chicken-lapack

Chicken Scheme bindings for the LAPACK and ATLAS libraries.

ATLAS (http://math-atlas.sourceforge.net) stands for Automatically Tuned Linear Algebra Software. Its purpose is to provide portably optimal linear algebra routines. The current version provides a complete BLAS (http://www.netlib.org/blas) API (for both C and Fortran77), and a small subset of the LAPACK (http://www.netlib.org/lapack) API.

Naming conventions for routines

Every routine in the LAPACK library comes in four flavors, each prefixed by the letters S, D, C, and Z, respectively. Each letter indicates the format of input data:

• S stands for single-precision (32-bit IEEE floating point numbers),
• D stands for double-precision (64-bit IEEE floating point numbers),
• C stands for complex numbers (represented by pairs of 32-bit IEEE floating point numbers),
• Z stands for double complex numbers (represented by pairs of 64-bit IEEE floating point numbers)

In addition, each ATLAS-LAPACK routine in this egg comes in three flavors:

• Safe, pure: safe routines check the sizes of their input arguments. For example, if a routine is supplied arguments that indicate that an input matrix is of dimensions M-by-N, then the argument corresponding to that matrix is checked that it is of size M * N. ''Pure'' routines do not alter their arguments in any way. A new matrix or vector is allocated for the return value of the routine.
• Safe, destructive (suffix: !): safe routines check the sizes of their input arguments. For example, if a routine is supplied arguments that indicate that an input matrix is of dimensions M-by-N, then the argument corresponding to that matrix is checked that it is of size M * N. Destructive routines can modify some or all of their arguments. They are given names ending in exclamation mark. The matrix factorization routines in LAPACK overwrite the input matrix argument with the result of the factorization, and the linear system solvers overwrite the right-hand side vector with the system solution. Please consult the LAPACK documentation to determine which functions modify their input arguments.
• Unsafe, destructive (prefix: unsafe-:, suffix: !). Unsafe routines do not check the sizes of their input arguments. They invoke the corresponding ATLAS-LAPACK routines directly. Unsafe routines do not have pure variants.

For example, function xGESV (N-by-N linear system solver) comes in the following variants:

LAPACK name	Safe, pure	Safe, destructive	Unsafe, destructive
SGESV	sgesv	sgesv!	unsafe-sgesv!
DGESV	dgesv	dgesv!	unsafe-dgesv!
CGESV	cgesv	cgesv!	unsafe-cgesv!
ZGESV	zgesv	zgesv!	unsafe-zgesv!

LAPACK datatype conventions

The datatype constructors described below are defined in the blas library. The blas library must be loaded before using any of the routines in this library.

Argument ORDER is one of RowMajor or ColMajor to indicate that the input and output matrices are in row-major or column-major form, respectively.

Where present, argument TRANS can be one of NoTrans or Trans to indicate whether the input matrix is to be transposed or not.

Where present, argument UPLO can be one of Upper or Lower to indicate whether the upper or lower triangular part of an input symmetric matrix is to referenced,or to specify the type of an input triangular matrix.

Where present, argument DIAG can be one of NonUnit or Unit to indicate whether an input triangular matrix is unit triangular or not.

LAPACK driver routines

General linear system solving

• sgesv:: ORDER * N * NRHS * A * B * [LDA] * [LDB] -> F32VECTOR * F32VECTOR * S32VECTOR
• dgesv:: ORDER * N * NRHS * A * B * [LDA] * [LDB] -> F64VECTOR * F64VECTOR * S32VECTOR

• cgesv:: ORDER * N * NRHS * A * B * [LDA] * [LDB] -> F32VECTOR * F32VECTOR * S32VECTOR

• zgesv:: ORDER * N * NRHS * A * B * [LDA] * [LDB] -> F64VECTOR * F64VECTOR * S32VECTOR

The routines compute the solution to a system of linear equations A

• X = B, where A is an N-by-N matrix and X and B are N-by-NRHS matrices. Optional arguments LDA and LDB are the leading dimensions of arrays A and B, respectively. LU decomposition with partial pivoting and row interchanges is used to factor A as A = P * L * U, where P is a permutation matrix, L is unit lower triangular, and U is upper triangular. The factored form of A is then used to solve the system. The return values are:

• a matrix containing the factors L and U from the factorization A = PLU;

• the N-by-NRHS solution matrix X

• a vector with pivot indices: for 1 <= i <= min(M,N), row i of the matrix A was interchanged with row pivot(i)

