SRC/chetrs_3.f(3)

💅 SRC/chetrs_3.f(3) — Library Functions Manual ✨

🌸 NAME 🌸

SRC/chetrs_3.f — bestie, that’s literally the name.

✨ SYNOPSIS ✨

🫶 Functions/Subroutines 🫶

subroutine chetrs_3 (uplo, n, nrhs, a, lda, e, ipiv, b, ldb, info)
    CHETRS_3

📚 Function/Subroutine Documentation 📚

subroutine chetrs_3 (character uplo, integer n, integer nrhs, complex,
     dimension( lda, * ) a, integer lda, complex, dimension( * ) e, integer,
     dimension( * ) ipiv, complex, dimension( ldb, * ) b, integer ldb,
     integer info)

CHETRS_3

💖 Purpose 💖

okay so CHETRS_3 lowkey solves a system of linear equations A * X = B with a complex Hermitian matrix A using the factorization computed by CHETRF_RK or CHETRF_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. periodt. 🔥

🎀 Parameters 🎀

• UPLO — 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 — 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 array, dimension (LDA,N). Diagonal of the block diagonal matrix D and factors U or L as computed by CHETRF_RK and CHETRF_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 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 CHETRF_RK or CHETRF_BK.
• B — B is COMPLEX 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 📌

Definition at line 163 of file chetrs_3.f.

💌 Author 💌

Generated automatically by Doxygen for LAPACK from the source code.

okay bestie, that’s the whole vibe — LAPACK, Version 3.12.0, SRC/chetrs_3.f(3) 💖✨