SRC/sormhr.f(3)

✨ NAME ✨

SRC/sormhr.f — okay bestie, this is the page for SRC/sormhr.f, from the Library Functions Manual. It's all about SORMHR, and we are keeping every single detail. No cap. 💅

✨ SYNOPSIS ✨

Functions/Subroutines

• subroutine sormhr (...) — SORMHR. Here's the signature, periodt:

subroutine sormhr (side, trans, m, n, ilo, ihi, a, lda, tau, c, ldc,
           work, lwork, info)

✨ Function/Subroutine Documentation ✨

subroutine sormhr (...)

subroutine sormhr (character side, character trans, integer m, integer n,
       integer ilo, integer ihi, real, dimension( lda, * ) a, integer lda,
       real, dimension( * ) tau, real, dimension( ldc, * ) c, integer ldc,
       real, dimension( * ) work, integer lwork, integer info)

SORMHR

✨ Purpose ✨

Okay so here's the whole vibe: SORMHR 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 IHI-ILO elementary reflectors, as returned by SGEHRD:

Q = H(ilo) H(ilo+1) . . . H(ihi-1).

✨ 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.
• ILO — ILO is INTEGER.
• IHI — IHI is INTEGER. ILO and IHI must have the same values as in the previous call of SGEHRD. Q is equal to the unit matrix except in the submatrix Q(ilo+1:ihi,ilo+1:ihi). If SIDE = 'L', then 1 <= ILO <= IHI <= M, if M > 0, and ILO = 1 and IHI = 0, if M = 0; if SIDE = 'R', then 1 <= ILO <= IHI <= N, if N > 0, and ILO = 1 and IHI = 0, if N = 0.
• A — A is REAL array, dimension (LDA,M) if SIDE = 'L', (LDA,N) if SIDE = 'R'. The vectors which define the elementary reflectors, as returned by SGEHRD.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'.
• TAU — TAU is REAL 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 SGEHRD.
• 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 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 — INFO is INTEGER. = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value.

Bestie note: LWORK = -1 is the special workspace-query vibe — it only calculates the optimal size of the WORK array and returns that value as the first entry of WORK, and XERBLA does not issue a LWORK-related error message for that case. That's in the original, fr fr.

✨ Author ✨

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

✨ Definition ✨

Definition at line 177 of file sormhr.f.

✨ Author ✨

Generated automatically by Doxygen for LAPACK from the source code.

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💖 okay that's the whole page, bestie. Footer vibe: LAPACK Version 3.12.0 and SRC/sormhr.f(3) — generated automatically by Doxygen for LAPACK from the source code. You ate that. 🫶