basic linear algebra operations for full matrices More...

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

subroutine, public	cp_fm_scale_and_add (alpha, matrix_a, beta, matrix_b)
	calc A <- alphaA + betaB optimized for alpha == 1.0 (just add beta*B) and beta == 0.0 (just scale A) More...

subroutine, public	cp_fm_geadd (alpha, trans, matrix_a, beta, matrix_b)
	interface to BLACS geadd: matrix_b = betamatrix_b + alphaopt(matrix_a) where opt(matrix_a) can be either: 'N': matrix_a 'T': matrix_a^T 'C': matrix_a^H (Hermitian conjugate) note that this is a level three routine, use cp_fm_scale_and_add if that is sufficient for your needs More...

subroutine, public	cp_fm_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)
	computes matrix_c = beta * matrix_c + alpha * ( matrix_a ** transa ) * ( matrix_b ** transb ) More...

subroutine, public	cp_fm_symm (side, uplo, m, n, alpha, matrix_a, matrix_b, beta, matrix_c)
	computes matrix_c = beta * matrix_c + alpha * matrix_a * matrix_b computes matrix_c = beta * matrix_c + alpha * matrix_b * matrix_a where matrix_a is symmetric More...

real(kind=dp) function, public	cp_fm_frobenius_norm (matrix_a)
	computes the Frobenius norm of matrix_a More...

subroutine, public	cp_fm_syrk (uplo, trans, k, alpha, matrix_a, ia, ja, beta, matrix_c)
	performs a rank-k update of a symmetric matrix_c matrix_c = beta * matrix_c + alpha * matrix_a * transpose ( matrix_a ) More...

subroutine, public	cp_fm_schur_product (matrix_a, matrix_b, matrix_c)
	computes the schur product of two matrices c_ij = a_ij * b_ij More...

subroutine, public	cp_fm_triangular_multiply (triangular_matrix, matrix_b, side, transpose_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 transpose_tr=.false. and invert_tr=.false.) triangular_matrix^T (if transpose_tr=.true. and invert_tr=.false.) triangular_matrix^(-1) (if transpose_tr=.false. and invert_tr=.true.) triangular_matrix^(-T) (if transpose_tr=.true. and invert_tr=.true.) More...

subroutine, public	cp_fm_scale (alpha, matrix_a)
	scales a matrix matrix_a = alpha * matrix_b More...

subroutine, public	cp_fm_transpose (matrix, matrixt)
	transposes a matrix matrixt = matrix ^ T More...

subroutine, public	cp_fm_upper_to_full (matrix, work)
	given an upper triangular matrix computes the corresponding full matrix More...

subroutine, public	cp_fm_column_scale (matrixa, scaling)
	scales column i of matrix a with scaling(i) More...

subroutine, public	cp_fm_row_scale (matrixa, scaling)
	scales row i of matrix a with scaling(i) More...

subroutine, public	cp_fm_invert (matrix_a, matrix_inverse, det_a, eps_svd, eigval)
	Inverts a cp_fm_type matrix, optionally returning the determinant of the input matrix. More...

subroutine, public	cp_fm_triangular_invert (matrix_a, uplo_tr)
	inverts a triangular matrix More...

subroutine, public	cp_fm_qr_factorization (matrix_a, matrix_r, nrow_fact, ncol_fact, first_row, first_col)
	performs a QR factorization of the input rectangular matrix A or of a submatrix of A the computed upper triangular matrix R is in output in the submatrix sub(A) of size NxN M and M give the dimension of the submatrix that has to be factorized (MxN) with M>N More...

subroutine, public	cp_fm_solve (matrix_a, general_a)
	computes the the solution to A*b=A_general using lu decomposition pay attention, both matrices are overwritten, a_general contais the result More...

subroutine, public	cp_complex_fm_gemm (transa, transb, m, n, k, alpha, A_re, A_im, B_re, B_im, beta, C_re, C_im, a_first_col, a_first_row, b_first_col, b_first_row, c_first_col, c_first_row)
	Convenience function. Computes the matrix multiplications needed for the multiplication of complex matrices. C = beta * C + alpha * ( A ** transa ) * ( B ** transb ) More...

real(kind=dp) function, public	cp_fm_norm (matrix, mode)
	norm of matrix using (p)dlange More...

subroutine, public	cp_fm_pdgeqpf (matrix, tau, nrow, ncol, first_row, first_col)
	compute a QR factorization with column pivoting of a M-by-N distributed matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) More...

