DTPTRI(3f)

NAME
DTPTRI - the inverse of a real upper or lower triangular matrix A stored in packed format

SYNOPSIS

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

CHARACTER
    DIAG, UPLO

INTEGER
    INFO, N

DOUBLE
    PRECISION AP( * )

PURPOSE
DTPTRI computes the inverse of a real 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) DOUBLE PRECISION 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