Basic linear algebra operations for complex full matrices. More...

Functions/Subroutines
subroutine, public	cp_cfm_det (matrix_a, det_a)
	Computes the determinant (with a correct sign even in parallel environment!) of a complex square matrix. More...

subroutine, public	cp_cfm_schur_product (matrix_a, matrix_b, matrix_c)
	Computes the element-wise (Schur) product of two matrices: C = A \circ B . More...

subroutine, public	cp_cfm_scale_and_add (alpha, matrix_a, beta, matrix_b)
	Scale and add two BLACS matrices (a = alphaa + betab). More...

subroutine, public	cp_cfm_scale_and_add_fm (alpha, matrix_a, beta, matrix_b)
	Scale and add two BLACS matrices (a = alphaa + betab). where b is a real matrix (adapted from cp_cfm_scale_and_add). More...

subroutine, public	cp_cfm_lu_decompose (matrix_a, determinant)
	Computes LU decomposition of a given matrix. More...

subroutine, public	cp_cfm_gemm (transa, transb, m, n, k, alpha, matrix_a, matrix_b, beta, matrix_c, a_first_col, a_first_row, b_first_col, b_first_row, c_first_col, c_first_row)
	Performs one of the matrix-matrix operations: matrix_c = alpha * op1( matrix_a ) * op2( matrix_b ) + beta*matrix_c. More...

subroutine, public	cp_cfm_column_scale (matrix_a, scaling)
	Scales columns of the full matrix by corresponding factors. More...

subroutine, public	cp_cfm_solve (matrix_a, general_a, determinant)
	Solve the system of linear equations A*b=A_general using LU decomposition. Pay attention that both matrices are overwritten on exit and that the result is stored into the matrix 'general_a'. More...

subroutine, public	cp_cfm_lu_invert (matrix, info_out)
	Inverts a matrix using LU decomposition. The input matrix will be overwritten. More...

subroutine, public	cp_cfm_cholesky_decompose (matrix, n, info_out)
	Used to replace a symmetric positive definite matrix M with its Cholesky decomposition U: M = U^T * U, with U upper triangular. More...

subroutine, public	cp_cfm_cholesky_invert (matrix, n, info_out)
	Used to replace Cholesky decomposition by the inverse. More...

subroutine, public	cp_cfm_trace (matrix_a, matrix_b, trace)
	Returns the trace of matrix_a^T matrix_b, i.e sum_{i,j}(matrix_a(i,j)*matrix_b(i,j)) . More...

subroutine, public	cp_cfm_triangular_multiply (triangular_matrix, matrix_b, side, transa_tr, invert_tr, uplo_tr, unit_diag_tr, n_rows, n_cols, alpha)
	Multiplies in place by a triangular matrix: matrix_b = alpha op(triangular_matrix) matrix_b or (if side='R') matrix_b = alpha matrix_b op(triangular_matrix) op(triangular_matrix) is: triangular_matrix (if transa="N" and invert_tr=.false.) triangular_matrix^T (if transa="T" and invert_tr=.false.) triangular_matrix^H (if transa="C" and invert_tr=.false.) triangular_matrix^(-1) (if transa="N" and invert_tr=.true.) triangular_matrix^(-T) (if transa="T" and invert_tr=.true.) triangular_matrix^(-H) (if transa="C" and invert_tr=.true.) More...

subroutine, public	cp_cfm_triangular_invert (matrix_a, uplo, info_out)
	Inverts a triangular matrix. More...

subroutine, public	cp_cfm_transpose (matrix, trans, matrixt)
	Transposes a BLACS distributed complex matrix. More...

real(kind=dp) function, public	cp_cfm_norm (matrix, mode)
	Norm of matrix using (p)zlange. More...

subroutine, public	cp_cfm_rot_rows (matrix, irow, jrow, cs, sn)
	Applies a planar rotation defined by cs and sn to the i'th and j'th rows. More...

subroutine, public	cp_cfm_rot_cols (matrix, icol, jcol, cs, sn)
	Applies a planar rotation defined by cs and sn to the i'th and j'th columnns. More...

