/usr/include/af/lapack.h is in libarrayfire-dev 3.3.2+dfsg1-4ubuntu1.
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* Copyright (c) 2014, ArrayFire
* All rights reserved.
*
* This file is distributed under 3-clause BSD license.
* The complete license agreement can be obtained at:
* http://arrayfire.com/licenses/BSD-3-Clause
********************************************************/
#pragma once
#include <af/array.h>
#include <af/defines.h>
#ifdef __cplusplus
namespace af
{
#if AF_API_VERSION >= 31
/**
C++ Interface for SVD decomposition
\param[out] u is the output array containing U
\param[out] s is the output array containing the diagonal values of sigma, (singular values of the input matrix))
\param[out] vt is the output array containing V^H
\param[in] in is the input matrix
\ingroup lapack_factor_func_svd
*/
AFAPI void svd(array &u, array &s, array &vt, const array &in);
#endif
#if AF_API_VERSION >= 31
/**
C++ Interface for SVD decomposition
\param[out] u is the output array containing U
\param[out] s is the output array containing the diagonal values of sigma, (singular values of the input matrix))
\param[out] vt is the output array containing V^H
\param[inout] in is the input matrix and will contain random data after this operation
\ingroup lapack_factor_func_svd
*/
AFAPI void svdInPlace(array &u, array &s, array &vt, array &in);
#endif
/**
C++ Interface for LU decomposition in packed format
\param[out] out is the output array containing the packed LU decomposition
\param[out] pivot will contain the permutation indices to map the input to the decomposition
\param[in] in is the input matrix
\param[in] is_lapack_piv specifies if the pivot is returned in original LAPACK compliant format
\note This function is not supported in GFOR
\ingroup lapack_factor_func_lu
*/
AFAPI void lu(array &out, array &pivot, const array &in, const bool is_lapack_piv=true);
/**
C++ Interface for LU decomposition
\param[out] lower will contain the lower triangular matrix of the LU decomposition
\param[out] upper will contain the upper triangular matrix of the LU decomposition
\param[out] pivot will contain the permutation indices to map the input to the decomposition
\param[in] in is the input matrix
\note This function is not supported in GFOR
\ingroup lapack_factor_func_lu
*/
AFAPI void lu(array &lower, array &upper, array &pivot, const array &in);
/**
C++ Interface for in place LU decomposition
\param[out] pivot will contain the permutation indices to map the input to the decomposition
\param[inout] in contains the input on entry, the packed LU decomposition on exit
\param[in] is_lapack_piv specifies if the pivot is returned in original LAPACK compliant format
\note This function is not supported in GFOR
\ingroup lapack_factor_func_lu
*/
AFAPI void luInPlace(array &pivot, array &in, const bool is_lapack_piv=true);
/**
C++ Interface for QR decomposition in packed format
\param[out] out is the output array containing the packed QR decomposition
\param[out] tau will contain additional information needed for unpacking the data
\param[in] in is the input matrix
\note This function is not supported in GFOR
\ingroup lapack_factor_func_qr
*/
AFAPI void qr(array &out, array &tau, const array &in);
/**
C++ Interface for QR decomposition
\param[out] q is the orthogonal matrix from QR decomposition
\param[out] r is the upper triangular matrix from QR decomposition
\param[out] tau will contain additional information needed for solving a least squares problem using \p q and \p r
\param[in] in is the input matrix
\note This function is not supported in GFOR
\ingroup lapack_factor_func_qr
*/
AFAPI void qr(array &q, array &r, array &tau, const array &in);
/**
C++ Interface for QR decomposition
\param[out] tau will contain additional information needed for unpacking the data
\param[inout] in is the input matrix on entry. It contains packed QR decomposition on exit
\note This function is not supported in GFOR
\ingroup lapack_factor_func_qr
*/
AFAPI void qrInPlace(array &tau, array &in);
/**
C++ Interface for cholesky decomposition
\param[out] out contains the triangular matrix. Multiply \p out with its conjugate transpose reproduces the input \p in.
\param[in] in is the input matrix
\param[in] is_upper a boolean determining if \p out is upper or lower triangular
\returns \p 0 if cholesky decomposition passes, if not it returns the rank at which the decomposition failed.
\note The input matrix \b has to be a positive definite matrix, if it is not zero, the cholesky decomposition functions return a non-zero output.
\note This function is not supported in GFOR
\ingroup lapack_factor_func_cholesky
*/
AFAPI int cholesky(array &out, const array &in, const bool is_upper = true);
/**
C++ Interface for in place cholesky decomposition
\param[inout] in is the input matrix on entry. It contains the triangular matrix on exit.
\param[in] is_upper a boolean determining if \p in is upper or lower triangular
\returns \p 0 if cholesky decomposition passes, if not it returns the rank at which the decomposition failed.
\note The input matrix \b has to be a positive definite matrix, if it is not zero, the cholesky decomposition functions return a non-zero output.
