NAME¶

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

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.