Detailed Description

Basic linear algebra operations for complex full matrices.

Note

not all functionality implemented

History: Nearly literal copy of Fawzi's routines

Author: Joost VandeVondele

Function/Subroutine Documentation

◆ cp_cfm_det()

subroutine, public cp_cfm_basic_linalg::cp_cfm_det	(	type(cp_cfm_type), intent(in)	matrix_a,
		complex(kind=dp), intent(out)	det_a
	)

Computes the determinant (with a correct sign even in parallel environment!) of a complex square matrix.

Parameters

matrix_a	...
det_a	...

Author: A. Sinyavskiy (andre.nosp@m.y.si.nosp@m.nyavs.nosp@m.kiy@.nosp@m.chem..nosp@m.uzh..nosp@m.ch)

Definition at line 75 of file cp_cfm_basic_linalg.F.

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◆ cp_cfm_schur_product()

subroutine, public cp_cfm_basic_linalg::cp_cfm_schur_product	(	type(cp_cfm_type), intent(in)	matrix_a,
		type(cp_cfm_type), intent(in)	matrix_b,
		type(cp_cfm_type), intent(in)	matrix_c
	)

Computes the element-wise (Schur) product of two matrices: C = A \circ B .

Parameters

matrix_a	the first input matrix
matrix_b	the second input matrix
matrix_c	matrix to store the result

Definition at line 156 of file cp_cfm_basic_linalg.F.

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◆ cp_cfm_scale_and_add()

subroutine, public cp_cfm_basic_linalg::cp_cfm_scale_and_add	(	complex(kind=dp), intent(in)	alpha,
		type(cp_cfm_type), intent(in)	matrix_a,
		complex(kind=dp), intent(in), optional	beta,
		type(cp_cfm_type), intent(in), optional	matrix_b
	)

Scale and add two BLACS matrices (a = alpha*a + beta*b).

Parameters

alpha	...
matrix_a	...
beta	...
matrix_b	...

Date: 11.06.2001

Author: Matthias Krack

Version: 1.0

Note: Use explicit loops to avoid temporary arrays, as a compiler reasonably assumes that arrays matrix_alocal_data and matrix_blocal_data may overlap (they are referenced by pointers). In general case (alpha*a + beta*b) explicit loops appears to be up to two times more efficient than equivalent LAPACK calls (zscale, zaxpy). This is because using LAPACK calls implies two passes through each array, so data need to be retrieved twice if arrays are large enough to not fit into the processor's cache.

Definition at line 243 of file cp_cfm_basic_linalg.F.

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◆ cp_cfm_scale_and_add_fm()

subroutine, public cp_cfm_basic_linalg::cp_cfm_scale_and_add_fm	(	complex(kind=dp), intent(in)	alpha,
		type(cp_cfm_type), intent(in)	matrix_a,
		complex(kind=dp), intent(in)	beta,
		type(cp_fm_type), intent(in)	matrix_b
	)

Scale and add two BLACS matrices (a = alpha*a + beta*b). where b is a real matrix (adapted from cp_cfm_scale_and_add).

Parameters

alpha	...
matrix_a	...
beta	...
matrix_b	...

Date: 01.08.2014

Author: JGH

Version: 1.0

Definition at line 354 of file cp_cfm_basic_linalg.F.

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◆ cp_cfm_lu_decompose()

subroutine, public cp_cfm_basic_linalg::cp_cfm_lu_decompose	(	type(cp_cfm_type), intent(in)	matrix_a,
		complex(kind=dp), intent(out)	determinant
	)

Computes LU decomposition of a given matrix.

Parameters

matrix_a	full matrix
determinant	determinant

Date: 11.06.2001

Author: Matthias Krack

Version: 1.0

Note: The actual purpose right now is to efficiently compute the determinant of a given matrix. The original content of the matrix is destroyed.

Definition at line 461 of file cp_cfm_basic_linalg.F.

