SRC/dormtr.f(3)

🎀 SRC/dormtr.f — Library Functions Manual 🎀

🌸 NAME 🌸

SRC/dormtr.f — bestie, this is the page for the DORMTR subroutine. It's giving “apply a real orthogonal matrix without forming it” energy, and it lives at SRC/dormtr.f. 💅

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

subroutine dormtr (side, uplo, trans, m, n, a, lda, tau, c, ldc, work,
    lwork, info)

DORMTR

💅 Function/Subroutine Documentation 💅

subroutine dormtr (character side, character uplo, character trans, integer
    m, integer n, 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)

DORMTR

🎀 Purpose: 🎀

Okay so DORMTR 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 of order nq, with nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of nq-1 elementary reflectors, as returned by DSYTRD:

if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);

if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).

🍓 Parameters 🍓

• SIDE — CHARACTER*1. = 'L': apply Q or Q**T from the Left; = 'R': apply Q or Q**T from the Right.
• UPLO — CHARACTER*1. = 'U': Upper triangle of A contains elementary reflectors from DSYTRD; = 'L': Lower triangle of A contains elementary reflectors from DSYTRD.
• TRANS — CHARACTER*1. = 'N': No transpose, apply Q; = 'T': Transpose, apply Q**T.
• M — INTEGER. The number of rows of the matrix C. M >= 0.
• N — INTEGER. The number of columns of the matrix C. N >= 0.
• A — DOUBLE PRECISION array, dimension (LDA,M) if SIDE = 'L', (LDA,N) if SIDE = 'R'. The vectors which define the elementary reflectors, as returned by DSYTRD.
• LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'.
• TAU — DOUBLE PRECISION array, dimension (M-1) if SIDE = 'L', (N-1) if SIDE = 'R'. TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by DSYTRD.
• C — 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 — INTEGER. The leading dimension of the array C. LDC >= max(1,M).
• WORK — DOUBLE PRECISION array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
• LWORK — INTEGER. The dimension of the array WORK. If SIDE = 'L', LWORK >= max(1,N); if SIDE = 'R', LWORK >= max(1,M). For optimum performance LWORK >= N*NB if SIDE = 'L', and LWORK >= M*NB if SIDE = 'R', where NB is the optimal blocksize.

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 — 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 169 of file dormtr.f.

💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code.

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✨ And that's the whole vibe, bestie! This iconic page is from LAPACK Version 3.12.0 and its source path is SRC/dormtr.f(3) — now go apply those orthogonal matrices responsibly! 💖👑