subroutine, public	cp_fm_pdorgqr (matrix, tau, nrow, first_row, first_col)
	generates an M-by-N real distributed matrix Q denoting A(IA:IA+M-1,JA:JA+N-1) with orthonormal columns, which is defined as the first N columns of a product of K elementary reflectors of order M More...

subroutine, public	cp_fm_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_fm_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...

subroutine, public	cp_fm_gram_schmidt_orthonorm (matrix_a, B, nrows, ncols, start_row, start_col, do_norm, do_print)
	Orthonormalizes selected rows and columns of a full matrix, matrix_a. More...

subroutine, public	cp_fm_potrf (fm_matrix, n)
	Cholesky decomposition. More...

subroutine, public	cp_fm_potri (fm_matrix, n)
	Invert trianguar matrix. More...

subroutine, public	cp_fm_cholesky_restore (fm_matrix, neig, fm_matrixb, fm_matrixout, op, pos, transa)
	... More...

Detailed Description

basic linear algebra operations for full matrices

History: 08.2002 split out of qs_blacs [fawzi]

Author: Fawzi Mohamed

Function/Subroutine Documentation

◆ cp_fm_det()

subroutine, public cp_fm_basic_linalg::cp_fm_det	(	type(cp_fm_type), intent(in)	matrix_a,
		real(kind=dp), intent(out)	det_a
	)

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

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 96 of file cp_fm_basic_linalg.F.

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◆ cp_fm_scale_and_add()

subroutine, public cp_fm_basic_linalg::cp_fm_scale_and_add	(	real(kind=dp), intent(in)	alpha,
		type(cp_fm_type), intent(in)	matrix_a,
		real(kind=dp), intent(in), optional	beta,
		type(cp_fm_type), intent(in), optional	matrix_b
	)

calc A <- alpha*A + beta*B optimized for alpha == 1.0 (just add beta*B) and beta == 0.0 (just scale A)

Parameters

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

Definition at line 166 of file cp_fm_basic_linalg.F.

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◆ cp_fm_geadd()

subroutine, public cp_fm_basic_linalg::cp_fm_geadd	(	real(kind=dp), intent(in)	alpha,
		character, intent(in)	trans,
		type(cp_fm_type), intent(in)	matrix_a,
		real(kind=dp), intent(in)	beta,
		type(cp_fm_type), intent(in)	matrix_b
	)

interface to BLACS geadd: matrix_b = beta*matrix_b + alpha*opt(matrix_a) where opt(matrix_a) can be either: 'N': matrix_a 'T': matrix_a^T 'C': matrix_a^H (Hermitian conjugate) note that this is a level three routine, use cp_fm_scale_and_add if that is sufficient for your needs

Parameters

alpha	: complex scalar
trans	: 'N' normal, 'T' transposed
matrix_a	: input matrix_a
beta	: complex scalar
matrix_b	: input matrix_b, upon out put the updated matrix_b

Author: Lianheng Tong

Definition at line 273 of file cp_fm_basic_linalg.F.

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◆ cp_fm_gemm()

subroutine, public cp_fm_basic_linalg::cp_fm_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,
		real(kind=dp), intent(in)	alpha,
		type(cp_fm_type), intent(in)	matrix_a,
		type(cp_fm_type), intent(in)	matrix_b,
		real(kind=dp), intent(in)	beta,
		type(cp_fm_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
	)

computes matrix_c = beta * matrix_c + alpha * ( matrix_a ** transa ) * ( matrix_b ** transb )

Parameters

transa	: 'N' -> normal 'T' -> transpose alpha,beta :: can be 0.0_dp and 1.0_dp
transb	...
m	...
n	...
k	...
alpha	...
matrix_a	: m x k matrix ( ! for transa = 'N')
matrix_b	: k x n matrix ( ! for transb = 'N')
beta	...
matrix_c	: m x n matrix
a_first_col	...
a_first_row	...
b_first_col	: the k x n matrix starts at col b_first_col of matrix_b (avoid usage)
b_first_row	...
c_first_col	...
c_first_row	...

Author: Matthias Krack

Note: matrix_c should have no overlap with matrix_a, matrix_b

Definition at line 437 of file cp_fm_basic_linalg.F.

