cp_fm_basic_linalg Module Reference

basic linear algebra operations for full matrices More...

Data Types
interface	cp_fm_contracted_trace
interface	cp_fm_trace

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.
subroutine, public	cp_fm_scale_and_add (alpha, matrix_a, beta, matrix_b)
	calc A <- alpha*A + beta*B optimized for alpha == 1.0 (just add beta*B) and beta == 0.0 (just scale A)
subroutine, public	cp_fm_geadd (alpha, trans, matrix_a, beta, 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
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 )
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
real(kind=dp) function, public	cp_fm_frobenius_norm (matrix_a)
	computes the Frobenius norm of matrix_a
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 )
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
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.)
subroutine, public	cp_fm_scale (alpha, matrix_a)
	scales a matrix matrix_a = alpha * matrix_b
subroutine, public	cp_fm_transpose (matrix, matrixt)
	transposes a matrix matrixt = matrix ^ T
subroutine, public	cp_fm_uplo_to_full (matrix, work, uplo)
	given a triangular matrix according to uplo, computes the corresponding full matrix
subroutine, public	cp_fm_column_scale (matrixa, scaling)
	scales column i of matrix a with scaling(i)
subroutine, public	cp_fm_row_scale (matrixa, scaling)
	scales row i of matrix a with scaling(i)
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.
subroutine, public	cp_fm_triangular_invert (matrix_a, uplo_tr)
	inverts a triangular matrix
subroutine, public	cp_fm_qr_factorization (matrix_a, matrix_r, nrow_fact, ncol_fact, first_row, first_col, uplo)
	performs a QR factorization of the input rectangular matrix A or of a submatrix of A the computed triangular matrix R is in output of 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
subroutine, public	cp_fm_solve (matrix_a, general_a)
	computes the the solution to A*b=A_general using lu decomposition
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 )
real(kind=dp) function, public	cp_fm_norm (matrix, mode)
	norm of matrix using (p)dlange
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)
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
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.
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.
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.
subroutine, public	cp_fm_potrf (fm_matrix, n, uplo)
	Cholesky decomposition.
subroutine, public	cp_fm_potri (fm_matrix, n, uplo)
	Invert trianguar matrix.
subroutine, public	cp_fm_cholesky_restore (fm_matrix, neig, fm_matrixb, fm_matrixout, op, pos, transa)
	...
subroutine, public	cp_fm_matvec (amat, xv, yv, alpha, beta)
	Calculates yv = alpha*amat*xv + beta*yv where amat: fm matrix xv : vector replicated yv : vector replicated Defaults: alpha = 1, beta = 0.

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 97 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 270 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	triangular format
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 triangular according to uplo matrix_a is always an m x m matrix typically slower than cp_fm_gemm (especially in parallel easily 50 percent)

Definition at line 562 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

computes the Frobenius norm of matrix_a

Parameters

matrix_a

: m x n matrix

Returns

...

Author

VW

Definition at line 615 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

Definition at line 659 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 712 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 1574 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 1664 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_uplo_to_full to symmetrise a matrix)

Definition at line 1694 of file cp_fm_basic_linalg.F.

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cp_fm_uplo_to_full()

subroutine, public cp_fm_basic_linalg::cp_fm_uplo_to_full	(	type(cp_fm_type), intent(in)	matrix,
		type(cp_fm_type), intent(in)	work,
		character, intent(in), optional	uplo
	)

given a triangular matrix according to uplo, computes the corresponding full matrix

Parameters

matrix	the triangular matrix as input, the full matrix as output
work	a matrix of the same size as matrix
uplo	triangular format; defaults to 'U'

Author

Matthias Krack

Note

the opposite triangular part is irrelevant

Definition at line 1746 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 1884 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 1947 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 2018 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	triangular format; defaults to 'U'

Author

MI

Definition at line 2196 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,
		character, intent(in), optional	uplo
	)

performs a QR factorization of the input rectangular matrix A or of a submatrix of A the computed triangular matrix R is in output of 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 2244 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

Parameters

matrix_a	input matrix; will be overwritten
general_a	contains the result

Author

Florian Schiffmann

Definition at line 2337 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 2407 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 2594 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 2746 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 2818 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 2878 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 2920 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 2965 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,
		character, intent(in), optional	uplo
	)

Cholesky decomposition.

Parameters

fm_matrix	...
n	...
uplo	triangular format; defaults to 'U'

Definition at line 3100 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,
		character, intent(in), optional	uplo
	)

Invert trianguar matrix.

Parameters

fm_matrix	the matrix to invert (triangular matrix according to uplo)
n	size of the matrix to invert
uplo	triangular format; defaults to 'U'

Definition at line 3143 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 3188 of file cp_fm_basic_linalg.F.

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cp_fm_matvec()

subroutine, public cp_fm_basic_linalg::cp_fm_matvec	(	type(cp_fm_type), intent(in)	amat,
		real(kind=dp), dimension(:), intent(in)	xv,
		real(kind=dp), dimension(:), intent(inout)	yv,
		real(kind=dp), intent(in), optional	alpha,
		real(kind=dp), intent(in), optional	beta
	)

Calculates yv = alpha*amat*xv + beta*yv where amat: fm matrix xv : vector replicated yv : vector replicated Defaults: alpha = 1, beta = 0.

Definition at line 3276 of file cp_fm_basic_linalg.F.

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