unmlq(3)

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version 3.12.1 · 9 versions
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🦋 unmlq(3) — {un,or}mlq: multiply by Q from gelqf 🦋

okay bestie, this is the unmlq(3) page from the Library Functions Manual, and it's giving "four LAPACK routines, one very specific mission" energy. No cap: this is part 1, and it's all about multiplying by Q from gelqf. Let's go ✨

🍓 NAME 🍓

unmlq — {un,or}mlq: multiply by Q from gelqf.

✨ SYNOPSIS ✨

🧚 Functions

subroutine cunmlq (side, trans, m, n, k, a, lda, tau, c, ldc, work,
    lwork, info)
    CUNMLQ
subroutine dormlq (side, trans, m, n, k, a, lda, tau, c, ldc, work,
    lwork, info)
    DORMLQ
subroutine sormlq (side, trans, m, n, k, a, lda, tau, c, ldc, work,
    lwork, info)
    SORMLQ
subroutine zunmlq (side, trans, m, n, k, a, lda, tau, c, ldc, work,
    lwork, info)
    ZUNMLQ

🦋 Detailed Description 🦋

This is where the page gets into the actual routines, bestie — the Function Documentation below is the main character energy ✨

🔥 Function Documentation 🔥

👑 subroutine cunmlq 👑

subroutine cunmlq (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 lwork, integer info)

CUNMLQ

🌸 Purpose

Bestie, CUNMLQ overwrites the general complex M-by-N matrix C with

                 SIDE = 'L'     SIDE = 'R'
 TRANS = 'N':      Q * C          C * Q
 TRANS = 'C':      Q**H * C       C * Q**H

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'.

🎀 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': No transpose, apply Q;
    • = 'C': Conjugate transpose, apply Q**H.
  • 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 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.
  • 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 CGELQF.
  • 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 (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
  • LWORK — LWORK is INTEGER. The dimension of the array WORK. If SIDE = 'L', LWORK >= max(1,N); if SIDE = 'R', LWORK >= max(1,M). For good performance, LWORK should generally be larger. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
  • 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 166 of file cunmlq.f.

👑 subroutine dormlq 👑

subroutine dormlq (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 lwork,
    integer info)

DORMLQ

🌸 Purpose

Bestie, DORMLQ overwrites the general real M-by-N matrix C with

                 SIDE = 'L'     SIDE = 'R'
 TRANS = 'N':      Q * C          C * Q
 TRANS = 'T':      Q**T * C       C * Q**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'.

🎀 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': No transpose, apply Q;
    • = 'T': Transpose, apply Q**T.
  • 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 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 — 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 DGELQF.
  • 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 (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
  • LWORK — LWORK is INTEGER. The dimension of the array WORK. If SIDE = 'L', LWORK >= max(1,N); if SIDE = 'R', LWORK >= max(1,M). For good performance, LWORK should generally be larger. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
  • 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 165 of file dormlq.f.

👑 subroutine sormlq 👑

subroutine sormlq (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 lwork, integer info)

SORMLQ

🌸 Purpose

Bestie, SORMLQ overwrites the general real M-by-N matrix C with

                 SIDE = 'L'     SIDE = 'R'
 TRANS = 'N':      Q * C          C * Q
 TRANS = 'T':      Q**T * C       C * Q**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'.

🎀 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': No transpose, apply Q;
    • = 'T': Transpose, apply Q**T.
  • 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 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.
  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,K).
  • TAU — bestie, part 2 picks up right here with the TAU tea ☕
  • TAU — REAL array, dimension (K). TAU(i) has to hold the scalar factor of the elementary reflector H(i), exactly like SGELQF handed it to you. No improvising, bestie 💅
  • C — REAL array, dimension (LDC,N). On entry? The M-by-N matrix C. On exit? It's been overwritten by Q*C or Q**T*C or C*Q**T or C*Q. She's a main character who reinvents herself, okay 🦋
  • LDC — INTEGER, the leading dimension of the array C. Constraint: LDC >= max(1,M). Respect the boundary, girl 🎀
  • WORK — REAL array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, then WORK(1) gives you back the optimal LWORK. A little thank-you note in slot one ✨
  • LWORK — INTEGER, the dimension of the array WORK.
    • If SIDE = 'L', then LWORK >= max(1,N)
    • If SIDE = 'R', then LWORK >= max(1,M)
    • For good performance, LWORK should generally be larger. Like, be generous, she thrives 🫶
If LWORK = -1, then a workspace query is assumed: the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. It's a vibe check, not a full commit 😌
  • INFO — 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 166 of file sormlq.f.

🧚 subroutine zunmlq (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 lwork, integer info)

subroutine zunmlq (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 lwork, integer info)

🌸 ZUNMLQ

💖 Purpose:

ZUNMLQ overwrites the general complex M-by-N matrix C with:

                SIDE = 'L'     SIDE = 'R'
TRANS = 'N':      Q * C          C * Q
TRANS = 'C':      Q**H * C       C * Q**H

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. Like, Q is of order M if SIDE = 'L', and of order N if SIDE = 'R'. Depends on the side, and honestly? Relatable 🌈

✨ Parameters

  • SIDE — CHARACTER*1
    • = 'L': apply Q or Q**H from the Left
    • = 'R': apply Q or Q**H from the Right

Pick a side, any side 💅

  • TRANS — CHARACTER*1
    • = 'N': No transpose, apply Q
    • = 'C': Conjugate transpose, apply Q**H
  • M — INTEGER, the number of rows of the matrix C. Constraint: M >= 0.
  • N — INTEGER, the number of columns of the matrix C. Constraint: N >= 0.
  • K — INTEGER, the number of elementary reflectors whose product defines the matrix Q.
    • If SIDE = 'L', then M >= K >= 0
    • If SIDE = 'R', then N >= K >= 0

Boundaries: respected 📏

  • A — 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. So like… don't rearrange her rows, she was already perfect 😭

  • LDA — INTEGER, the leading dimension of the array A. Constraint: LDA >= max(1,K).
  • TAU — COMPLEX*16 array, dimension (K). TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by ZGELQF. Same energy as above, just complex now 💜
  • C — 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 — INTEGER, the leading dimension of the array C. Constraint: LDC >= max(1,M).
  • WORK — COMPLEX*16 array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, then WORK(1) returns the optimal LWORK. Iconic little receipt 🧾
  • LWORK — INTEGER, the dimension of the array WORK.
    • If SIDE = 'L', then LWORK >= max(1,N)
    • If SIDE = 'R', then LWORK >= max(1,M)
    • For good performance, LWORK should generally be larger. Bigger workspace, better life ⭐
If LWORK = -1, then a workspace query is assumed: the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. Just peeking, not touching 🙈
  • INFO — 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 165 of file zunmlq.f.

🫶 Author

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Ok bestie, that's the whole page 💖 This one was auto-generated by Doxygen for LAPACK straight from the source code — LAPACK, Version 3.12.0, filed under unmlq(3). Go forth and apply your reflectors correctly, no cap 👑🌸
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