# csptri.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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csptri.f

## SYNOPSIS

### Functions/Subroutines

subroutine csptri (UPLO, N, AP, IPIV, WORK, INFO)
CSPTRI

## Function/Subroutine Documentation

### subroutine csptri (character UPLO, integer N, complex, dimension( * ) AP, integer, dimension( * ) IPIV, complex, dimension( * ) WORK, integer INFO)

CSPTRI

Purpose:

``` CSPTRI computes the inverse of a complex symmetric indefinite matrix
A in packed storage using the factorization A = U*D*U**T or
A = L*D*L**T computed by CSPTRF.
```

Parameters:

UPLO

```          UPLO is CHARACTER*1
Specifies whether the details of the factorization are stored
as an upper or lower triangular matrix.
= 'U':  Upper triangular, form is A = U*D*U**T;
= 'L':  Lower triangular, form is A = L*D*L**T.
```

N

```          N is INTEGER
The order of the matrix A.  N >= 0.
```

AP

```          AP is COMPLEX array, dimension (N*(N+1)/2)
On entry, the block diagonal matrix D and the multipliers
used to obtain the factor U or L as computed by CSPTRF,
stored as a packed triangular matrix.

On exit, if INFO = 0, the (symmetric) inverse of the original
matrix, stored as a packed triangular matrix. The j-th column
of inv(A) is stored in the array AP as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j;
if UPLO = 'L',
AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n.
```

IPIV

```          IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by CSPTRF.
```

WORK

```          WORK is COMPLEX array, dimension (N)
```

INFO

```          INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
inverse could not be computed.
```

Author:

Univ. of Tennessee

Univ. of California Berkeley