Data Types
interface	inv

interface	invl

interface	invu

interface	l1lm

interface	ldlm

interface	ldum

interface	swpvv

interface	udlmm

Public Member Functions
subroutine	cldumf (a, ipiv, d, ff)
	Perform l-d-u decomposition of square matrix a in place with pivoting. More...

subroutine	cudlmm (a, b, ipiv)
	Use l-u factors in A to back-substitute for several rhs in B, using ipiv to define the pivoting permutation used in the l-u decomposition. More...

subroutine	cudlmv (a, b, ipiv)
	Use l-u factors in A to back-substitute for 1 rhs in B, using ipiv to define the pivoting permutation used in the l-u decomposition. More...

subroutine	dinvl (a)
	Invert lower triangular matrix in place. More...

subroutine	dinvmtf (a, ff)
	Invert a double precision matrix in place, or flag if process fails. More...

subroutine	dl1lmf (a, b, ff)
	Cholesky, M -> L*U, U(i,j)=L(j,i) More...

subroutine	dldlmf (a, b, d, ff)
	Modified Cholesky Q –> LDU, U(i,j)=L(j,i) More...

subroutine	dldumf (a, ipiv, d, ff)
	Perform l-d-u decomposition of square matrix a in place with pivoting. More...

subroutine	dudlmm (a, b, ipiv)
	Use l-u factors in A to back-substitute for several rhs in B, using ipiv to define the pivoting permutation used in the l-u decomposition. More...

subroutine	dudlmv (a, b, ipiv)
	Use l-u factors in A to back-substitute for 1 rhs in B, using ipiv to define the pivoting permutation used in the l-u decomposition. More...

subroutine	sinvu (a)
	Invert the upper triangular matrix in place by transposing, calling invl, and transposing again. More...

subroutine	sl1lm (a, b)
	Cholesky, M -> L*U, U(i,j)=L(j,i) More...

subroutine	sldlm (a, b, d)
	Modified Cholesky decompose Q –> LDU, U(i,j)=L(j,i) More...

subroutine	slinlv (a, u)
	Solve linear system involving lower triangular system matrix. More...

subroutine	slinmmt (a, b)
	Invert linear system with multiple right-hand side vectors. More...

subroutine	sudlmm (a, b, ipiv)
	Use l-u factors in A to back-substitute for several rhs in B, using ipiv to define the pivoting permutation used in the l-u decomposition. More...

subroutine	sudlmv (a, b, ipiv)
	Use l-u factors in A to back-substitute for 1 rhs in B, using ipiv to define the pivoting permutation used in the l-u decomposition. More...

Private Member Functions
subroutine	cinvmt (a)
	Invert complex matrix in place. More...

subroutine	cinvmtf (a, ff)
	Invert a complex matrix in place, or flag if process fails. More...

subroutine	cldum (a, ipiv, d)
	Perform LDU decomposition, with pivoting, of square matrix. More...

subroutine	clinmmt (a, b)
	Invert complex linear system with multiple right-hand side vectors. More...

subroutine	clinmmtf (a, b, ff)
	Invert linear system with multiple right-hand side vectors, or flag failure. More...

subroutine	clinmvt (a, b)
	Invert linear system with single right-hand side vector. More...

subroutine	clinmvtf (a, b, ff)
	Invert complex linear system with single right-hand side vector. More...

subroutine	cswpvv (d, e)
	Swap a pair of complex vectors. More...

subroutine	dinvmt (a)
	Invert double precision matrix in place. More...

subroutine	dinvu (a)
	Invert the upper triangular matrix in place by transposing, calling invl, and transposing again. More...

subroutine	dl1lm (a, b)
	Cholesky, M -> L*U, U(i,j)=L(j,i) More...

subroutine	dldlm (a, b, d)
	Modified Cholesky decompose Q –> LDU, U(i,j)=L(j,i) More...

