SRC/zhesv_rook.f(3)

💖 NAME 💖

Okay so this is the Library Functions Manual page for SRC/zhesv_rook.f(3), and bestie, the actual NAME is literally SRC/zhesv_rook.f — the Fortran home of zhesv_rook. Slay. 💅

✨ 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") diagonal pivoting method. Iconic.

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🌸 Function/Subroutine Documentation 🌸

👑 subroutine zhesv_rook 👑

The full typed-out signature, 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)

The tagline is exactly: 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. Obsessed with her. 💖

🦋 Purpose 🦋

• 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 ("rook") 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 Hermitian matrix A using the bounded Bunch-Kaufman ("rook") diagonal pivoting method.
• The factored form of A is then used to solve the system of equations A * X = B by calling ZHETRS_ROOK (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 interchanged, and 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 interchanged, and 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.
• 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

The source block also has the Doxygen marker !> in front of those notes, and it ends with .fi. Cute.

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Definition at line 203 of file zhesv_rook.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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💖 That's the whole page, bestie: LAPACK Version 3.12.0, source SRC/zhesv_rook.f(3) — and the dates living on this page are the November 2013 and September 2007 author notes up above. Mwah! 💋