SRC/sormlq.f(3)

🌸 NAME 🌸

okay so this is the page for SRC/sormlq.f from the Library Functions Manual, bestie. It's literally all about SORMLQ, the real orthogonal-matrix-applying subroutine, and we're gonna get into every single detail. 💅✨

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

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

💖 Function/Subroutine Documentation 💖

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 🦋

okay so SORMLQ overwrites the general real M-by-N matrix C with the following, and yes this is the moment:

                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'. periodt. 💜

🌈 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 — 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 (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 sormlq.f. 🎯

🎀 Author 🎀

Generated automatically by Doxygen for LAPACK from the source code. 🫶

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okay bestie, that's the whole thing — this cutie is from LAPACK, Version 3.12.0, and the page source is SRC/sormlq.f(3). mwah! 💖✨🎀