Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

ID 766686
Date 3/31/2023
Public

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?hesv_aa

Computes the solution to system of linear equations for HE matrices.

call chesv_aa(uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info)

call zhesv_aa(uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info)

Description

?hesv_aa computes the solution to a complex system of linear equations A * X = B, where A is an n-by-n Hermitian matrix and X and B are n-by-nrhs matrices. Aasen's algorithm is used to factor A as

A = U * T * UH if uplo = 'U', or

A = L * T * LH if uplo = 'L',

where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and T is Hermitian and tridiagonal. The factored form of A is then used to solve the system of equations A * X = B.

Input Parameters
uplo

CHARACTER*1.

If uplo = 'U': The upper triangle of A is stored.

If uplo = 'L': the lower triangle of A is stored.

n

INTEGER. The number of linear equations or the order of the matrix A. n 0.

nrhs

INTEGER. The number of right hand sides or the number of columns of the matrix B. nrhs 0.

a

COMPLEX for chesv_aa

COMPLEX*16 for zhesv_aa

Array of size (lda, n). On entry, the Hermitian matrix A.

If uplo = 'U', the leading n-by-n upper triangular part of a contains the upper triangular part of the matrix A, and the strictly lower triangular part of a is not referenced.

If uplo = 'L', the leading n-by-n lower triangular part of a contains the lower triangular part of the matrix A, and the strictly upper triangular part of a is not referenced.

lda

INTEGER. The leading dimension of the array a. lda max(1,n).

b

COMPLEX for chesv_aa

COMPLEX*16 for zhesv_aa

Array of size (ldb, nrhs). On entry, the n-by-nrhs right hand side matrix B.

ldb

INTEGER. The leading dimension of the array b. ldb max(1,n).

lwork

INTEGER. The length of work. lwork max(1, 2*n, 3*n-2), and for best performance lwork max(1,n*nb), where nb is the optimal blocksize for ?hetrf.

If lwork < n, TRS is done with Level BLAS 2. If lworkn, TRS is done with Level BLAS 3.

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
a

On exit, if info = 0, the tridiagonal matrix T and the multipliers used to obtain the factor U or L from the factorization A = U*T*UH or A = L*T*LH as computed by ?hetrf_aa.

ipiv

INTEGER . Array of size (n) On exit, it contains the details of the interchanges: row and column k of A were interchanged with the row and column ipiv(k).

b

On exit, if info = 0, the n-by-nrhs solution matrix X.

work

COMPLEX for chesv_aa

COMPLEX*16 for zhesv_aa

Array of size (max(1, lwork)). On exit, if info = 0, work(1) returns the optimal lwork.

info

INTEGER.

If info = 0: successful exit.

If info < 0: if info = -i, the i-th argument had an illegal value.

If info > 0: if info = i, Di, i is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, so the solution could not be computed.