potrf2(3)

NAME
potrf2 - potrf2: triangular factor panel, recursive?

SYNOPSIS

  Functions
recursive subroutine cpotrf2 (uplo, n, a, lda, info)
CPOTRF2
recursive subroutine dpotrf2 (uplo, n, a, lda, info)
DPOTRF2
recursive subroutine spotrf2 (uplo, n, a, lda, info)
SPOTRF2
recursive subroutine zpotrf2 (uplo, n, a, lda, info)
ZPOTRF2

Detailed Description

Function Documentation

  recursive subroutine cpotrf2 (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, integer info)

CPOTRF2

Purpose:

     CPOTRF2 computes the Cholesky factorization of a Hermitian
     positive definite matrix A using the recursive algorithm.
     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 recursive version of the algorithm. It divides
     the matrix into four submatrices:
            [  A11 | A12  ]  where A11 is n1 by n1 and A22 is n2 by n2
        A = [ -----|----- ]  with n1 = n/2
            [  A21 | A22  ]       n2 = n-n1
     The subroutine calls itself to factor A11. Update and scale A21
     or A12, update A22 then calls itself to factor A22.

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.

Definition at line 105 of file cpotrf2.f.

  recursive subroutine dpotrf2 (character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, integer info)

DPOTRF2

Purpose:

     DPOTRF2 computes the Cholesky factorization of a real symmetric
     positive definite matrix A using the recursive algorithm.
     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 recursive version of the algorithm. It divides
     the matrix into four submatrices:
            [  A11 | A12  ]  where A11 is n1 by n1 and A22 is n2 by n2
        A = [ -----|----- ]  with n1 = n/2
            [  A21 | A22  ]       n2 = n-n1
     The subroutine calls itself to factor A11. Update and scale A21
     or A12, update A22 then calls itself to factor A22.

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.

Definition at line 105 of file dpotrf2.f.

  recursive subroutine spotrf2 (character uplo, integer n, real, dimension( lda, * ) a, integer lda, integer info)

SPOTRF2

Purpose:

     SPOTRF2 computes the Cholesky factorization of a real symmetric
     positive definite matrix A using the recursive algorithm.
     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 recursive version of the algorithm. It divides
     the matrix into four submatrices:
            [  A11 | A12  ]  where A11 is n1 by n1 and A22 is n2 by n2
        A = [ -----|----- ]  with n1 = n/2
            [  A21 | A22  ]       n2 = n-n1
     The subroutine calls itself to factor A11. Update and scale A21
     or A12, update A22 then call itself to factor A22.

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.

Definition at line 105 of file spotrf2.f.

  recursive subroutine zpotrf2 (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, integer info)

ZPOTRF2

Purpose:

     ZPOTRF2 computes the Cholesky factorization of a Hermitian
     positive definite matrix A using the recursive algorithm.
     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 recursive version of the algorithm. It divides
     the matrix into four submatrices:
            [  A11 | A12  ]  where A11 is n1 by n1 and A22 is n2 by n2
        A = [ -----|----- ]  with n1 = n/2
            [  A21 | A22  ]       n2 = n-n1
     The subroutine calls itself to factor A11. Update and scale A21
     or A12, update A22 then call itself to factor A22.

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.

Definition at line 105 of file zpotrf2.f.

Author

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