DTPTRI(l) — LAPACK routine (version 2.0)

NAME

DTPTRI - compute 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