ZHETRS_3(3)

🎀 NAME 🎀

okay bestie, this manual page is for /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zhetrs_3.f — and the manual name is folded in right here: it’s from the Library Functions Manual, page path /home/abui.../zhetrs_3.f(3) 🫶

✨ SYNOPSIS ✨

Functions/Subroutines

subroutine ZHETRS_3 (uplo, n, nrhs, a, lda, e, ipiv, b, ldb, info)
    ZHETRS_3

💅 Function/Subroutine Documentation 💅

subroutine ZHETRS_3 (character uplo, integer n, integer nrhs, complex*16,
       dimension( lda, * ) a, integer lda, complex*16, dimension( * ) e,
       integer, dimension( * ) ipiv, complex*16, dimension( ldb, * ) b, integer
       ldb, integer info)
       ZHETRS_3

🎯 Purpose 🎯

okay so ZHETRS_3 solves a system of linear equations A * X = B with a complex Hermitian matrix A using the factorization computed by ZHETRF_RK or ZHETRF_BK:

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 Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

This algorithm is using Level 3 BLAS. 🔥

🧸 Parameters 🧸

UPLO

UPLO is CHARACTER*1. It 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

N is INTEGER. The order of the matrix A. N >= 0.

NRHS

NRHS is INTEGER. The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.

A

A is COMPLEX*16 array, dimension (LDA,N). Diagonal of the block diagonal matrix D and factors U or L as computed by ZHETRF_RK and ZHETRF_BK:

• a) ONLY diagonal elements of the Hermitian block diagonal matrix D on the diagonal of A, i.e. D(k,k) = A(k,k); (superdiagonal (or subdiagonal) elements of D should be provided on entry in array E), and
• b) If UPLO = 'U': factor U in the superdiagonal part of A. If UPLO = 'L': factor L in the subdiagonal part of A.

LDA

LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).

E

E is COMPLEX*16 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, where

• If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced;
• If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.

NOTE: For 1-by-1 diagonal block D(k), where 1 <= k <= N, the element E(k) is not referenced in both UPLO = 'U' or UPLO = 'L' cases.

IPIV

IPIV is INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by ZHETRF_RK or ZHETRF_BK.

B

B is COMPLEX*16 array, dimension (LDB,NRHS). On entry, the right hand side matrix B. On exit, the solution matrix X.

LDB

LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N).

INFO

INFO is INTEGER.

• = 0: successful exit
• < 0: if INFO = -i, the i-th argument had an illegal value

👑 Author 👑

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

🌟 Contributors 🌟

• June 2017, Igor Kozachenko, Computer Science Division, University of California, Berkeley
• September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, School of Mathematics, University of Manchester

Definition at line 163 of file zhetrs_3.f.

🪄 Author 🪄

Generated automatically by Doxygen for LAPACK from the source code.

---

that’s the whole vibe bestie — LAPACK Version 3.12.0, page /home/abui.../zhetrs_3.f(3) 💖✨