.TH STPTRI 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) " .SH NAME STPTRI - the inverse of a real upper or lower triangular matrix A stored in packed format .SH SYNOPSIS .TP 19 SUBROUTINE STPTRI( UPLO, DIAG, N, AP, INFO ) .TP 19 .ti +4 CHARACTER DIAG, UPLO .TP 19 .ti +4 INTEGER INFO, N .TP 19 .ti +4 REAL AP( * ) .SH PURPOSE STPTRI computes the inverse of a real upper or lower triangular matrix A stored in packed format. .SH ARGUMENTS .TP 8 UPLO (input) CHARACTER*1 = \(aqU\(aq: A is upper triangular; .br = \(aqL\(aq: A is lower triangular. .TP 8 DIAG (input) CHARACTER*1 .br = \(aqN\(aq: A is non-unit triangular; .br = \(aqU\(aq: A is unit triangular. .TP 8 N (input) INTEGER The order of the matrix A. N >= 0. .TP 8 AP (input/output) REAL 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 = \(aqU\(aq, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = \(aqL\(aq, 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. .TP 8 INFO (output) INTEGER = 0: successful exit .br < 0: if INFO = -i, the i-th argument had an illegal value .br > 0: if INFO = i, A(i,i) is exactly zero. The triangular matrix is singular and its inverse can not be computed. .SH FURTHER DETAILS A triangular matrix A can be transferred to packed storage using one of the following program segments: .br UPLO = \(aqU\(aq: UPLO = \(aqL\(aq: .br JC = 1 JC = 1 .br DO 2 J = 1, N DO 2 J = 1, N .br DO 1 I = 1, J DO 1 I = J, N .br AP(JC+I-1) = A(I,J) AP(JC+I-J) = A(I,J) 1 CONTINUE 1 CONTINUE .br JC = JC + J JC = JC + N - J + 1 2 CONTINUE 2 CONTINUE .br