linalg.h File Reference

Provide linalg APIs. More...

#include "kids/Types.h"

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Namespaces
namespace	PROJECT_NS
	< http://warp.povusers.org/FunctionParser/fparser.html

Macros
#define	KIDS_LINALG_BIND_EIGEN_NOT_USE_TEMPLATE

Functions
bool	PROJECT_NS::ARRAY_ISFINITE (kids_real *A, size_t n)
	Check if all elements of a real array are finite.
bool	PROJECT_NS::ARRAY_ISFINITE (kids_complex *A, size_t n)
	Check if all elements of a complex array are finite.
void	PROJECT_NS::ARRAY_CLEAR (kids_int *A, size_t N)
	Set all elements of an integer array to zero.
void	PROJECT_NS::ARRAY_CLEAR (kids_real *A, size_t N)
	Set all elements of a real array to zero.
void	PROJECT_NS::ARRAY_CLEAR (kids_complex *A, size_t N)
	Set all elements of a complex array to zero.
void	PROJECT_NS::ARRAY_MATMUL (kids_real *A, kids_real *B, kids_real *C, size_t N1, size_t N2, size_t N3)
	Perform matrix multiplication where A = B * C for real matrices.
void	PROJECT_NS::ARRAY_MATMUL (kids_complex *A, kids_complex *B, kids_complex *C, size_t N1, size_t N2, size_t N3)
	Perform matrix multiplication where A = B * C for complex matrices.
void	PROJECT_NS::ARRAY_MATMUL (kids_complex *A, kids_real *B, kids_complex *C, size_t N1, size_t N2, size_t N3)
	Perform matrix multiplication where A = B * C for complex and real matrices.
void	PROJECT_NS::ARRAY_MATMUL (kids_complex *A, kids_complex *B, kids_real *C, size_t N1, size_t N2, size_t N3)
	Perform matrix multiplication where A = B * C for complex and real matrices.
void	PROJECT_NS::ARRAY_MATMUL_TRANS1 (kids_real *A, kids_real *B, kids_real *C, size_t N1, size_t N2, size_t N3)
	Perform matrix multiplication where A = B^T * C for real matrices.
void	PROJECT_NS::ARRAY_MATMUL_TRANS1 (kids_complex *A, kids_complex *B, kids_complex *C, size_t N1, size_t N2, size_t N3)
	Perform matrix multiplication where A = B^T * C for complex matrices.
void	PROJECT_NS::ARRAY_MATMUL_TRANS1 (kids_complex *A, kids_real *B, kids_complex *C, size_t N1, size_t N2, size_t N3)
	Perform matrix multiplication where A = B^T * C for complex and real matrices.
void	PROJECT_NS::ARRAY_MATMUL_TRANS1 (kids_complex *A, kids_complex *B, kids_real *C, size_t N1, size_t N2, size_t N3)
	Perform matrix multiplication where A = B^T * C for complex and real matrices.
void	PROJECT_NS::ARRAY_MATMUL_TRANS2 (kids_real *A, kids_real *B, kids_real *C, size_t N1, size_t N2, size_t N3)
	Perform matrix multiplication where A = B * C^T for real matrices.
void	PROJECT_NS::ARRAY_MATMUL_TRANS2 (kids_complex *A, kids_complex *B, kids_complex *C, size_t N1, size_t N2, size_t N3)
	Perform matrix multiplication where A = B * C^T for complex matrices.
void	PROJECT_NS::ARRAY_MATMUL_TRANS2 (kids_complex *A, kids_real *B, kids_complex *C, size_t N1, size_t N2, size_t N3)
	Perform matrix multiplication where A = B * C^T for complex and real matrices.
void	PROJECT_NS::ARRAY_MATMUL_TRANS2 (kids_complex *A, kids_complex *B, kids_real *C, size_t N1, size_t N2, size_t N3)
	Perform matrix multiplication where A = B * C^T for complex and real matrices.
void	PROJECT_NS::ARRAY_OUTER_TRANS2 (kids_real *A, kids_real *B, kids_real *C, size_t N1, size_t N2)
