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posv(3) Library Functions Manual posv(3)

NAME

posv - posv: factor and solve

SYNOPSIS

Functions


subroutine CPOSV (uplo, n, nrhs, a, lda, b, ldb, info)
CPOSV computes the solution to system of linear equations A * X = B for PO matrices subroutine DPOSV (uplo, n, nrhs, a, lda, b, ldb, info)
DPOSV computes the solution to system of linear equations A * X = B for PO matrices subroutine SPOSV (uplo, n, nrhs, a, lda, b, ldb, info)
SPOSV computes the solution to system of linear equations A * X = B for PO matrices subroutine ZPOSV (uplo, n, nrhs, a, lda, b, ldb, info)
ZPOSV computes the solution to system of linear equations A * X = B for PO matrices

Detailed Description

Function Documentation

subroutine CPOSV (character uplo, integer n, integer nrhs, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldb, * ) b, integer ldb, integer info)

CPOSV computes the solution to system of linear equations A * X = B for PO matrices

Purpose:

!>
!> CPOSV computes the solution to a complex system of linear equations
!>    A * X = B,
!> where A is an N-by-N Hermitian positive definite matrix and X and B
!> are N-by-NRHS matrices.
!>
!> The Cholesky decomposition is used to factor A as
!>    A = U**H* U,  if UPLO = 'U', or
!>    A = L * L**H,  if UPLO = 'L',
!> where U is an upper triangular matrix and  L is a lower triangular
!> matrix.  The factored form of A is then used to solve the system of
!> equations A * X = B.
!>

Parameters

UPLO 

!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangle of A is stored;
!>          = 'L':  Lower triangle of A is stored.
!>

N

!>          N is INTEGER
!>          The number of linear equations, i.e., the order of the
!>          matrix A.  N >= 0.
!>

NRHS

!>          NRHS is INTEGER
!>          The number of right hand sides, i.e., the number of columns
!>          of the matrix B.  NRHS >= 0.
!>

A

!>          A is COMPLEX array, dimension (LDA,N)
!>          On entry, the Hermitian matrix A.  If UPLO = 'U', the leading
!>          N-by-N upper triangular part of A contains the upper
!>          triangular part of the matrix A, and the strictly lower
!>          triangular part of A is not referenced.  If UPLO = 'L', the
!>          leading N-by-N lower triangular part of A contains the lower
!>          triangular part of the matrix A, and the strictly upper
!>          triangular part of A is not referenced.
!>
!>          On exit, if INFO = 0, the factor U or L from the Cholesky
!>          factorization A = U**H*U or A = L*L**H.
!>

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,N).
!>

B

!>          B is COMPLEX array, dimension (LDB,NRHS)
!>          On entry, the N-by-NRHS right hand side matrix B.
!>          On exit, if INFO = 0, the N-by-NRHS solution matrix X.
!>

LDB

!>          LDB is INTEGER
!>          The leading dimension of the array B.  LDB >= max(1,N).
!>

INFO

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>          > 0:  if INFO = i, the leading principal minor of order i
!>                of A is not positive, so the factorization could not
!>                be completed, and the solution has not been computed.
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 129 of file cposv.f.

subroutine DPOSV (character uplo, integer n, integer nrhs, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldb, * ) b, integer ldb, integer info)

DPOSV computes the solution to system of linear equations A * X = B for PO matrices

Purpose:

!>
!> DPOSV computes the solution to a real system of linear equations
!>    A * X = B,
!> where A is an N-by-N symmetric positive definite matrix and X and B
!> are N-by-NRHS matrices.
!>
!> The Cholesky decomposition is used to factor A as
!>    A = U**T* U,  if UPLO = 'U', or
!>    A = L * L**T,  if UPLO = 'L',
!> where U is an upper triangular matrix and L is a lower triangular
!> matrix.  The factored form of A is then used to solve the system of
!> equations A * X = B.
!>

Parameters

UPLO 

!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangle of A is stored;
!>          = 'L':  Lower triangle of A is stored.
!>

N

!>          N is INTEGER
!>          The number of linear equations, i.e., the order of the
!>          matrix A.  N >= 0.
!>

NRHS

!>          NRHS is INTEGER
!>          The number of right hand sides, i.e., the number of columns
!>          of the matrix B.  NRHS >= 0.
!>

A

!>          A is DOUBLE PRECISION array, dimension (LDA,N)
!>          On entry, the symmetric matrix A.  If UPLO = 'U', the leading
!>          N-by-N upper triangular part of A contains the upper
!>          triangular part of the matrix A, and the strictly lower
!>          triangular part of A is not referenced.  If UPLO = 'L', the
!>          leading N-by-N lower triangular part of A contains the lower
!>          triangular part of the matrix A, and the strictly upper
!>          triangular part of A is not referenced.
!>
!>          On exit, if INFO = 0, the factor U or L from the Cholesky
!>          factorization A = U**T*U or A = L*L**T.
!>

