laqp2(3)

📦
version 3.12.1 · 9 versions
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✨ laqp2(3) ✨

okay so this is laqp2(3), straight out of the Library Functions Manual, and bestie… it's a whole family of subroutines that all do the same iconic thing in different precisions. Think of it as the same slay outfit in four different colorways 💅. It's one step of geqp3, and it's the one doing the QR-with-column-pivoting moment. Let's get into it 🫶

🎀 NAME 🎀

laqp2 — literally just: laqp2: step of geqp3. That's the whole name section. Short, sweet, does what it says on the tin ✨.

🦋 SYNOPSIS 🦋

💫 Functions

  • subroutine claqp2 (m, n, offset, a, lda, jpvt, tau, vn1, vn2, work) — CLAQP2 computes a QR factorization with column pivoting of the matrix block. (complex era 💜)
  • subroutine dlaqp2 (m, n, offset, a, lda, jpvt, tau, vn1, vn2, work) — DLAQP2 computes a QR factorization with column pivoting of the matrix block. (double precision era 🔥)
  • subroutine slaqp2 (m, n, offset, a, lda, jpvt, tau, vn1, vn2, work) — SLAQP2 computes a QR factorization with column pivoting of the matrix block. (real era 🌸)
  • subroutine zlaqp2 (m, n, offset, a, lda, jpvt, tau, vn1, vn2, work) — ZLAQP2 computes a QR factorization with column pivoting of the matrix block. (double complex era 👑)

🌈 Detailed Description

(no cap, the original page just puts this heading here and then Beelines straight into the function docs — so that's exactly what we're doing too. all the real tea is below ⬇️)

💖 Function Documentation 💖

🌸 claqp2 🌸

subroutine claqp2 (integer m, integer n, integer offset, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) jpvt, complex, dimension( * ) tau, real, dimension( * ) vn1, real, dimension( * ) vn2, complex, dimension( * ) work)

CLAQP2 computes a QR factorization with column pivoting of the matrix block. The complex icon of the group 💅.

⭐ Purpose

ok so CLAQP2 computes a QR factorization with column pivoting of the block A(OFFSET+1:M,1:N).

And the block A(1:OFFSET,1:N)? It gets accordingly pivoted, but it does not get factorized. Pivoted yes, factorized no. Know the difference bestie 🫶

🎯 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.
  • OFFSET — OFFSET is INTEGER. The number of rows of the matrix A that must be pivoted but not factorized. OFFSET >= 0.
  • A — A is COMPLEX array, dimension (LDA,N). On entry: the M-by-N matrix A. On exit: the upper triangle of block A(OFFSET+1:M,1:N) is the triangular factor obtained; the elements in block A(OFFSET+1:M,1:N) below the diagonal, together with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors. Block A(1:OFFSET,1:N) has been accordingly pivoted, but not factorized.
  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M).
  • JPVT — JPVT is INTEGER array, dimension (N). On entry: if JPVT(i) .ne. 0, the i-th column of A is permuted to the front of A*P (a leading column); if JPVT(i) = 0, the i-th column of A is a free column. On exit: if JPVT(i) = k, then the i-th column of A*P was the k-th column of A.
  • TAU — TAU is COMPLEX array, dimension (min(M,N)). The scalar factors of the elementary reflectors.
  • VN1 — VN1 is REAL array, dimension (N). The vector with the partial column norms.
  • VN2 — VN2 is REAL array, dimension (N). The vector with the exact column norms.
  • WORK — WORK is COMPLEX array, dimension (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 147 of file claqp2.f.

🔥 dlaqp2 🔥

subroutine dlaqp2 (integer m, integer n, integer offset, 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( * ) work)

DLAQP2 computes a QR factorization with column pivoting of the matrix block. The double precision one, serving exact same energy, just with bigger vibes 💜.

⭐ Purpose

DLAQP2 computes a QR factorization with column pivoting of the block A(OFFSET+1:M,1:N).

The block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized. That's it. That's the whole deal 🫶

🎯 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.
  • OFFSET — OFFSET is INTEGER. The number of rows of the matrix A that must be pivoted but not factorized. OFFSET >= 0.
  • A — A is DOUBLE PRECISION array, dimension (LDA,N). On entry: the M-by-N matrix A. On exit: the upper triangle of block A(OFFSET+1:M,1:N) is the triangular factor obtained; the elements in block A(OFFSET+1:M,1:N) below the diagonal, together with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors. Block A(1:OFFSET,1:N) has been accordingly pivoted, but not factorized.
  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M).
  • JPVT — JPVT is INTEGER array, dimension (N). On entry: if JPVT(i) .ne. 0, the i-th column of A is permuted to the front of A*P (a leading column); if JPVT(i) = 0, the i-th column of A is a free column. On exit: if JPVT(i) = k, then the i-th column of A*P was the k-th column of A.
  • TAU — TAU is DOUBLE PRECISION array, dimension (min(M,N)). The scalar factors of the elementary reflectors.
  • VN1 — VN1 is DOUBLE PRECISION array, dimension (N). The vector with the partial column norms.
  • VN2 — VN2 is DOUBLE PRECISION array, dimension (N). The vector with the exact column norms.
  • WORK — WORK is DOUBLE PRECISION array, dimension (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 147 of file dlaqp2.f.

