TESTING/MATGEN/dlaror.f(3)

✨ NAME ✨

okay so bestie, this page is for TESTING/MATGEN/dlaror.f — and yes, that’s the same TESTING/MATGEN/dlaror.f(3) from the Library Functions Manual. It’s giving LAPACK testing/matgen energy, and we’re about to make it make sense. 💅

✨ SYNOPSIS ✨

Functions/Subroutines 🎀

• subroutine dlaror (side, init, m, n, a, lda, iseed, x, info) — DLAROR

✨ Function/Subroutine Documentation ✨

Here’s the full signature, literally exactly as it appears:

subroutine dlaror (character side, character init, integer m, integer n,
    double precision, dimension( lda, * ) a, integer lda, integer,
    dimension( 4 ) iseed, double precision, dimension( * ) x, integer info)

DLAROR 👑

Purpose 🎯

DLAROR pre- or post-multiplies an M by N matrix A by a random orthogonal matrix U, overwriting A. A may optionally be initialized to the identity matrix before multiplying by U. U is generated using the method of G.W. Stewart (SIAM J. Numer. Anal. 17, 1980, 403-409).

no cap, that’s the whole vibe of this subroutine. 🦋

Parameters 🧚

SIDE

SIDE is CHARACTER*1. It specifies whether A is multiplied on the left or right by U. The values are:

• = 'L': Multiply A on the left (premultiply) by U
• = 'R': Multiply A on the right (postmultiply) by U'
• = 'C' or 'T': Multiply A on the left by U and the right by U' (Here, U' means U-transpose.)

INIT

INIT is CHARACTER*1. It specifies whether or not A should be initialized to the identity matrix. The values are:

• = 'I': Initialize A to (a section of) the identity matrix before applying U.
• = 'N': No initialization. Apply U to the input matrix A.

INIT = 'I' may be used to generate square or rectangular orthogonal matrices:

• For M = N and SIDE = 'L' or 'R', the rows will be orthogonal to each other, as will the columns.
• If M < N, SIDE = 'R' produces a dense matrix whose rows are orthogonal and whose columns are not, while SIDE = 'L' produces a matrix whose rows are orthogonal, and whose first M columns are orthogonal, and whose remaining columns are zero.
• If M > N, SIDE = 'L' produces a dense matrix whose columns are orthogonal and whose rows are not, while SIDE = 'R' produces a matrix whose columns are orthogonal, and whose first M rows are orthogonal, and whose remaining rows are zero.

M

M is INTEGER. The number of rows of A.

N

N is INTEGER. The number of columns of A.

A

A is DOUBLE PRECISION array, dimension (LDA, N).

On entry, the array A. On exit, overwritten by:

• U A if SIDE = 'L',
• A U if SIDE = 'R',
• U A U' if SIDE = 'C' or 'T'.

LDA

LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M).

ISEED

ISEED is INTEGER array, dimension (4).

On entry ISEED specifies the seed of the random number generator. The array elements should be between 0 and 4095; if not they will be reduced mod 4096. Also, ISEED(4) must be odd. The random number generator uses a linear congruential sequence limited to small integers, and so should produce machine independent random numbers. The values of ISEED are changed on exit, and can be used in the next call to DLAROR to continue the same random number sequence.

🫶 tiny vibe check: ISEED(4) must be odd, bestie. That part is not optional.

X

X is DOUBLE PRECISION array, dimension (3*MAX( M, N )).

Workspace of length:

• 2*M + N if SIDE = 'L',
• 2*N + M if SIDE = 'R',
• 3*N if SIDE = 'C' or 'T'.

INFO

INFO is INTEGER. An error flag. It is set to:

• = 0: normal return
• < 0: if INFO = -k, the k-th argument had an illegal value
• = 1: if the random numbers generated by DLARND are bad.

Author 👑

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 145 of file dlaror.f.

Author 🤖

Generated automatically by Doxygen for LAPACK from the source code.

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