subroutine	dldum (a, ipiv, d)
	Perform LDU decomposition, with pivoting, of square matrix. More...

subroutine	dlinlv (a, u)
	Solve linear system involving lower triangular system matrix. More...

subroutine	dlinmmt (a, b)
	Invert linear system with multiple right-hand side vectors. More...

subroutine	dlinmmtf (a, b, ff)
	Invert linear system with multiple right-hand side vectors, or flag failure. More...

subroutine	dlinmvt (a, b)
	Invert linear system with single right-hand side vector. More...

subroutine	dlinmvtf (a, b, ff)
	Invert linear system with single right-hand side vector. More...

subroutine	dlinuv (a, u)
	Solve linear system involving upper triangular system matrix. More...

subroutine	dswpvv (d, e)
	Swap a pair of double precision vectors. More...

subroutine	iinvf (imat, ff)
	Invert integer square matrix, imat, if possible, but flag ff=.true. More...

subroutine	sinvl (a)
	Invert lower triangular matrix in place. More...

subroutine	sinvmt (a)
	Invert single precision matrix in place. More...

subroutine	sinvmtf (a, ff)
	Invert a single precision matrix in place, or flag if process fails. More...

subroutine	sl1lmf (a, b, ff)
	Cholesky, M -> L*U, U(i,j)=L(j,i) More...

subroutine	sldlmf (a, b, d, ff)
	Modified Cholesky decompose Q –> LDU, U(i,j)=L(j,i) More...

subroutine	sldum (a, ipiv, d)
	Perform LDU decomposition, with pivoting, of square matrix. More...

subroutine	sldumf (a, ipiv, d, ff)
	Perform l-d-u decomposition of square matrix a in place with pivoting. More...

subroutine	slinmmtf (a, b, ff)
	Invert linear system with multiple right-hand side vectors, or flag failure. More...

subroutine	slinmvt (a, b)
	Invert linear system with single right-hand side vector. More...

subroutine	slinmvtf (a, b, ff)
	Invert linear system with single right-hand side vector. More...

subroutine	slinuv (a, u)
	Solve linear system involving upper triangular system matrix. More...

subroutine	sswpvv (d, e)
	Swap a pair of single precision vectors. More...

Detailed Description

Definition at line 20 of file pmat.f90.

Member Function/Subroutine Documentation

subroutine pmat::cinvmt ( complex(dpc), dimension(:,:), intent(inout) a )

private

Invert complex matrix in place.

Parameters

[in,out] a matrix

Author: R. J. Purser

Definition at line 103 of file pmat.f90.

References pmat::inv::cinvmtf().

subroutine pmat::cinvmtf	(	complex(dpc), dimension(:,:), intent(inout)	a,
		logical, intent(out)	ff
	)

private

Invert a complex matrix in place, or flag if process fails.

Parameters

[in,out]	a	matrix
[out]	ff	flag for error condition

Author: R. J. Purser

Definition at line 190 of file pmat.f90.

References pmat::ldum::cldumf(), and pmat::swpvv::cswpvv().

subroutine pmat::cldum	(	complex(dpc), dimension(:,:), intent(inout)	a,
		integer(spi), dimension(:), intent(out)	ipiv,
		complex(dpc), intent(out)	d
	)

private

Perform L*D*U decomposition, with pivoting, of square matrix.

Complex double precision version.

Parameters

[in,out]	a	input square matrix, output L,D,U factors
[out]	d	determinant sign change indicator (+1 or -1)
[out]	ipiv	vector of pivots

Author: R. J. Purser

Definition at line 508 of file pmat.f90.

References pmat::ldum::cldumf().

subroutine pmat::cldumf	(	complex(dpc), dimension(:,:), intent(inout)	a,
		integer(spi), dimension(:), intent(out)	ipiv,
		complex(dpc), intent(out)	d,
		logical, intent(out)	ff
	)

Perform l-d-u decomposition of square matrix a in place with pivoting.

