CTPTRI (3lapack)

compute the inverse of a complex upper or lower triangular matrix A stored in packed format

SYNOPSIS

  SUBROUTINE CTPTRI( UPLO, DIAG, N, AP, INFO )

      CHARACTER      DIAG, UPLO

      INTEGER        INFO, N

      COMPLEX        AP( * )

PURPOSE

  CTPTRI computes the inverse of a complex upper or lower triangular matrix A
  stored in packed format.

ARGUMENTS

  UPLO    (input) CHARACTER*1
          = 'U':  A is upper triangular;
          = 'L':  A is lower triangular.

  DIAG    (input) CHARACTER*1
          = 'N':  A is non-unit triangular;
          = 'U':  A is unit triangular.

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

  AP      (input/output) COMPLEX array, dimension (N*(N+1)/2)
          On entry, the upper or lower triangular matrix A, stored 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)*((2*n-j)/2) = A(i,j) for j<=i<=n.  See
          below for further details.  On exit, the (triangular) inverse of
          the original matrix, in the same packed storage format.

  INFO    (output) INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value
          > 0:  if INFO = i, A(i,i) is exactly zero.  The triangular matrix
          is singular and its inverse can not be computed.

FURTHER DETAILS

  A triangular matrix A can be transferred to packed storage using one of the
  following program segments:

  UPLO = 'U':                      UPLO = 'L':

        JC = 1                           JC = 1
        DO 2 J = 1, N                    DO 2 J = 1, N
           DO 1 I = 1, J                    DO 1 I = J, N
              AP(JC+I-1) = A(I,J)              AP(JC+I-J) = A(I,J)
      1    CONTINUE                    1    CONTINUE
           JC = JC + J                      JC = JC + N - J + 1
      2 CONTINUE                       2 CONTINUE