VK3FNG/soundmodem
1
0
Fork 0
mirror of https://github.com/VK3FNG/soundmodem.git synced 2025-12-06 03:01:59 +01:00
Code Issues Actions Packages Projects Releases Wiki Activity
soundmodem/matlib/mat.hh
Matt Grice f4c4438e0e First commit
2018-06-17 22:19:22 +10:00

503 lines
12 KiB
C++
Raw Blame History

/*
* Matrix operations library
*
* Copyright (C) 1999-2000, 2003
* Thomas Sailer, <t.sailer@alumni.ethz.ch>
*
* 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
*/
#ifndef _MAT_HH
#define _MAT_HH
#ifdef HAVE_CONFIG_H
#include <config.h>
#endif
/* AIX requires this to be the first thing in the file. */
#ifndef __GNUC__
# if HAVE_ALLOCA_H
# include <alloca.h>
# else
# ifdef _AIX
#pragma alloca
# else
# ifndef alloca /* predefined by HP cc +Olibcalls */
char *alloca ();
# endif
# endif
# endif
#endif
#include <exception>
#include <string>
#include <sstream>
class matrix_exception : public exception
{
public:
matrix_exception(const string& e) throw() : err(e) {}
virtual ~matrix_exception() throw() {}
virtual const char* what() const throw() { return err.c_str(); }
private:
const string err;
};
/*
* Simple matrix operations
*/
template<typename T> void madd(T *c, const T *a, const T *b, unsigned int d1, unsigned int d2)
{
unsigned int i, j = d1 * d2;
for (i = 0; i < j; i++)
c[i] = a[i] + b[i];
}
template<typename T> void msub(T *c, const T *a, const T *b, unsigned int d1, unsigned int d2)
{
unsigned int i, j = d1 * d2;
for (i = 0; i < j; i++)
c[i] = a[i] - b[i];
}
/* c el R^{d1 x d3}, a el R^{d1 x d2}, b el R^{d2 x d3} */
template<typename T> void mmul(T *c, const T *a, const T *b, unsigned int d1, unsigned int d2, unsigned int d3)
{
T *r = c, s;
unsigned int i, j, k;
if (c == a || c == b)
r = (T *)alloca(d1 * d3 * sizeof(r[0]));
for (i = 0; i < d1; i++)
for (k = 0; k < d3; k++) {
for (s = 0, j = 0; j < d2; j++)
s += a[i*d2+j] * b[j*d3+k];
r[i*d3+k] = s;
}
if (r != c)
memcpy(c, r, d1 * d3 * sizeof(c[0]));
}
template<typename T> void mdet(const T *c, unsigned int d)
{
T *c2;
unsigned int i, j, k, l;
T det = 0, dr;
if (!d)
return 0;
if (d == 1)
return c[0];
if (d == 2)
return c[0] * c[3] - c[1] * c[2];
c2 = alloca(sizeof(T)*(d-1)*(d-1));
for (i = 0; i < d; i++) {
for (j = k = 0; j < d; j++) {
if (j == i)
continue;
for (l = 0; l < d-1; l++)
c2[l*(d-1)+k] = c[(l+1)*d+j];
k++;
}
dr = mdet(c2, d-1);
if (i & 1)
det -= dr * c[i];
else
det += dr * c[i];
}
return det;
}
/* Transpose a matrix (a el C^{d1 x d2}, b el C^{d2 x d1}) */
template<typename T> void mtranspose(T *b, const T *a, unsigned int d1, unsigned int d2)
{
const T *c = a;
unsigned int ci, bi, i, j;
if (b == a) {
void *cc = alloca(d1 * d2 * sizeof(c[0]));
memcpy(cc, a, d1 * d2 * sizeof(c[0]));
c = (const T *)cc;
}
for (i = 0; i < d1; i++)
for (j = 0; j < d2; j++) {
ci = i*d2+j;
bi = j*d1+i;
b[bi] = c[ci];
}
}
/* Transpose a matrix (a el C^{d1 x d2}, b el C^{d2 x d1}) */