	Perform outer product with transpose where A = B^T * C for real matrices.
void	PROJECT_NS::ARRAY_OUTER_TRANS2 (kids_complex *A, kids_complex *B, kids_complex *C, size_t N1, size_t N2)
	Perform outer product with transpose where A = B^T * C for complex matrices.
void	PROJECT_NS::ARRAY_MATMUL3_TRANS1 (kids_real *A, kids_real *B, kids_real *C, kids_real *D, size_t N1, size_t N2, size_t N0, size_t N3)
	Perform matrix multiplication where A = B^T * C * D for real matrices.
void	PROJECT_NS::ARRAY_MATMUL3_TRANS1 (kids_complex *A, kids_complex *B, kids_complex *C, kids_complex *D, size_t N1, size_t N2, size_t N0, size_t N3)
	Perform matrix multiplication where A = B^T * C * D for complex matrices.
void	PROJECT_NS::ARRAY_MATMUL3_TRANS1 (kids_complex *A, kids_real *B, kids_complex *C, kids_real *D, size_t N1, size_t N2, size_t N0, size_t N3)
	Perform matrix multiplication where A = B^T * C * D for complex and real matrices.
void	PROJECT_NS::ARRAY_MATMUL3_TRANS1 (kids_complex *A, kids_complex *B, kids_real *C, kids_complex *D, size_t N1, size_t N2, size_t N0, size_t N3)
	Perform matrix multiplication where A = B^T * C * D for complex and real matrices.
void	PROJECT_NS::ARRAY_MATMUL3_TRANS2 (kids_real *A, kids_real *B, kids_real *C, kids_real *D, size_t N1, size_t N2, size_t N0, size_t N3)
	Perform matrix multiplication where A = B * C * D^T for real matrices.
void	PROJECT_NS::ARRAY_MATMUL3_TRANS2 (kids_complex *A, kids_complex *B, kids_complex *C, kids_complex *D, size_t N1, size_t N2, size_t N0, size_t N3)
	Perform matrix multiplication where A = B * C * D^T for complex matrices.
void	PROJECT_NS::ARRAY_MATMUL3_TRANS2 (kids_complex *A, kids_real *B, kids_complex *C, kids_real *D, size_t N1, size_t N2, size_t N0, size_t N3)
	Perform matrix multiplication where A = B * C * D^T for complex and real matrices.
void	PROJECT_NS::ARRAY_MATMUL3_TRANS2 (kids_complex *A, kids_complex *B, kids_real *C, kids_complex *D, size_t N1, size_t N2, size_t N0, size_t N3)
	Perform matrix multiplication where A = B * C * D^T for complex and real matrices.
kids_real	PROJECT_NS::ARRAY_TRACE2 (kids_real *B, kids_real *C, size_t N1, size_t N2)
	Compute the trace of the matrix product B * C for real matrices.
kids_complex	PROJECT_NS::ARRAY_TRACE2 (kids_complex *B, kids_complex *C, size_t N1, size_t N2)
	Compute the trace of the matrix product B * C for complex matrices.
kids_complex	PROJECT_NS::ARRAY_TRACE2 (kids_complex *B, kids_real *C, size_t N1, size_t N2)
	Compute the trace of the matrix product B * C for complex and real matrices.
kids_complex	PROJECT_NS::ARRAY_TRACE2 (kids_real *B, kids_complex *C, size_t N1, size_t N2)
	Compute the trace of the matrix product B * C for real and complex matrices.
kids_real	PROJECT_NS::ARRAY_TRACE2_DIAG (kids_real *B, kids_real *C, size_t N1, size_t N2)
	Compute the trace of the diagonal elements of the matrix product B * C for real matrices.
kids_complex	PROJECT_NS::ARRAY_TRACE2_DIAG (kids_complex *B, kids_complex *C, size_t N1, size_t N2)
	Compute the trace of the diagonal elements of the matrix product B * C for complex matrices.
kids_complex	PROJECT_NS::ARRAY_TRACE2_DIAG (kids_complex *B, kids_real *C, size_t N1, size_t N2)