Symmetric positive definite linear system solving

sposv:: ORDER * UPLO * N * NRHS * A * B * [LDA] * [LDB] -> F32VECTOR * F32VECTOR

dposv:: ORDER * UPLO * N * NRHS * A * B * [LDA] * [LDB] -> F64VECTOR * F64VECTOR

cposv:: ORDER * UPLO * N * NRHS * A * B * [LDA] * [LDB] -> F32VECTOR * F32VECTOR

zposv:: ORDER * UPLO * N * NRHS * A * B * [LDA] * [LDB] -> F64VECTOR * F64VECTOR

The routines compute the solution to a system of linear equations A * X = B, where A is an N-by-N symmetric positive definite matrix and X and B are N-by-NRHS matrices. Optional arguments LDA and LDB are the leading dimensions of arrays A and B, respectively. Cholesky decomposition is used to factor A as * A = U**T * U if UPLO = 'Upper'

• A = L * L**T if UPLO = 'Lower' where U is an upper triangular, and L is a lower triangular matrix. The factored form of A is then used to solve the system. The return values are:

the factor U or Lfrom the Cholesky factorization, depending on the value of argument UPLO.

the N-by-NRHS solution matrix X

LAPACK computational routines

General matrix factorization

sgetrf:: ORDER * M * N * A * [LDA] -> F32VECTOR * S32VECTOR

dgetrf:: ORDER * M * N * A * [LDA] -> F64VECTOR * S32VECTOR

cgetrf:: ORDER * M * N * A * [LDA] -> F32VECTOR * S32VECTOR

zgetrf:: ORDER * M * N * A * [LDA] -> F64VECTOR * S32VECTOR

These routines compute an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges. Optional argument LDA is the leading dimension of array A. The return values are:

• a matrix containing the factors L and U from the factorization A = PLU;
• a vector with pivot indices: for 1 <= i <= min(M,N), row i of the matrix was interchanged with row pivot(i)

General linear system solving using factorization

sgetrs:: ORDER * TRANSPOSE * N * NRHS * A * B * [LDA] * [LDB] -> F32VECTOR

dgetrs:: ORDER * TRANSPOSE * N * NRHS * A * B * [LDA] * [LDB] -> F64VECTOR

cgetrs:: ORDER * TRANSPOSE * N * NRHS * A * B * [LDA] * [LDB] -> F32VECTOR

zgetrs:: ORDER * TRANSPOSE * N * NRHS * A * B * [LDA] * [LDB] -> F64VECTOR

These routines solve a system of linear equations A * X = B or A' * X = B with a general N-by-N matrix A using the LU factorization computed by the xGETRF routines. Argument NRHS is the number of right-hand sides (i.e. number of columns in B). Optional arguments LDA and LDB are the leading dimensions of arrays A and B, respectively. The return value is the solution matrix X.

General matrix invert using factorization

sgetri:: ORDER * N * A * PIVOT * [LDA] -> F32VECTOR

dgetri:: ORDER * N * A * PIVOT * [LDA] -> F64VECTOR

cgetri:: ORDER * N * A * PIVOT * [LDA] -> F32VECTOR

zgetri:: ORDER * N * A * PIVOT * [LDA] -> F64VECTOR

These routines compute the inverse of a matrix using the LU factorization computed by the xGETRF routines. Argument A must contain the factors L and U from the LU factorization computed by xGETRF. Argument PIVOT must be the pivot vector returned by the factorization routine. Optional argument LDA is the leading dimension of array A. The return value is the inverse of the original matrix A.

Symmetric positive definite matrix factorization

spotrf:: ORDER * UPLO * N * A * [LDA] -> F32VECTOR

dpotrf:: ORDER * UPLO * N * A * [LDA] -> F64VECTOR

cpotrf:: ORDER * UPLO * N * A * [LDA] -> F32VECTOR

zpotrf:: ORDER * UPLO * N * A * [LDA] -> F64VECTOR

These routines compute the Cholesky factorization of a symmetric positive definite matrix A. The factorization has the form:

• A = U**T * U if UPLO = 'Upper'
• A = L * L**T if UPLO = 'Lower'

where U is an upper triangular, and L is a lower triangular matrix. Optional argument LDA is the leading dimension of array A. The return value is the factor U or Lfrom the Cholesky factorization, depending on the value of argument UPLO.

