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.

  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.

  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.

  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.

Author

Generated automatically by Doxygen for LAPACK from the source code.