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.

  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.

  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.

  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.

Author

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