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◆ cp_fm_symm()

subroutine, public cp_fm_basic_linalg::cp_fm_symm	(	character(len=1), intent(in)	side,
		character(len=1), intent(in)	uplo,
		integer, intent(in)	m,
		integer, intent(in)	n,
		real(kind=dp), intent(in)	alpha,
		type(cp_fm_type), intent(in)	matrix_a,
		type(cp_fm_type), intent(in)	matrix_b,
		real(kind=dp), intent(in)	beta,
		type(cp_fm_type), intent(in)	matrix_c
	)

computes matrix_c = beta * matrix_c + alpha * matrix_a * matrix_b computes matrix_c = beta * matrix_c + alpha * matrix_b * matrix_a where matrix_a is symmetric

Parameters

side	: 'L' -> matrix_a is on the left 'R' -> matrix_a is on the right alpha,beta :: can be 0.0_dp and 1.0_dp
uplo	...
m	...
n	...
alpha	...
matrix_a	: m x m matrix
matrix_b	: m x n matrix
beta	...
matrix_c	: m x n matrix

Author: Matthias Krack

Note: matrix_c should have no overlap with matrix_a, matrix_b all matrices in QS are upper triangular, so uplo should be 'U' always matrix_a is always an m x m matrix it is typically slower to do cp_fm_symm than cp_fm_gemm (especially in parallel easily 50 percent !)

Definition at line 575 of file cp_fm_basic_linalg.F.

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◆ cp_fm_frobenius_norm()

real(kind=dp) function, public cp_fm_basic_linalg::cp_fm_frobenius_norm ( type(cp_fm_type), intent(in) matrix_a )

computes the Frobenius norm of matrix_a

Parameters

matrix_a : m x n matrix

Returns: ...

Author: VW

Definition at line 628 of file cp_fm_basic_linalg.F.

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◆ cp_fm_syrk()

subroutine, public cp_fm_basic_linalg::cp_fm_syrk	(	character(len=1), intent(in)	uplo,
		character(len=1), intent(in)	trans,
		integer, intent(in)	k,
		real(kind=dp), intent(in)	alpha,
		type(cp_fm_type), intent(in)	matrix_a,
		integer, intent(in)	ia,
		integer, intent(in)	ja,
		real(kind=dp), intent(in)	beta,
		type(cp_fm_type), intent(in)	matrix_c
	)

performs a rank-k update of a symmetric matrix_c matrix_c = beta * matrix_c + alpha * matrix_a * transpose ( matrix_a )

Parameters

uplo	: 'U' ('L')
trans	: 'N' ('T')
k	: number of cols to use in matrix_a ia,ja :: 1,1 (could be used for selecting subblock of a)
alpha	...
matrix_a	...
ia	...
ja	...
beta	...
matrix_c	...

Author: Matthias Krack

Note: In QS uplo should 'U' (upper part updated)

Definition at line 674 of file cp_fm_basic_linalg.F.

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◆ cp_fm_schur_product()

subroutine, public cp_fm_basic_linalg::cp_fm_schur_product	(	type(cp_fm_type), intent(in)	matrix_a,
		type(cp_fm_type), intent(in)	matrix_b,
		type(cp_fm_type), intent(in)	matrix_c
	)

computes the schur product of two matrices c_ij = a_ij * b_ij

Parameters

matrix_a	...
matrix_b	...
matrix_c	...

Author: Joost VandeVondele

Definition at line 727 of file cp_fm_basic_linalg.F.

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◆ cp_fm_triangular_multiply()

subroutine, public cp_fm_basic_linalg::cp_fm_triangular_multiply	(	type(cp_fm_type), intent(in)	triangular_matrix,
		type(cp_fm_type), intent(in)	matrix_b,
		character, intent(in), optional	side,
		logical, intent(in), optional	transpose_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,
		real(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 transpose_tr=.false. and invert_tr=.false.) triangular_matrix^T (if transpose_tr=.true. and invert_tr=.false.) triangular_matrix^(-1) (if transpose_tr=.false. and invert_tr=.true.) triangular_matrix^(-T) (if transpose_tr=.true. 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')
transpose_tr	if the triangular matrix should be transposed (defaults to false)
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 1589 of file cp_fm_basic_linalg.F.

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◆ cp_fm_scale()

subroutine, public cp_fm_basic_linalg::cp_fm_scale	(	real(kind=dp), intent(in)	alpha,
		type(cp_fm_type), intent(in)	matrix_a
	)

scales a matrix matrix_a = alpha * matrix_b

Parameters

alpha	...
matrix_a	...

