lahef(3)

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version 3.12.1 · 9 versions
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💅 lahef(3) — Library Functions Manual 🎀

okay bestie, so this is lahef(3) from the Library Functions Manual, and it's literally the group chat of LAPACK auxiliary routines. no cap, it's a whole family of them. let's get into it ✨

🌸 NAME 🌸

lahef — la{he,sy}f: step in hetrf

like, that's the whole name section. short and iconic. moving on 💅

✨ SYNOPSIS ✨

🦋 Functions

  • 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).
  • subroutine clasyf (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info) — CLASYF computes a partial factorization of a complex symmetric matrix using the Bunch-Kaufman diagonal pivoting method.
  • subroutine dlasyf (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info) — DLASYF computes a partial factorization of a real symmetric matrix using the Bunch-Kaufman diagonal pivoting method.
  • subroutine slasyf (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info) — SLASYF computes a partial factorization of a real symmetric matrix using the Bunch-Kaufman diagonal pivoting method.
  • subroutine zlahef (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info) — ZLAHEF computes a partial factorization of a complex Hermitian indefinite matrix using the Bunch-Kaufman diagonal pivoting method (blocked algorithm, calling Level 3 BLAS).
  • subroutine zlasyf (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info) — ZLASYF computes a partial factorization of a complex symmetric matrix using the Bunch-Kaufman diagonal pivoting method.

see how they all take the exact same argument list? it's giving coordinated outfit energy. uplo, n, nb, kb, a, lda, ipiv, w, ldw, info — every single one. obsessed 🫶

💜 Detailed Description 💜

(yeah so this section exists but there's genuinely nothing written under it in the original — it's just sitting there, empty, main character energy with no lines. respect honestly.)

🔥 Function 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:

ok so 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. (important!! don't skip that one, bestie 💀)

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.

note the index flip between the two cases — k-1 one way, k+1 the other. it's giving mirror-image twins, don't mix them up 🙈

W

W is COMPLEX array, dimension (LDW,NB).

(yes that's genuinely all it says. no elaboration. mysterious. we love her for it 💅)

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.
⚠️ okay so that second one is the vibe-killer case: positive INFO means the factorization finished, but D came out exactly singular. it's not an error mid-way, it's a "we got there and the answer is cursed" situation. note it accordingly, bestie 😭

👑 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

Definition at line 176 of file clahef.f.

⭐ subroutine clasyf (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)

CLASYF computes a partial factorization of a complex symmetric matrix using the Bunch-Kaufman diagonal pivoting method.

🎀 Purpose:

ok so CLASYF computes a partial factorization of a complex symmetric 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**T U22**T )

A  =  ( L11  0 ) ( D    0  ) ( L11**T L21**T )  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**T denotes the transpose of U.

spot the difference from CLAHEF: it's plain transpose **T, not conjugate transpose **H, because this one is symmetric, not Hermitian. iykyk 🦋

CLASYF is an auxiliary routine called by CSYTRF. 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 symmetric 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 symmetric 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.

(identical wording to CLAHEF's IPIV, bestie — these two routines are genuinely twinning 🫶)

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.
⚠️ same caveat as before and it's a real one: INFO > 0 does not mean the factorization bailed. it means it completed and D turned out exactly singular. keep that distinction, it matters 😭

👑 Author

  • Univ. of Tennessee

Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd. — that's the whole author squad, no cap 💖

Contributors:

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

Definition at line 176 of file clasyf.f.

🌸 dlasyf

subroutine dlasyf (character uplo, integer n, integer nb, integer kb, double
precision, dimension( lda, * ) a, integer lda, integer, dimension( * )
ipiv, double precision, dimension( ldw, * ) w, integer ldw, integer
info)

DLASYF computes a partial factorization of a real symmetric matrix using the Bunch-Kaufman diagonal pivoting method. Same energy as its siblings, just double precision 💅

Purpose:

DLASYF computes a partial factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method, and the partial factorization has the form:

