# ctptri (l) - Linux Man Pages

## NAME

CTPTRI - computes the inverse of a complex upper or lower triangular matrix A stored in packed format

## SYNOPSIS

SUBROUTINE CTPTRI(
UPLO, DIAG, N, AP, INFO )

CHARACTER DIAG, UPLO

INTEGER INFO, N

COMPLEX AP( * )

## PURPOSE

CTPTRI computes the inverse of a complex upper or lower triangular matrix A stored in packed format.

## ARGUMENTS

UPLO (input) CHARACTER*1
= aqUaq: A is upper triangular;
= aqLaq: A is lower triangular.
DIAG (input) CHARACTER*1

= aqNaq: A is non-unit triangular;
= aqUaq: A is unit triangular.
N (input) INTEGER
The order of the matrix A. N >= 0.
AP (input/output) COMPLEX 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 = aqUaq, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = aqLaq, 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 = aqUaq: UPLO = aqLaq:

JC                           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)
CONTINUE                       CONTINUE

JC JC                      JC JC N - J 1
2 CONTINUE                       2 CONTINUE