ZHESV_ROOK(3)

💅 ZHESV_ROOK(3) — Library Functions Manual 💅

okay so this is the ZHESV_ROOK(3) page, bestie. It’s a LAPACK library-functions-manual moment, and the whole NAME situation is literally just a file path. Iconic behavior, honestly.

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zhesv_rook.f

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

       subroutine ZHESV_ROOK (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork,
           info)
           ZHESV_ROOK computes the solution to a system of linear equations A *
           X = B for HE matrices using the bounded Bunch-Kaufman
           (rook")diagonalpivotingmethod

🦋 Function/Subroutine Documentation 🦋

The actual signature, verbatim, no cap:

   subroutine ZHESV_ROOK (character uplo, integer n, integer nrhs, complex*16,
       dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv,
       complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( *
       ) work, integer lwork, integer info)

ZHESV_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. Slay.

💖 Purpose 💖

Okay so ZHESV_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.

ZHETRF_ROOK is called to compute the factorization of a complex Hermition matrix A using the bounded Bunch-Kaufman () diagonal pivoting method. (The page says Hermition, and I’m keeping that spelling, periodt.)

The factored form of A is then used to solve the system of equations A * X = B by calling <cyan>ZHETRS_ROOK</cyan> (uses BLAS 2).

🎀 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*16 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 ZHETRF_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.

✨ B ✨

B is COMPLEX*16 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*16 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 ZHETRF_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.

🌈 Author 🌈

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

And here’s the little !> credit block, kept exactly:

!>
!>  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 zhesv_rook.f.

🧚 Author 🧚

Generated automatically by Doxygen for LAPACK from the source code.

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LAPACK Version 3.12.0, footer path /home/abui...hesv_rook.f(3) — dates floating around this page are November 2013 and September 2007. Byeee bestie, go solve that Hermitian system 💖✨👑