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NAME DTPTRI - compute the inverse of a real upper or lower tri- angular 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 tri- angular 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. (N*(N+1)/2) AP (input/output) DOUBLE PRECISION array, dimension 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((j-1)*j/2 + i) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = 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 tri- angular 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