Complex double precision version.

Parameters

[in,out]	a	square matrix to be factorized
[out]	ipiv	vector encoding the pivoting sequence
[out]	d	indicator for possible sign change of determinant
[out]	ff,:	failure flag, set to .true. when determinant of a vanishes.

Author: R. J. Purser

Definition at line 659 of file pmat.f90.

References pmat::swpvv::cswpvv().

subroutine pmat::clinmmt	(	complex(dpc), dimension(:,:), intent(inout)	a,
		complex(dpc), dimension(:,:), intent(inout)	b
	)

private

Invert complex linear system with multiple right-hand side vectors.

Complex double precision version.

Parameters

[in,out]	a	Invertible system matrix, destroyed on output
[in,out]	b	input RHS vectors, output solution vectors

Author: R. J. Purser

Definition at line 255 of file pmat.f90.

References pmat::inv::clinmmtf().

subroutine pmat::clinmmtf	(	complex(dpc), dimension(:,:), intent(inout)	a,
		complex(dpc), dimension(:,:), intent(inout)	b,
		logical, intent(out)	ff
	)

private

Invert linear system with multiple right-hand side vectors, or flag failure.

Complex double precision version.

Parameters

[in,out]	a	Invertible system matrix, destroyed on output
[in,out]	b	input RHS vectors, output solution vectors
[out]	ff	failure flag

Author: R. J. Purser

Definition at line 319 of file pmat.f90.

References pmat::ldum::cldumf(), and pmat::udlmm::cudlmm().

subroutine pmat::clinmvt	(	complex(dpc), dimension(:,:), intent(inout)	a,
		complex(dpc), dimension(:), intent(inout)	b
	)

private

Invert linear system with single right-hand side vector.

Complex double precision version.

Parameters

[in,out]	a	Invertible system matrix, destroyed on output
[in,out]	b	input RHS vector, output solution vector

Author: R. J. Purser

Definition at line 371 of file pmat.f90.

References pmat::inv::clinmvtf().

subroutine pmat::clinmvtf	(	complex(dpc), dimension(:,:), intent(inout)	a,
		complex(dpc), dimension(:), intent(inout)	b,
		logical, intent(out)	ff
	)

private

Invert complex linear system with single right-hand side vector.

Parameters

[in,out]	a	Invertible system matrix, destroyed on output
[in,out]	b	input RHS vector, output solution vector
[out]	ff	failure flag

Author: R. J. Purser

Definition at line 429 of file pmat.f90.

References pmat::ldum::cldumf(), and pmat::udlmm::cudlmv().

subroutine pmat::cswpvv	(	complex(dpc), dimension(:), intent(inout)	d,
		complex(dpc), dimension(:), intent(inout)	e
	)

private

Swap a pair of complex vectors.

Parameters

[in,out]	d	vector
[in,out]	e	vector

Author: R. J. Purser

Definition at line 71 of file pmat.f90.

subroutine pmat::cudlmm	(	complex(dpc), dimension(:,:), intent(in)	a,
		complex(dpc), dimension(:,:), intent(inout)	b,
		integer(spi), dimension(:), intent(in)	ipiv
	)

Use l-u factors in A to back-substitute for several rhs in B, using ipiv to define the pivoting permutation used in the l-u decomposition.

Parameters

[in]	a	square matrix to be factorized
[in,out]	b	rt-hand-sides vectors on input, corresponding solutions on return
[in]	ipiv	vector encoding the pivoting sequence

Author: R. J. Purser

Definition at line 797 of file pmat.f90.

subroutine pmat::cudlmv	(	complex(dpc), dimension(:,:), intent(in)	a,
		complex(dpc), dimension(:), intent(inout)	b,
		integer(spi), dimension(:), intent(in)	ipiv
	)

Use l-u factors in A to back-substitute for 1 rhs in B, using ipiv to define the pivoting permutation used in the l-u decomposition.

