SRC/zhetrs_3.f(3)

💖 SRC/zhetrs_3.f(3) 💖

okay so bestie, welcome to the SRC/zhetrs_3.f(3) page from the Library Functions Manual — it's giving Fortran subroutine main-character energy, and we're gonna go through every single detail together, no cap. 💅✨

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🌸 NAME 🌸

SRC/zhetrs_3.f

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✨ SYNOPSIS ✨

🌈 Functions/Subroutines 🌈

• subroutine zhetrs_3 (uplo, n, nrhs, a, lda, e, ipiv, b, ldb, info) — ZHETRS_3

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🧚 Function/Subroutine Documentation 🧚

okay so the full signature is literally this, and yes we're keeping it exactly:

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

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🎀 Purpose 🎀

so here's the tea: 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. 🔥

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🌸 Parameters 🌸

• UPLO is 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 is INTEGER — the order of the matrix A. N >= 0.
• NRHS is INTEGER — the number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
• 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 is INTEGER — the leading dimension of the array A. LDA >= max(1,N).
• 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 is INTEGER array, dimension (N) — details of the interchanges and the block structure of D as determined by ZHETRF_RK or ZHETRF_BK.
• B is COMPLEX*16 array, dimension (LDB,NRHS) — on entry, the right hand side matrix B. On exit, the solution matrix X.
• LDB is INTEGER — the leading dimension of the array B. LDB >= max(1,N).
• INFO is INTEGER:
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

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👑 Author 👑

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

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🦋 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

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Definition at line 163 of file zhetrs_3.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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and that's the whole vibe, bestie — this page is from LAPACK Version 3.12.0, file SRC/zhetrs_3.f(3), and it was generated automatically by Doxygen for LAPACK from the source code. catch you later, mwah 💖✨🎀