SLAORHR_COL_GETRFNP(3)

💅 SRC/slaorhr_col_getrfnp.f — Library Functions Manual 💅

okay bestie, this is the Library Functions Manual page for SRC/slaorhr_col_getrfnp.f — manual name folded in near the top, exactly as requested. It's the SLAORHR_COL_GETRFNP subroutine page, and it's lowkey iconic for being an auxiliary piece in Householder reconstruction. 🦋

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✨ NAME ✨

SRC/slaorhr_col_getrfnp.f — that's the page name, 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 — the one and only, bestie. 💖

💖 Purpose 💖

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 is not possible during the division by the diagonal element).
• L is a M-by-N lower triangular matrix with unit diagonal elements (lower trapezoidal if M > N).
• 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.

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🌸 Parameters 🌸

• M — M is INTEGER. The number of rows of the matrix A. M >= 0.
• N — N is INTEGER. 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

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👑 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.

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🧚 Definition at line 🧚

Definition at line 145 of file slaorhr_col_getrfnp.f.

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👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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cute sign-off time, bestie: this page's footer energy is LAPACK Version 3.12.0 and source/page SRC/slaorh...l_getrfnp.f(3), with the date noted in contributors being November 2019. Mwah 💖🫶🎀