Parameters

[in]	a	square matrix to be factorized
[in,out]	b	right-hand side vector on input, corresponding solution on return
[in]	ipiv	array encoding the pivoting sequence

Author: R. J. Purser

Definition at line 892 of file pmat.f90.

subroutine pmat::dinvl ( real(dp), dimension(:,:), intent(inout) a )

Invert lower triangular matrix in place.

Double precision.

Parameters

[in,out] a lower triangular matrix.

Author: R. J. Purser

Definition at line 1153 of file pmat.f90.

subroutine pmat::dinvmt ( real(dp), dimension(:,:), intent(inout) a )

private

Invert double precision matrix in place.

Parameters

[in,out] a matrix

Author: R. J. Purser

Definition at line 92 of file pmat.f90.

References pmat::inv::dinvmtf().

subroutine pmat::dinvmtf	(	real(dp), dimension(:,:), intent(inout)	a,
		logical, intent(out)	ff
	)

Invert a double precision matrix in place, or flag if process fails.

Parameters

[in,out]	a	matrix
[out]	ff	flag for error condition

Author: R. J. Purser

Definition at line 153 of file pmat.f90.

References pmat::ldum::dldumf(), and pmat::swpvv::dswpvv().

subroutine pmat::dinvu ( real(dp), dimension(:,:), intent(inout) a )

private

Invert the upper triangular matrix in place by transposing, calling invl, and transposing again.

Double precision version.

Parameters

[in,out] a upper triangular matrix.

Author: R. J. Purser

Definition at line 1126 of file pmat.f90.

References pmat::invl::dinvl().

subroutine pmat::dl1lm	(	real(dp), dimension(:,:), intent(in)	a,
		real(dp), dimension(:,:), intent(inout)	b
	)

private

Cholesky, M -> L*U, U(i,j)=L(j,i)

Parameters

[in]	a	symmetric matrix.
[in,out]	b	Cholesky factor matrix.

Author: R. J. Purser

Definition at line 933 of file pmat.f90.

References pmat::l1lm::dl1lmf().

subroutine pmat::dl1lmf	(	real(dp), dimension(:,:), intent(in)	a,
		real(dp), dimension(:,:), intent(inout)	b,
		logical, intent(out)	ff
	)

Cholesky, M -> L*U, U(i,j)=L(j,i)

Parameters

[in]	a	symmetric matrix.
[in,out]	b	Cholesky factor matrix.
[out]	ff	failure flag

Author: R. J. Purser

Definition at line 981 of file pmat.f90.

subroutine pmat::dldlm	(	real(dp), dimension(:,:), intent(in)	a,
		real(dp), dimension(:,:), intent(inout)	b,
		real(dp), dimension(:), intent(out)	d
	)

private

Modified Cholesky decompose Q –> L*D*U, U(i,j)=L(j,i)

Parameters

[in]	a	symmetric matrix.
[in,out]	b	output modified cholesky factor, L.
[out]	d	diagonal matrix, D.

Author: R. J. Purser

Definition at line 1030 of file pmat.f90.

References pmat::ldlm::dldlmf().

subroutine pmat::dldlmf	(	real(dp), dimension(:,:), intent(in)	a,
		real(dp), dimension(:,:), intent(inout)	b,
		real(dp), dimension(:), intent(out)	d,
		logical, intent(out)	ff
	)

Modified Cholesky Q –> L*D*U, U(i,j)=L(j,i)

Parameters

[in]	a	symmetric matrix.
[in,out]	b	modified Cholesky factor, L.
[out]	d	diagonal matrix, D.
[out]	ff	error flag

Author: R. J. Purser

Definition at line 1083 of file pmat.f90.

subroutine pmat::dldum	(	real(dp), dimension(:,:), intent(inout)	a,
		integer(spi), dimension(:), intent(out)	ipiv,
		real(dp), intent(out)	d
	)

private

Perform L*D*U decomposition, with pivoting, of square matrix.

