NAME

       pptri - pptri: triangular inverse

SYNOPSIS

   Functions
       subroutine cpptri (uplo, n, ap, info)
           CPPTRI
       subroutine dpptri (uplo, n, ap, info)
           DPPTRI
       subroutine spptri (uplo, n, ap, info)
           SPPTRI
       subroutine zpptri (uplo, n, ap, info)
           ZPPTRI

Detailed Description

Function Documentation

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

       Purpose:

            CPPTRI computes the inverse of a complex Hermitian positive definite
            matrix A using the Cholesky factorization A = U**H*U or A = L*L**H
            computed by CPPTRF.

       Parameters
           UPLO

                     UPLO is CHARACTER*1
                     = 'U':  Upper triangular factor is stored in AP;
                     = 'L':  Lower triangular factor is stored in AP.

           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 triangular factor U or L from the Cholesky
                     factorization A = U**H*U or A = L*L**H, packed columnwise as
                     a linear array.  The j-th column of U or L is stored in the
                     array AP as follows:
                     if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
                     if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.

                     On exit, the upper or lower triangle of the (Hermitian)
                     inverse of A, overwriting the input factor U or L.

           INFO

                     INFO is INTEGER
                     = 0:  successful exit
                     < 0:  if INFO = -i, the i-th argument had an illegal value
                     > 0:  if INFO = i, the (i,i) element of the factor U or L is
                           zero, and the inverse could not be computed.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

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

       Purpose:

            DPPTRI computes the inverse of a real symmetric positive definite
            matrix A using the Cholesky factorization A = U**T*U or A = L*L**T
            computed by DPPTRF.

       Parameters
           UPLO

                     UPLO is CHARACTER*1
                     = 'U':  Upper triangular factor is stored in AP;
                     = 'L':  Lower triangular factor is stored in AP.

           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 triangular factor U or L from the Cholesky
                     factorization A = U**T*U or A = L*L**T, packed columnwise as
                     a linear array.  The j-th column of U or L is stored in the
                     array AP as follows:
                     if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
                     if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.

                     On exit, the upper or lower triangle of the (symmetric)
                     inverse of A, overwriting the input factor U or L.

           INFO

                     INFO is INTEGER
                     = 0:  successful exit
                     < 0:  if INFO = -i, the i-th argument had an illegal value
                     > 0:  if INFO = i, the (i,i) element of the factor U or L is
                           zero, and the inverse could not be computed.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

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

       Purpose:

            SPPTRI computes the inverse of a real symmetric positive definite
            matrix A using the Cholesky factorization A = U**T*U or A = L*L**T
            computed by SPPTRF.

       Parameters
           UPLO

                     UPLO is CHARACTER*1
                     = 'U':  Upper triangular factor is stored in AP;
                     = 'L':  Lower triangular factor is stored in AP.

           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 triangular factor U or L from the Cholesky
                     factorization A = U**T*U or A = L*L**T, packed columnwise as
                     a linear array.  The j-th column of U or L is stored in the
                     array AP as follows:
                     if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
                     if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.

                     On exit, the upper or lower triangle of the (symmetric)
                     inverse of A, overwriting the input factor U or L.

           INFO

                     INFO is INTEGER
                     = 0:  successful exit
                     < 0:  if INFO = -i, the i-th argument had an illegal value
                     > 0:  if INFO = i, the (i,i) element of the factor U or L is
                           zero, and the inverse could not be computed.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

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

       Purpose:

            ZPPTRI computes the inverse of a complex Hermitian positive definite
            matrix A using the Cholesky factorization A = U**H*U or A = L*L**H
            computed by ZPPTRF.

       Parameters
           UPLO

                     UPLO is CHARACTER*1
                     = 'U':  Upper triangular factor is stored in AP;
                     = 'L':  Lower triangular factor is stored in AP.

           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 triangular factor U or L from the Cholesky
                     factorization A = U**H*U or A = L*L**H, packed columnwise as
                     a linear array.  The j-th column of U or L is stored in the
                     array AP as follows:
                     if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
                     if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.

                     On exit, the upper or lower triangle of the (Hermitian)
                     inverse of A, overwriting the input factor U or L.

           INFO

                     INFO is INTEGER
                     = 0:  successful exit
                     < 0:  if INFO = -i, the i-th argument had an illegal value
                     > 0:  if INFO = i, the (i,i) element of the factor U or L is
                           zero, and the inverse could not be computed.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

Author

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