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◆ cp_cfm_gemm()

subroutine, public cp_cfm_basic_linalg::cp_cfm_gemm	(	character(len=1), intent(in)	transa,
		character(len=1), intent(in)	transb,
		integer, intent(in)	m,
		integer, intent(in)	n,
		integer, intent(in)	k,
		complex(kind=dp), intent(in)	alpha,
		type(cp_cfm_type), intent(in)	matrix_a,
		type(cp_cfm_type), intent(in)	matrix_b,
		complex(kind=dp), intent(in)	beta,
		type(cp_cfm_type), intent(in)	matrix_c,
		integer, intent(in), optional	a_first_col,
		integer, intent(in), optional	a_first_row,
		integer, intent(in), optional	b_first_col,
		integer, intent(in), optional	b_first_row,
		integer, intent(in), optional	c_first_col,
		integer, intent(in), optional	c_first_row
	)

Performs one of the matrix-matrix operations: matrix_c = alpha * op1( matrix_a ) * op2( matrix_b ) + beta*matrix_c.

Parameters

transa	form of op1( matrix_a ): op1( matrix_a ) = matrix_a, when transa == 'N' , op1( matrix_a ) = matrix_a^T, when transa == 'T' , op1( matrix_a ) = matrix_a^H, when transa == 'C' ,
transb	form of op2( matrix_b )
m	number of rows of the matrix op1( matrix_a )
n	number of columns of the matrix op2( matrix_b )
k	number of columns of the matrix op1( matrix_a ) as well as number of rows of the matrix op2( matrix_b )
alpha	scale factor
matrix_a	matrix A
matrix_b	matrix B
beta	scale factor
matrix_c	matrix C
a_first_col	(optional) the first column of the matrix_a to multiply
a_first_row	(optional) the first row of the matrix_a to multiply
b_first_col	(optional) the first column of the matrix_b to multiply
b_first_row	(optional) the first row of the matrix_b to multiply
c_first_col	(optional) the first column of the matrix_c
c_first_row	(optional) the first row of the matrix_c

Date: 07.06.2001

Author: Matthias Krack

Version: 1.0

Definition at line 564 of file cp_cfm_basic_linalg.F.

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◆ cp_cfm_column_scale()

subroutine, public cp_cfm_basic_linalg::cp_cfm_column_scale	(	type(cp_cfm_type), intent(in)	matrix_a,
		complex(kind=dp), dimension(:), intent(in)	scaling
	)

Scales columns of the full matrix by corresponding factors.

Parameters

matrix_a	matrix to scale
scaling	scale factors for every column. The actual number of scaled columns is limited by the number of scale factors given or by the actual number of columns whichever is smaller.

Author: Joost VandeVondele

Definition at line 648 of file cp_cfm_basic_linalg.F.

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◆ cp_cfm_solve()

subroutine, public cp_cfm_basic_linalg::cp_cfm_solve	(	type(cp_cfm_type), intent(in)	matrix_a,
		type(cp_cfm_type), intent(in)	general_a,
		complex(kind=dp), optional	determinant
	)

Solve the system of linear equations A*b=A_general using LU decomposition. Pay attention that both matrices are overwritten on exit and that the result is stored into the matrix 'general_a'.

Parameters

matrix_a	matrix A (overwritten on exit)
general_a	(input) matrix A_general, (output) matrix B
determinant	(optional) determinant

Author: Florian Schiffmann

Definition at line 747 of file cp_cfm_basic_linalg.F.

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◆ cp_cfm_lu_invert()

subroutine, public cp_cfm_basic_linalg::cp_cfm_lu_invert	(	type(cp_cfm_type), intent(in)	matrix,
		integer, intent(out), optional	info_out
	)

Inverts a matrix using LU decomposition. The input matrix will be overwritten.

Parameters

matrix	input a general square non-singular matrix, outputs its inverse
info_out	optional, if present outputs the info from (p)zgetri

Author: Lianheng Tong

Definition at line 839 of file cp_cfm_basic_linalg.F.

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◆ cp_cfm_cholesky_decompose()

subroutine, public cp_cfm_basic_linalg::cp_cfm_cholesky_decompose	(	type(cp_cfm_type), intent(in)	matrix,
		integer, intent(in), optional	n,
		integer, intent(out), optional	info_out
	)

Used to replace a symmetric positive definite matrix M with its Cholesky decomposition U: M = U^T * U, with U upper triangular.

