pmat.f90 File Reference

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

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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.
subroutine	pmat::cinvmtf (a, ff)
	Invert a complex matrix in place, or flag if process fails.
subroutine	pmat::cldum (a, ipiv, d)
	Perform L*D*U decomposition, with pivoting, of square matrix.
subroutine	pmat::cldumf (a, ipiv, d, ff)
	Perform l-d-u decomposition of square matrix a in place with pivoting.
subroutine	pmat::clinmmt (a, b)
	Invert complex linear system with multiple right-hand side vectors.
subroutine	pmat::clinmmtf (a, b, ff)
	Invert linear system with multiple right-hand side vectors, or flag failure.
subroutine	pmat::clinmvt (a, b)
	Invert linear system with single right-hand side vector.
subroutine	pmat::clinmvtf (a, b, ff)
	Invert complex linear system with single right-hand side vector.
subroutine	pmat::cswpvv (d, e)
	Swap a pair of complex vectors.
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.
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.
subroutine	pmat::dinvl (a)
	Invert lower triangular matrix in place.
subroutine	pmat::dinvmt (a)
	Invert double precision matrix in place.
subroutine	pmat::dinvmtf (a, ff)
	Invert a double precision matrix in place, or flag if process fails.
subroutine	pmat::dinvu (a)
	Invert the upper triangular matrix in place by transposing, calling invl, and transposing again.
subroutine	pmat::dl1lm (a, b)
	Cholesky, M -> L*U, U(i,j)=L(j,i)
subroutine	pmat::dl1lmf (a, b, ff)
	Cholesky, M -> L*U, U(i,j)=L(j,i)
subroutine	pmat::dldlm (a, b, d)
	Modified Cholesky decompose Q --> L*D*U, U(i,j)=L(j,i)
subroutine	pmat::dldlmf (a, b, d, ff)
	Modified Cholesky Q --> L*D*U, U(i,j)=L(j,i)
subroutine	pmat::dldum (a, ipiv, d)
	Perform L*D*U decomposition, with pivoting, of square matrix.
subroutine	pmat::dldumf (a, ipiv, d, ff)
	Perform l-d-u decomposition of square matrix a in place with pivoting.
subroutine	pmat::dlinlv (a, u)
	Solve linear system involving lower triangular system matrix.
subroutine	pmat::dlinmmt (a, b)
	Invert linear system with multiple right-hand side vectors.
subroutine	pmat::dlinmmtf (a, b, ff)
	Invert linear system with multiple right-hand side vectors, or flag failure.
subroutine	pmat::dlinmvt (a, b)
	Invert linear system with single right-hand side vector.
subroutine	pmat::dlinmvtf (a, b, ff)
	Invert linear system with single right-hand side vector.
subroutine	pmat::dlinuv (a, u)
	Solve linear system involving upper triangular system matrix.
subroutine	pmat::dswpvv (d, e)
	Swap a pair of double precision vectors.
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.
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.
subroutine	pmat::iinvf (imat, ff)
	Invert integer square matrix, imat, if possible, but flag ff=.true.
subroutine	pmat::sinvl (a)
	Invert lower triangular matrix in place.
subroutine	pmat::sinvmt (a)
	Invert single precision matrix in place.
subroutine	pmat::sinvmtf (a, ff)
	Invert a single precision matrix in place, or flag if process fails.
subroutine	pmat::sinvu (a)
	Invert the upper triangular matrix in place by transposing, calling invl, and transposing again.
subroutine	pmat::sl1lm (a, b)
	Cholesky, M -> L*U, U(i,j)=L(j,i)
subroutine	pmat::sl1lmf (a, b, ff)
	Cholesky, M -> L*U, U(i,j)=L(j,i)
subroutine	pmat::sldlm (a, b, d)
	Modified Cholesky decompose Q --> L*D*U, U(i,j)=L(j,i)
subroutine	pmat::sldlmf (a, b, d, ff)
	Modified Cholesky decompose Q --> L*D*U, U(i,j)=L(j,i)
subroutine	pmat::sldum (a, ipiv, d)
	Perform L*D*U decomposition, with pivoting, of square matrix.
subroutine	pmat::sldumf (a, ipiv, d, ff)
	Perform l-d-u decomposition of square matrix a in place with pivoting.
subroutine	pmat::slinlv (a, u)
	Solve linear system involving lower triangular system matrix.
subroutine	pmat::slinmmt (a, b)
	Invert linear system with multiple right-hand side vectors.
subroutine	pmat::slinmmtf (a, b, ff)
	Invert linear system with multiple right-hand side vectors, or flag failure.
subroutine	pmat::slinmvt (a, b)
	Invert linear system with single right-hand side vector.
subroutine	pmat::slinmvtf (a, b, ff)
	Invert linear system with single right-hand side vector.
subroutine	pmat::slinuv (a, u)
	Solve linear system involving upper triangular system matrix.
subroutine	pmat::sswpvv (d, e)
	Swap a pair of single precision vectors.
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.
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.

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 103 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 190 of file pmat.f90.

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 508 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 )

private

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.

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 255 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 319 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 371 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 429 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 71 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 )

private

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.

cudlmv()

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

private

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.

dinvl()

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

private

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.

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 92 of file pmat.f90.

dinvmtf()

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

private

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.

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 1126 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 933 of file pmat.f90.

dl1lmf()

subroutine pmat::dl1lmf ( real(dp), dimension(:,:), intent(in) a, real(dp), 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 981 of file pmat.f90.

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 1030 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 )

private

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.

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 492 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 )

private

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.

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 1188 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 242 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 294 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 357 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 407 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 1218 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 60 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 )

private

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.

dudlmv()

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

private

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.

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 451 of file pmat.f90.

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 1135 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 81 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 115 of file pmat.f90.

sinvu()

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

private

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.

sl1lm()

subroutine pmat::sl1lm ( real(sp), dimension(:,:), intent(in) a, real(sp), 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 920 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 947 of file pmat.f90.

sldlm()

subroutine pmat::sldlm ( real(sp), dimension(:,:), intent(in) a, real(sp), dimension(:,:), intent(inout) b, real(sp), 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 1015 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 1046 of file pmat.f90.

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 476 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 525 of file pmat.f90.

slinlv()

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

private

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.

slinmmt()

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

private

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.

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.

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 343 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 385 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 1203 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 49 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 )

private

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.

sudlmv()

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

private

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.