Note: use cp_fm_set_all to zero (avoids problems with nan)

Definition at line 1679 of file cp_fm_basic_linalg.F.

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◆ cp_fm_transpose()

subroutine, public cp_fm_basic_linalg::cp_fm_transpose	(	type(cp_fm_type), intent(in)	matrix,
		type(cp_fm_type), intent(in)	matrixt
	)

transposes a matrix matrixt = matrix ^ T

Parameters

matrix	...
matrixt	...

Note: all matrix elements are transposed (see cp_fm_upper_to_half to symmetrise a matrix)

Definition at line 1709 of file cp_fm_basic_linalg.F.

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◆ cp_fm_upper_to_full()

subroutine, public cp_fm_basic_linalg::cp_fm_upper_to_full	(	type(cp_fm_type), intent(in)	matrix,
		type(cp_fm_type), intent(in)	work
	)

given an upper triangular matrix computes the corresponding full matrix

Parameters

matrix	the upper triangular matrix as input, the full matrix as output
work	a matrix of the same size as matrix

Author: Matthias Krack

Note: the lower triangular part is irrelevant

Definition at line 1758 of file cp_fm_basic_linalg.F.

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◆ cp_fm_column_scale()

subroutine, public cp_fm_basic_linalg::cp_fm_column_scale	(	type(cp_fm_type), intent(in)	matrixa,
		real(kind=dp), dimension(:), intent(in)	scaling
	)

scales column i of matrix a with scaling(i)

Parameters

matrixa	...
scaling	: an array used for scaling the columns, SIZE(scaling) determines the number of columns to be scaled

Author: Joost VandeVondele

Note: this is very useful as a first step in the computation of C = sum_i alpha_i A_i transpose (A_i) that is a rank-k update (cp_fm_syrk , cp_sm_plus_fm_fm_t) this procedure can be up to 20 times faster than calling cp_fm_syrk n times where every vector has a different prefactor

Definition at line 1881 of file cp_fm_basic_linalg.F.

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◆ cp_fm_row_scale()

subroutine, public cp_fm_basic_linalg::cp_fm_row_scale	(	type(cp_fm_type), intent(in)	matrixa,
		real(kind=dp), dimension(:), intent(in)	scaling
	)

scales row i of matrix a with scaling(i)

Parameters

matrixa	...
scaling	: an array used for scaling the columns,

Author: JGH

Note

Definition at line 1944 of file cp_fm_basic_linalg.F.

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◆ cp_fm_invert()

subroutine, public cp_fm_basic_linalg::cp_fm_invert	(	type(cp_fm_type), intent(in)	matrix_a,
		type(cp_fm_type), intent(in)	matrix_inverse,
		real(kind=dp), intent(out), optional	det_a,
		real(kind=dp), intent(in), optional	eps_svd,
		real(kind=dp), dimension(:), intent(inout), optional, pointer	eigval
	)

Inverts a cp_fm_type matrix, optionally returning the determinant of the input matrix.

Parameters

matrix_a	the matrix to invert
matrix_inverse	the inverse of matrix_a
det_a	the determinant of matrix_a
eps_svd	optional parameter to active SVD based inversion, singular values below eps_svd are screened
eigval	optionally return matrix eigenvalues/singular values

History

note of Jan Wilhelm (12.2015)

computation of determinant corrected
determinant only computed if det_a is present 12.2016 added option to use SVD instead of LU [Nico Holmberg]
Use cp_fm_get diag instead of n times cp_fm_get_element (A. Bussy)

Author: Florian Schiffmann(02.2007)

Definition at line 2014 of file cp_fm_basic_linalg.F.

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◆ cp_fm_triangular_invert()

subroutine, public cp_fm_basic_linalg::cp_fm_triangular_invert	(	type(cp_fm_type), intent(in)	matrix_a,
		character, intent(in), optional	uplo_tr
	)

inverts a triangular matrix

Parameters

matrix_a	...
uplo_tr	...

Author: MI

Definition at line 2192 of file cp_fm_basic_linalg.F.

