SRC/clahef.f(3)

🌸 NAME 🌸

okay so bestie, this page is literally SRC/clahef.f — from the Library Functions Manual. It’s giving “I do linear algebra and I do it fabulously.” 💅

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✨ SYNOPSIS ✨

Functions/Subroutines

subroutine clahef (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info)

CLAHEF computes a partial factorization of a complex Hermitian indefinite matrix using the Bunch-Kaufman diagonal pivoting method (blocked algorithm, calling Level 3 BLAS). 🔥

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💖 Function/Subroutine Documentation 💖

subroutine clahef (character uplo, integer n, integer nb, integer kb,
       complex, dimension( lda, * ) a, integer lda, integer, dimension( * )
       ipiv, complex, dimension( ldw, * ) w, integer ldw, integer info)

CLAHEF computes a partial factorization of a complex Hermitian indefinite matrix using the Bunch-Kaufman diagonal pivoting method (blocked algorithm, calling Level 3 BLAS). ✨

🎀 Purpose 🎀

okay so here’s the whole vibe: CLAHEF computes a partial factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method. The partial factorization has the form:

A  =  ( I  U12 ) ( A11  0  ) (  I      0     )  if UPLO = 'U', or:
      ( 0  U22 ) (  0   D  ) ( U12**H U22**H )

A  =  ( L11  0 ) (  D   0  ) ( L11**H L21**H )  if UPLO = 'L'
      ( L21  I ) (  0  A22 ) (  0      I     )

where the order of D is at most NB. The actual order is returned in the argument KB, and is either NB or NB-1, or N if N <= NB. Note that U**H denotes the conjugate transpose of U. 🦋

CLAHEF is an auxiliary routine called by CHETRF. It uses blocked code (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or A22 (if UPLO = 'L'). 💜

🌈 Parameters 🌈

• UPLO — UPLO is CHARACTER*1. Specifies whether the upper or lower triangular part of the Hermitian matrix A is stored:
  • = 'U': Upper triangular
  • = 'L': Lower triangular
• N — N is INTEGER. The order of the matrix A. N >= 0.
• NB — NB is INTEGER. The maximum number of columns of the matrix A that should be factored. NB should be at least 2 to allow for 2-by-2 pivot blocks.
• KB — KB is INTEGER. The number of columns of A that were actually factored. KB is either NB-1 or NB, or N if N <= NB.
• 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, A contains details of the partial factorization.
• 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) = IPIV(k-1) < 0, then rows and columns k-1 and -IPIV(k) 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) = IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
• W — W is COMPLEX array, dimension (LDW,NB).
• LDW — LDW is INTEGER. The leading dimension of the array W. LDW >= max(1,N).
• INFO — INFO is INTEGER.
  • = 0: successful exit
  • > 0: if INFO = k, D(k,k) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular.

👑 Author 👑

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

🌟 Contributors 🌟

November 2013, Igor Kozachenko, Computer Science Division, University of California, Berkeley

Definition at line 176 of file clahef.f.

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🤖 Author 🤖

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