2 * Copyright © 2011 Keith Packard <keithp@keithp.com>
4 * This program is free software; you can redistribute it and/or modify
5 * it under the terms of the GNU General Public License as published by
6 * the Free Software Foundation; version 2 of the License.
8 * This program is distributed in the hope that it will be useful, but
9 * WITHOUT ANY WARRANTY; without even the implied warranty of
10 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
11 * General Public License for more details.
13 * You should have received a copy of the GNU General Public License along
14 * with this program; if not, write to the Free Software Foundation, Inc.,
15 * 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA.
19 public typedef real[*] vec_t;
20 public typedef real[*,*] mat_t;
22 public mat_t transpose(mat_t m) {
24 return (real[d[1],d[0]]) { [i,j] = m[j,i] };
27 public void print_mat(string name, mat_t m) {
29 printf ("%s {\n", name);
30 for (int y = 0; y < d[0]; y++) {
31 for (int x = 0; x < d[1]; x++)
32 printf (" %14.8f", m[y,x]);
38 public void print_vec(string name, vec_t v) {
40 printf ("%s {", name);
41 for (int x = 0; x < d; x++)
42 printf (" %14.8f", v[x]);
46 public mat_t multiply(mat_t a, mat_t b) {
50 assert(da[1] == db[0], "invalid matrix dimensions");
52 real dot(int rx, int ry) {
54 for (int i = 0; i < da[1]; i++)
55 r += a[ry, i] * b[i, rx];
59 mat_t r = (real[da[0], db[1]]) { [ry,rx] = dot(rx,ry) };
63 public mat_t multiply_mat_val(mat_t m, real value) {
65 for (int j = 0; j < d[1]; j++)
66 for (int i = 0; i < d[0]; i++)
71 public mat_t add(mat_t a, mat_t b) {
75 assert(da[0] == db[0] && da[1] == db[1], "mismatching dim in plus");
76 return (real[da[0], da[1]]) { [y,x] = a[y,x] + b[y,x] };
79 public mat_t subtract(mat_t a, mat_t b) {
83 assert(da[0] == db[0] && da[1] == db[1], "mismatching dim in minus");
84 return (real[da[0], da[1]]) { [y,x] = a[y,x] - b[y,x] };
87 public mat_t inverse(mat_t m) {
90 real[1,1] inverse_1(real[1,1] m) {
91 return (real[1,1]) { { 1/m[0,0] } };
94 if (d[0] == 1 && d[1] == 1)
97 real[2,2] inverse_2(real[2,2] m) {
98 real a = m[0,0], b = m[0,1];
99 real c = m[1,0], d = m[1,1];
100 real det = a * d - b * c;
101 return multiply_mat_val((real[2,2]) {
102 { d, -b }, { -c, a } }, 1/det);
105 if (d[0] == 2 && d[1] == 2)
108 real[3,3] inverse_3(real[3,3] m) {
109 real a = m[0,0], b = m[0,1], c = m[0, 2];
110 real d = m[1,0], e = m[1,1], f = m[1, 2];
111 real g = m[2,0], h = m[2,1], k = m[2, 2];
112 real Z = a*(e*k-f*h) + b*(f*g - d*k) + c*(d*h-e*g);
113 real A = (e*k-f*h), B = (c*h-b*k), C=(b*f-c*e);
114 real D = (f*g-d*k), E = (a*k-c*g), F=(c*d-a*f);
115 real G = (d*h-e*g), H = (b*g-a*h), K=(a*e-b*d);
116 return multiply_mat_val((real[3,3]) {
117 { A, B, C }, { D, E, F }, { G, H, K }},
121 if (d[0] == 3 && d[1] == 3)
123 assert(false, "cannot invert %v\n", d);
127 public mat_t identity(int d) {
128 return (real[d,d]) { [i,j] = (i == j) ? 1 : 0 };
131 public vec_t vec_subtract(vec_t a, vec_t b) {
135 assert(da == db, "mismatching dim in minus");
136 return (real[da]) { [x] = a[x] - b[x] };
139 public vec_t vec_add(vec_t a, vec_t b) {
143 assert(da == db, "mismatching dim in plus");
144 return (real[da]) { [x] = a[x] + b[x] };
147 public vec_t multiply_vec_mat(vec_t v, mat_t m) {
148 mat_t r2 = matrix::multiply((real[dim(v),1]) { [y,x] = v[y] }, m);
149 return (real[dim(v)]) { [y] = r2[y,0] };
152 public vec_t multiply_mat_vec(mat_t m, vec_t v) {
153 mat_t r2 = matrix::multiply(m, (real[dim(v), 1]) { [y,x] = v[y] });
155 return (real[d[0]]) { [y] = r2[y,0] };