SRC/chesv_rook.f(3)

💖 SRC/chesv_rook.f(3) — Library Functions Manual 💖

Okay bestie, this is the page for SRC/chesv_rook.f, and it’s giving complex Hermitian linear-solve with bounded Bunch-Kaufman rook pivoting energy. Let’s unpack it with zero gatekeeping 💅✨

🎀 NAME 🎀

SRC/chesv_rook.f — that’s the file, bestie. Main character file behavior. 🫶

🌈 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

Yes, the synopsis really says (rook")diagonalpivotingmethod all mashed together — iconic, no cap 💀✨

🦋 Function/Subroutine Documentation 🦋

Here’s the full signature, character-for-character:

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 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. Slay 💅

CHETRF_ROOK is called to compute the factorization of a complex Hermition matrix A using the bounded Bunch-Kaufman () diagonal pivoting method. (Yes: Hermition is exactly what the source says. We do not edit the queen’s typo 😭)

The factored form of A is then used to solve the system of equations A * X = B by calling CHETRS_ROOK (uses BLAS 2). 🔥

🎀 Parameters 🎀

• UPLO — is CHARACTER*1
  • = 'U': Upper triangle of A is stored;
  • = 'L': Lower triangle of A is stored.
• N — is INTEGER. The number of linear equations, i.e., 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 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 — is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• 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.
• 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 — is INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• WORK — is COMPLEX array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal 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 — 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.

🌸 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. ✨

💀 Author 💀

Generated automatically by Doxygen for LAPACK from the source code.

---

And that’s the page, bestie. Footer flex: LAPACK Version 3.12.0 and SRC/chesv_rook.f(3). Periodt. 💖✨