pptrf(3)

NAME
pptrf - pptrf: triangular factor

SYNOPSIS

  Functions

subroutine cpptrf (uplo, n, ap, info)
CPPTRF
subroutine dpptrf (uplo, n, ap, info)
DPPTRF
subroutine spptrf (uplo, n, ap, info)
SPPTRF
subroutine zpptrf (uplo, n, ap, info)
ZPPTRF

Detailed Description

Function Documentation

  subroutine cpptrf (character uplo, integer n, complex, dimension( * ) ap, integer info)

CPPTRF

Purpose:

    !>
    !> CPPTRF computes the Cholesky factorization of a complex Hermitian
    !> positive definite matrix A stored in packed format.
    !>
    !> 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.
    !>

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.
    !>

    AP

    !>          AP is COMPLEX array, dimension (N*(N+1)/2)
    !>          On entry, the upper or lower triangle of the Hermitian matrix
    !>          A, packed columnwise in a linear array.  The j-th column of A
    !>          is stored in the array AP as follows:
    !>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
    !>          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
    !>          See below for further details.
    !>
    !>          On exit, if INFO = 0, the triangular factor U or L from the
    !>          Cholesky factorization A = U**H*U or A = L*L**H, in the same
    !>          storage format as A.
    !>

    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 definite, and the factorization could
    !>                not be completed.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

    !>
    !>  The packed storage scheme is illustrated by the following example
    !>  when N = 4, UPLO = 'U':
    !>
    !>  Two-dimensional storage of the Hermitian matrix A:
    !>
    !>     a11 a12 a13 a14
    !>         a22 a23 a24
    !>             a33 a34     (aij = conjg(aji))
    !>                 a44
    !>
    !>  Packed storage of the upper triangle of A:
    !>
    !>  AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
    !>

  subroutine dpptrf (character uplo, integer n, double precision, dimension( * ) ap, integer info)

DPPTRF

Purpose:

    !>
    !> DPPTRF computes the Cholesky factorization of a real symmetric
    !> positive definite matrix A stored in packed format.
    !>
    !> 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.
    !>

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.
    !>

    AP

    !>          AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
    !>          On entry, the upper or lower triangle of the symmetric matrix
    !>          A, packed columnwise in a linear array.  The j-th column of A
    !>          is stored in the array AP as follows:
    !>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
    !>          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
    !>          See below for further details.
    !>
    !>          On exit, if INFO = 0, the triangular factor U or L from the
    !>          Cholesky factorization A = U**T*U or A = L*L**T, in the same
    !>          storage format as A.
    !>

    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.

Further Details:

    !>
    !>  The packed storage scheme is illustrated by the following example
    !>  when N = 4, UPLO = 'U':
    !>
    !>  Two-dimensional storage of the symmetric matrix A:
    !>
    !>     a11 a12 a13 a14
    !>         a22 a23 a24
    !>             a33 a34     (aij = aji)
    !>                 a44
    !>
    !>  Packed storage of the upper triangle of A:
    !>
    !>  AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
    !>

  subroutine spptrf (character uplo, integer n, real, dimension( * ) ap, integer info)

SPPTRF

Purpose:

    !>
    !> SPPTRF computes the Cholesky factorization of a real symmetric
    !> positive definite matrix A stored in packed format.
    !>
    !> 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.
    !>

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.
    !>

    AP

    !>          AP is REAL array, dimension (N*(N+1)/2)
    !>          On entry, the upper or lower triangle of the symmetric matrix
    !>          A, packed columnwise in a linear array.  The j-th column of A
    !>          is stored in the array AP as follows:
    !>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
    !>          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
    !>          See below for further details.
    !>
    !>          On exit, if INFO = 0, the triangular factor U or L from the
    !>          Cholesky factorization A = U**T*U or A = L*L**T, in the same
    !>          storage format as A.
    !>

    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.

Further Details:

    !>
    !>  The packed storage scheme is illustrated by the following example
    !>  when N = 4, UPLO = 'U':
    !>
    !>  Two-dimensional storage of the symmetric matrix A:
    !>
    !>     a11 a12 a13 a14
    !>         a22 a23 a24
    !>             a33 a34     (aij = aji)
    !>                 a44
    !>
    !>  Packed storage of the upper triangle of A:
    !>
    !>  AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
    !>

  subroutine zpptrf (character uplo, integer n, complex*16, dimension( * ) ap, integer info)

ZPPTRF

Purpose:

    !>
    !> ZPPTRF computes the Cholesky factorization of a complex Hermitian
    !> positive definite matrix A stored in packed format.
    !>
    !> 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.
    !>

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.
    !>

    AP

    !>          AP is COMPLEX*16 array, dimension (N*(N+1)/2)
    !>          On entry, the upper or lower triangle of the Hermitian matrix
    !>          A, packed columnwise in a linear array.  The j-th column of A
    !>          is stored in the array AP as follows:
    !>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
    !>          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
    !>          See below for further details.
    !>
    !>          On exit, if INFO = 0, the triangular factor U or L from the
    !>          Cholesky factorization A = U**H*U or A = L*L**H, in the same
    !>          storage format as A.
    !>

    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.

Further Details:

    !>
    !>  The packed storage scheme is illustrated by the following example
    !>  when N = 4, UPLO = 'U':
    !>
    !>  Two-dimensional storage of the Hermitian matrix A:
    !>
    !>     a11 a12 a13 a14
    !>         a22 a23 a24
    !>             a33 a34     (aij = conjg(aji))
    !>                 a44
    !>
    !>  Packed storage of the upper triangle of A:
    !>
    !>  AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
    !>

Author

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