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

okay bestie, this page lives in the Library Functions Manual and its title is /home/abui..._getrfnp.f(3) — yes, the whole filename is the title, iconic behavior 💅. let’s get into it.

💖 NAME 💖

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

like, that’s the path, periodt 🎀

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✨ SYNOPSIS ✨

🌈 Functions/Subroutines 🌈

• subroutine SLAORHR_COL_GETRFNP (m, n, a, lda, d, info) — SLAORHR_COL_GETRFNP

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🎀 Function/Subroutine Documentation 🎀

subroutine SLAORHR_COL_GETRFNP (integer m, integer n, real, dimension( lda,
* ) a, integer lda, real, dimension( * ) d, integer info)

SLAORHR_COL_GETRFNP

💅 Purpose: 💅

okay so SLAORHR_COL_GETRFNP computes the modified LU factorization without pivoting of a real general M-by-N matrix A. The factorization has the form:

A - S = L * U,

where:

• S is a m-by-n diagonal sign matrix with the diagonal D, so that D(i) = S(i,i), 1 <= i <= min(M,N). The diagonal D is constructed as D(i)=-SIGN(A(i,i)), where A(i,i) is the value after performing i-1 steps of Gaussian elimination. This means that the diagonal element at each step of Gaussian elimination is at least one in absolute value (so that division-by-zero not not possible during the division by the diagonal element — yes, the source really says “not not,” keep it 100 😭);
• L is a M-by-N lower triangular matrix with unit diagonal elements (lower trapezoidal if M > N);
• and U is a M-by-N upper triangular matrix (upper trapezoidal if M < N).

This routine is an auxiliary routine used in the Householder reconstruction routine SORHR_COL. In SORHR_COL, this routine is applied to an M-by-N matrix A with orthonormal columns, where each element is bounded by one in absolute value. With the choice of the matrix S above, one can show that the diagonal element at each step of Gaussian elimination is the largest (in absolute value) in the column on or below the diagonal, so that no pivoting is required for numerical stability [1].

For more details on the Householder reconstruction algorithm, including the modified LU factorization, see [1].

This is the blocked right-looking version of the algorithm, calling Level 3 BLAS to update the submatrix. To factorize a block, this routine calls the recursive routine SLAORHR_COL_GETRFNP2.

[1] ,
    G. Ballard, J. Demmel, L. Grigori, M. Jacquelin, H.D. Nguyen,
    E. Solomonik, J. Parallel Distrib. Comput.,
    vol. 85, pp. 3-31, 2015.

🦋 Parameters 🦋

• M — M is INTEGER. M is the number of rows of the matrix A. M >= 0.
• N — N is INTEGER. N is the number of columns of the matrix A. N >= 0.
• A — A is REAL array, dimension (LDA,N). On entry, the M-by-N matrix to be factored. On exit, the factors L and U from the factorization A-S=L*U; the unit diagonal elements of L are not stored.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M).
• D — D is REAL array, dimension min(M,N). The diagonal elements of the diagonal M-by-N sign matrix S, D(i) = S(i,i), where 1 <= i <= min(M,N). The elements can be only plus or minus one.
• INFO — INFO is INTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

💜 Author 💜

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

🌸 Contributors: 🌸

November 2019, Igor Kozachenko,
               Computer Science Division,
               University of California, Berkeley

Definition at line 145 of file slaorhr_col_getrfnp.f.

💖 Author 💖

Generated automatically by Doxygen for LAPACK from the source code.

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okay bestie, that’s the whole page 🫶. the footer says LAPACK and Version 3.12.0, and the page is /home/abui..._getrfnp.f(3) — there’s no date in the original footer, so I’m not inventing one, no cap 🎀✨. byeee 💜