Double precision version.

Parameters

[in,out]	a	input square matrix, output L,D,U factors
[out]	d	determinant sign change indicator (+1 or -1)
[out]	ipiv	vector of pivots

Author: R. J. Purser

Definition at line 492 of file pmat.f90.

References pmat::ldum::dldumf().

subroutine pmat::dldumf	(	real(dp), dimension(:,:), intent(inout)	a,
		integer, dimension(:), intent(out)	ipiv,
		real(dp), intent(out)	d,
		logical(spi), intent(out)	ff
	)

Perform l-d-u decomposition of square matrix a in place with pivoting.

Double precision version.

Parameters

[in,out]	a	square matrix to be factorized
[out]	ipiv	vector encoding the pivoting sequence
[out]	d	indicator for possible sign change of determinant
[out]	ff,:	failure flag, set to .true. when determinant of a vanishes.

Author: R. J. Purser

Definition at line 592 of file pmat.f90.

References pmat::swpvv::dswpvv().

subroutine pmat::dlinlv	(	real(dp), dimension(:,:), intent(in)	a,
		real(dp), dimension(:), intent(inout)	u
	)

private

Solve linear system involving lower triangular system matrix.

Double precision version.

Parameters

[in]	a	lower triangular matrix.
[in,out]	u	input RHS vector, output solution vector.

Author: R. J. Purser

Definition at line 1188 of file pmat.f90.

subroutine pmat::dlinmmt	(	real(dp), dimension(:,:), intent(inout)	a,
		real(dp), dimension(:,:), intent(inout)	b
	)

private

Invert linear system with multiple right-hand side vectors.

Double precision version

Parameters

[in,out]	a	Invertible system matrix, destroyed on output
[in,out]	b	input RHS vectors, output solution vectors

Author: R. J. Purser

Definition at line 242 of file pmat.f90.

References pmat::inv::dlinmmtf().

subroutine pmat::dlinmmtf	(	real(dp), dimension(:,:), intent(inout)	a,
		real(dp), dimension(:,:), intent(inout)	b,
		logical, intent(out)	ff
	)

private

Invert linear system with multiple right-hand side vectors, or flag failure.

Double precision version.

Parameters

[in,out]	a	Invertible system matrix, destroyed on output
[in,out]	b	input RHS vectors, output solution vectors
[out]	ff	failure flag

Author: R. J. Purser

Definition at line 294 of file pmat.f90.

References pmat::ldum::dldumf(), and pmat::udlmm::dudlmm().

subroutine pmat::dlinmvt	(	real(dp), dimension(:,:), intent(inout)	a,
		real(dp), dimension(:), intent(inout)	b
	)

private

Invert linear system with single right-hand side vector.

Double precision version.

Parameters

[in,out]	a	Invertible system matrix, destroyed on output
[in,out]	b	input RHS vector, output solution vector

Author: R. J. Purser

Definition at line 357 of file pmat.f90.

References pmat::inv::dlinmvtf().

subroutine pmat::dlinmvtf	(	real(dp), dimension(:,:), intent(inout)	a,
		real(dp), dimension(:), intent(inout)	b,
		logical, intent(out)	ff
	)

private

Invert linear system with single right-hand side vector.

Parameters

[in,out]	a	Invertible system matrix, destroyed on output
[in,out]	b	input RHS vector, output solution vector
[out]	ff	failure flag

Author: R. J. Purser

Definition at line 407 of file pmat.f90.

References pmat::ldum::dldumf(), and pmat::udlmm::dudlmv().

subroutine pmat::dlinuv	(	real(dp), dimension(:,:), intent(in)	a,
		real(dp), dimension(:), intent(inout)	u
	)

private

Solve linear system involving upper triangular system matrix.

Double precision version.

