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########################################################################
##
## Copyright (C) 2004-2024 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
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