\note This function is not supported in GFOR
\ingroup lapack_factor_func_cholesky
*/
AFAPI int choleskyInPlace(array &in, const bool is_upper = true);
/**
C++ Interface for solving a system of equations
\param[in] a is the coefficient matrix
\param[in] b is the measured values
\param[in] options determining various properties of matrix \p a
\returns \p x, the matrix of unknown variables
\note \p options needs to be one of \ref AF_MAT_NONE, \ref AF_MAT_LOWER or \ref AF_MAT_UPPER
\note This function is not supported in GFOR
\ingroup lapack_solve_func_gen
*/
AFAPI array solve(const array &a, const array &b, const matProp options = AF_MAT_NONE);
/**
C++ Interface for solving a system of equations
\param[in] a is the output matrix from packed LU decomposition of the coefficient matrix
\param[in] piv is the pivot array from packed LU decomposition of the coefficient matrix
\param[in] b is the matrix of measured values
\param[in] options determining various properties of matrix \p a
\returns \p x, the matrix of unknown variables
\ingroup lapack_solve_lu_func_gen
\note \p options currently needs to be \ref AF_MAT_NONE
\note This function is not supported in GFOR
*/
AFAPI array solveLU(const array &a, const array &piv,
const array &b, const matProp options = AF_MAT_NONE);
/**
C++ Interface for inverting a matrix
\param[in] in is input matrix
\param[in] options determining various properties of matrix \p in
\returns \p x, the inverse of the input matrix
\note \p options currently needs to be \ref AF_MAT_NONE
\note This function is not supported in GFOR
\ingroup lapack_ops_func_inv
*/
AFAPI array inverse(const array &in, const matProp options = AF_MAT_NONE);
/**
C++ Interface for finding the rank of a matrix
\param[in] in is input matrix
\param[in] tol is the tolerance value
\returns the rank of the matrix
\ingroup lapack_ops_func_rank
*/
AFAPI unsigned rank(const array &in, const double tol=1E-5);
/**
C++ Interface for finding the determinant of a matrix
\param[in] in is input matrix
\returns the determinant of the matrix
\ingroup lapack_ops_func_det
*/
template<typename T> T det(const array &in);
/**
C++ Interface for norm of a matrix
\param[in] in is the input matrix
\param[in] type specifies the \ref af::normType. Default: \ref AF_NORM_VECTOR_1
\param[in] p specifies the value of P when \p type is one of \ref AF_NORM_VECTOR_P, AF_NORM_MATRIX_L_PQ is used. It is ignored for other values of \p type
\param[in] q specifies the value of Q when \p type is AF_NORM_MATRIX_L_PQ. This parameter is ignored if \p type is anything else
\returns the norm of \p inbased on \p type
\ingroup lapack_ops_func_norm
*/
AFAPI double norm(const array &in, const normType type=AF_NORM_EUCLID,
const double p=1, const double q=1);
#if AF_API_VERSION >= 33
/**
Returns true is ArrayFire is compiled with LAPACK support
\returns true is LAPACK support is available, false otherwise
\ingroup lapack_ops_func_norm
*/
AFAPI bool isLAPACKAvailable();
#endif
}
#endif
#ifdef __cplusplus
extern "C" {
#endif
#if AF_API_VERSION >= 31
/**
C Interface for SVD decomposition
\param[out] u is the output array containing U
\param[out] s is the output array containing the diagonal values of sigma, (singular values of the input matrix))
\param[out] vt is the output array containing V^H
\param[in] in is the input matrix
\ingroup lapack_factor_func_svd
*/
AFAPI af_err af_svd(af_array *u, af_array *s, af_array *vt, const af_array in);
#endif
#if AF_API_VERSION >= 31
/**
C Interface for SVD decomposition
\param[out] u is the output array containing U
\param[out] s is the output array containing the diagonal values of sigma, (singular values of the input matrix))
\param[out] vt is the output array containing V^H
\param[inout] in is the input matrix that will contain random data after this operation
\ingroup lapack_factor_func_svd
*/
AFAPI af_err af_svd_inplace(af_array *u, af_array *s, af_array *vt, af_array in);
#endif
/**
C Interface for LU decomposition
\param[out] lower will contain the lower triangular matrix of the LU decomposition
\param[out] upper will contain the upper triangular matrix of the LU decomposition
\param[out] pivot will contain the permutation indices to map the input to the decomposition
\param[in] in is the input matrix
\ingroup lapack_factor_func_lu
*/
AFAPI af_err af_lu(af_array *lower, af_array *upper, af_array *pivot, const af_array in);
/**
C Interface for in place LU decomposition
\param[out] pivot will contain the permutation indices to map the input to the decomposition
\param[inout] in contains the input on entry, the packed LU decomposition on exit
\param[in] is_lapack_piv specifies if the pivot is returned in original LAPACK compliant format
\ingroup lapack_factor_func_lu
*/
AFAPI af_err af_lu_inplace(af_array *pivot, af_array in, const bool is_lapack_piv);
/**
C Interface for QR decomposition
\param[out] q is the orthogonal matrix from QR decomposition
\param[out] r is the upper triangular matrix from QR decomposition
\param[out] tau will contain additional information needed for solving a least squares problem using \p q and \p r
\param[in] in is the input matrix
\ingroup lapack_factor_func_qr
*/
AFAPI af_err af_qr(af_array *q, af_array *r, af_array *tau, const af_array in);
/**
C Interface for QR decomposition
\param[out] tau will contain additional information needed for unpacking the data
\param[inout] in is the input matrix on entry. It contains packed QR decomposition on exit
\ingroup lapack_factor_func_qr
*/
AFAPI af_err af_qr_inplace(af_array *tau, af_array in);
/**
C++ Interface for cholesky decomposition
\param[out] out contains the triangular matrix. Multiply \p out with it conjugate transpose reproduces the input \p in.
