
double zSqJacob_rr_zm_mult = 0;
double zSqJacob_zz_rm_mult = 0;
double zSqJacob_zz_zm_mult = 0;
double zSqJacob_rz_rm_mult = 0;
double zSqJacob_rz_zm_mult = 0;
double zSqJacob_zr_rm_mult = 0;
double zSqJacob_zr_zm_mult = 0;
double zSqJacob_mr_mult = 0;
double zSqJacob_rm_mult = 0;
double zSqJacob_mz_mult = 0;
double zSqJacob_zm_mult = 0;
for( coeffIT = srcList[srcNum].A_Coeff.begin();
coeffIT !=srcList[srcNum].A_Coeff.end();
coeffIT ++ )
{
double n = coeffIT->order;
currentState.value += coeffIT->coeff * std::pow(pMag,n);
if( n==0 )
{
colNum ++;
continue;
}
double Pn = LegandrePolynomial(cTh, n, 0); // Legandre Polynomial at cos(theta)
double Pn_1 = LegandrePolynomial(cTh, n, 1); // First Derivative of Legandre Polynomial at cos(theta)
double Pn_2 = LegandrePolynomial(cTh, n, 2); // Second Derivative of Legandre Polynomial at cos(theta)
double Pn_3 = LegandrePolynomial(cTh, n, 3); // Second Derivative of Legandre Polynomial at cos(theta)
double c1 = 0;
double c2 = 0;
double c3 = 0;
double tmp = 1;
if( n > 1 )
tmp *= pow(pMag,n-1);
c2 += tmp;
tmp *= n;
c1 += tmp;
if( n > 1)
{
tmp *= n-1;
c3 += tmp;
}
// field terms
double field_r_mult = c2*cTh*Pn_1-c1*Pn;
double field_z_mult = -c2*Pn_1;
currentStateJacob.firstSpatialDerivative_A_CoeffDerivative.col(colNum) = field_r_mult*p + field_z_mult*z;
// how field changes with source direction
double dBdz_grz_rrt_mult = Pn_1*(c1-c2) - cTh*Pn_2*c2;
double dBdz_zzt_mult = c2*(Pn_1+cTh*Pn_2);
double dBdz_zrt_mult = -1.0*c2*Pn_2;
double dBdz_I_mult = -1.0*c2*Pn_1;
// field gradient
double grad_I_mult = (c2*cTh*Pn_1-c1*Pn);
double grad_rr_mult = ((c1-c3)*Pn + (2.0*c1-3.0*c2)*cTh*Pn_1 - c2*cThsq*Pn_2);
double grad_zz_mult = -c2*Pn_2;
double grad_rzzr_mult = ((c2-c1)*Pn_1+c2*cTh*Pn_2);
// claculate field spatial gradient
Eigen::Matrix3d GradMat = -1*((grad_I_mult/pMag)*I
+(grad_rr_mult/pMag)*(ppt)
+(grad_zz_mult/pMag)*(zzt)
+(grad_rzzr_mult/pMag)*(pzt_zpt));
Eigen::Matrix3d HeadMat = dBdz_grz_rrt_mult*(cTh*rzt-ppt)
+ dBdz_zzt_mult*zzt
+ dBdz_zrt_mult*zrt
+ dBdz_I_mult *I;
// this is needed because we actually want d(B'X)/dAdHeading
//HeadMat.transposeInPlace();
for( int i=0; i<3; i++ )
{
currentStateJacob.firstSpatialDerivative_dA_dPosition.block<3,1>(i*3,colNum) = GradMat.transpose().col(i);
currentStateJacob.firstSpatialDerivative_dA_dHeading.block<3,1>(i*3,colNum) = HeadMat.col(i);
}
// The second zHat deritive
c1 *= coeffIT->coeff;
c2 *= coeffIT->coeff;
c3 *= coeffIT->coeff;
zSqJacob_I_rm_mult += ((-c2)*Pn_2);
zSqJacob_I_zm_mult += c2*Pn_1 + (c2*cTh)*Pn_2;
zSqJacob_rr_rm_mult += (2*c2 - c1)*Pn_2 + (c2*cTh)*Pn_3;
zSqJacob_rr_zm_mult += (c1 - c2)*Pn_1 + (c1*cTh - 3*c2*cTh)*Pn_2 + (-c2*cThsq)*Pn_3;
zSqJacob_zz_rm_mult += c2*Pn_2 + (c2*cTh)*Pn_3;
zSqJacob_zz_zm_mult += (-2*c2)*Pn_1 + (-4*c2*cTh)*Pn_2 + (-c2*cThsq)*Pn_3;
zSqJacob_rz_rm_mult += (c1*cTh - 2*c2*cTh)*Pn_2 + (-c2*cThsq)*Pn_3;
zSqJacob_rz_zm_mult += (2*c2*cTh - 2*c1*cTh)*Pn_1 + (4*c2*cThsq - c1*cThsq)*Pn_2 + (c2*cThsq*cTh)*Pn_3;
zSqJacob_zr_rm_mult += (-c2)*Pn_3;
zSqJacob_zr_zm_mult += (2*c2)*Pn_2 + (c2*cTh)*Pn_3;
zSqJacob_mr_mult += (-c2)*Pn_2;
zSqJacob_rm_mult += (c1*cTh - c2*cTh)*Pn_1 + (-c2*cThsq)*Pn_2;
zSqJacob_mz_mult += (c2*cTh)*Pn_2;