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◆ cp_fm_qr_factorization()

subroutine, public cp_fm_basic_linalg::cp_fm_qr_factorization	(	type(cp_fm_type), intent(in)	matrix_a,
		type(cp_fm_type), intent(in)	matrix_r,
		integer, intent(in), optional	nrow_fact,
		integer, intent(in), optional	ncol_fact,
		integer, intent(in), optional	first_row,
		integer, intent(in), optional	first_col
	)

performs a QR factorization of the input rectangular matrix A or of a submatrix of A the computed upper triangular matrix R is in output in the submatrix sub(A) of size NxN M and M give the dimension of the submatrix that has to be factorized (MxN) with M>N

Parameters

matrix_a	...
matrix_r	...
nrow_fact	...
ncol_fact	...
first_row	...
first_col	...

Author: MI

Definition at line 2241 of file cp_fm_basic_linalg.F.

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◆ cp_fm_solve()

subroutine, public cp_fm_basic_linalg::cp_fm_solve	(	type(cp_fm_type), intent(in)	matrix_a,
		type(cp_fm_type), intent(in)	general_a
	)

computes the the solution to A*b=A_general using lu decomposition pay attention, both matrices are overwritten, a_general contais the result

Parameters

matrix_a	...
general_a	...

Author: Florian Schiffmann

Definition at line 2323 of file cp_fm_basic_linalg.F.

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◆ cp_complex_fm_gemm()

subroutine, public cp_fm_basic_linalg::cp_complex_fm_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,
		real(kind=dp), intent(in)	alpha,
		type(cp_fm_type), intent(in)	A_re,
		type(cp_fm_type), intent(in)	A_im,
		type(cp_fm_type), intent(in)	B_re,
		type(cp_fm_type), intent(in)	B_im,
		real(kind=dp), intent(in)	beta,
		type(cp_fm_type), intent(in)	C_re,
		type(cp_fm_type), intent(in)	C_im,
		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
	)

Convenience function. Computes the matrix multiplications needed for the multiplication of complex matrices. C = beta * C + alpha * ( A ** transa ) * ( B ** transb )

Parameters

transa	: 'N' -> normal 'T' -> transpose alpha,beta :: can be 0.0_dp and 1.0_dp
transb	...
m	...
n	...
k	...
alpha	...
A_re	m x k matrix ( ! for transa = 'N'), real part
A_im	m x k matrix ( ! for transa = 'N'), imaginary part
B_re	k x n matrix ( ! for transa = 'N'), real part
B_im	k x n matrix ( ! for transa = 'N'), imaginary part
beta	...
C_re	m x n matrix, real part
C_im	m x n matrix, imaginary part
a_first_col	...
a_first_row	...
b_first_col	: the k x n matrix starts at col b_first_col of matrix_b (avoid usage)
b_first_row	...
c_first_col	...
c_first_row	...

Author: Samuel Andermatt

Note: C should have no overlap with A, B

Definition at line 2392 of file cp_fm_basic_linalg.F.

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◆ cp_fm_norm()

real(kind=dp) function, public cp_fm_basic_linalg::cp_fm_norm	(	type(cp_fm_type), intent(in)	matrix,
		character, intent(in)	mode
	)

norm of matrix using (p)dlange

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 2579 of file cp_fm_basic_linalg.F.

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◆ cp_fm_pdgeqpf()

subroutine, public cp_fm_basic_linalg::cp_fm_pdgeqpf	(	type(cp_fm_type), intent(in)	matrix,
		real(kind=dp), dimension(:), pointer	tau,
		integer, intent(in)	nrow,
		integer, intent(in)	ncol,
		integer, intent(in)	first_row,
		integer, intent(in)	first_col
	)

compute a QR factorization with column pivoting of a M-by-N distributed matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1)

Parameters

matrix	: input M-by-N distributed matrix sub( A ) which is to be factored
tau	: scalar factors TAU of the elementary reflectors. TAU is tied to the distributed matrix A
nrow	...
ncol	...
first_row	...
first_col	...

Author: MI

Definition at line 2731 of file cp_fm_basic_linalg.F.

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◆ cp_fm_pdorgqr()

subroutine, public cp_fm_basic_linalg::cp_fm_pdorgqr	(	type(cp_fm_type), intent(in)	matrix,
		real(kind=dp), dimension(:), pointer	tau,
		integer, intent(in)	nrow,
		integer, intent(in)	first_row,
		integer, intent(in)	first_col
	)

generates an M-by-N real distributed matrix Q denoting A(IA:IA+M-1,JA:JA+N-1) with orthonormal columns, which is defined as the first N columns of a product of K elementary reflectors of order M

Parameters

matrix	: On entry, the j-th column must contain the vector which defines the elementary reflector as returned from PDGEQRF On exit it contains the M-by-N distributed matrix Q
tau	: contains the scalar factors TAU of elementary reflectors as returned by PDGEQRF
nrow	...
first_row	...
first_col	...

