potrf(3)

NAME
potrf - potrf: triangular factor

SYNOPSIS

  Functions

subroutine cpotrf (uplo, n, a, lda, info)
CPOTRF
subroutine dpotrf (uplo, n, a, lda, info)
DPOTRF
subroutine spotrf (uplo, n, a, lda, info)
SPOTRF
subroutine zpotrf (uplo, n, a, lda, info)
ZPOTRF

Detailed Description

Function Documentation

  subroutine cpotrf (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, integer info)

CPOTRF

Purpose:

    !>
    !> CPOTRF computes the Cholesky factorization of a complex Hermitian
    !> positive definite matrix A.
    !>
    !> The factorization has the form
    !>    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 lower triangular.
    !>
    !> This is the block version of the algorithm, calling Level 3 BLAS.
    !>

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.
    !>

    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).
    !>

    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
    !>                is not positive, and the factorization could not be
    !>                completed.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine dpotrf (character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, integer info)

DPOTRF

Purpose:

    !>
    !> DPOTRF computes the Cholesky factorization of a real symmetric
    !> positive definite matrix A.
    !>
    !> The factorization has the form
    !>    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 lower triangular.
    !>
    !> This is the block version of the algorithm, calling Level 3 BLAS.
    !>

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.
    !>

    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).
    !>

    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
    !>                is not positive, and the factorization could not be
    !>                completed.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine spotrf (character uplo, integer n, real, dimension( lda, * ) a, integer lda, integer info)

SPOTRF

Purpose:

    !>
    !> SPOTRF computes the Cholesky factorization of a real symmetric
    !> positive definite matrix A.
    !>
    !> The factorization has the form
    !>    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 lower triangular.
    !>
    !> This is the block version of the algorithm, calling Level 3 BLAS.
    !>

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.
    !>

    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).
    !>

    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
    !>                is not positive, and the factorization could not be
    !>                completed.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine zpotrf (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, integer info)

ZPOTRF

Purpose:

    !>
    !> ZPOTRF computes the Cholesky factorization of a complex Hermitian
    !> positive definite matrix A.
    !>
    !> The factorization has the form
    !>    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 lower triangular.
    !>
    !> This is the block version of the algorithm, calling Level 3 BLAS.
    !>

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.
    !>

    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).
    !>

    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
    !>                is not positive, and the factorization could not be
    !>                completed.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Author

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