template<typename T> void mhermtranspose(complex<T> *b, const complex<T> *a, unsigned int d1, unsigned int d2)
{
const complex<T> *c = a;
unsigned int ci, bi, i, j;
if (b == a) {
void *cc = alloca(d1 * d2 * sizeof(c[0]));
memcpy(cc, a, d1 * d2 * sizeof(c[0]));
c = (const complex<T> *)cc;
}
for (i = 0; i < d1; i++)
for (j = 0; j < d2; j++) {
ci = i*d2+j;
bi = j*d1+i;
b[bi] = conj(c[ci]);
}
}
template<typename T> void mconj(complex<T> *c, const complex<T> *a, unsigned int d1, unsigned int d2)
{
unsigned int i, j = d1 * d2;
for (i = 0; i < j; i++)
c[i] = conj(a[i]);
}
/*
* complex cholesky factorization
*/
/*
* A el C^{d x d}
* This routine calculates G*G^H = A, where G is lower triangular, and then uses this to solve
* A*c=b for c
* G*G^H*c=b
* G*t=b
* G^H*c=t
*/
template<typename T> inline T complex_pwr(complex<T> c)
{
return real(c) * real(c) + imag(c) * imag(c);
}
template<typename T> void mcholfactor(const complex<T> *a, complex<T> *g, unsigned int d)
{
unsigned int i, j, k;
complex<T> sc;
T s;
memset(g, 0, d*d*sizeof(g[0]));
for (i = 0; i < d; i++) {
s = real(a[i*d+i]);
for (j = 0; j < i; j++)
s -= complex_pwr(g[i*d+j]);
if (s <= 0 || imag(a[i*d+i]) != 0) {
ostringstream os;
os << "mcholfactor: matrix not positive definite a[" << i << "][" << i << "]=" << a[i*d+i] << " s=" << s << "\n";
throw matrix_exception(os.str());
}
s = T(1) / sqrt(s);
g[i*d+i] = s;
for (j = i+1; j < d; j++) {
sc = a[j*d+i];
for (k = 0; k < i; k++)
sc -= g[j*d+k] * conj(g[i*d+k]);
g[j*d+i] = sc * s;
}
}
}
template<typename T> void mcholapply(const complex<T> *g, const complex<T> *b, complex<T> *c, unsigned int d)
{
complex<T> *t, s, s2;
unsigned int i, j;
t = alloca(d*sizeof(t[0]));
for (i = 0; i < d; i++) {
s = b[i];
for (j = 0; j < i; j++)
s -= g[i*d+j] * t[j];
/* g's diagonal is real, therefore we have a division by a real */
t[i] = s * real(g[i*d+i]);
}
for (i = d; i > 0; i--) {
s = t[i-1];
for (j = i; j < d; j++)
s -= conj(g[j*d+(i-1)]) * c[j];
/* g's diagonal is real, therefore we have a division by a real */
c[i-1] = s * real(g[(i-1)*d+(i-1)]);
}
}
/*
* real cholesky factorization
*/
/*
* A el R^{d x d}
* This routine calculates G*G^T = A, where G is lower triangular, and then uses this to solve
* A*c=b for c
* G*G^T*c=b
* G*t=b
* G^T*c=t
*/
template<typename T> void mcholfactor(const T *a, T *g, unsigned int d)
{
unsigned int i, j, k;
T s, s1;
memset(g, 0, d*d*sizeof(g[0]));
for (i = 0; i < d; i++) {
s = a[i*d+i];
for (j = 0; j < i; j++)
s -= g[i*d+j] * g[i*d+j];
if (s <= 0) {
ostringstream os;
os << "mcholfactor: matrix not positive definite a[" << i << "][" << i << "]=" << a[i*d+i] << " s=" << s << "\n";
throw matrix_exception(os.str());
}
s = T(1) / sqrt(s);
g[i*d+i] = s;
for (j = i+1; j < d; j++) {
s1 = a[j*d+i];
for (k = 0; k < i; k++)
s1 -= g[j*d+k] * g[i*d+k];
g[j*d+i] = s * s1;
}
}
}