	Compute the trace of the diagonal elements of the matrix product B * C for complex and real matrices.
kids_complex	PROJECT_NS::ARRAY_TRACE2_DIAG (kids_real *B, kids_complex *C, size_t N1, size_t N2)
	Compute the trace of the diagonal elements of the matrix product B * C for real and complex matrices.
kids_real	PROJECT_NS::ARRAY_TRACE2_OFFD (kids_real *B, kids_real *C, size_t N1, size_t N2)
	Compute the trace of the off-diagonal elements of the matrix product B * C for real matrices.
kids_complex	PROJECT_NS::ARRAY_TRACE2_OFFD (kids_complex *B, kids_complex *C, size_t N1, size_t N2)
	Compute the trace of the off-diagonal elements of the matrix product B * C for complex matrices.
kids_complex	PROJECT_NS::ARRAY_TRACE2_OFFD (kids_complex *B, kids_real *C, size_t N1, size_t N2)
	Compute the trace of the off-diagonal elements of the matrix product B * C for complex and real matrices.
kids_complex	PROJECT_NS::ARRAY_TRACE2_OFFD (kids_real *B, kids_complex *C, size_t N1, size_t N2)
	Compute the trace of the off-diagonal elements of the matrix product B * C for real and complex matrices.
kids_real	PROJECT_NS::ARRAY_INNER_TRANS1 (kids_real *B, kids_real *C, size_t N1)
	Compute the inner product of the transpose of B with C for real matrices.
kids_complex	PROJECT_NS::ARRAY_INNER_TRANS1 (kids_complex *B, kids_complex *C, size_t N1)
	Compute the inner product of the conjugate transpose of B with C for complex matrices.
kids_complex	PROJECT_NS::ARRAY_INNER_TRANS1 (kids_complex *B, kids_real *C, size_t N1)
	Compute the inner product of the conjugate transpose of B with C for complex and real matrices.
kids_complex	PROJECT_NS::ARRAY_INNER_TRANS1 (kids_real *B, kids_complex *C, size_t N1)
	Compute the inner product of the transpose of B with C for real and complex matrices.
kids_real	PROJECT_NS::ARRAY_INNER_VMV_TRANS1 (kids_real *B, kids_real *C, kids_real *D, size_t N1, size_t N2)
	Compute the inner product of the transpose of the real vector B with the matrix C, element-wise multiplication with the real vector D.
kids_complex	PROJECT_NS::ARRAY_INNER_VMV_TRANS1 (kids_complex *B, kids_complex *C, kids_complex *D, size_t N1, size_t N2)
	Compute the inner product of the conjugate transpose of the complex vector B with the complex matrix C, element-wise multiplication with the complex vector D.
kids_complex	PROJECT_NS::ARRAY_INNER_VMV_TRANS1 (kids_complex *B, kids_real *C, kids_complex *D, size_t N1, size_t N2)
	Compute the inner product of the conjugate transpose of the complex vector B with the real matrix C, element-wise multiplication with the complex vector D.
kids_complex	PROJECT_NS::ARRAY_INNER_VMV_TRANS1 (kids_real *B, kids_complex *C, kids_real *D, size_t N1, size_t N2)
	Compute the inner product of the transpose of the real vector B with the complex matrix C, element-wise multiplication with the real vector D.
void	PROJECT_NS::ARRAY_EYE (kids_real *A, size_t n)
	Generate an identity matrix of size n for real numbers.
void	PROJECT_NS::ARRAY_EYE (kids_complex *A, size_t n)
	Generate an identity matrix of size n for complex numbers.
void	PROJECT_NS::ARRAY_MAT_DIAG (kids_real *A, kids_real *B, size_t N1)
