TESTING/MATGEN/slaror.f(3)

TESTING/MATGEN/slaror.f(3) 💅

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NAME 🎀

TESTING/MATGEN/slaror.f

SYNOPSIS 🦋

Functions/Subroutines ✨

• subroutine slaror (side, init, m, n, a, lda, iseed, x, info) — SLAROR

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

Function/Subroutine Documentation 💖

subroutine slaror (character side, character init, integer m, integer n,
   real, dimension( lda, * ) a, integer lda, integer, dimension( 4 ) iseed,
   real, dimension( * ) x, integer info)

SLAROR 👑

This is the main-character subroutine page, bestie — all the deets are below. 🫶

Purpose 🌸

SLAROR 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).

Parameters 🎀

• SIDE — SIDE is CHARACTER*1
  • 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 the right by U' (Here, U' means U-transpose.)
• INIT — INIT is CHARACTER*1
  • 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.
  • 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 REAL 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').
• 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 SLAROR to continue the same random number sequence.
• X — X is REAL 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 SLARND are bad.

Author 🌟

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

Definition at line 145 of file slaror.f. 📍

Author 🫶

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