\param[out] info is \p 0 if cholesky decomposition passes, if not it returns the rank at which the decomposition failed.
\param[in] in is the input matrix
\param[in] is_upper a boolean determining if \p out is upper or lower triangular
\note The input matrix \b has to be a positive definite matrix, if it is not zero, the cholesky decomposition functions return a non zero output.
\ingroup lapack_factor_func_cholesky
*/
AFAPI af_err af_cholesky(af_array *out, int *info, const af_array in, const bool is_upper);
/**
C Interface for in place cholesky decomposition
\param[out] info is \p 0 if cholesky decomposition passes, if not it returns the rank at which the decomposition failed.
\param[inout] in is the input matrix on entry. It contains the triangular matrix on exit.
\param[in] is_upper a boolean determining if \p in is upper or lower triangular
\note The input matrix \b has to be a positive definite matrix, if it is not zero, the cholesky decomposition functions return a non zero output.
\ingroup lapack_factor_func_cholesky
*/
AFAPI af_err af_cholesky_inplace(int *info, af_array in, const bool is_upper);
/**
C Interface for solving a system of equations
\param[out] x is the matrix of unknown variables
\param[in] a is the coefficient matrix
\param[in] b is the measured values
\param[in] options determining various properties of matrix \p a
\ingroup lapack_solve_func_gen
\note \p options needs to be one of \ref AF_MAT_NONE, \ref AF_MAT_LOWER or \ref AF_MAT_UPPER
*/
AFAPI af_err af_solve(af_array *x, const af_array a, const af_array b,
const af_mat_prop options);
/**
C Interface for solving a system of equations
\param[out] x will contain the matrix of unknown variables
\param[in] a is the output matrix from packed LU decomposition of the coefficient matrix
\param[in] piv is the pivot array from packed LU decomposition of the coefficient matrix
\param[in] b is the matrix of measured values
\param[in] options determining various properties of matrix \p a
\ingroup lapack_solve_lu_func_gen
\note \p options currently needs to be \ref AF_MAT_NONE
\note This function is not supported in GFOR
*/
AFAPI af_err af_solve_lu(af_array *x, const af_array a, const af_array piv,
const af_array b, const af_mat_prop options);
/**
C Interface for inverting a matrix
\param[out] out will contain the inverse of matrix \p in
\param[in] in is input matrix
\param[in] options determining various properties of matrix \p in
\ingroup lapack_ops_func_inv
\note currently options needs to be \ref AF_MAT_NONE
*/
AFAPI af_err af_inverse(af_array *out, const af_array in, const af_mat_prop options);
/**
C Interface for finding the rank of a matrix
\param[out] rank will contain the rank of \p in
\param[in] in is input matrix
\param[in] tol is the tolerance value
\ingroup lapack_ops_func_rank
*/
AFAPI af_err af_rank(unsigned *rank, const af_array in, const double tol);
/**
C Interface for finding the determinant of a matrix
\param[out] det_real will contain the real part of the determinant of \p in
\param[out] det_imag will contain the imaginary part of the determinant of \p in
\param[in] in is input matrix
\ingroup lapack_ops_func_det
*/
AFAPI af_err af_det(double *det_real, double *det_imag, const af_array in);
/**
C Interface for norm of a matrix
\param[out] out will contain the norm of \p in
\param[in] in is the input matrix
\param[in] type specifies the \ref af::normType. Default: \ref AF_NORM_VECTOR_1
\param[in] p specifies the value of P when \p type is one of \ref AF_NORM_VECTOR_P, AF_NORM_MATRIX_L_PQ is used. It is ignored for other values of \p type
\param[in] q specifies the value of Q when \p type is AF_NORM_MATRIX_L_PQ. This parameter is ignored if \p type is anything else
\ingroup lapack_ops_func_norm
*/
AFAPI af_err af_norm(double *out, const af_array in, const af_norm_type type, const double p, const double q);
#if AF_API_VERSION >= 33
/**
Returns true is ArrayFire is compiled with LAPACK support
\param[out] out is true if LAPACK support is available, false otherwise
\returns AF_SUCCESS if successful (does not depend on the value of out)
\ingroup lapack_ops_func_norm
*/
AFAPI af_err af_is_lapack_available(bool *out);
#endif
#ifdef __cplusplus
}
#endif
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