Provided by: liblapack-doc_3.3.1-1_all #### NAME

```       LAPACK-3  - computes the inverse of a real symmetric indefinite matrix A in packed storage
using the factorization A = U*D*U**T or A = L*D*L**T computed by DSPTRF

```

#### SYNOPSIS

```       SUBROUTINE DSPTRI( UPLO, N, AP, IPIV, WORK, INFO )

CHARACTER      UPLO

INTEGER        INFO, N

INTEGER        IPIV( * )

DOUBLE         PRECISION AP( * ), WORK( * )

```

#### PURPOSE

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

```

#### ARGUMENTS

```        UPLO    (input) 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       (input) INTEGER
The order of the matrix A.  N >= 0.

AP      (input/output) DOUBLE PRECISION 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 DSPTRF,
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    (input) INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by DSPTRF.

WORK    (workspace) DOUBLE PRECISION array, dimension (N)

INFO    (output) 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.

LAPACK routine (version 3.3.1)             April 2011                            DSPTRI(3lapack)
```