Computes the inverse of a Hermitian indefinite matrix through setting the leading dimension of the workspace and calling ?hetri2x.
FORTRAN 77:
call chetri2( uplo, n, a, lda, ipiv, work, lwork, info )
call zhetri2( uplo, n, a, lda, ipiv, work, lwork, info )
FORTRAN 95:
call hetri2( a,ipiv[,uplo][,info] )
C:
lapack_int LAPACKE_<?>hetri2( int matrix_order, char uplo, lapack_int n, <datatype>* a, lapack_int lda, const lapack_int* ipiv );
The routine computes the inverse inv(A) of a Hermitian indefinite matrix A using the factorization A = U*D*UH or A = L*D*LH computed by ?hetrf.
The ?hetri2 routine sets the leading dimension of the workspace before calling ?hetri2x that actually computes the inverse.
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 |
CHARACTER*1. Must be 'U' or 'L'. Indicates how the input matrix A has been factored: If uplo = 'U', the array a stores the factorization A = U*D*UH. If uplo = 'L', the array a stores the factorization A = L*D*LH. |
n |
INTEGER. The order of the matrix A; n ≥ 0. |
a, work |
COMPLEX for chetri2 DOUBLE COMPLEX for zhetri2 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 ?hetrf. |
lwork |
INTEGER. The dimension of the work array. lwork ≥ (n+nb+1)*(nb+3) where nb is the block size parameter as returned by hetrf. 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. |
a |
If info = 0, the 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. |
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 hetri2 interface are as follows:
a |
Holds the matrix A of size (n,n). |
ipiv |
Holds the vector of length n. |
uplo |
Indicates how the input matrix A has been factored. Must be 'U' or 'L'. |