Parameters

matrix	the matrix to replace with its Cholesky decomposition
n	the number of row (and columns) of the matrix & (defaults to the min(size(matrix)))
info_out	if present, outputs info from (p)zpotrf

History: 05.2002 created [JVdV] 12.2002 updated, added n optional parm [fawzi] 09.2021 removed CPASSERT(info == 0) since there is already check of info [Jan Wilhelm]

Author: Joost

Definition at line 925 of file cp_cfm_basic_linalg.F.

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◆ cp_cfm_cholesky_invert()

subroutine, public cp_cfm_basic_linalg::cp_cfm_cholesky_invert	(	type(cp_cfm_type), intent(in)	matrix,
		integer, intent(in), optional	n,
		integer, intent(out), optional	info_out
	)

Used to replace Cholesky decomposition by the inverse.

Parameters

matrix	: the matrix to invert (must be an upper triangular matrix), and is the output of Cholesky decomposition
n	: size of the matrix to invert (defaults to the min(size(matrix)))
info_out	: if present, outputs info of (p)zpotri

History: 05.2002 created Lianheng Tong, based on cp_fm_cholesky_invert

Author: Lianheng Tong

Definition at line 981 of file cp_cfm_basic_linalg.F.

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◆ cp_cfm_trace()

subroutine, public cp_cfm_basic_linalg::cp_cfm_trace	(	type(cp_cfm_type), intent(in)	matrix_a,
		type(cp_cfm_type), intent(in)	matrix_b,
		complex(kind=dp), intent(out)	trace
	)

Returns the trace of matrix_a^T matrix_b, i.e sum_{i,j}(matrix_a(i,j)*matrix_b(i,j)) .

Parameters

matrix_a	a complex matrix
matrix_b	another complex matrix
trace	value of the trace operator

History

09.2017 created [Sergey Chulkov]

Author: Sergey Chulkov

Note: Based on the subroutine cp_fm_trace(). Note the transposition of matrix_a!

Definition at line 1036 of file cp_cfm_basic_linalg.F.

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◆ cp_cfm_triangular_multiply()

subroutine, public cp_cfm_basic_linalg::cp_cfm_triangular_multiply	(	type(cp_cfm_type), intent(in)	triangular_matrix,
		type(cp_cfm_type), intent(in)	matrix_b,
		character, intent(in), optional	side,
		character, intent(in), optional	transa_tr,
		logical, intent(in), optional	invert_tr,
		character, intent(in), optional	uplo_tr,
		logical, intent(in), optional	unit_diag_tr,
		integer, intent(in), optional	n_rows,
		integer, intent(in), optional	n_cols,
		complex(kind=dp), intent(in), optional	alpha
	)

Multiplies in place by a triangular matrix: matrix_b = alpha op(triangular_matrix) matrix_b or (if side='R') matrix_b = alpha matrix_b op(triangular_matrix) op(triangular_matrix) is: triangular_matrix (if transa="N" and invert_tr=.false.) triangular_matrix^T (if transa="T" and invert_tr=.false.) triangular_matrix^H (if transa="C" and invert_tr=.false.) triangular_matrix^(-1) (if transa="N" and invert_tr=.true.) triangular_matrix^(-T) (if transa="T" and invert_tr=.true.) triangular_matrix^(-H) (if transa="C" and invert_tr=.true.)

Parameters

triangular_matrix	the triangular matrix that multiplies the other
matrix_b	the matrix that gets multiplied and stores the result
side	on which side of matrix_b stays op(triangular_matrix) (defaults to 'L')
transa_tr	...
invert_tr	if the triangular matrix should be inverted (defaults to false)
uplo_tr	if triangular_matrix is stored in the upper ('U') or lower ('L') triangle (defaults to 'U')
unit_diag_tr	if the diagonal elements of triangular_matrix should be assumed to be 1 (defaults to false)
n_rows	the number of rows of the result (defaults to size(matrix_b,1))
n_cols	the number of columns of the result (defaults to size(matrix_b,2))
alpha	...

