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/*
* Copyright © 2011 Keith Packard <keithp@keithp.com>
*
* This program 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 2 of the License, or
* (at your option) any later version.
*
* This program 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 this program; if not, write to the Free Software Foundation, Inc.,
* 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA.
*/
namespace matrix {
public typedef real[*] vec_t;
public typedef real[*,*] mat_t;
public mat_t transpose(mat_t m) {
int[2] d = dims(m);
return (real[d[1],d[0]]) { [i,j] = m[j,i] };
}
public void print_mat(string name, mat_t m) {
int[2] d = dims(m);
printf ("%s {\n", name);
for (int y = 0; y < d[0]; y++) {
for (int x = 0; x < d[1]; x++)
printf (" %14.8f", m[y,x]);
printf ("\n");
}
printf ("}\n");
}
public void print_vec(string name, vec_t v) {
int d = dim(v);
printf ("%s {", name);
for (int x = 0; x < d; x++)
printf (" %14.8f", v[x]);
printf (" }\n");
}
public mat_t multiply(mat_t a, mat_t b) {
int[2] da = dims(a);
int[2] db = dims(b);
assert(da[1] == db[0], "invalid matrix dimensions");
real dot(int rx, int ry) {
real r = 0.0;
for (int i = 0; i < da[1]; i++)
r += a[ry, i] * b[i, rx];
return imprecise(r);
}
mat_t r = (real[da[0], db[1]]) { [ry,rx] = dot(rx,ry) };
return r;
}
public mat_t multiply_mat_val(mat_t m, real value) {
int[2] d = dims(m);
for (int j = 0; j < d[1]; j++)
for (int i = 0; i < d[0]; i++)
m[i,j] *= value;
return m;
}
public mat_t add(mat_t a, mat_t b) {
int[2] da = dims(a);
int[2] db = dims(b);
assert(da[0] == db[0] && da[1] == db[1], "mismatching dim in plus");
return (real[da[0], da[1]]) { [y,x] = a[y,x] + b[y,x] };
}
public mat_t subtract(mat_t a, mat_t b) {
int[2] da = dims(a);
int[2] db = dims(b);
assert(da[0] == db[0] && da[1] == db[1], "mismatching dim in minus");
return (real[da[0], da[1]]) { [y,x] = a[y,x] - b[y,x] };
}
public mat_t inverse(mat_t m) {
int[2] d = dims(m);
real[1,1] inverse_1(real[1,1] m) {
return (real[1,1]) { { 1/m[0,0] } };
}
if (d[0] == 1 && d[1] == 1)
return inverse_1(m);
real[2,2] inverse_2(real[2,2] m) {
real a = m[0,0], b = m[0,1];
real c = m[1,0], d = m[1,1];
real det = a * d - b * c;
return multiply_mat_val((real[2,2]) {
{ d, -b }, { -c, a } }, 1/det);
}
if (d[0] == 2 && d[1] == 2)
return inverse_2(m);
real[3,3] inverse_3(real[3,3] m) {
real a = m[0,0], b = m[0,1], c = m[0, 2];
real d = m[1,0], e = m[1,1], f = m[1, 2];
real g = m[2,0], h = m[2,1], k = m[2, 2];
real Z = a*(e*k-f*h) + b*(f*g - d*k) + c*(d*h-e*g);
real A = (e*k-f*h), B = (c*h-b*k), C=(b*f-c*e);
real D = (f*g-d*k), E = (a*k-c*g), F=(c*d-a*f);
real G = (d*h-e*g), H = (b*g-a*h), K=(a*e-b*d);
return multiply_mat_val((real[3,3]) {
{ A, B, C }, { D, E, F }, { G, H, K }},
1/Z);
}
if (d[0] == 3 && d[1] == 3)
return inverse_3(m);
assert(false, "cannot invert %v\n", d);
return m;
}
public mat_t identity(int d) {
return (real[d,d]) { [i,j] = (i == j) ? 1 : 0 };
}
public vec_t vec_subtract(vec_t a, vec_t b) {
int da = dim(a);
int db = dim(b);
assert(da == db, "mismatching dim in minus");
return (real[da]) { [x] = a[x] - b[x] };
}
public vec_t vec_add(vec_t a, vec_t b) {
int da = dim(a);
int db = dim(b);
assert(da == db, "mismatching dim in plus");
return (real[da]) { [x] = a[x] + b[x] };
}
public vec_t multiply_vec_mat(vec_t v, mat_t m) {
mat_t r2 = matrix::multiply((real[dim(v),1]) { [y,x] = v[y] }, m);
return (real[dim(v)]) { [y] = r2[y,0] };
}
public vec_t multiply_mat_vec(mat_t m, vec_t v) {
mat_t r2 = matrix::multiply(m, (real[dim(v), 1]) { [y,x] = v[y] });
int[2] d = dims(m);
return (real[d[0]]) { [y] = r2[y,0] };
}
}
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