/home/abui...N/dlaror.f(3)

🎀 NAME 🎀

Okay so bestie, this is dlaror.f(3) from the Library Functions Manual — and it is literally the glow-up page for:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/MATGEN/dlaror.f

That's the whole name section, no cap. 💅

✨ SYNOPSIS ✨

Functions/Subroutines

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

📚 Function/Subroutine Documentation 📚

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 — the main character. 👑

🎯 Purpose 🎯

Okay so DLAROR pre- or post-multiplies an M by N matrix A by a random orthogonal matrix U, overwriting A. Before multiplying by U, A may optionally be initialized to the identity matrix. U is generated using the method of G.W. Stewart (SIAM J. Numer. Anal. 17, 1980, 403-409). Not me obsessing over the citation. 🦋

🧾 Parameters 🧾

• SIDE — bestie, SIDE is CHARACTER*1, and it specifies whether A is multiplied on the left or right by U. = '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 on 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. = 'I': initialize A to (a section of) the identity matrix before applying U. = 'N': no initialization; apply U to the input matrix A. Also, 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. It's the number of rows of A. 🍓
• N — N is INTEGER. It's the number of columns of A. 🌸
• A — A is a DOUBLE PRECISION array, dimension (LDA, N). On entry, the array A. On exit, overwritten by U A (if SIDE = 'L'), or by A U (if SIDE = 'R'), or by U A U' (if SIDE = 'C' or 'T'). It's giving full overwrite realness. ✨
• LDA — LDA is INTEGER, the leading dimension of the array A. Constraint: LDA >= max(1,M). Don't play with it. 💀
• ISEED — ISEED is an 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. 🎲

🫶 bestie PSA: ISEED(4) must be odd, and if elements aren't between 0 and 4095, they get reduced mod 4096. That's the rule, fr fr.

• X — X is a DOUBLE PRECISION array, dimension (3*MAX( M, N )). It's 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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Okay bestie, cute sign-off time: this footer is giving LAPACK Version 3.12.0 energy, with the page stamp /home/abui...N/dlaror.f(3) — that's the source/version and date/path situation, iykyk. Bye! 💖🎀