?hetrs

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 12/16/2022

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?hetrs_3

Solves a system of linear equations A * X = B with a complex Hermitian matrix using the factorization computed by ?hetrf_rk.

call chetrs_3(uplo, n, nrhs, A, lda, e, ipiv, B, ldb, info)

call zhetrs_3(uplo, n, nrhs, A, lda, e, ipiv, B, ldb, info)

Description

?hetrs_3 solves a system of linear equations A * X = B with a complex Hermitian matrix A using the factorization computed by ?hetrf_rk: A = P*U*D*(U^H)*(P^T) or A = P*L*D*(L^H)*(P^T), where U (or L) is unit upper (or lower) triangular matrix, U^H (or L^H) is the conjugate of U (or L), P is a permutation matrix, P^T is the transpose of P, and D is a Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

This algorithm uses Level 3 BLAS.

Input Parameters

uplo

CHARACTER*1

Specifies whether the details of the factorization are stored as an upper or lower triangular matrix:

= 'U': Upper triangular; form is A = P*U*D*(U^H)*(P^T).
= 'L': Lower triangular; form is A = P*L*D*(L^H)*(P^T).

n

INTEGER

The order of the matrix A. n ≥ 0.

nrhs

INTEGER

The number of right-hand sides; that is, the number of columns in the matrix B. nrhs ≥ 0.

A

COMPLEX for chetrs_3

COMPLEX*16 for zhetrs_3

Array, dimension (lda,n). Diagonal of the block diagonal matrix D and factor U or L as computed by ?hetrf_rk:

Only diagonal elements of the Hermitian block diagonal matrix D on the diagonal of A; that is, D(k,k) = A(k,k). Superdiagonal (or subdiagonal) elements of D should be provided on entry in array e.
If uplo = 'U', factor U in the superdiagonal part of A. If uplo = 'L', factor L in the subdiagonal part of A.

lda

INTEGER

The leading dimension of the array A.lda ≥ max(1, n).

e

COMPLEX for chetrs_3

COMPLEX*16 for zhetrs_3

Array, dimension (n). On entry, contains the superdiagonal (or subdiagonal) elements of the Hermitian block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks. If uplo = 'U', e(i) = D(i-1,i),i=2:N, and e(1) is not referenced. If uplo = 'L', e(i) = D(i+1,i),i=1:N-1, and e(n) is not referenced.

NOTE:

For 1-by-1 diagonal block D(k), where 1 ≤ k ≤ n, the element e(k) is not referenced in both the uplo = 'U' and uplo = 'L' cases.

ipiv

INTEGER

Array, dimension (n). Details of the interchanges and the block structure of D as determined by ?hetrf_rk.

B

COMPLEX for chetrs_3

COMPLEX*16 for zhetrs_3

On entry, the right-hand side matrix B.

The second dimension of B must be at least max(1, nrhs).

ldb

INTEGER

The leading dimension of the array B. ldb ≥ max(1, n).

Output Parameters

B

COMPLEX for chetrs_3

COMPLEX*16 for zhetrs_3

On exit, the solution matrix X.

info

INTEGER

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

Parent topic: Solving Systems of Linear Equations: LAPACK Computational Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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