SORMHR(3)

hey bestie 💖 welcome to /home/abui...RC/sormhr.f(3) — yep, that’s the page, and it lives in the Library Functions Manual. It’s giving “linear algebra bestie goes to the group chat,” and we are so here for it. ✨

💅 NAME 💅

okay so the name section is literally this file path, no cap:

/home/abuild/rpmbuild/BUILD/lapack-
static-3.12.0-build/lapack-3.12.0/SRC/sormhr.f

✨ SYNOPSIS ✨

🧮 Functions/Subroutines 🧮

Under Functions/Subroutines, we’ve got this iconic little declaration:

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

💖 Function/Subroutine Documentation 💖

Here’s the full signature, bestie — every type, every dimension, every argument, exactly as it appears:

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 SORMHR overwrites the general real M-by-N matrix C with this whole situation:

                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).

periodt. 💅

🌸 Parameters 🌸

🦋 SIDE 🦋

SIDE is CHARACTER*1 — here’s the tea:

• = '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. It’s the number of rows of the matrix C. Constraint check: M >= 0. ✨

🦋 N 🦋

N is INTEGER. It’s the number of columns of the matrix C. Constraint check: N >= 0. ✨

🦋 ILO 🦋

ILO is INTEGER.

🦋 IHI 🦋

IHI is INTEGER.

and okay, important bestie note: 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'

These are the vectors which define the elementary reflectors, as returned by SGEHRD. 🫶

🦋 LDA 🦋

LDA is INTEGER. It’s 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. no cap. 💜

🦋 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. It’s the leading dimension of the array C. Constraint: 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. It’s 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. okay that’s actually kinda iconic. ✨

🦋 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 177 of file sormhr.f.

👑 Author 👑 (the auto-gen one)

Generated automatically by Doxygen for LAPACK from the source code.

okay that’s a wrap, bestie 🫶 — footer check: LAPACK Version 3.12.0 and /home/abui...RC/sormhr.f(3). bye 💅✨🌸