ung2r(3)

📦
version 3.12.1 · 9 versions
, in arch rolling

✨ ung2r(3) — the Q-glow-up manual ✨

🌸 NAME 🌸

  • ung2r — {un,or}g2r: generate explicit Q from geqrf, level 2

🦋 SYNOPSIS 🦋

🌈 Functions 🌈

  • subroutine cung2r (m, n, k, a, lda, tau, work, info) — CUNG2R
  • subroutine dorg2r (m, n, k, a, lda, tau, work, info) — DORG2R generates all or part of the orthogonal matrix Q from a QR factorization determined by sgeqrf (unblocked algorithm).
  • subroutine sorg2r (m, n, k, a, lda, tau, work, info) — SORG2R generates all or part of the orthogonal matrix Q from a QR factorization determined by sgeqrf (unblocked algorithm).
  • subroutine zung2r (m, n, k, a, lda, tau, work, info) — ZUNG2R

💖 Detailed Description 💖

Okay bestie, this is where the actual function docs live. No cap, all four routines are here, and every parameter is getting its moment. 🫶

🎀 Function Documentation 🎀

subroutine cung2r

subroutine cung2r (integer m, integer n, integer k, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work, integer info)

CUNG2R

Purpose:

CUNG2R generates an m by n complex matrix Q with orthonormal columns, which is defined as the first n columns of a product of k elementary reflectors of order m

Q  =  H(1) H(2) . . . H(k)

as returned by CGEQRF.

Parameters

  • M — M is INTEGER. The number of rows of the matrix Q. M >= 0.
  • N — N is INTEGER. The number of columns of the matrix Q. M >= N >= 0.
  • K — K is INTEGER. The number of elementary reflectors whose product defines the matrix Q. N >= K >= 0.
  • A — A is COMPLEX array, dimension (LDA,N). On entry, the i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by CGEQRF in the first k columns of its array argument A. On exit, the m by n matrix Q.
  • LDA — LDA is INTEGER. The first dimension of the array A. LDA >= max(1,M).
  • TAU — TAU is COMPLEX array, dimension (K). TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by CGEQRF.
  • WORK — WORK is COMPLEX array, dimension (N).
  • INFO — INFO is INTEGER. = 0: successful exit. < 0: if INFO = -i, the i-th argument has an illegal value.

Author

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

Definition at line 113 of file cung2r.f.

subroutine dorg2r

subroutine dorg2r (integer m, integer n, integer k, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer info)

DORG2R generates all or part of the orthogonal matrix Q from a QR factorization determined by sgeqrf (unblocked algorithm).

Purpose:

DORG2R generates an m by n real matrix Q with orthonormal columns, which is defined as the first n columns of a product of k elementary reflectors of order m

Q  =  H(1) H(2) . . . H(k)

as returned by DGEQRF.

Parameters

  • M — M is INTEGER. The number of rows of the matrix Q. M >= 0.
  • N — N is INTEGER. The number of columns of the matrix Q. M >= N >= 0.
  • K — K is INTEGER. The number of elementary reflectors whose product defines the matrix Q. N >= K >= 0.
  • A — A is DOUBLE PRECISION array, dimension (LDA,N). On entry, the i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by DGEQRF in the first k columns of its array argument A. On exit, the m-by-n matrix Q.
  • LDA — LDA is INTEGER. The first dimension of the array A. LDA >= max(1,M).
  • TAU — TAU is DOUBLE PRECISION array, dimension (K). TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by DGEQRF.
  • WORK — WORK is DOUBLE PRECISION array, dimension (N).
  • INFO — INFO is INTEGER. = 0: successful exit. < 0: if INFO = -i, the i-th argument has an illegal value.

Author

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

Definition at line 113 of file dorg2r.f.

subroutine sorg2r

subroutine sorg2r (integer m, integer n, integer k, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer info)

SORG2R generates all or part of the orthogonal matrix Q from a QR factorization determined by sgeqrf (unblocked algorithm).

Purpose:

SORG2R generates an m by n real matrix Q with orthonormal columns, which is defined as the first n columns of a product of k elementary reflectors of order m

Q  =  H(1) H(2) . . . H(k)

as returned by SGEQRF.

Parameters

  • M — M is INTEGER. The number of rows of the matrix Q. M >= 0.
  • N — N is INTEGER. The number of columns of the matrix Q. M >= N >= 0.
  • K — K is INTEGER. The number of elementary reflectors whose product defines the matrix Q. N >= K >= 0.
  • A — A is REAL array, dimension (LDA,N). On entry, the i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by SGEQRF in the first k columns of its array argument A. On exit, the m-by-n matrix Q.
  • LDA — LDA is INTEGER. The first dimension of the array A. LDA >= max(1,M).
  • TAU — TAU is REAL array, dimension (K). TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by SGEQRF.
  • WORK — WORK is REAL array, dimension (N).
  • INFO — INFO is INTEGER. = 0: successful exit. < 0: if INFO = -i, the i-th argument has an illegal value.

Author

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

Definition at line 113 of file sorg2r.f.

subroutine zung2r

subroutine zung2r (integer m, integer n, integer k, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer info)

ZUNG2R

Purpose:

ZUNG2R generates an m by n complex matrix Q with orthonormal columns, which is defined as the first n columns of a product of k elementary reflectors of order m

Q  =  H(1) H(2) . . . H(k)

as returned by ZGEQRF.

Parameters

  • M — M is INTEGER. The number of rows of the matrix Q. M >= 0.
  • N — N is INTEGER. The number of columns of the matrix Q. M >= N >= 0.
  • K — K is INTEGER. The number of elementary reflectors whose product defines the matrix Q. N >= K >= 0.
  • A — A is COMPLEX*16 array, dimension (LDA,N). On entry, the i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by ZGEQRF in the first k columns of its array argument A. On exit, the m by n matrix Q.
  • LDA — LDA is INTEGER. The first dimension of the array A. LDA >= max(1,M).
  • TAU — TAU is COMPLEX*16 array, dimension (K). TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by ZGEQRF.
  • WORK — WORK is COMPLEX*16 array, dimension (N).
  • INFO — INFO is INTEGER. = 0: successful exit. < 0: if INFO = -i, the i-th argument has an illegal value.

Author

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

Definition at line 113 of file zung2r.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

🫶✨ That’s the whole glow-up! This page is from LAPACK Version 3.12.0 and it’s the ung2r(3) manual, bestie — slay. 🎀💅
📦 where this page comes from