Contents

• NAME
• SYNOPSIS
  • F95 INTERFACE
  • C INTERFACE
• PURPOSE
• ARGUMENTS

NAME

     csptri - compute the inverse of a complex symmetric indefin-
     ite  matrix  A in packed storage using the factorization A =
     U*D*U**T or A = L*D*L**T computed by CSPTRF

SYNOPSIS

     SUBROUTINE CSPTRI(UPLO, N, AP, IPIVOT, WORK, INFO)

     CHARACTER * 1 UPLO
     COMPLEX AP(*), WORK(*)
     INTEGER N, INFO
     INTEGER IPIVOT(*)

     SUBROUTINE CSPTRI_64(UPLO, N, AP, IPIVOT, WORK, INFO)

     CHARACTER * 1 UPLO
     COMPLEX AP(*), WORK(*)
     INTEGER*8 N, INFO
     INTEGER*8 IPIVOT(*)

  F95 INTERFACE
     SUBROUTINE SPTRI(UPLO, N, AP, IPIVOT, [WORK], [INFO])

     CHARACTER(LEN=1) :: UPLO
     COMPLEX, DIMENSION(:) :: AP, WORK
     INTEGER :: N, INFO
     INTEGER, DIMENSION(:) :: IPIVOT

     SUBROUTINE SPTRI_64(UPLO, N, AP, IPIVOT, [WORK], [INFO])

     CHARACTER(LEN=1) :: UPLO
     COMPLEX, DIMENSION(:) :: AP, WORK
     INTEGER(8) :: N, INFO
     INTEGER(8), DIMENSION(:) :: IPIVOT

  C INTERFACE
     #include <sunperf.h>

     void csptri(char uplo, int n, complex *ap, int *ipivot,  int
               *info);

     void csptri_64(char uplo, long n, complex *ap, long *ipivot,
               long *info);

PURPOSE

     csptri  computes  the  inverse  of   a   complex   symmetric
     indefinite  matrix  A in packed storage using the factoriza-
     tion A = U*D*U**T or A = L*D*L**T computed by CSPTRF.

ARGUMENTS

     UPLO (input)
               Specifies whether the details of the factorization
               are stored as an upper or lower triangular matrix.
               = 'U':  Upper triangular, form is A = U*D*U**T;
               = 'L':  Lower triangular, form is A = L*D*L**T.

     N (input) The order of the matrix A.  N >= 0.

     AP (input/output)
               Complex array, dimension (N*(N+1)/2) On entry, the
               block  diagonal  matrix D and the multipliers used
               to obtain the factor U or L as computed by CSPTRF,
               stored as a packed triangular matrix.

               On exit, if INFO = 0, the (symmetric)  inverse  of
               the original matrix, stored as a packed triangular
               matrix. The j-th column of inv(A) is stored in the
               array  AP  as  follows:  if UPLO = 'U', AP(i + (j-
               1)*j/2) = inv(A)(i,j) for 1<=i<=j; if UPLO =  'L',
               AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n.

     IPIVOT (input)
               Integer array, dimension (N) Details of the inter-
               changes and the block structure of D as determined
               by CSPTRF.

     WORK (workspace)
               Complex array, dimension (N)

     INFO (output)
               = 0: successful exit
               < 0: if INFO = -i, the i-th argument had an  ille-
               gal value
               > 0: if INFO = i, D(i,i) = 0; the matrix is singu-
               lar and its inverse could not be computed.