man dtptri (Fonctions bibliothèques) - compute the inverse of a real upper or lower triangular matrix A stored in packed format

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