unml2(3)

📦

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okay bestie, welcome to unml2(3) — straight from the Library Functions Manual and honestly it's giving "the LQ glow-up nobody told you about" 💅 this is the level-2 (unblocked) step in unmlq, and it's literally four subroutines doing the same gorgeous thing in four different flavours. buckle up 🎀

✨ NAME ✨

unml2 — {un,or}ml2: multiply by Q, level 2, step in unmlq 🦋

🌸 SYNOPSIS 🌸

🫶 Functions

subroutine cunml2 (side, trans, m, n, k, a, lda, tau, c, ldc, work, info) — CUNML2 multiplies a general matrix by the unitary matrix from a LQ factorization determined by cgelqf (unblocked algorithm). 💜
subroutine dorml2 (side, trans, m, n, k, a, lda, tau, c, ldc, work, info) — DORML2 multiplies a general matrix by the orthogonal matrix from a LQ factorization determined by sgelqf (unblocked algorithm). no cap, it really does say sgelqf in there 😭
subroutine sorml2 (side, trans, m, n, k, a, lda, tau, c, ldc, work, info) — SORML2 multiplies a general matrix by the orthogonal matrix from a LQ factorization determined by sgelqf (unblocked algorithm). 👑
subroutine zunml2 (side, trans, m, n, k, a, lda, tau, c, ldc, work, info) — ZUNML2 multiplies a general matrix by the unitary matrix from a LQ factorization determined by cgelqf (unblocked algorithm). ✨

🔥 Detailed Description 🔥

Function Documentation — yes, that's the whole section title, we're getting into the good part now.

🧚 Function Documentation 🧚

💖 subroutine cunml2

subroutine cunml2 (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)

CUNML2 multiplies a general matrix by the unitary matrix from a LQ factorization determined by cgelqf (unblocked algorithm). 🦋

⭐ Purpose

okay so CUNML2 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(k)**H . . . H(2)**H H(1)**H

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

🎀 Parameters

SIDE — is CHARACTER*1
- = 'L': apply Q or Q**H from the Left
- = 'R': apply Q or Q**H from the Right
TRANS — is CHARACTER*1
- = 'N': apply Q (No transpose)
- = 'C': apply Q**H (Conjugate transpose)
M — is INTEGER
- The number of rows of the matrix C. M >= 0.
N — is INTEGER
- The number of columns of the matrix C. N >= 0.
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 — 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 CGELQF in the first k rows of its array argument A.
- A is modified by the routine but restored on exit. 🫶 (we give it back, promise)
LDA — is INTEGER
- The leading dimension of the array A. LDA >= max(1,K).
TAU — is COMPLEX array, dimension (K)
- TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by CGELQF.
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 — is INTEGER
- The leading dimension of the array C. LDC >= max(1,M).
WORK — is COMPLEX array, dimension
- (N) if SIDE = 'L',
- (M) if SIDE = 'R'
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 cunml2.f.

💜 subroutine dorml2

subroutine dorml2 (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)

DORML2 multiplies a general matrix by the orthogonal matrix from a LQ factorization determined by sgelqf (unblocked algorithm). 🌸

⭐ Purpose

DORML2 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(k) . . . H(2) H(1)

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

🎀 Parameters

SIDE — is CHARACTER*1
- = 'L': apply Q or Q**T from the Left
- = 'R': apply Q or Q**T from the Right
TRANS — is CHARACTER*1
- = 'N': apply Q (No transpose)
- = 'T': apply Q**T (Transpose)
M — is INTEGER
- The number of rows of the matrix C. M >= 0.
N — is INTEGER
- The number of columns of the matrix C. N >= 0.
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 — 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 DGELQF in the first k rows of its array argument A.
LDA — is INTEGER
- The leading dimension of the array A. LDA >= max(1,K).
TAU — is DOUBLE PRECISION array, dimension (K)
- TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by DGELQF.
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 — is INTEGER
- The leading dimension of the array C. LDC >= max(1,M).
WORK — is DOUBLE PRECISION array, dimension
- (N) if SIDE = 'L',
- (M) if SIDE = 'R'
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 156 of file dorml2.f.

🦋 subroutine sorml2

subroutine sorml2 (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)

SORML2 multiplies a general matrix by the orthogonal matrix from a LQ factorization determined by sgelqf (unblocked algorithm). ✨

⭐ Purpose

SORML2 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(k) . . . H(2) H(1)

as returned by SGELQF. Q is of order m if SIDE = 'L' and of order n if SIDE = 'R'. highkey obsessed. 💖

🎀 Parameters

SIDE — is CHARACTER*1
- = 'L': apply Q or Q**T from the Left
- = 'R': apply Q or Q**T from the Right
TRANS — is CHARACTER*1
- = 'N': apply Q (No transpose)
- = 'T': apply Q**T (Transpose)
M — is INTEGER
- The number of rows of the matrix C. M >= 0.
N — is INTEGER
- The number of columns of the matrix C. N >= 0.
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 — 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 SGELQF in the first k rows of its array argument A.
- A is modified by the routine but restored on exit. 🫶
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 SGELQF. 💖
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 sorml2.f.

🌈 subroutine zunml2 🌈

   subroutine zunml2 (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)

ZUNML2 multiplies a general matrix by the unitary matrix from the LQ factorization determined by cgelqf (unblocked algorithm). 🦋

✨ Purpose ✨

ZUNML2 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(k)**H . . . H(2)**H H(1)**H

as returned by ZGELQF. 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 ZGELQF in the first 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 ZGELQF. 💜
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 zunml2.f.

🫶 Author 🫶

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