CHESV_ROOK(3)

💖 NAME

okay so bestie, this page is literally the home of /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/chesv_rook.f — yes that's the whole path, she's got a long name and she's iconic for it 🎀

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✨ SYNOPSIS

Functions/Subroutines

subroutine CHESV_ROOK (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork,
    info)

CHESV_ROOK computes the solution to a system of linear equations A * X = B for HE matrices using the bounded Bunch-Kaufman (rook")diagonalpivotingmethod

yeah that's how it got typeset, "rook")diagonalpivotingmethod, no spaces, she's a little scruffy but we love her 💅

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🫶 Function/Subroutine Documentation

subroutine CHESV_ROOK (character uplo, integer n, integer nrhs, complex,
    dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv,
    complex, dimension( ldb, * ) b, integer ldb, complex, dimension( * )
    work, integer lwork, integer info)

CHESV_ROOK computes the solution to a system of linear equations A * X = B for HE matrices using the bounded Bunch-Kaufman ("rook") diagonal pivoting method

🦋 Purpose

!>
!> CHESV_ROOK 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.
!>
!> The bounded Bunch-Kaufman () diagonal pivoting method is used
!> to factor A as
!>    A = U * D * U**T,  if UPLO = 'U', or
!>    A = L * D * L**T,  if UPLO = 'L',
!> where U (or L) is a product of permutation and unit upper (lower)
!> triangular matrices, and D is Hermitian and block diagonal with
!> 1-by-1 and 2-by-2 diagonal blocks.
!>
!> CHETRF_ROOK is called to compute the factorization of a complex
!> Hermition matrix A using the bounded Bunch-Kaufman () diagonal
!> pivoting method.
!>
!> The factored form of A is then used to solve the system
!> of equations A * X = B by calling CHETRS_ROOK (uses BLAS 2).
!>

so like, in human words: she takes your Hermitian matrix A and your right-hand-side B, factors A with the bounded Bunch-Kaufman ("rook") diagonal pivoting method into U*D*U**T (if UPLO = 'U') or L*D*L**T (if UPLO = 'L'), where U/L is a product of permutation and unit triangular matrices and D is Hermitian block diagonal with 1-by-1 and 2-by-2 diagonal blocks. then she solves for X. the factorization itself comes from CHETRF_ROOK, and the solve comes from CHETRS_ROOK (uses BLAS 2). two besties, one job ✨

(and yes, the original really does say "Hermition" — we're keeping it fr fr, typos are part of the lore 😭)

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🎀 Parameters

• UPLO — UPLO is CHARACTER*1
  • = 'U': Upper triangle of A is stored;
  • = 'L': Lower triangle of A is stored.
• N — N is INTEGER. The number of linear equations, i.e., 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). 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. On exit, if INFO = 0, the block diagonal matrix D and the multipliers used to obtain the factor U or L from the factorization A = U*D*U**H or A = L*D*L**H as computed by CHETRF_ROOK.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• IPIV — IPIV is INTEGER array, dimension (N). Details of the interchanges and the block structure of D.
  • If UPLO = 'U':
    • Only the last KB elements of IPIV are set.
    • If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged and D(k,k) is a 1-by-1 diagonal block.
    • If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and columns k and -IPIV(k) were interchanged and rows and columns k-1 and -IPIV(k-1) were inerchaged, D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
  • If UPLO = 'L':
    • Only the first KB elements of IPIV are set.
    • If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged and D(k,k) is a 1-by-1 diagonal block.
    • If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and columns k and -IPIV(k) were interchanged and rows and columns k+1 and -IPIV(k+1) were inerchaged, D(k:k+1,k:k+1) is a 2-by-2 diagonal block.

ngl "inerchaged" is in the source too and it's giving typo era, but we do not gatekeep 🫶

• B — B is COMPLEX array, dimension (LDB,NRHS). On entry, the N-by-NRHS right hand side matrix B. On exit, if INFO = 0, the N-by-NRHS solution matrix X.
• LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• WORK — WORK is COMPLEX array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
• LWORK — LWORK is INTEGER. The length of WORK. LWORK >= 1, and for best performance LWORK >= max(1,N*NB), where NB is the optimal blocksize for CHETRF_ROOK.
  • for LWORK < N, TRS will be done with Level BLAS 2
  • for LWORK >= N, TRS will be 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.
• INFO — INFO is INTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
  • > 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.

bestie listen: INFO > 0 means D is exactly singular and the solution literally could not be computed. like, she finished the factorization, she did her part, but the answer is not coming. no cap, check your matrix 💀

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👑 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

!>
!>  November 2013,  Igor Kozachenko,
!>                  Computer Science Division,
!>                  University of California, Berkeley
!>
!>  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
!>                  School of Mathematics,
!>                  University of Manchester
!>
!> .fi

Definition at line 203 of file chesv_rook.f.

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🌸 Author

Generated automatically by Doxygen for LAPACK from the source code.

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and that's the whole vibe check, bestie 💜 this page is LAPACK, Version 3.12.0 — mwah, stan her, periodt ✨🎀🦋