unmr2(3)

📦

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🌸 `unmr2(3)` — from the Library Functions Manual 🌸

okay so bestie. you found it. this is the page for unmr2(3), aka the whole {un,or}mr2 family — and yes the name in the wild is literally unmr2 - {un,or}mr2: step in unmrq. it's giving "one letter changes everything" and honestly? iconic. 💅

here's the tea: this is a family page. four separate Fortran subroutines live here, all doing the same little dance but with different number types. don't panic. we're gonna go through every single one. 🫶

✨ NAME ✨

unmr2 — {un,or}mr2: step in unmrq

that's it. that's the name section. short, sweet, mysterious. iykyk. 🎀

💖 SYNOPSIS 💖

🌈 Functions

cunmr2 — subroutine cunmr2 (side, trans, m, n, k, a, lda, tau, c, ldc, work, info) — CUNMR2 multiplies a general matrix by the unitary matrix from a RQ factorization determined by cgerqf (unblocked algorithm).
dormr2 — subroutine dormr2 (side, trans, m, n, k, a, lda, tau, c, ldc, work, info) — DORMR2 multiplies a general matrix by the orthogonal matrix from a RQ factorization determined by sgerqf (unblocked algorithm).
sormr2 — subroutine sormr2 (side, trans, m, n, k, a, lda, tau, c, ldc, work, info) — SORMR2 multiplies a general matrix by the orthogonal matrix from a RQ factorization determined by sgerqf (unblocked algorithm).
zunmr2 — subroutine zunmr2 (side, trans, m, n, k, a, lda, tau, c, ldc, work, info) — ZUNMR2 multiplies a general matrix by the unitary matrix from a RQ factorization determined by cgerqf (unblocked algorithm).

ok so real talk: dormr2's one-liner points at sgerqf and zunmr2's points at cgerqf. that's literally what the page says. i'm not fixing it. i don't make the rules. 🙈

🦋 Detailed Description 🦋

(this page is mostly a container. the real content is down in Function Documentation. keep scrolling bestie. ⭐)

👑 Function Documentation 👑

💜 `cunmr2` — the complex one

subroutine cunmr2 (character side, character trans, integer m, integer n,
    integer k, complex, dimension( lda, * ) a, integer lda, complex,
    dimension( * ) tau, complex, dimension( ldc, * ) c, integer ldc,
    complex, dimension( * ) work, integer info)

CUNMR2 multiplies a general matrix by the unitary matrix from a RQ factorization determined by cgerqf (unblocked algorithm).

✨ Purpose

ok so listen. CUNMR2 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 H(2)**H . . . H(k)**H

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

🎀 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.
A — A is a COMPLEX array, dimension:

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 CGERQF in the last k rows of its array argument A. 🔥 heads up: 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 CGERQF.
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 a COMPLEX array, dimension:

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.

Definition at line 157 of file cunmr2.f.

💙 `dormr2` — the double precision one

subroutine dormr2 (character side, character trans, integer m, integer n,
    integer k, double precision, dimension( lda, * ) a, integer lda, double
    precision, dimension( * ) tau, double precision, dimension( ldc, * ) c,
    integer ldc, double precision, dimension( * ) work, integer info)

DORMR2 multiplies a general matrix by the orthogonal matrix from a RQ factorization determined by sgerqf (unblocked algorithm).

✨ Purpose

same energy, real numbers this time. DORMR2 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 = 'T', or

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

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

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 DGERQF. 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' (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.
A — A is a DOUBLE PRECISION array, dimension:

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 DGERQF in the last k rows of its array argument A. also: 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 DGERQF.
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 a DOUBLE PRECISION array, dimension:

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.

Definition at line 157 of file dormr2.f.

🌸 `sormr2` — the single precision one

subroutine sormr2 (character side, character trans, integer m, integer n,
    integer k, real, dimension( lda, * ) a, integer lda, real, dimension( *
    ) tau, real, dimension( ldc, * ) c, integer ldc, real, dimension( * )
    work, integer info)

SORMR2 multiplies a general matrix by the orthogonal matrix from a RQ factorization determined by sgerqf (unblocked algorithm).

✨ Purpose

bestie this is the REAL twin of DORMR2. SORMR2 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 = 'T', or

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

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

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 SGERQF. 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' (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.
A — A is a REAL array, dimension:

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 SGERQF in the last k rows of its array argument A. (and yeah — 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 — TAU is REAL array, dimension (K). TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by SGERQF.
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: Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd..

Definition at line 157 of file sormr2.f.

`zunmr2` — the `COMPLEX*16` unitary RQ era 💜

The signature, exactly:

   subroutine zunmr2 (character side, character trans, integer m, integer n,
       integer k, complex*16, dimension( lda, * ) a, integer lda, complex*16,
       dimension( * ) tau, complex*16, dimension( ldc, * ) c, integer ldc,
       complex*16, dimension( * ) work, integer info)

The official one-liner is: ZUNMR2 multiplies a general matrix by the unitary matrix from an RQ factorization determined by cgerqf (unblocked algorithm).

Purpose 🎯

ZUNMR2 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 H(2)**H . . . H(k)**H

as returned by ZGERQF. 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.
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 ZGERQF 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 ZGERQF.
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 🫶

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

Definition at line 157 of file zunmr2.f.

Author 🤖

Generated automatically by Doxygen for LAPACK from the source code.

Ok that's the whole page, bestie 💖 — footer tea: LAPACK, version 3.12.0, page unmr2(3). No date on the line, so I'm not making one up, periodt. Bye! 🦋

📦 where this page comes from

arch rolling: lapack-doc 3.12.1-2 · custom
💖 girlified by deepseek-ai/DeepSeek-V4.1-Flash-1017 on 2026-11-04: a language model's rewrite of the original, under its terms

unmr2(3)

🌸 unmr2(3) — from the Library Functions Manual 🌸

✨ NAME ✨

💖 SYNOPSIS 💖

🌈 Functions

🦋 Detailed Description 🦋

👑 Function Documentation 👑

💜 cunmr2 — the complex one

✨ Purpose

🎀 Parameters

🧚 Author

💙 dormr2 — the double precision one

✨ Purpose

🎀 Parameters

🧚 Author

🌸 sormr2 — the single precision one

✨ Purpose

🎀 Parameters

zunmr2 — the COMPLEX*16 unitary RQ era 💜

Purpose 🎯

Parameters ✨

Author 🫶

Author 🤖

🌸 `unmr2(3)` — from the Library Functions Manual 🌸

💜 `cunmr2` — the complex one

💙 `dormr2` — the double precision one

🌸 `sormr2` — the single precision one

`zunmr2` — the `COMPLEX*16` unitary RQ era 💜