unmr3(3)

📦
version 3.12.1 · 9 versions
, in arch rolling

💅 unmr3(3) — the {un,or}mr3 girlies 💖

okay so you're reading unmr3(3) out of the Library Functions Manual, and honestly? iconic. this is the page for the {un,or}mr3 crew — a little family of routines whose entire personality is "step in unmrz" ✨. no cap, that's the whole NAME line, and we're gonna get into all of it.

🌸 NAME 🌸

unmr3 — {un,or}mr3: step in unmrz

✨ SYNOPSIS ✨

🫶 Functions

  • subroutine cunmr3 (side, trans, m, n, k, l, a, lda, tau, c, ldc, work, info) — CUNMR3 multiplies a general matrix by the unitary matrix from a RZ factorization determined by ctzrzf (unblocked algorithm).
  • subroutine dormr3 (side, trans, m, n, k, l, a, lda, tau, c, ldc, work, info) — DORMR3 multiplies a general matrix by the orthogonal matrix from a RZ factorization determined by stzrzf (unblocked algorithm).
  • subroutine sormr3 (side, trans, m, n, k, l, a, lda, tau, c, ldc, work, info) — SORMR3 multiplies a general matrix by the orthogonal matrix from a RZ factorization determined by stzrzf (unblocked algorithm).
  • subroutine zunmr3 (side, trans, m, n, k, l, a, lda, tau, c, ldc, work, info) — ZUNMR3 multiplies a general matrix by the unitary matrix from a RZ factorization determined by ctzrzf (unblocked algorithm).
yes bestie, dormr3 says stzrzf and not dtzrzf in that one-line summary. that's literally what the page says, so that's what I'm giving you. don't shoot the messenger 💀

🌈 Detailed Description 🌈

(the page keeps this heading and then… nothing. a vibe, an empty stage, main character energy with no dialogue. moving on 🎀)

👑 Function Documentation 👑

💜 subroutine cunmr3

subroutine cunmr3 (character side, character trans, integer m, integer n,
    integer k, integer l, complex, dimension( lda, * ) a, integer lda,
    complex, dimension( * ) tau, complex, dimension( ldc, * ) c, integer
    ldc, complex, dimension( * ) work, integer info)

CUNMR3 multiplies a general matrix by the unitary matrix from a RZ factorization determined by ctzrzf (unblocked algorithm).

🌟 Purpose:

CUNMR3 overwrites the general complex m by n matrix C with

Q * C  if SIDE = 'L' and TRANS = 'N', or

Q**H* C  if SIDE = 'L' and TRANS = 'C', or

C * Q  if SIDE = 'R' and TRANS = 'N', or

C * Q**H if SIDE = 'R' and TRANS = 'C',

where Q is a complex unitary matrix defined as the product of k elementary reflectors

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

as returned by CTZRZF. Q is of order m if SIDE = 'L' and of order n if SIDE = 'R'.

🍓 Parameters

  • SIDE — SIDE is CHARACTER*1. = 'L': apply Q or Q**H from the Left. = 'R': apply Q or Q**H from the Right.
  • TRANS — TRANS is CHARACTER*1. = 'N': apply Q (No transpose). = 'C': apply Q**H (Conjugate transpose).
  • M — M is INTEGER. The number of rows of the matrix C. M >= 0.
  • N — N is INTEGER. The number of columns of the matrix C. N >= 0.
  • K — K is INTEGER. The number of elementary reflectors whose product defines the matrix Q. If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >= 0.
  • L — L is INTEGER. The number of columns of the matrix A containing the meaningful part of the Householder reflectors. If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
  • A — A is COMPLEX array, dimension (LDA,M) if SIDE = 'L', (LDA,N) if SIDE = 'R'. The i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by CTZRZF in the last k rows of its array argument A. A is modified by the routine but restored on exit.
  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,K).
  • TAU — TAU is COMPLEX array, dimension (K). TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by CTZRZF.
  • C — C is COMPLEX array, dimension (LDC,N). On entry, the m-by-n matrix C. On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
  • LDC — LDC is INTEGER. The leading dimension of the array C. LDC >= max(1,M).
  • WORK — WORK is COMPLEX array, dimension (N) if SIDE = 'L', (M) if SIDE = 'R'.
  • INFO — INFO is INTEGER. = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value.