Author: MI

Definition at line 2803 of file cp_fm_basic_linalg.F.

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◆ cp_fm_rot_rows()

subroutine, public cp_fm_basic_linalg::cp_fm_rot_rows	(	type(cp_fm_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

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

Author: Ole Schuett

Definition at line 2863 of file cp_fm_basic_linalg.F.

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◆ cp_fm_rot_cols()

subroutine, public cp_fm_basic_linalg::cp_fm_rot_cols	(	type(cp_fm_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

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

Author: Ole Schuett

Definition at line 2905 of file cp_fm_basic_linalg.F.

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◆ cp_fm_gram_schmidt_orthonorm()

subroutine, public cp_fm_basic_linalg::cp_fm_gram_schmidt_orthonorm	(	type(cp_fm_type), intent(in)	matrix_a,
		real(kind=dp), dimension(:, :), intent(out)	B,
		integer, intent(in), optional	nrows,
		integer, intent(in), optional	ncols,
		integer, intent(in), optional	start_row,
		integer, intent(in), optional	start_col,
		logical, intent(in), optional	do_norm,
		logical, intent(in), optional	do_print
	)

Orthonormalizes selected rows and columns of a full matrix, matrix_a.

Parameters

matrix_a	...
B	...
nrows	number of rows of matrix_a, optional, defaults to size(matrix_a,1)
ncols	number of columns of matrix_a, optional, defaults to size(matrix_a, 2)
start_row	starting index of rows, optional, defaults to 1
start_col	starting index of columns, optional, defaults to 1
do_norm	...
do_print	...

Definition at line 2950 of file cp_fm_basic_linalg.F.

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◆ cp_fm_potrf()

subroutine, public cp_fm_basic_linalg::cp_fm_potrf	(	type(cp_fm_type)	fm_matrix,
		integer, intent(in)	n
	)

Cholesky decomposition.

Parameters

fm_matrix	...
n	...

Definition at line 3084 of file cp_fm_basic_linalg.F.

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◆ cp_fm_potri()

subroutine, public cp_fm_basic_linalg::cp_fm_potri	(	type(cp_fm_type)	fm_matrix,
		integer, intent(in)	n
	)

Invert trianguar matrix.

Parameters

fm_matrix	the matrix to invert (must be an upper triangular matrix)
n	size of the matrix to invert

Definition at line 3121 of file cp_fm_basic_linalg.F.

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◆ cp_fm_cholesky_restore()

subroutine, public cp_fm_basic_linalg::cp_fm_cholesky_restore	(	type(cp_fm_type)	fm_matrix,
		integer, intent(in)	neig,
		type(cp_fm_type)	fm_matrixb,
		type(cp_fm_type)	fm_matrixout,
		character(len=*), intent(in)	op,
		character(len=*), intent(in)	pos,
		character(len=*), intent(in)	transa
	)

...

Parameters

fm_matrix	...
neig	...
fm_matrixb	...
fm_matrixout	...
op	...
pos	...
transa	...

Definition at line 3161 of file cp_fm_basic_linalg.F.

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Functions/Subroutines

Detailed Description

Function/Subroutine Documentation

◆ cp_fm_det()

◆ cp_fm_scale_and_add()

◆ cp_fm_geadd()

◆ cp_fm_gemm()

◆ cp_fm_symm()

◆ cp_fm_frobenius_norm()

◆ cp_fm_syrk()

◆ cp_fm_schur_product()

◆ cp_fm_triangular_multiply()

◆ cp_fm_scale()

◆ cp_fm_transpose()

◆ cp_fm_upper_to_full()

◆ cp_fm_column_scale()

◆ cp_fm_row_scale()

◆ cp_fm_invert()

◆ cp_fm_triangular_invert()

◆ cp_fm_qr_factorization()

◆ cp_fm_solve()

◆ cp_complex_fm_gemm()

◆ cp_fm_norm()

◆ cp_fm_pdgeqpf()

◆ cp_fm_pdorgqr()

◆ cp_fm_rot_rows()

◆ cp_fm_rot_cols()

◆ cp_fm_gram_schmidt_orthonorm()

◆ cp_fm_potrf()

◆ cp_fm_potri()

◆ cp_fm_cholesky_restore()