Parameters

[in]	a	upper triangular matrix.
[in,out]	u	input RHS vector, output solution vector.

Author: R. J. Purser

Definition at line 1218 of file pmat.f90.

subroutine pmat::dswpvv	(	real(dp), dimension(:), intent(inout)	d,
		real(dp), dimension(:), intent(inout)	e
	)

private

Swap a pair of double precision vectors.

Parameters

[in,out]	d	vector
[in,out]	e	vector

Author: R. J. Purser

Definition at line 60 of file pmat.f90.

subroutine pmat::dudlmm	(	real(dp), dimension(:,:), intent(in)	a,
		real(dp), dimension(:,:), intent(inout)	b,
		integer(spi), dimension(:), intent(in)	ipiv
	)

Use l-u factors in A to back-substitute for several rhs in B, using ipiv to define the pivoting permutation used in the l-u decomposition.

Parameters

[in]	a	square matrix to be factorized
[in,out]	b	rt-hand-sides vectors on input, corresponding solutions on return
[in]	ipiv	vector encoding the pivoting sequence

Author: R. J. Purser

Definition at line 763 of file pmat.f90.

subroutine pmat::dudlmv	(	real(dp), dimension(:,:), intent(in)	a,
		real(dp), dimension(:), intent(inout)	b,
		integer(spi), dimension(:), intent(in)	ipiv
	)

Use l-u factors in A to back-substitute for 1 rhs in B, using ipiv to define the pivoting permutation used in the l-u decomposition.

Parameters

[in]	a	square matrix to be factorized
[in,out]	b	right-hand side vector on input, corresponding solution on return
[in]	ipiv	array encoding the pivoting sequence

Author: R. J. Purser

Definition at line 861 of file pmat.f90.

subroutine pmat::iinvf	(	integer(spi), dimension(:,:), intent(inout)	imat,
		logical, intent(out)	ff
	)

private

Invert integer square matrix, imat, if possible, but flag ff=.true.

if not possible. (Determinant of imat must be +1 or -1)

Parameters

[in,out]	imat	integer square matrix
[out]	ff	error flag

Author: R. J. Purser

Definition at line 451 of file pmat.f90.

subroutine pmat::sinvl ( real(sp), dimension(:,:), intent(inout) a )

private

Invert lower triangular matrix in place.

Single precision.

Parameters

[in,out] a lower triangular matrix.

Author: R. J. Purser

Definition at line 1135 of file pmat.f90.

subroutine pmat::sinvmt ( real(sp), dimension(:,:), intent(inout) a )

private

Invert single precision matrix in place.

Parameters

[in,out] a matrix

Author: R. J. Purser

Definition at line 81 of file pmat.f90.

References pmat::inv::sinvmtf().

subroutine pmat::sinvmtf	(	real(sp), dimension(:,:), intent(inout)	a,
		logical, intent(out)	ff
	)

private

Invert a single precision matrix in place, or flag if process fails.

Parameters

[in,out]	a	matrix
[out]	ff	flag for error condition

Author: R. J. Purser

Definition at line 115 of file pmat.f90.

References pmat::ldum::sldumf(), and pmat::swpvv::sswpvv().

subroutine pmat::sinvu ( real(sp), dimension(:,:), intent(inout) a )

Invert the upper triangular matrix in place by transposing, calling invl, and transposing again.

Single precision version.

Parameters

[in,out] a upper triangular matrix.

Author: R. J. Purser

Definition at line 1116 of file pmat.f90.

References pmat::invl::sinvl().

subroutine pmat::sl1lm	(	real(sp), dimension(:,:), intent(in)	a,
		real(sp), dimension(:,:), intent(inout)	b
	)

Cholesky, M -> L*U, U(i,j)=L(j,i)

Parameters

[in]	a	symmetric matrix.
[in,out]	b	Cholesky factor matrix.

Author: R. J. Purser

Definition at line 920 of file pmat.f90.

