pptrs(3)

NAME
pptrs - pptrs: triangular solve using factor

SYNOPSIS

  Functions

subroutine cpptrs (uplo, n, nrhs, ap, b, ldb, info)
CPPTRS
subroutine dpptrs (uplo, n, nrhs, ap, b, ldb, info)
DPPTRS
subroutine spptrs (uplo, n, nrhs, ap, b, ldb, info)
SPPTRS
subroutine zpptrs (uplo, n, nrhs, ap, b, ldb, info)
ZPPTRS

Detailed Description

Function Documentation

  subroutine cpptrs (character uplo, integer n, integer nrhs, complex, dimension( * ) ap, complex, dimension( ldb, * ) b, integer ldb, integer info)

CPPTRS

Purpose:

    !>
    !> CPPTRS solves a system of linear equations A*X = B with a Hermitian
    !> positive definite matrix A in packed storage using the Cholesky
    !> factorization A = U**H*U or A = L*L**H computed by CPPTRF.
    !>

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 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.
    !>

    AP

    !>          AP is COMPLEX array, dimension (N*(N+1)/2)
    !>          The triangular factor U or L from the Cholesky factorization
    !>          A = U**H*U or A = L*L**H, packed columnwise in a linear
    !>          array.  The j-th column of U or L is stored in the array AP
    !>          as follows:
    !>          if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
    !>          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.
    !>

    B

    !>          B is COMPLEX array, dimension (LDB,NRHS)
    !>          On entry, the right hand side matrix B.
    !>          On exit, the 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
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine dpptrs (character uplo, integer n, integer nrhs, double precision, dimension( * ) ap, double precision, dimension( ldb, * ) b, integer ldb, integer info)

DPPTRS

Purpose:

    !>
    !> DPPTRS solves a system of linear equations A*X = B with a symmetric
    !> positive definite matrix A in packed storage using the Cholesky
    !> factorization A = U**T*U or A = L*L**T computed by DPPTRF.
    !>

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 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.
    !>

    AP

    !>          AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
    !>          The triangular factor U or L from the Cholesky factorization
    !>          A = U**T*U or A = L*L**T, packed columnwise in a linear
    !>          array.  The j-th column of U or L is stored in the array AP
    !>          as follows:
    !>          if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
    !>          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.
    !>

    B

    !>          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
    !>          On entry, the right hand side matrix B.
    !>          On exit, the 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
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine spptrs (character uplo, integer n, integer nrhs, real, dimension( * ) ap, real, dimension( ldb, * ) b, integer ldb, integer info)

SPPTRS

Purpose:

    !>
    !> SPPTRS solves a system of linear equations A*X = B with a symmetric
    !> positive definite matrix A in packed storage using the Cholesky
    !> factorization A = U**T*U or A = L*L**T computed by SPPTRF.
    !>

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 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.
    !>

    AP

    !>          AP is REAL array, dimension (N*(N+1)/2)
    !>          The triangular factor U or L from the Cholesky factorization
    !>          A = U**T*U or A = L*L**T, packed columnwise in a linear
    !>          array.  The j-th column of U or L is stored in the array AP
    !>          as follows:
    !>          if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
    !>          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.
    !>

    B

    !>          B is REAL array, dimension (LDB,NRHS)
    !>          On entry, the right hand side matrix B.
    !>          On exit, the 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
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine zpptrs (character uplo, integer n, integer nrhs, complex*16, dimension( * ) ap, complex*16, dimension( ldb, * ) b, integer ldb, integer info)

ZPPTRS

Purpose:

    !>
    !> ZPPTRS solves a system of linear equations A*X = B with a Hermitian
    !> positive definite matrix A in packed storage using the Cholesky
    !> factorization A = U**H * U or A = L * L**H computed by ZPPTRF.
    !>

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 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.
    !>

    AP

    !>          AP is COMPLEX*16 array, dimension (N*(N+1)/2)
    !>          The triangular factor U or L from the Cholesky factorization
    !>          A = U**H * U or A = L * L**H, packed columnwise in a linear
    !>          array.  The j-th column of U or L is stored in the array AP
    !>          as follows:
    !>          if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
    !>          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.
    !>

    B

    !>          B is COMPLEX*16 array, dimension (LDB,NRHS)
    !>          On entry, the right hand side matrix B.
    !>          On exit, the 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
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Author

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