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# stptri

```
NAME
STPTRI - compute the inverse of a real upper or lower tri-
angular matrix A stored in packed format

SYNOPSIS
SUBROUTINE STPTRI( UPLO, DIAG, N, AP, INFO )

CHARACTER      DIAG, UPLO

INTEGER        INFO, N

REAL           AP( * )

PURPOSE
STPTRI 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.

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 = '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
```