	Copy the diagonal elements from matrix B to matrix A for real matrices.
void	PROJECT_NS::ARRAY_MAT_DIAG (kids_complex *A, kids_complex *B, size_t N1)
	Copy the diagonal elements from matrix B to matrix A for complex matrices.
void	PROJECT_NS::ARRAY_MAT_DIAG (kids_complex *A, kids_real *B, size_t N1)
	Copy the diagonal elements from matrix B to matrix A for complex and real matrices.
void	PROJECT_NS::ARRAY_MAT_OFFD (kids_real *A, kids_real *B, size_t N1)
	Copy the off-diagonal elements from matrix B to matrix A for real matrices.
void	PROJECT_NS::ARRAY_MAT_OFFD (kids_complex *A, kids_complex *B, size_t N1)
	Copy the off-diagonal elements from matrix B to matrix A for complex matrices.
void	PROJECT_NS::ARRAY_MAT_OFFD (kids_complex *A, kids_real *B, size_t N1)
	Copy the off-diagonal elements from matrix B to matrix A for complex and real matrices.
void	PROJECT_NS::LinearSolve (kids_real *x, kids_real *A, kids_real *b, size_t N)
	Solve a linear system Ax = b for real matrices.
void	PROJECT_NS::EigenSolve (kids_real *E, kids_real *T, kids_real *A, size_t N)
	Solve the eigenvalue problem for real matrices.
void	PROJECT_NS::EigenSolve (kids_real *E, kids_complex *T, kids_complex *A, size_t N)
	Solve the eigenvalue problem for (hermite) complex matrices.
void	PROJECT_NS::EigenSolve (kids_complex *E, kids_complex *T, kids_complex *A, size_t N)
	Solve the eigenvalue problem for general complex matrices.
void	PROJECT_NS::PseudoInverse (kids_real *A, kids_real *invA, size_t N, kids_real e=1E-5)
	Compute the pseudo-inverse of a matrix for real numbers.
void	PROJECT_NS::MatrixInverse (kids_real *invA, kids_real *A, size_t N)
	Compute the inverse of a matrix for real numbers.
void	PROJECT_NS::ARRAY_INV_MAT (kids_complex *invA, kids_complex *A, size_t N)
	Compute the inverse of a matrix for complex numbers.
void	PROJECT_NS::ARRAY_EXP_MAT_GENERAL (kids_complex *expkA, kids_complex *A, kids_complex k, size_t N)
void	PROJECT_NS::ARRAY_CORRECT_U (kids_complex *U, size_t N)
void	PROJECT_NS::ARRAY_TRANSPOSE (kids_real *A, size_t N1, size_t N2)
void	PROJECT_NS::ARRAY_TRANSPOSE (kids_complex *A, size_t N1, size_t N2)

Detailed Description

Provide linalg APIs.

unified APIs, and realization can be based on either Eigen or MKL

See also

eigen: https://eigen.tuxfamily.org/dox/ mkl : https://www.intel.com/content/www/us/en/develop/documentation/onemkl-lapack-examples/top.html

Author

Xin He

Date

2024-03

Version

1.0

Copyright

GNU Lesser General Public License (LGPL)

         Copyright (c) 2024 Xin He, Liu-Group

This software is a product of Xin's PhD research conducted by Professor Liu's Group at the College of Chemistry and Molecular Engineering, Peking University. All rights are reserved by Peking University. You should have received a copy of the GNU Lesser General Public License along with this software. If not, see https://www.gnu.org/licenses/lgpl-3.0.en.html

revision:

Date	Description
2024-04-25	split from tpl APIs, which is slow in compilation

Definition in file linalg.h.

Macro Definition Documentation

KIDS_LINALG_BIND_EIGEN_NOT_USE_TEMPLATE

#define KIDS_LINALG_BIND_EIGEN_NOT_USE_TEMPLATE

Definition at line 35 of file linalg.h.