ungr2(3)

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🎀 ungr2 vibes — Library Functions Manual

okay so bestie, welcome to the ungr2 page from the Library Functions Manual 💅 this is the whole thing, no skipped tea, no cap 🫶

🌸 NAME

ungr2 — {un,or}gr2: step in ungrq ✨

🦋 SYNOPSIS

Functions

  • subroutine cungr2 (m, n, k, a, lda, tau, work, info) — CUNGR2 generates all or part of the unitary matrix Q from an RQ factorization determined by cgerqf (unblocked algorithm). 💜
  • subroutine dorgr2 (m, n, k, a, lda, tau, work, info) — DORGR2 generates all or part of the orthogonal matrix Q from an RQ factorization determined by sgerqf (unblocked algorithm). 🦋
  • subroutine sorgr2 (m, n, k, a, lda, tau, work, info) — SORGR2 generates all or part of the orthogonal matrix Q from an RQ factorization determined by sgerqf (unblocked algorithm). 🌸
  • subroutine zungr2 (m, n, k, a, lda, tau, work, info) — ZUNGR2 generates all or part of the unitary matrix Q from an RQ factorization determined by cgerqf (unblocked algorithm). ✨

💜 Detailed Description

this section is short and sweet in the original: it just hands you over to the function docs below 🫶

🔥 Function Documentation

four routines, all iconic, no cap 👑

cungr2 ✨

subroutine cungr2 (integer m, integer n, integer k, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work, integer info)

CUNGR2 generates all or part of the unitary matrix Q from an RQ factorization determined by cgerqf (unblocked algorithm).

Purpose

CUNGR2 generates an m by n complex matrix Q with orthonormal rows, which is defined as the last m rows of a product of k elementary reflectors of order n

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

as returned by CGERQF. 💅

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. N >= M.
  • K — K is INTEGER; the number of elementary reflectors whose product defines the matrix Q. M >= K >= 0.
  • A — A is COMPLEX array, dimension (LDA,N). On entry, the (m-k+i)-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by CGERQF in the last k rows 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 CGERQF.
  • WORK — WORK is COMPLEX array, dimension (M).
  • 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

Definition at line 113 of file cungr2.f.

dorgr2 🦋

subroutine dorgr2 (integer m, integer n, integer k, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer info)

DORGR2 generates all or part of the orthogonal matrix Q from an RQ factorization determined by sgerqf (unblocked algorithm).

Purpose

DORGR2 generates an m by n real matrix Q with orthonormal rows, which is defined as the last m rows of a product of k elementary reflectors of order n

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

as returned by DGERQF. 💖

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. N >= M.
  • K — K is INTEGER; the number of elementary reflectors whose product defines the matrix Q. M >= K >= 0.
  • A — A is DOUBLE PRECISION array, dimension (LDA,N). On entry, the (m-k+i)-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by DGERQF in the last k rows 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 DGERQF.
  • WORK — WORK is DOUBLE PRECISION array, dimension (M).
  • 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

Definition at line 113 of file dorgr2.f.

sorgr2 🌸

subroutine sorgr2 (integer m, integer n, integer k, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer info)

SORGR2 generates all or part of the orthogonal matrix Q from an RQ factorization determined by sgerqf (unblocked algorithm).

Purpose

SORGR2 generates an m by n real matrix Q with orthonormal rows, which is defined as the last m rows of a product of k elementary reflectors of order n

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

as returned by SGERQF. 🌈

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. N >= M.
  • K — K is INTEGER; the number of elementary reflectors whose product defines the matrix Q. M >= K >= 0.
  • A — A is REAL array, dimension (LDA,N). On entry, the (m-k+i)-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by SGERQF in the last k rows 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 SGERQF.
  • WORK — WORK is REAL array, dimension (M).
  • 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

Definition at line 113 of file sorgr2.f.

zungr2 👑

subroutine zungr2 (integer m, integer n, integer k, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer info)

ZUNGR2 generates all or part of the unitary matrix Q from an RQ factorization determined by cgerqf (unblocked algorithm).

Purpose

ZUNGR2 generates an m by n complex matrix Q with orthonormal rows, which is defined as the last m rows of a product of k elementary reflectors of order n

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

as returned by ZGERQF. 💜

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. N >= M.
  • K — K is INTEGER; the number of elementary reflectors whose product defines the matrix Q. M >= K >= 0.
  • A — A is COMPLEX*16 array, dimension (LDA,N). On entry, the (m-k+i)-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by ZGERQF in the last k rows 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 ZGERQF.
  • WORK — WORK is COMPLEX*16 array, dimension (M).
  • 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

Definition at line 113 of file zungr2.f.

🌈 Author

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