🌸 slaqp2 🌸

subroutine slaqp2 (integer m, integer n, integer offset, real, dimension( lda, * ) a, integer lda, integer, dimension( * ) jpvt, real, dimension( * ) tau, real, dimension( * ) vn1, real, dimension( * ) vn2, real, dimension( * ) work)

SLAQP2 computes a QR factorization with column pivoting of the matrix block. Real precision, real cute, same algorithm 🎀.

⭐ Purpose

SLAQP2 computes a QR factorization with column pivoting of the block A(OFFSET+1:M,1:N).

And once again: the block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized. It's the family motto at this point fr fr ✨

🎯 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.
  • OFFSET — OFFSET is INTEGER. The number of rows of the matrix A that must be pivoted but not factorized. OFFSET >= 0.
  • A — A is REAL array, dimension (LDA,N). On entry: the M-by-N matrix A. On exit: the upper triangle of block A(OFFSET+1:M,1:N) is the triangular factor obtained; the elements in block A(OFFSET+1:M,1:N) below the diagonal, together with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors. Block A(1:OFFSET,1:N) has been accordingly pivoted, but not factorized.
  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M).
  • JPVT — JPVT is INTEGER array, dimension (N). On entry: if JPVT(i) .ne. 0, the i-th column of A is permuted to the front of A*P (a leading column); if JPVT(i) = 0, the i-th column of A is a free column. On exit: if JPVT(i) = k, then the i-th column of A*P was the k-th column of A.
  • TAU — TAU is REAL array, dimension (min(M,N)). The scalar factors of the elementary reflectors.
  • VN1 — VN1 is REAL array, dimension (N). The vector with the partial column norms.
  • VN2 — VN2 is REAL array, dimension (N). The vector with the exact column norms.
  • WORK — WORK is REAL array, dimension (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 147 of file slaqp2.f.

👑 zlaqp2 👑

subroutine zlaqp2 (integer m, integer n, integer offset, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) jpvt, complex*16, dimension( * ) tau, double precision, dimension( * ) vn1, double precision, dimension( * ) vn2, complex*16, dimension( * ) work)

ZLAQP2 computes a QR factorization with column pivoting of the matrix block. The double complex main character of the family — note that a, tau and work are complex*16 but vn1 and vn2 stay double precision, because norms are real and they know it 💅.

⭐ Purpose

ZLAQP2 computes a QR factorization with column pivoting of the block A(OFFSET+1:M,1:N).

The block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized. Same energy, double complex edition 🔥

🎯 Parameters

  • M — M is INTEGER. The number of rows of the matrix A. M >= 0.
  • M — M is INTEGER. It’s the number of rows of matrix A. Constraint: M >= 0. Zero rows is valid, bestie, don’t panic ✨
  • N — N is INTEGER. Number of columns of matrix A. Constraint: N >= 0.
  • OFFSET — OFFSET is INTEGER. The number of rows of matrix A that must be pivoted but not factorized. Constraint: OFFSET >= 0.
  • A — A is COMPLEX*16 array, dimension (LDA,N). On entry, it’s the M-by-N matrix A. On exit, the upper triangle of block A(OFFSET+1:M,1:N) is the triangular factor obtained; the elements in block A(OFFSET+1:M,1:N) below the diagonal, together with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors. Block A(1:OFFSET,1:N) has been pivoted accordingly, but not factorized. Yes, the whole block gets shuffled; it just doesn’t get factorized 🫶
  • LDA — LDA is INTEGER. The leading dimension of the array A. Constraint: LDA >= max(1,M). Don’t skimp on the leading dimension, bestie 😭
  • JPVT — JPVT is INTEGER array, dimension (N). On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted to the front of A*P (a leading column); if JPVT(i) = 0, the i-th column of A is a free column. On exit, if JPVT(i) = k, then the i-th column of A*P was the k-th column of A. The .ne. is Fortran for “not equal,” iykyk 💀
  • TAU — TAU is COMPLEX*16 array, dimension (min(M,N)). Holds the scalar factors of the elementary reflectors.
  • VN1 — VN1 is DOUBLE PRECISION array, dimension (N). The vector with the partial column norms.
  • VN2 — VN2 is DOUBLE PRECISION array, dimension (N). The vector with the exact column norms.
  • WORK — WORK is COMPLEX*16 array, dimension (N). That’s it, no extra lore 💅

👑 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 147 of file zlaqp2.f.

🤖 Author (the Doxygen one)

Generated automatically by Doxygen for LAPACK from the source code.

And that’s the footer tea, bestie: LAPACK Version 3.12.0, page laqp2(3) — no separate date shown on that line, so that’s the whole vibe 🙈💖 Byeee ✨

📦 where this page comes from