/home/abui...trf_rook.f(3)

💖 /home/abui...trf_rook.f(3) — Library Functions Manual 💖

Okay bestie, this is the manual page for /home/abui...trf_rook.f(3), and the manual name is Library Functions Manual. We're about to get into ZHETRF_ROOK, and yes, she is iconic. 🎀

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🌸 NAME 🌸

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

That's the full dramatic path, no cap. This is the LAPACK page for ZHETRF_ROOK, the complex Hermitian indefinite factorization bestie using the bounded Bunch-Kaufman (“rook”) diagonal pivoting method. 💅

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✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

• subroutine ZHETRF_ROOK (uplo, n, a, lda, ipiv, work, lwork, info) — ZHETRF_ROOK computes the factorization of a complex Hermitian indefinite matrix using the bounded Bunch-Kaufman (“rook”) diagonal pivoting method (blocked algorithm, calling Level 3 BLAS).

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💜 Function/Subroutine Documentation 💜

🦋 subroutine ZHETRF_ROOK 🦋

subroutine ZHETRF_ROOK (character uplo, integer n, complex*16, dimension(
     lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16,
     dimension( * ) work, integer lwork, integer info)

ZHETRF_ROOK computes the factorization of a complex Hermitian indefinite matrix using the bounded Bunch-Kaufman (“rook”) diagonal pivoting method (blocked algorithm, calling Level 3 BLAS). Periodt. 💖

🌸 Purpose 🌸

ZHETRF_ROOK computes the factorization of a complex Hermitian matrix A using the bounded Bunch-Kaufman () diagonal pivoting method. The form of the factorization is

A = U*D*U**T  or  A = L*D*L**T

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.

This is the blocked version of the algorithm, calling Level 3 BLAS. She is not doing tiny unblocked loops unless she has to, okay? ✨

🎀 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 order of the matrix A. N >= 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, the block diagonal matrix D and the multipliers used to obtain the factor U or L (see below for further details).

💅 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, 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, D(k:k+1,k:k+1) is a 2-by-2 diagonal block.

💅 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. For best performance LWORK >= N*NB, where NB is the block size returned by ILAENV.
  • 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, and division by zero will occur if it is used to solve a system of equations.

🚨 Bestie, that INFO > 0 case is the “math said no” warning. D is exactly singular, and dividing by zero is not a vibe. 😭

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🌈 Author 🌈

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

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🔥 Further Details 🔥

If UPLO = 'U', then A = U*D*U**T, where

U = P(n)*U(n)* ... *P(k)U(k)* ...,

i.e., U is a product of terms P(k)*U(k), where k decreases from n to 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as defined by IPIV(k), and U(k) is a unit upper triangular matrix, such that if the diagonal block D(k) is of order s (s = 1 or 2), then

            (   I    v    0   )   k-s
    U(k) =  (   0    I    0   )   s
            (   0    0    I   )   n-k
               k-s   s   n-k

If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k). If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k), and A(k,k), and v overwrites A(1:k-2,k-1:k).

If UPLO = 'L', then A = L*D*L**T, where

L = P(1)*L(1)* ... *P(k)*L(k)* ...,

i.e., L is a product of terms P(k)*L(k), where k increases from 1 to n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as defined by IPIV(k), and L(k) is a unit lower triangular matrix, such that if the diagonal block D(k) is of order s (s = 1 or 2), then

            (   I    0     0   )  k-1
    L(k) =  (   0    I     0   )  s
            (   0    v     I   )  n-k-s+1
               k-1   s  n-k-s+1

If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k). If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k), and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).

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🫶 Contributors 🫶

• June 2016, Igor Kozachenko, Computer Science Division, University of California, Berkeley
• September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, School of Mathematics, University of Manchester

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📌 Definition 📌

Definition at line 211 of file zhetrf_rook.f.

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💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code.

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Byeee bestie, this page is LAPACK Version 3.12.0, and the footer is /home/abui...trf_rook.f(3). Mwah 💋✨