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ZTPTRI(l)) ZTPTRI(l)NAMEZTPTRI - compute the inverse of a complex upper or lower triangular matrix A stored in packed formatSYNOPSISSUBROUTINE ZTPTRI( UPLO, DIAG, N, AP, INFO ) CHARACTER DIAG, UPLO INTEGER INFO, N COMPLEX*16 AP( * )PURPOSEZTPTRI computes the inverse of a complex upper or lower triangular matrix A stored in packed format.ARGUMENTSUPLO (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*16 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 =, 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.-iFURTHER DETAILSA triangular matrix A can be transferred to packed storage using one of the following pro- gram 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 CONTINUELAPACK version 3.015 June 2000 ZTPTRI(l)

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