References pmat::l1lm::sl1lmf().

subroutine pmat::sl1lmf	(	real(sp), dimension(:,:), intent(in)	a,
		real(sp), dimension(:,:), intent(inout)	b,
		logical, intent(out)	ff
	)

private

Cholesky, M -> L*U, U(i,j)=L(j,i)

Parameters

[in]	a	symmetric matrix.
[in,out]	b	Cholesky factor matrix.
[out]	ff	failure flag

Author: R. J. Purser

Definition at line 947 of file pmat.f90.

subroutine pmat::sldlm	(	real(sp), dimension(:,:), intent(in)	a,
		real(sp), dimension(:,:), intent(inout)	b,
		real(sp), dimension(:), intent(out)	d
	)

Modified Cholesky decompose Q –> L*D*U, U(i,j)=L(j,i)

Parameters

[in]	a	symmetric matrix.
[in,out]	b	output modified cholesky factor, L.
[out]	d	diagonal matrix, D.

Author: R. J. Purser

Definition at line 1015 of file pmat.f90.

References pmat::ldlm::sldlmf().

subroutine pmat::sldlmf	(	real(sp), dimension(:,:), intent(in)	a,
		real(sp), dimension(:,:), intent(inout)	b,
		real(sp), dimension(:), intent(out)	d,
		logical, intent(out)	ff
	)

private

Modified Cholesky decompose Q –> L*D*U, U(i,j)=L(j,i)

Parameters

[in]	a	symmetric matrix
[in,out]	b	modified cholesky factor, L.
[out]	d	diagonal matrix, D.
[out]	ff	error flag

Author: R. J. Purser

Definition at line 1046 of file pmat.f90.

subroutine pmat::sldum	(	real(sp), dimension(:,:), intent(inout)	a,
		integer(spi), dimension(:), intent(out)	ipiv,
		real(sp), intent(out)	d
	)

private

Perform L*D*U decomposition, with pivoting, of square matrix.

Single precision version.

Parameters

[in,out]	a	input square matrix, output L,D,U factors
[out]	d	determinant sign change indicator (+1 or -1)
[out]	ipiv	vector of pivots

Author: R. J. Purser

Definition at line 476 of file pmat.f90.

References pmat::ldum::sldumf().

subroutine pmat::sldumf	(	real(sp), dimension(:,:), intent(inout)	a,
		integer(spi), dimension(:), intent(out)	ipiv,
		real(sp), intent(out)	d,
		logical, intent(out)	ff
	)

private

Perform l-d-u decomposition of square matrix a in place with pivoting.

Single precision version.

Parameters

[in,out]	a	square matrix to be factorized
[out]	ipiv	vector encoding the pivoting sequence
[out]	d	indicator for possible sign change of determinant
[out]	ff,:	failure flag, set to .true. when determinant of a vanishes.

Author: R. J. Purser

Definition at line 525 of file pmat.f90.

References pmat::swpvv::sswpvv().

subroutine pmat::slinlv	(	real(sp), dimension(:,:), intent(in)	a,
		real(sp), dimension(:), intent(inout)	u
	)

Solve linear system involving lower triangular system matrix.

Single precision version.

Parameters

[in]	a	lower triangular matrix.
[in,out]	u	input RHS vector, output solution vector.

Author: R. J. Purser

Definition at line 1173 of file pmat.f90.

subroutine pmat::slinmmt	(	real(sp), dimension(:,:), intent(inout)	a,
		real(sp), dimension(:,:), intent(inout)	b
	)

Invert linear system with multiple right-hand side vectors.

Single precision version.

Parameters

[in,out]	a	Invertible system matrix, destroyed on output
[in,out]	b	input RHS vectors, output solution vectors

Author: R. J. Purser

Definition at line 229 of file pmat.f90.

