cp_fm_cholesky Module Reference

various cholesky decomposition related routines More...

Functions/Subroutines
subroutine, public	cp_fm_cholesky_decompose (matrix, n, info_out)
	used to replace a symmetric positive def. matrix M with its cholesky decomposition U: M = U^T * U, with U upper triangular
subroutine, public	cp_fm_cholesky_solve (matrix, matrixb, n, info_out)
	solves A*X = B for X, given the Cholesky decomposition U of the symmetric positive def. matrix A (A = U^T*U, U upper triangular), as produced by cp_fm_cholesky_decompose
subroutine, public	cp_fm_cholesky_invert (matrix, n, info_out)
	used to replace the cholesky decomposition by the inverse
subroutine, public	cp_fm_cholesky_reduce (matrix, matrixb, itype)
	reduce a matrix pencil A,B to normal form B has to be cholesky decomposed with cp_fm_cholesky_decompose before calling this routine A,B -> inv(U^T)*A*inv(U),1 (AX=BX -> inv(U^T)*A*inv(U)*U*X=U*X hence evecs U*X)
subroutine, public	cp_fm_cholesky_restore (fm_matrix, neig, fm_matrixb, fm_matrixout, op, pos, transa)
	apply Cholesky decomposition op can be "SOLVE" (out = U^-1 * in) or "MULTIPLY" (out = U * in) pos can be "LEFT" or "RIGHT" (U at the left or at the right)

Variables
integer, save, public	cholesky_type = 0
integer, save, public	dlaf_cholesky_n_min = 0
integer, parameter, public	fm_cholesky_type_scalapack = 101
integer, parameter, public	fm_cholesky_type_dlaf = 104
integer, parameter, public	fm_cholesky_type_default = FM_CHOLESKY_TYPE_SCALAPACK

Detailed Description

various cholesky decomposition related routines

History

09.2002 created [fawzi]

Author

Fawzi Mohamed

Function/Subroutine Documentation

cp_fm_cholesky_decompose()

subroutine, public cp_fm_cholesky::cp_fm_cholesky_decompose	(	type(cp_fm_type), intent(in)	matrix,
		integer, intent(in), optional	n,
		integer, intent(out), optional	info_out
	)

used to replace a symmetric positive def. 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	...

History

05.2002 created [JVdV] 12.2002 updated, added n optional parm [fawzi]

Author

Joost

Definition at line 60 of file cp_fm_cholesky.F.

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cp_fm_cholesky_solve()

subroutine, public cp_fm_cholesky::cp_fm_cholesky_solve	(	type(cp_fm_type), intent(in)	matrix,
		type(cp_fm_type), intent(inout)	matrixb,
		integer, intent(in), optional	n,
		integer, intent(out), optional	info_out
	)

solves A*X = B for X, given the Cholesky decomposition U of the symmetric positive def. matrix A (A = U^T*U, U upper triangular), as produced by cp_fm_cholesky_decompose

Parameters

matrix	the Cholesky factor U of A, as produced by cp_fm_cholesky_decompose
matrixb	on input the right-hand side(s) B, on output the solution(s) X
n	the number of rows (and columns) of matrix (defaults to the min(size(matrix)))
info_out	...

Definition at line 125 of file cp_fm_cholesky.F.

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cp_fm_cholesky_invert()

subroutine, public cp_fm_cholesky::cp_fm_cholesky_invert	(	type(cp_fm_type), intent(in)	matrix,
		integer, intent(in), optional	n,
		integer, intent(out), optional	info_out
	)

used to replace the cholesky decomposition by the inverse

Parameters

matrix	the matrix to invert (must be an upper triangular matrix)
n	size of the matrix to invert (defaults to the min(size(matrix)))
info_out	...

History

05.2002 created [JVdV]

Author

Joost VandeVondele

Definition at line 181 of file cp_fm_cholesky.F.

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cp_fm_cholesky_reduce()

subroutine, public cp_fm_cholesky::cp_fm_cholesky_reduce	(	type(cp_fm_type), intent(in)	matrix,
		type(cp_fm_type), intent(in)	matrixb,
		integer, optional	itype
	)

reduce a matrix pencil A,B to normal form B has to be cholesky decomposed with cp_fm_cholesky_decompose before calling this routine A,B -> inv(U^T)*A*inv(U),1 (AX=BX -> inv(U^T)*A*inv(U)*U*X=U*X hence evecs U*X)

Parameters

matrix	the symmetric matrix A
matrixb	the cholesky decomposition of matrix B
itype	...

History

05.2002 created [JVdV]

Author

Joost VandeVondele

Definition at line 254 of file cp_fm_cholesky.F.

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cp_fm_cholesky_restore()

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

apply Cholesky decomposition op can be "SOLVE" (out = U^-1 * in) or "MULTIPLY" (out = U * in) pos can be "LEFT" or "RIGHT" (U at the left or at the right)

Parameters

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

Definition at line 312 of file cp_fm_cholesky.F.

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Variable Documentation

cholesky_type

integer, save, public cp_fm_cholesky::cholesky_type = 0

Definition at line 36 of file cp_fm_cholesky.F.

dlaf_cholesky_n_min

integer, save, public cp_fm_cholesky::dlaf_cholesky_n_min = 0

Definition at line 39 of file cp_fm_cholesky.F.

fm_cholesky_type_scalapack

integer, parameter, public cp_fm_cholesky::fm_cholesky_type_scalapack = 101

Definition at line 41 of file cp_fm_cholesky.F.

fm_cholesky_type_dlaf

integer, parameter, public cp_fm_cholesky::fm_cholesky_type_dlaf = 104

Definition at line 41 of file cp_fm_cholesky.F.

fm_cholesky_type_default

integer, parameter, public cp_fm_cholesky::fm_cholesky_type_default = FM_CHOLESKY_TYPE_SCALAPACK

Definition at line 43 of file cp_fm_cholesky.F.