🧚 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

🎀 Contributors:

A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

⭐ Further Details:

(this heading exists and then it's just an empty !> — the void, the silence, the drama 🫶)

Definition at line 176 of file cunmr3.f.

💜 subroutine dormr3

subroutine dormr3 (character side, character trans, integer m, integer n,
    integer k, integer l, double precision, dimension( lda, * ) a, integer
    lda, double precision, dimension( * ) tau, double precision, dimension(
    ldc, * ) c, integer ldc, double precision, dimension( * ) work, integer
    info)

DORMR3 multiplies a general matrix by the orthogonal matrix from a RZ factorization determined by stzrzf (unblocked algorithm).

🌟 Purpose:

DORMR3 overwrites the general real m by n matrix C with

Q * C  if SIDE = 'L' and TRANS = 'N', or

Q**T* C  if SIDE = 'L' and TRANS = 'C', or

C * Q  if SIDE = 'R' and TRANS = 'N', or

C * Q**T if SIDE = 'R' and TRANS = 'C',

where Q is a real orthogonal matrix defined as the product of k elementary reflectors

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

as returned by DTZRZF. Q is of order m if SIDE = 'L' and of order n if SIDE = 'R'.

🍓 Parameters

  • SIDE — SIDE is CHARACTER*1. = 'L': apply Q or Q**T from the Left. = 'R': apply Q or Q**T from the Right.
  • TRANS — TRANS is CHARACTER*1. = 'N': apply Q (No transpose). = 'T': apply Q**T (Transpose).
  • M — M is INTEGER. The number of rows of the matrix C. M >= 0.
  • N — N is INTEGER. The number of columns of the matrix C. N >= 0.
  • K — K is INTEGER. The number of elementary reflectors whose product defines the matrix Q. If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >= 0.
  • L — L is INTEGER. The number of columns of the matrix A containing the meaningful part of the Householder reflectors. If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
  • A — A is DOUBLE PRECISION array, dimension (LDA,M) if SIDE = 'L', (LDA,N) if SIDE = 'R'. The i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by DTZRZF in the last k rows of its array argument A. A is modified by the routine but restored on exit.
  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,K).
  • TAU — TAU is DOUBLE PRECISION array, dimension (K). TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by DTZRZF.
  • C — C is DOUBLE PRECISION array, dimension (LDC,N). On entry, the m-by-n matrix C. On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
  • LDC — LDC is INTEGER. The leading dimension of the array C. LDC >= max(1,M).
  • WORK — WORK is DOUBLE PRECISION array, dimension (N) if SIDE = 'L', (M) if SIDE = 'R'.
  • INFO — INFO is INTEGER. = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value.

🧚 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

🎀 Contributors:

A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

⭐ Further Details:

(again: heading, then nothing but an empty !>. we respect the mystery.)

Definition at line 176 of file dormr3.f.

💜 subroutine sormr3

subroutine sormr3 (character side, character trans, integer m, integer n,
    integer k, integer l, real, dimension( lda, * ) a, integer lda, real,
    dimension( * ) tau, real, dimension( ldc, * ) c, integer ldc, real,
    dimension( * ) work, integer info)

SORMR3 multiplies a general matrix by the orthogonal matrix from a RZ factorization determined by stzrzf (unblocked algorithm).

🌟 Purpose:

SORMR3 overwrites the general real m by n matrix C with

Q * C  if SIDE = 'L' and TRANS = 'N', or

Q**T* C  if SIDE = 'L' and TRANS = 'C', or

C * Q  if SIDE = 'R' and TRANS = 'N', or

C * Q**T if SIDE = 'R' and TRANS = 'C',

where Q is a real orthogonal matrix defined as the product of k elementary reflectors

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

as returned by STZRZF. Q is of order m if SIDE = 'L' and of order n if SIDE = 'R'.

