SRC/dlaqps.f(3)

💖 NAME 💖

Okay bestie, this page is for SRC/dlaqps.f, and it lives in the Library Functions Manual — that’s the manual-name vibe folded in right at the top, no boring header line needed. Minimal. Iconic. 🎀

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✨ SYNOPSIS ✨

🌈 Functions/Subroutines 🌈

• subroutine dlaqps (m, n, offset, nb, kb, a, lda, jpvt, tau, vn1, vn2, auxv, f, ldf) — DLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3.

       subroutine dlaqps (m, n, offset, nb, kb, a, lda, jpvt, tau, vn1, vn2,
           auxv, f, ldf)

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🧚 Function/Subroutine Documentation 🧚

       subroutine dlaqps (integer m, integer n, integer offset, integer nb, integer
           kb, double precision, dimension( lda, * ) a, integer lda, integer,
           dimension( * ) jpvt, double precision, dimension( * ) tau, double
           precision, dimension( * ) vn1, double precision, dimension( * ) vn2,
           double precision, dimension( * ) auxv, double precision, dimension( ldf,
           * ) f, integer ldf)

DLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3. That’s the short story, and the full tea is below. 🫶

🎯 Purpose 🎯

DLAQPS computes a step of QR factorization with column pivoting of a real M-by-N matrix A by using Blas-3. It tries to factorize NB columns from A starting from the row OFFSET+1, and updates all of the matrix with Blas-3 xGEMM.

👀 Real talk: in some cases, due to catastrophic cancellations, it cannot factorize NB columns. Hence, the actual number of factorized columns is returned in KB.

Block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized.

🧸 Parameters 🧸

• M — M is INTEGER. It’s the number of rows of the matrix A. M >= 0.
• N — N is INTEGER. It’s the number of columns of the matrix A. N >= 0.
• OFFSET — OFFSET is INTEGER. It’s the number of rows of A that have been factorized in previous steps.
• NB — NB is INTEGER. It’s the number of columns to factorize.
• KB — KB is INTEGER. It’s the number of columns actually factorized.
• A — A is a DOUBLE PRECISION array, dimension (LDA,N). On entry, it’s the M-by-N matrix A. On exit, block A(OFFSET+1:M,1:KB) is the triangular factor obtained, and block A(1:OFFSET,1:N) has been accordingly pivoted but not factorized. The rest of the matrix, block A(OFFSET+1:M,KB+1:N), has been updated.
• LDA — LDA is INTEGER. It’s the leading dimension of the array A. LDA >= max(1,M).
• JPVT — JPVT is an INTEGER array, dimension (N). The docs say: JPVT(I) = K <==> Column K of the full matrix A has been permuted into position I in AP.
• TAU — TAU is a DOUBLE PRECISION array, dimension (KB). These are the scalar factors of the elementary reflectors.
• VN1 — VN1 is a DOUBLE PRECISION array, dimension (N). It’s the vector with the partial column norms.
• VN2 — VN2 is a DOUBLE PRECISION array, dimension (N). It’s the vector with the exact column norms.
• AUXV — AUXV is a DOUBLE PRECISION array, dimension (NB). It’s an auxiliary vector.
• F — F is a DOUBLE PRECISION array, dimension (LDF,NB). Matrix F**T = L*Y**T*A.
• LDF — LDF is INTEGER. It’s the leading dimension of the array F. LDF >= max(1,N).

👑 Author 👑

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

🫶 Contributors 🫶

• G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
• X. Sun, Computer Science Dept., Duke University, USA
• Partial column norm updating strategy modified on April 2011 Z. Drmac and Z. Bujanovic, Dept. of Mathematics, University of Zagreb, Croatia.

📚 References 📚

• LAPACK Working Note 176

Definition at line 175 of file dlaqps.f.

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📝 Author 📝

Generated automatically by Doxygen for LAPACK from the source code.

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💖 That’s the whole page, bestie! The footer’s source/version energy is LAPACK Version 3.12.0, SRC/dlaqps.f(3) — and yes, we ate. Periodt. 💅✨