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,N).
!>

B

!>          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
!>          On entry, the N-by-NRHS right hand side matrix B.
!>          On exit, if INFO = 0, the N-by-NRHS solution matrix X.
!>

LDB

!>          LDB is INTEGER
!>          The leading dimension of the array B.  LDB >= max(1,N).
!>

INFO

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>          > 0:  if INFO = i, the leading principal minor of order i
!>                of A is not positive, so the factorization could not
!>                be completed, and the solution has not been computed.
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 129 of file dposv.f.

subroutine SPOSV (character uplo, integer n, integer nrhs, real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, integer info)

SPOSV computes the solution to system of linear equations A * X = B for PO matrices

Purpose:

!>
!> SPOSV computes the solution to a real system of linear equations
!>    A * X = B,
!> where A is an N-by-N symmetric positive definite matrix and X and B
!> are N-by-NRHS matrices.
!>
!> The Cholesky decomposition is used to factor A as
!>    A = U**T* U,  if UPLO = 'U', or
!>    A = L * L**T,  if UPLO = 'L',
!> where U is an upper triangular matrix and L is a lower triangular
!> matrix.  The factored form of A is then used to solve the system of
!> equations A * X = B.
!>

Parameters

UPLO 

!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangle of A is stored;
!>          = 'L':  Lower triangle of A is stored.
!>

N

!>          N is INTEGER
!>          The number of linear equations, i.e., the order of the
!>          matrix A.  N >= 0.
!>

NRHS

!>          NRHS is INTEGER
!>          The number of right hand sides, i.e., the number of columns
!>          of the matrix B.  NRHS >= 0.
!>

A

!>          A is REAL array, dimension (LDA,N)
!>          On entry, the symmetric matrix A.  If UPLO = 'U', the leading
!>          N-by-N upper triangular part of A contains the upper
!>          triangular part of the matrix A, and the strictly lower
!>          triangular part of A is not referenced.  If UPLO = 'L', the
!>          leading N-by-N lower triangular part of A contains the lower
!>          triangular part of the matrix A, and the strictly upper
!>          triangular part of A is not referenced.
!>
!>          On exit, if INFO = 0, the factor U or L from the Cholesky
!>          factorization A = U**T*U or A = L*L**T.
!>

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,N).
!>

B

!>          B is REAL array, dimension (LDB,NRHS)
!>          On entry, the N-by-NRHS right hand side matrix B.
!>          On exit, if INFO = 0, the N-by-NRHS solution matrix X.
!>

LDB

!>          LDB is INTEGER
!>          The leading dimension of the array B.  LDB >= max(1,N).
!>

INFO

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>          > 0:  if INFO = i, the leading principal minor of order i
!>                of A is not positive, so the factorization could not
!>                be completed, and the solution has not been computed.
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 129 of file sposv.f.

subroutine ZPOSV (character uplo, integer n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b, integer ldb, integer info)

ZPOSV computes the solution to system of linear equations A * X = B for PO matrices

Purpose:

!>
!> ZPOSV computes the solution to a complex system of linear equations
!>    A * X = B,
!> where A is an N-by-N Hermitian positive definite matrix and X and B
!> are N-by-NRHS matrices.
!>
!> The Cholesky decomposition is used to factor A as
!>    A = U**H* U,  if UPLO = 'U', or
!>    A = L * L**H,  if UPLO = 'L',
!> where U is an upper triangular matrix and  L is a lower triangular
!> matrix.  The factored form of A is then used to solve the system of
!> equations A * X = B.
!>

Parameters

UPLO 

!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangle of A is stored;
!>          = 'L':  Lower triangle of A is stored.
!>

N

!>          N is INTEGER
!>          The number of linear equations, i.e., the order of the
!>          matrix A.  N >= 0.
!>

NRHS

!>          NRHS is INTEGER
!>          The number of right hand sides, i.e., the number of columns
!>          of the matrix B.  NRHS >= 0.
!>

A

!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          On entry, the Hermitian matrix A.  If UPLO = 'U', the leading
!>          N-by-N upper triangular part of A contains the upper
!>          triangular part of the matrix A, and the strictly lower
!>          triangular part of A is not referenced.  If UPLO = 'L', the
!>          leading N-by-N lower triangular part of A contains the lower
!>          triangular part of the matrix A, and the strictly upper
!>          triangular part of A is not referenced.
!>
!>          On exit, if INFO = 0, the factor U or L from the Cholesky
!>          factorization A = U**H *U or A = L*L**H.
!>

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,N).
!>

B

!>          B is COMPLEX*16 array, dimension (LDB,NRHS)
!>          On entry, the N-by-NRHS right hand side matrix B.
!>          On exit, if INFO = 0, the N-by-NRHS solution matrix X.
!>

LDB

!>          LDB is INTEGER
!>          The leading dimension of the array B.  LDB >= max(1,N).
!>

INFO

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>          > 0:  if INFO = i, the leading principal minor of order i
!>                of A is not positive, so the factorization could not
!>                be completed, and the solution has not been computed.
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 129 of file zposv.f.

Author

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