History: 08.2002 created [fawzi]

Author: Fawzi Mohamed

Note: needs an mpi env

Definition at line 1104 of file cp_cfm_basic_linalg.F.

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◆ cp_cfm_triangular_invert()

subroutine, public cp_cfm_basic_linalg::cp_cfm_triangular_invert	(	type(cp_cfm_type), intent(in)	matrix_a,
		character, intent(in), optional	uplo,
		integer, intent(out), optional	info_out
	)

Inverts a triangular matrix.

Parameters

matrix_a	...
uplo	...
info_out	...

Author: MI

Definition at line 1188 of file cp_cfm_basic_linalg.F.

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◆ cp_cfm_transpose()

subroutine, public cp_cfm_basic_linalg::cp_cfm_transpose	(	type(cp_cfm_type), intent(in)	matrix,
		character, intent(in)	trans,
		type(cp_cfm_type), intent(in)	matrixt
	)

Transposes a BLACS distributed complex matrix.

Parameters

matrix	input matrix
trans	'T' for transpose, 'C' for Hermitian conjugate
matrixt	output matrix

Author: Lianheng Tong

Definition at line 1238 of file cp_cfm_basic_linalg.F.

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◆ cp_cfm_norm()

real(kind=dp) function, public cp_cfm_basic_linalg::cp_cfm_norm	(	type(cp_cfm_type), intent(in)	matrix,
		character, intent(in)	mode
	)

Norm of matrix using (p)zlange.

Parameters

matrix	input a general matrix
mode	'M' max abs element value, '1' or 'O' one norm, i.e. maximum column sum, 'I' infinity norm, i.e. maximum row sum, 'F' or 'E' Frobenius norm, i.e. sqrt of sum of all squares of elements

Returns: the norm according to mode

Author: Lianheng Tong

Definition at line 1311 of file cp_cfm_basic_linalg.F.

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◆ cp_cfm_rot_rows()

subroutine, public cp_cfm_basic_linalg::cp_cfm_rot_rows	(	type(cp_cfm_type), intent(in)	matrix,
		integer, intent(in)	irow,
		integer, intent(in)	jrow,
		real(dp), intent(in)	cs,
		real(dp), intent(in)	sn
	)

Applies a planar rotation defined by cs and sn to the i'th and j'th rows.

Parameters

matrix	...
irow	...
jrow	...
cs	cosine of the rotation angle
sn	sinus of the rotation angle

Author: Ole Schuett

Definition at line 1382 of file cp_cfm_basic_linalg.F.

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◆ cp_cfm_rot_cols()

subroutine, public cp_cfm_basic_linalg::cp_cfm_rot_cols	(	type(cp_cfm_type), intent(in)	matrix,
		integer, intent(in)	icol,
		integer, intent(in)	jcol,
		real(dp), intent(in)	cs,
		real(dp), intent(in)	sn
	)

Applies a planar rotation defined by cs and sn to the i'th and j'th columnns.

Parameters

matrix	...
icol	...
jcol	...
cs	cosine of the rotation angle
sn	sinus of the rotation angle

Author: Ole Schuett

Definition at line 1427 of file cp_cfm_basic_linalg.F.

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Functions/Subroutines

Detailed Description

Function/Subroutine Documentation

◆ cp_cfm_det()

◆ cp_cfm_schur_product()

◆ cp_cfm_scale_and_add()

◆ cp_cfm_scale_and_add_fm()

◆ cp_cfm_lu_decompose()

◆ cp_cfm_gemm()

◆ cp_cfm_column_scale()

◆ cp_cfm_solve()

◆ cp_cfm_lu_invert()

◆ cp_cfm_cholesky_decompose()

◆ cp_cfm_cholesky_invert()

◆ cp_cfm_trace()

◆ cp_cfm_triangular_multiply()

◆ cp_cfm_triangular_invert()

◆ cp_cfm_transpose()

◆ cp_cfm_norm()

◆ cp_cfm_rot_rows()

◆ cp_cfm_rot_cols()