🍓 Parameters

  • SIDE — SIDE is CHARACTER*1. = 'L': apply Q or Q**T from the Left. = 'R': apply Q or Q**T from the Right.
  • TRANS — TRANS is CHARACTER*1. = 'N': apply Q (No transpose). = 'T': apply Q**T (Transpose).
  • M — M is INTEGER. The number of rows of the matrix C. M >= 0.
  • N — N is INTEGER. The number of columns of the matrix C. N >= 0.
  • K — K is INTEGER.

okay so we're still rolling through the sormr3 parameter list — here's the rest of the cast, and yes every single one matters, bestie 💅

  • K — K is INTEGER. The number of elementary reflectors whose product defines the matrix Q. If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >= 0.
  • L — L is INTEGER. The number of columns of the matrix A containing the meaningful part of the Householder reflectors. If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
  • A — A is REAL array, dimension (LDA,M) if SIDE = 'L', (LDA,N) if SIDE = 'R'. The i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by STZRZF in the last k rows of its array argument A. A is modified by the routine but restored on exit.
  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,K).
  • TAU — TAU is REAL array, dimension (K). TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by STZRZF.
  • C — C is REAL array, dimension (LDC,N). On entry, the m-by-n matrix C. On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
  • LDC — LDC is INTEGER. The leading dimension of the array C. LDC >= max(1,M).
  • WORK — WORK is REAL array, dimension (N) if SIDE = 'L', (M) if SIDE = 'R'.
  • INFO — INFO is INTEGER. = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value.

Author 👑

the icons who brought you this routine:

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

Contributors: 🫶

  • A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

Further Details: 🙈

literally just !> — no extra lore here, bestie. The source leaves it empty.

Definition at line 176 of file sormr3.f. 📍

🌟 zunmr3 — the complex twin, same unblocked energy 🦋

here's the signature, copy-paste energy, exactly as it lives in the source:

subroutine zunmr3 (character side, character trans, integer m, integer n,
       integer k, integer l, complex*16, dimension( lda, * ) a, integer lda,
       complex*16, dimension( * ) tau, complex*16, dimension( ldc, * ) c,
       integer ldc, complex*16, dimension( * ) work, integer info)

ZUNMR3 multiplies a general matrix by the unitary matrix from a RZ factorization determined by ctzrzf (unblocked algorithm).

Purpose 🎯

ZUNMR3 overwrites the general complex m by n matrix C with:

Q * C  if SIDE = 'L' and TRANS = 'N', or

Q**H* C  if SIDE = 'L' and TRANS = 'C', or

C * Q  if SIDE = 'R' and TRANS = 'N', or

C * Q**H if SIDE = 'R' and TRANS = 'C',

where Q is a complex unitary matrix defined as the product of k elementary reflectors

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

as returned by ZTZRZF. Q is of order m if SIDE = 'L' and of order n if SIDE = 'R'.

Parameters ✨

  • SIDE — SIDE is CHARACTER*1. = 'L': apply Q or QH from the Left. = 'R': apply Q or QH from the Right.
  • TRANS — TRANS is CHARACTER*1. = 'N': apply Q (No transpose). = 'C': apply Q**H (Conjugate transpose).
  • M — M is INTEGER. The number of rows of the matrix C. M >= 0.
  • N — N is INTEGER. The number of columns of the matrix C. N >= 0.
  • K — K is INTEGER. The number of elementary reflectors whose product defines the matrix Q. If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >= 0.
  • L — L is INTEGER. The number of columns of the matrix A containing the meaningful part of the Householder reflectors. If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
  • A — A is COMPLEX*16 array, dimension (LDA,M) if SIDE = 'L', (LDA,N) if SIDE = 'R'. The i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by ZTZRZF in the last k rows of its array argument A. A is modified by the routine but restored on exit.
  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,K).
  • TAU — TAU is COMPLEX*16 array, dimension (K). TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by ZTZRZF.
  • C — C is COMPLEX*16 array, dimension (LDC,N). On entry, the m-by-n matrix C. On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
  • LDC — LDC is INTEGER. The leading dimension of the array C. LDC >= max(1,M).
  • WORK — WORK is COMPLEX*16 array, dimension (N) if SIDE = 'L', (M) if SIDE = 'R'.
  • INFO — INFO is INTEGER. = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value.

Author 👑

same iconic lineup:

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

Contributors: 🫶

  • A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

Further Details: 🙈

again, just !> — the section is empty, and we respect the minimalism.

Definition at line 176 of file zunmr3.f. 📍

Author (the page-footer energy) 🧚

Generated automatically by Doxygen for LAPACK from the source code.

signing off with LAPACK Version 3.12.0 and the unmr3(3) page stamp — that's the footer vibe, bestie, no extra date tea invented 💖✨

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