?sytri2

Computes the inverse of a symmetric indefinite matrix through setting the leading dimension of the workspace and calling ?sytri2x.

Syntax

FORTRAN 77:

call ssytri2( uplo, n, a, lda, ipiv, work, lwork, info )

call dsytri2( uplo, n, a, lda, ipiv, work, lwork, info )

call csytri2( uplo, n, a, lda, ipiv, work, lwork, info )

call zsytri2( uplo, n, a, lda, ipiv, work, lwork, info )

FORTRAN 95:

call sytri2( a,ipiv[,uplo][,info] )

lapack_int LAPACKE_<?>sytri2( int matrix_order, char uplo, lapack_int n, <datatype>* a, lapack_int lda, const lapack_int* ipiv );

Include Files

Fortran: mkl_lapack.fi and mkl_lapack.h
Fortran 95: lapack.f90
C: mkl_lapacke.h

Description

The routine computes the inverse inv(A) of a symmetric indefinite matrix A using the factorization A = U*D*U^T or A = L*D*L^T computed by ?sytrf.

The ?sytri2 routine sets the leading dimension of the workspace before calling ?sytri2x that actually computes the inverse.

Input Parameters

The data types are given for the Fortran interface. A <datatype> placeholder, if present, is used for the C interface data types in the C interface section above. See C Interface Conventions for the C interface principal conventions and type definitions.

uplo	CHARACTER1. Must be 'U' or 'L'. Indicates how the input matrix `A` has been factored: If `uplo = 'U'`, the array `a` stores the factorization `A = UDU^T`. If `uplo = 'L'`, the array `a` stores the factorization `A = LD*L^T`.
n	INTEGER. The order of the matrix `A`; `n ≥ 0`.
a, work	REAL for ssytri2 DOUBLE PRECISION for dsytri2 COMPLEX for csytri2 DOUBLE COMPLEX for zsytri2 Arrays: a(lda,) contains the block diagonal matrix `D` and the multipliers used to obtain the factor U or L as returned by ?sytrf. The second dimension of a must be at least `max(1,n)`. work is a workspace array of `(n+nb+1)(nb+3)` dimension.
lda	INTEGER. The leading dimension of `a`; `lda ≥ max(1, n)`.
ipiv	INTEGER. Array, DIMENSION at least `max(1, n)`. Details of the interchanges and the block structure of `D` as returned by ?sytrf.
lwork	INTEGER. The dimension of the work array. `lwork ≥ (n+nb+1)*(nb+3)` where `nb` is the block size parameter as returned by sytrf. If `lwork = -1`, then a workspace query is assumed; the routine only calculates the optimal size of the work array, returns this value as the first entry of the work array, and no error message related to lwork is issued by xerbla.

Output Parameters

If info = 0, the symmetric inverse of the original matrix.

If info = 'U', the upper triangular part of the inverse is formed and the part of A below the diagonal is not referenced.

If info = 'L', the lower triangular part of the inverse is formed and the part of A above the diagonal is not referenced.

info

INTEGER.

If info = 0, the execution is successful.

If info =-i, the i-th parameter had an illegal value.

If info = i, D(i,i) = 0; D is singular and its inversion could not be computed.

Fortran 95 Interface Notes

Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or reconstructible arguments, see Fortran 95 Interface Conventions.

Specific details for the routine sytri2 interface are as follows:

a	Holds the matrix `A` of size (`n,n`).
ipiv	Holds the vector of length `n`.
uplo	Indicates how the matrix `A` has been factored. Must be 'U' or 'L'.