Provided by: liblapack-doc_3.12.0-3build1.1_all bug

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

       Generated automatically by Doxygen for LAPACK from the source code.