laqps(3)

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version 3.12.1 · 9 versions
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💅 laqps(3) — the laqps page, but make it make sense

okay so bestie, this is laqps(3) from the Library Functions Manual, and it's literally the "step of geqp3" situation. Think of it as the little worker bee that does one chunk of a pivoted QR factorization. Not me about to explain pivoted QR in detail because honestly the page doesn't. Let's go 🔥

✨ NAME ✨

laqps — like, the whole name. laqps: step of geqp3. That's the vibe. Short, iconic, to the point 🎀

🌸 SYNOPSIS 🌸

🫶 Functions

  • subroutine claqps (m, n, offset, nb, kb, a, lda, jpvt, tau, vn1, vn2, auxv, f, ldf) — CLAQPS 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) — DLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3.
  • subroutine slaqps (m, n, offset, nb, kb, a, lda, jpvt, tau, vn1, vn2, auxv, f, ldf) — SLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3.
  • subroutine zlaqps (m, n, offset, nb, kb, a, lda, jpvt, tau, vn1, vn2, auxv, f, ldf) — ZLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3.
so yeah, four flavors — one per precision. same energy, different vibes ⭐

Detailed Description

(the page just vibes here — this heading exists, then it's straight into the function docs 💀)

🔥 Function Documentation 🔥

💜 subroutine claqps (integer m, integer n, integer offset, integer nb, integer kb, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) jpvt, complex, dimension( * ) tau, real, dimension( * ) vn1, real, dimension( * ) vn2, complex, dimension( * ) auxv, complex, dimension( ldf, * ) f, integer ldf)

CLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3.

Purpose:

!>
!> CLAQPS computes a step of QR factorization with column pivoting
!> of a complex 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.
!>
!> 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, 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 A that have been factorized in previous steps. !>
  • NB — !> NB is INTEGER, the number of columns to factorize. !>
  • KB — !> KB is INTEGER, the number of columns actually factorized. !>
  • A — !> A is COMPLEX array, dimension (LDA,N). On entry, 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 no factorized. The rest of the matrix, block A(OFFSET+1:M,KB+1:N) has been updated. !>
  • LDA — !> LDA is INTEGER, the leading dimension of the array A. LDA >= max(1,M). !>
  • JPVT — !> JPVT is INTEGER array, dimension (N). JPVT(I) = K <==> Column K of the full matrix A has been permuted into position I in AP. !>
  • TAU — !> TAU is COMPLEX array, dimension (KB), 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. !>
  • AUXV — !> AUXV is COMPLEX array, dimension (NB), auxiliary vector. !>
  • F — !> F is COMPLEX array, dimension (LDF,NB). Matrix F**H = L * Y**H * A. !>
  • LDF — !> LDF is INTEGER, 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 176 of file claqps.f.

🦋 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.

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.
!>
!> 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, 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 A that have been factorized in previous steps. !>
  • NB — !> NB is INTEGER, the number of columns to factorize. !>
  • KB — !> KB is INTEGER, the number of columns actually factorized. !>
  • A — !> A is DOUBLE PRECISION array, dimension (LDA,N). On entry, 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 no factorized. The rest of the matrix, block A(OFFSET+1:M,KB+1:N) has been updated. !>
  • LDA — !> LDA is INTEGER, the leading dimension of the array A. LDA >= max(1,M). !>
  • JPVT — !> JPVT is INTEGER array, dimension (N). JPVT(I) = K <==> Column K of the full matrix A has been permuted into position I in AP. !>
  • TAU — !> TAU is DOUBLE PRECISION array, dimension (KB), 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. !>
  • AUXV — !> AUXV is DOUBLE PRECISION array, dimension (NB), auxiliary vector. !>
  • F — !> F is DOUBLE PRECISION array, dimension (LDF,NB). Matrix F**T = L*Y**T*A. !>
  • LDF — !> LDF is INTEGER, 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.

🌈 subroutine slaqps (integer m, integer n, integer offset, integer nb, integer kb, real, dimension( lda, * ) a, integer lda, integer, dimension( * ) jpvt, real, dimension( * ) tau, real, dimension( * ) vn1, real, dimension( * ) vn2, real, dimension( * ) auxv, real, dimension( ldf, * ) f, integer ldf)

SLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3.

Purpose:

!>
!> SLAQPS 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.
!>
!> 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, 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 A that have been factorized in previous steps. !>
  • NB — !> NB is INTEGER, the number of columns to factorize. !>
  • KB — !> KB is INTEGER, the number of columns actually factorized. !>
  • A — !> A is REAL array, dimension (LDA,N). On entry, 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 no factorized. The rest of the matrix, block A(OFFSET+1:M,KB+1:N) has been updated. !>
  • LDA — !> LDA is INTEGER, the leading dimension of the array A. LDA >= max(1,M). !>
  • JPVT — JPVT is INTEGER array, dimension (N). The tea ☕: JPVT(I) = K <==> Column K of the full matrix A has been permuted into position I in AP. Basically the receipts for where every column ended up 💅
  • TAU — TAU is REAL array, dimension (KB). The scalar factors of the elementary reflectors. Iconic little scalars, no notes ✨
  • VN1 — VN1 is REAL array, dimension (N). The vector with the partial column norms. Keeping the vibe check on column sizes 🫶
  • VN2 — VN2 is REAL array, dimension (N). The vector with the exact column norms. The exact tea, not the approximations 🍓
  • AUXV — AUXV is REAL array, dimension (NB). Auxiliary vector. Sidekick energy 🧚
  • F — F is REAL array, dimension (LDF,NB). Matrix F**T = L*Y**T*A. Yes that's a transpose, not a typo 💀
  • LDF — LDF is INTEGER. The leading dimension of the array F. LDF >= max(1,N). Respect the leading dimension or else 😭

👑 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 176 of file slaqps.f.

💖 subroutine zlaqps

subroutine zlaqps (integer m, integer n, integer offset, integer nb, integer
    kb, 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( * )
    auxv, complex*16, dimension( ldf, * ) f, integer ldf)

ZLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3.

🔥 Purpose:

ZLAQPS computes a step of QR factorization with column pivoting of a complex 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.

Sometimes, 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. It's giving “we moved it but didn't do the work” energy 💅

🌸 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 A that have been factorized in previous steps.
  • NB — NB is INTEGER. The number of columns to factorize.
  • KB — KB is INTEGER. The number of columns actually factorized.
  • A — A is COMPLEX*16 array, dimension (LDA,N). On entry, 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 no factorized. The rest of the matrix, block A(OFFSET+1:M,KB+1:N) has been updated.
  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M).
  • JPVT — JPVT is INTEGER array, dimension (N). JPVT(I) = K <==> Column K of the full matrix A has been permuted into position I in AP.
  • TAU — TAU is COMPLEX*16 array, dimension (KB). 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.
  • AUXV — AUXV is COMPLEX*16 array, dimension (NB). Auxiliary vector.
  • F — F is COMPLEX*16 array, dimension (LDF,NB). Matrix F**H = L * Y**H * A.
  • LDF — LDF is INTEGER. 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 zlaqps.f.

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