SRC/dormqr.f(3)

okay bestie, welcome to SRC/dormqr.f — a page from the Library Functions Manual, and yes it’s giving very “linear algebra but make it fashion” 💅✨

💖 NAME 💖

SRC/dormqr.f — that’s the whole name, no cap. This is the DORMQR page, and it’s about applying that orthogonal matrix Q to a real matrix C 🫶

🦋 SYNOPSIS 🦋

✨ Functions/Subroutines ✨

subroutine dormqr (side, trans, m, n, k, a, lda, tau, c, ldc, work,
    lwork, info)
    DORMQR

🌈 Function/Subroutine Documentation 🌈

Here’s the full glow-up signature, bestie — every type and dimension exactly where it belongs:

subroutine dormqr (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)

This iconic little routine is called DORMQR 👑

🎯 Purpose 🎯

DORMQR 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(1) H(2) . . . H(k)

as returned by DGEQRF. 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,K)
  • The i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by DGEQRF in the first k columns of its array argument A.
• LDA — LDA is INTEGER
  • The leading dimension of the array A.
  • If SIDE = 'L', LDA >= max(1,M);
  • if SIDE = 'R', LDA >= max(1,N).
• TAU — TAU is DOUBLE PRECISION array, dimension (K)
  • TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by DGEQRF.
• 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 dormqr.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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byeee bestie 💖 — this page is from LAPACK Version 3.12.0, and the footer tag is SRC/dormqr.f(3). Go make those reflectors behave, mwah ✨👑