?hesv_aa

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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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 * U^H if uplo = 'U', or

A = L * T * L^H 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 lwork≥n, 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*U^H or A = L*T*L^H 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, D_{i, 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.

Parent topic: LAPACK Linear Equation Driver Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?hesv_aa