A  =  ( I  U12 ) ( A11  0  ) (  I       0    )  if UPLO = 'U', or:
      ( 0  U22 ) (  0   D  ) ( U12**T U22**T )
A  =  ( L11  0 ) (  D   0  ) ( L11**T L21**T )  if UPLO = 'L'
      ( L21  I ) (  0  A22 ) (  0       I    )

where the order of D is at most NB. The actual order gets handed back to you in the argument KB, and it's either NB or NB-1, or N if N <= NB. Lowkey the important bit 🫶

DLASYF is an auxiliary routine called by DSYTRF. It uses blocked code (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or A22 (if UPLO = 'L'). That's the whole slay ✨

Parameters

  • UPLO — is CHARACTER*1. Specifies whether the upper or lower triangular part of the symmetric matrix A is stored:
    • = 'U': Upper triangular
    • = 'L': Lower triangular
  • N — is INTEGER. The order of the matrix A. N >= 0.
  • 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 — 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 — is DOUBLE PRECISION array, dimension (LDA,N). On entry, the symmetric 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 — 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) = 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 — is DOUBLE PRECISION array, dimension (LDW,NB).
  • LDW — is INTEGER. The leading dimension of the array W. LDW >= max(1,N).
  • 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 175 of file dlasyf.f.

🌈 slasyf

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

SLASYF computes a partial factorization of a real symmetric matrix using the Bunch-Kaufman diagonal pivoting method. Yes bestie, it's the single-precision twin, and it ate 🔥

Purpose:

SLASYF computes a partial factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method, and the partial factorization has the form:

A  =  ( I  U12 ) ( A11  0  ) (  I       0    )  if UPLO = 'U', or:
      ( 0  U22 ) (  0   D  ) ( U12**T U22**T )
A  =  ( L11  0 ) (  D   0  ) ( L11**T L21**T )  if UPLO = 'L'
      ( L21  I ) (  0  A22 ) (  0       I    )

where the order of D is at most NB. The actual order comes back to you in the argument KB, and it's either NB or NB-1, or N if N <= NB. Fr fr, same deal as dlasyf 🎀

SLASYF is an auxiliary routine called by SSYTRF. It uses blocked code (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or A22 (if UPLO = 'L'). Main character energy ✨

Parameters

  • UPLO — is CHARACTER*1. Specifies whether the upper or lower triangular part of the symmetric matrix A is stored:
    • = 'U': Upper triangular
    • = 'L': Lower triangular
  • N — is INTEGER. The order of the matrix A. N >= 0.
  • 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 — 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 — is REAL array, dimension (LDA,N). On entry, the symmetric 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 — 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) = 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 — is REAL array, dimension (LDW,NB).
  • LDW — is INTEGER. The leading dimension of the array W. LDW >= max(1,N).
  • 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 175 of file slasyf.f.

💜 zlahef

subroutine zlahef (character uplo, integer n, integer nb, integer kb,
complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * )
ipiv, complex*16, dimension( ldw, * ) w, integer ldw, integer info)

ZLAHEF computes a partial factorization of a complex Hermitian indefinite matrix using the Bunch-Kaufman diagonal pivoting method (blocked algorithm, calling Level 3 BLAS). Hermitian and indefinite, we love a complicated icon 💅

Purpose:

so yeah — ZLAHEF 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.

ZLAHEF is an auxiliary routine called by ZHETRF. 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*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, 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*16 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 🌸

December 2016 — Igor Kozachenko, Computer Science Division, University of California, Berkeley.

Definition at line 176 of file zlahef.f.

🦋 subroutine zlasyf 🦋

subroutine zlasyf (character uplo, integer n, integer nb, integer kb,
    complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * )
    ipiv, complex*16, dimension( ldw, * ) w, integer ldw, integer info)

ZLASYF computes a partial factorization of a complex symmetric matrix using the Bunch-Kaufman diagonal pivoting method.

🌟 Purpose 🌟

ZLASYF computes a partial factorization of a complex symmetric 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**T U22**T )

A  =  ( L11  0 ) ( D    0  ) ( L11**T L21**T )  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**T denotes the transpose of U.

ZLASYF is an auxiliary routine called by ZSYTRF. 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 symmetric 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*16 array, dimension (LDA,N).
    • On entry, the symmetric 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*16 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 zlasyf.f.

💜 Author 💜

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