SRC/dormrq.f(3)

💖 SRC/dormrq.f(3) 💖

okay bestie, welcome to the SRC/dormrq.f(3) page from the Library Functions Manual. this one is literally all about DORMRQ, and it’s giving real orthogonal matrix energy — slay ✨

✨ NAME ✨

SRC/dormrq.f

🎀 SYNOPSIS 🎀

🧚 Functions/Subroutines 🧚

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

🌈 Function/Subroutine Documentation 🌈

🦋 subroutine dormrq 🦋

subroutine dormrq (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)

DORMRQ

✨ Purpose ✨

okay so DORMRQ 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 DGERQF. no cap, 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 QT from the Left; = 'R': apply Q or QT 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 DGERQF in the last k rows of its array argument A. iykyk.
• 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 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. obsessed with this iconic workspace-query behavior, honestly.
• 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 dormrq.f.

🌟 Author 🌟

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