Utility routines for various linear inversions and Cholesky. More...

Data Types
interface	pmat::inv

interface	pmat::invl

interface	pmat::invu

interface	pmat::l1lm

interface	pmat::ldlm

interface	pmat::ldum

interface	pmat::swpvv

interface	pmat::udlmm

Functions/Subroutines
subroutine	pmat::cinvmt (a)
	Invert complex matrix in place. More...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

subroutine	pmat::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	pmat::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...

Detailed Description

Utility routines for various linear inversions and Cholesky.

Author: R. J. Purser, NOAA/NCEP/EMC, Tsukasa Fujita, JMA.

Definition in file pmat.f90.

Function/Subroutine Documentation

◆ cinvmt()

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 104 of file pmat.f90.

◆ 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 191 of file pmat.f90.

References pietc::c1.

◆ cldum()

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 509 of file pmat.f90.

◆ 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 660 of file pmat.f90.

References pietc::c0, pietc::c1, pietc::u0, and pietc::u1.

◆ clinmmt()

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 256 of file pmat.f90.

◆ 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 320 of file pmat.f90.

◆ clinmvt()

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 372 of file pmat.f90.

◆ 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 430 of file pmat.f90.

◆ cswpvv()

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 72 of file pmat.f90.

◆ cudlmm()

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 798 of file pmat.f90.

References pietc::c1.

◆ cudlmv()

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 893 of file pmat.f90.

References pietc::c1.

◆ dinvl()

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 1154 of file pmat.f90.

References pietc::u0, and pietc::u1.

◆ dinvmt()

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 93 of file pmat.f90.

◆ 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 154 of file pmat.f90.

◆ dinvu()

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 1127 of file pmat.f90.

◆ dl1lm()

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 934 of file pmat.f90.

◆ 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 982 of file pmat.f90.

References pietc::u0, and pietc::u1.

◆ dldlm()

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 1031 of file pmat.f90.

◆ 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 1084 of file pmat.f90.

References pietc::u0, and pietc::u1.

◆ dldum()

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 493 of file pmat.f90.

◆ 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 593 of file pmat.f90.

References pietc::u0, and pietc::u1.

◆ dlinlv()

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 1189 of file pmat.f90.

◆ dlinmmt()

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 243 of file pmat.f90.

◆ 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 295 of file pmat.f90.

◆ dlinmvt()

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 358 of file pmat.f90.

◆ 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 408 of file pmat.f90.

◆ dlinuv()

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 1219 of file pmat.f90.

◆ dswpvv()

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 61 of file pmat.f90.

◆ dudlmm()

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 764 of file pmat.f90.

References pietc::u1.

◆ dudlmv()

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 862 of file pmat.f90.

References pietc::u1.

◆ iinvf()

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 452 of file pmat.f90.

References pietc::t.

◆ sinvl()

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 1136 of file pmat.f90.

◆ sinvmt()

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 82 of file pmat.f90.

◆ 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 116 of file pmat.f90.

◆ sinvu()

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 1117 of file pmat.f90.

◆ sl1lm()

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 921 of file pmat.f90.

◆ 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 948 of file pmat.f90.

References pietc::f.

◆ sldlm()

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 1016 of file pmat.f90.

◆ 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 1047 of file pmat.f90.

References pietc::f.

◆ sldum()

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 477 of file pmat.f90.

◆ 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 526 of file pmat.f90.

References pietc::f, and pietc::t.

◆ slinlv()

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 1174 of file pmat.f90.

◆ slinmmt()

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 230 of file pmat.f90.

◆ 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 270 of file pmat.f90.

◆ slinmvt()

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 344 of file pmat.f90.

◆ 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 386 of file pmat.f90.

◆ slinuv()

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 1204 of file pmat.f90.

◆ sswpvv()

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 50 of file pmat.f90.

◆ sudlmm()

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 730 of file pmat.f90.

◆ sudlmv()

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 831 of file pmat.f90.

Data Types

Functions/Subroutines

Detailed Description

Function/Subroutine Documentation

◆ cinvmt()

◆ cinvmtf()

◆ cldum()

◆ cldumf()

◆ clinmmt()

◆ clinmmtf()

◆ clinmvt()

◆ clinmvtf()

◆ cswpvv()

◆ cudlmm()

◆ cudlmv()

◆ dinvl()

◆ dinvmt()

◆ dinvmtf()

◆ dinvu()

◆ dl1lm()

◆ dl1lmf()

◆ dldlm()

◆ dldlmf()

◆ dldum()

◆ dldumf()

◆ dlinlv()

◆ dlinmmt()

◆ dlinmmtf()

◆ dlinmvt()

◆ dlinmvtf()

◆ dlinuv()

◆ dswpvv()

◆ dudlmm()

◆ dudlmv()

◆ iinvf()

◆ sinvl()

◆ sinvmt()

◆ sinvmtf()

◆ sinvu()

◆ sl1lm()

◆ sl1lmf()

◆ sldlm()

◆ sldlmf()

◆ sldum()

◆ sldumf()

◆ slinlv()

◆ slinmmt()

◆ slinmmtf()

◆ slinmvt()

◆ slinmvtf()

◆ slinuv()

◆ sswpvv()

◆ sudlmm()

◆ sudlmv()