Symmetric positive definite matrix solving using factorization

spotrs:: ORDER * UPLO * N * NRHS * A * B * [LDA] * [LDB] -> F32VECTOR

dpotrs:: ORDER * UPLO * N * NRHS * A * B * [LDA] * [LDB] -> F64VECTOR

cpotrs:: ORDER * UPLO * N * NRHS * A * B * [LDA] * [LDB] -> F32VECTOR

zpotrs:: ORDER * UPLO * N * NRHS * A * B * [LDA] * [LDB] -> F64VECTOR

These routines solve a system of linear equations A * X = B with a symmetric positive definite matrix A using the Cholesky factorization computed by the xPOTRF routines. Argument A is the triangular factor U or L as computed by xPOTRF. Argument NRHS is the number of right-hand sides (i.e. number of columns in B). Argument UPLO indicates whether upper or lower triangle of A is stored ('Upper' or 'Lower'). Optional arguments LDA and LDB are the leading dimensions of arrays A and B, respectively. The return value is the solution matrix X.

Symmetric positive definite matrix invert using factorization

spotri:: ORDER * UPLO * N * A * [LDA] -> F32VECTOR

dpotri:: ORDER * UPLO * N * A * [LDA] -> F64VECTOR

cpotri:: ORDER * UPLO * N * A * [LDA] -> F32VECTOR

zpotri:: ORDER * UPLO * N * A * [LDA] -> F64VECTOR

These routines compute the inverse of a symmetric positive definite matrix A using the Cholesky factorization A = UTU or A = LLT computed by xPOTRF. Argument A is the triangular factor U or L as computed by xPOTRF. Argument UPLO indicates whether upper or lower triangle of A is stored ('Upper' or 'Lower'). Optional argument LDA is the leading dimension of array A. The return value is the upper or lower triangle of the inverse of A.

Triangular matrix invert

strtri:: ORDER * UPLO * DIAG * N * A * [LDA] -> F32VECTOR

dtrtri:: ORDER * UPLO * DIAG * N * A * [LDA] -> F64VECTOR

ctrtri:: ORDER * UPLO * DIAG * N * A * [LDA] -> F32VECTOR

ztrtri:: ORDER * UPLO * DIAG * N * A * [LDA] -> F64VECTOR

These routines compute the inverse of a triangular matrix A. Argument A is the triangular factor U or L as computed by xPOTRF. Argument UPLO indicates whether upper or lower triangle of A is stored ('Upper' or 'Lower'). Argument DIAG indicates whether A is non-unit triangular or unit triangular ('NonUnit' or 'Unit'). Optional argument LDA is the leading dimension of array A. The return value is the triangular inverse of the input matrix, in the same storage format.

Auxilliary routines

slauum:: ORDER * UPLO * DIAG * N * A * [LDA] -> F32VECTOR

dlauum:: ORDER * UPLO * DIAG * N * A * [LDA] -> F64VECTOR

clauum:: ORDER * UPLO * DIAG * N * A * [LDA] -> F32VECTOR

zlauum:: ORDER * UPLO * DIAG * N * A * [LDA] -> F64VECTOR

These routines compute the product U * U' or L' * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A. Argument UPLO indicates whether upper or lower triangle of A is stored ('Upper' or Lower'). Optional argument LDA is the leading dimension of array A. The return value is the lower triangle of the lower triangular product, or the upper triangle of upper triangular product, in the respective storage format.

Examples

 (use srfi-4 blas atlas-lapack)
 
 (define order ColMajor)
 (define n 4)
 (define nrhs 1)
 
 ;; Solve the equations
 ;;
 ;; Ax = b,
 ;;
 ;; where A is the general matrix
 
 ;; column-major order
 (define A (f64vector 1.8   5.25   1.58 -1.11  
 		     2.88  -2.95 -2.69 -0.66 
 		     2.05  -0.95 -2.90 -0.59 
 		     -0.89 -3.80 -1.04  0.80))
 ;;
 ;; and b is
 ;;
 (define b (f64vector 9.52 24.35 0.77 -6.22))
 
 ;; A and b are not modified
 (define-values (LU x piv) (dgesv order n nrhs A b))
 
 ;; A is overwritten with its LU decomposition, and 
 ;; b is overwritten with the solution of the system
 (dgesv! order n nrhs A b)

Version history

3.0 : Using bind instead of easyffi 2.1 : Ensure that unit test script exists with a non-zero exit status on error (thanks to mario) 2.0 : Eliminated reduntant atlas-lapack: prefix from names of exported symbols

Requirements

• blas

License

Copyright 2007-2015 Ivan Raikov, Jeremy Steward

This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

A full copy of the GPL license can be found at http://www.gnu.org/licenses/.