References pmat::inv::slinmmtf().

subroutine pmat::slinmmtf	(	real(sp), dimension(:,:), intent(inout)	a,
		real(sp), dimension(:,:), intent(inout)	b,
		logical, intent(out)	ff
	)

private

Invert linear system with multiple right-hand side vectors, or flag failure.

Single precision version.

Parameters

[in,out]	a	Invertible system matrix, destroyed on output
[in,out]	b	input RHS vectors, output solution vectors
[out]	ff	failure flag

Author: R. J. Purser

Definition at line 269 of file pmat.f90.

References pmat::ldum::sldumf(), and pmat::udlmm::sudlmm().

subroutine pmat::slinmvt	(	real(sp), dimension(:,:), intent(inout)	a,
		real(sp), dimension(:), intent(inout)	b
	)

private

Invert linear system with single right-hand side vector.

Single precision version.

Parameters

[in,out]	a	Invertible system matrix, destroyed on output
[in,out]	b	input RHS vector, output solution vector

Author: R. J. Purser

Definition at line 343 of file pmat.f90.

References pmat::inv::slinmvtf().

subroutine pmat::slinmvtf	(	real(sp), dimension(:,:), intent(inout)	a,
		real(sp), dimension(:), intent(inout)	b,
		logical, intent(out)	ff
	)

private

Invert linear system with single right-hand side vector.

Parameters

[in,out]	a	Invertible system matrix, destroyed on output
[in,out]	b	input RHS vector, output solution vector
[out]	ff	failure flag

Author: R. J. Purser

Definition at line 385 of file pmat.f90.

References pmat::ldum::sldumf(), and pmat::udlmm::sudlmv().

subroutine pmat::slinuv	(	real(sp), dimension(:,:), intent(in)	a,
		real(sp), dimension(:), intent(inout)	u
	)

private

Solve linear system involving upper triangular system matrix.

Single precision version.

Parameters

[in]	a	upper triangular matrix.
[in,out]	u	input RHS vector, output solution vector.

Author: R. J. Purser

Definition at line 1203 of file pmat.f90.

subroutine pmat::sswpvv	(	real(sp), dimension(:), intent(inout)	d,
		real(sp), dimension(:), intent(inout)	e
	)

private

Swap a pair of single precision vectors.

Parameters

[in,out]	d	vector
[in,out]	e	vector

Author: R. J. Purser

Definition at line 49 of file pmat.f90.

subroutine pmat::sudlmm	(	real(sp), dimension(:,:), intent(in)	a,
		real(sp), dimension(:,:), intent(inout)	b,
		integer(spi), dimension(:), intent(in)	ipiv
	)

Use l-u factors in A to back-substitute for several rhs in B, using ipiv to define the pivoting permutation used in the l-u decomposition.

Parameters

[in]	a	L-D-U factorization of linear system matrux
[in,out]	b	rt-hand-sides vectors on input, corresponding solutions on return
[in]	ipiv	vector encoding the pivoting sequence

Author: R. J. Purser

Definition at line 729 of file pmat.f90.

subroutine pmat::sudlmv	(	real(sp), dimension(:,:), intent(in)	a,
		real(sp), dimension(:), intent(inout)	b,
		integer(spi), dimension(:), intent(in)	ipiv
	)

Use l-u factors in A to back-substitute for 1 rhs in B, using ipiv to define the pivoting permutation used in the l-u decomposition.

Parameters

[in]	a	L-D-U factorization of linear system matrix
[in,out]	b	right-hand-side vector on input, corresponding solution on return
[in]	ipiv	vector encoding the pivoting sequence

Author: R. J. Purser

Definition at line 830 of file pmat.f90.

The documentation for this module was generated from the following file:

/scratch1/NCEPDEV/da/George.Gayno/ufs_utils.git/UFS_UTILS.upstream/sorc/grid_tools.fd/regional_esg_grid.fd/pmat.f90

Data Types

Public Member Functions

Private Member Functions

Detailed Description

Member Function/Subroutine Documentation