Mercurial > octave
view scripts/sparse/private/__sprand__.m @ 30893:e1788b1a315f
maint: Use "fcn" as preferred abbreviation for "function" in m-files.
* accumarray.m, accumdim.m, quadl.m, quadv.m, randi.m, structfun.m,
__is_function__.m, uigetfile.m, uimenu.m, uiputfile.m, doc_cache_create.m,
colorspace_conversion_input_check.m, imageIO.m, argnames.m, vectorize.m,
vectorize.m, normest1.m, inputname.m, nthargout.m, display_info_file.m,
decic.m, ode15i.m, ode15s.m, ode23.m, ode23s.m, ode45.m, odeset.m,
check_default_input.m, integrate_adaptive.m, ode_event_handler.m,
runge_kutta_23.m, runge_kutta_23s.m, runge_kutta_45_dorpri.m,
runge_kutta_interpolate.m, starting_stepsize.m, __all_opts__.m, fminbnd.m,
fminsearch.m, fminunc.m, fsolve.m, fzero.m, sqp.m, fplot.m, plotyy.m,
__bar__.m, __ezplot__.m, flat_entry.html, profexport.m, movfun.m, bicg.m,
bicgstab.m, cgs.m, eigs.m, gmres.m, pcg.m, __alltohandles__.m, __sprand__.m,
qmr.m, tfqmr.m, dump_demos.m:
Replace "func", "fun", "fn" in documentation and variable names with "fcn".
author | Rik <rik@octave.org> |
---|---|
date | Mon, 04 Apr 2022 18:14:56 -0700 |
parents | 5d3faba0342e |
children | 597f3ee61a48 |
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######################################################################## ## ## Copyright (C) 2004-2022 The Octave Project Developers ## ## See the file COPYRIGHT.md in the top-level directory of this ## distribution or <https://octave.org/copyright/>. ## ## This file is part of Octave. ## ## Octave is free software: you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## <https://www.gnu.org/licenses/>. ## ######################################################################## ## ## Original version by Paul Kienzle distributed as free software in the ## public domain. ## -*- texinfo -*- ## @deftypefn {} {@var{S} =} __sprand__ (@var{s}, @var{randfcn}) ## @deftypefnx {} {@var{S} =} __sprand__ (@var{m}, @var{n}, @var{d}, @var{fcnname}, @var{randfcn}) ## @deftypefnx {} {@var{S} =} __sprand__ (@var{m}, @var{n}, @var{d}, @var{rc}, @var{fcnname}, @var{randfcn}) ## Undocumented internal function. ## @end deftypefn ## Actual implementation of sprand and sprandn happens here. function S = __sprand__ (varargin) if (nargin == 2) [m, randfcn] = deal (varargin{1:2}); [i, j] = find (m); [nr, nc] = size (m); S = sparse (i, j, randfcn (size (i)), nr, nc); else if (nargin == 5) [m, n, d, fcnname, randfcn] = deal (varargin{:}); else [m, n, d, rc, fcnname, randfcn] = deal (varargin{:}); endif if (! (isscalar (m) && m == fix (m) && m >= 0)) error ("%s: M must be a non-negative integer", fcnname); endif if (! (isscalar (n) && n == fix (n) && n >= 0)) error ("%s: N must be a non-negative integer", fcnname); endif if (d < 0 || d > 1) error ("%s: density D must be between 0 and 1", fcnname); endif if (m == 0 || n == 0) S = sparse (m, n); return; endif if (nargin == 5) mn = m*n; k = round (d*mn); if (mn > sizemax ()) ## randperm will overflow, so use alternative methods idx = unique (fix (rand (1.01*k, 1) * mn)) + 1; ## idx contains random numbers in [1,mn] ## Generate 1% more random values than necessary in order to reduce the ## probability that there are less than k distinct values; maybe a ## better strategy could be used but I don't think it's worth the price. ## actual number of entries in S k = min (length (idx), k); j = floor ((idx(1:k) - 1) / m); i = idx(1:k) - j * m; j += 1; else idx = randperm (mn, k); [i, j] = ind2sub ([m, n], idx); endif S = sparse (i, j, randfcn (k, 1), m, n); elseif (nargin == 6) ## Create a matrix with specified reciprocal condition number. if (! isscalar (rc) && ! isvector (rc)) error ("%s: RC must be a scalar or vector", fcnname); endif ## We want to reverse singular valued decomposition A=U*S*V'. ## First, first S is constructed and then U = U1*U2*..Un and ## V' = V1*V2*..Vn are seen as Jacobi rotation matrices with angles and ## planes of rotation randomized. Repeatedly apply rotations until the ## required density for A is achieved. if (isscalar (rc)) if (rc < 0 || rc > 1) error ("%s: reciprocal condition number RC must be between 0 and 1", fcnname); endif ## Reciprocal condition number is ratio of smallest SV to largest SV ## Generate singular values randomly and sort them to build S ## Random singular values in range [rc, 1]. v = rand (1, min (m,n)) * (1 - rc) + rc; v(1) = 1; v(end) = rc; v = sort (v, "descend"); S = sparse (diag (v, m, n)); else ## Only the min (m, n) greater singular values from rc vector are used. if (length (rc) > min (m,n)) rc = rc(1:min (m, n)); endif S = sparse (diag (sort (rc, "descend"), m, n)); endif Uinit = speye (m); Vinit = speye (n); k = round (d*m*n); while (nnz (S) < k) if (m > 1) ## Construct U randomized rotation matrix rot_angleu = 2 * pi * rand (); cu = cos (rot_angleu); su = sin (rot_angleu); rndtmp = randperm (m, 2); i = rndtmp(1); j = rndtmp(2); U = Uinit; U(i, i) = cu; U(i, j) = -su; U(j, i) = su; U(j, j) = cu; S = U * S; endif if (n > 1) ## Construct V' randomized rotation matrix rot_anglev = 2 * pi * rand (); cv = cos (rot_anglev); sv = sin (rot_anglev); rndtmp = randperm (n, 2); i = rndtmp(1); j = rndtmp(2); V = Vinit; V(i, i) = cv; V(i, j) = sv; V(j, i) = -sv; V(j, j) = cv; S *= V; endif endwhile endif endif endfunction