template<typename T> void mcholapply(const T *g, const T *b, T *c, unsigned int d)
{
T *t;
unsigned int i, j;
float s1;
t = (T *)alloca(d*sizeof(t[0]));
for (i = 0; i < d; i++) {
s1 = b[i];
for (j = 0; j < i; j++)
s1 -= g[i*d+j] * t[j];
t[i] = s1 * g[i*d+i];
}
for (i = d; i > 0; i--) {
s1 = t[i-1];
for (j = i; j < d; j++)
s1 -= g[j*d+(i-1)] * c[j];
c[i-1] = s1 * g[(i-1)*d+(i-1)];
}
}
template<typename T> void mchol(const T *a, const T *b, T *c, unsigned int d)
{
T *g;
g = (T *)alloca(d*d*sizeof(g[0]));
mcholfactor(a, g, d);
mcholapply(g, b, c, d);
}
/*
* Complex Gaussian Elimination
*/
/*
* Golub/van Loan, 3.1.3, p 112; PA=LU factorization with partial pivoting
*/
template<typename T> inline void swap(T& a, T& b)
{
T c = a;
a = b;
b = c;
}
template<typename T> void mlufact(complex<T> *u, unsigned int *p, const complex<T> *a, unsigned int d)
{
unsigned int i, j, k, mu;
complex<T> fm;
T f1, f2;
if (u != a)
memcpy(u, a, d*d*sizeof(u[0]));
for (k = 0; k < d-1; k++) {
/* search pivot index */
for (f1 = 0, i = mu = k; i < d; i++) {
f2 = complex_pwr(u[i*d+k]);
if (f2 > f1) {
f1 = f2;
mu = i;
}
}
/* exchange rows */
p[k] = mu;
for (i = k; i < d; i++)
swap(u[k*d+i], u[mu*d+i]);
fm = u[k*d+k];
if (real(fm) != 0 || imag(fm) != 0) {
fm = T(1) / fm;
for (i = k+1; i < d; i++)
u[i*d+k] *= fm;
for (i = k+1; i < d; i++)
for (j = k+1; j < d; j++)
u[i*d+j] -= u[i*d+k] * u[k*d+j];
}
}
}
template<typename T> void mlusolve(complex<T> *x, const complex<T> *b, const complex<T> *u, const unsigned int *p, unsigned int d)
{
complex<T> *y, s;
unsigned int k, i;
y = alloca(d * sizeof(y[0]));
memcpy(y, b, d * sizeof(y[0]));
for (k = 0; k < d-1; k++) {
i = p[k];
if (i != k)
swap(y[k], y[i]);
if (real(y[k]) == 0 && imag(y[k]) == 0)
continue;
for (i = k+1; i < d; i++)
y[i] -= y[k] * u[i*d+k];
}
/* solve Ux=y */
for (k = d; k > 0; k--) {
s = y[k-1];
for (i = k; i < d; i++)
s -= u[(k-1)*d+i] * x[i];
x[k-1] = s / u[(k-1)*d+(k-1)];
}
}
/*
* Real Gaussian Elimination
*/
/*
* Golub/van Loan, 3.1.3, p 112; PA=LU factorization with partial pivoting
*/
template<typename T> void mlufact(T *u, unsigned int *p, const T *a, unsigned int d)
{
unsigned int i, j, k, mu;
T f1, f2;
if (u != a)
memcpy(u, a, d*d*sizeof(u[0]));
for (k = 0; k < d-1; k++) {
/* search pivot index */
for (f1 = 0, i = mu = k; i < d; i++) {
f2 = fabs(u[i*d+k]);
if (f2 > f1) {
f1 = f2;
mu = i;
}
}
/* exchange rows */
p[k] = mu;
for (i = k; i < d; i++)
swap(u[k*d+i], u[mu*d+i]);
f1 = u[k*d+k];
if (f1 != 0) {
f1 = 1 / f1;
for (i = k+1; i < d; i++)
u[i*d+k] *= f1;
for (i = k+1; i < d; i++)
for (j = k+1; j < d; j++)
u[i*d+j] -= u[i*d+k] * u[k*d+j];
}
}
}
template<typename T> void mlusolve(T *x, const T *b, const T *u, const unsigned int *p, unsigned int d)
{
T *y, s;
unsigned int k, i;
y = alloca(d * sizeof(y[0]));
memcpy(y, b, d * sizeof(y[0]));
for (k = 0; k < d-1; k++) {
i = p[k];
if (i != k)
swap(y[k], y[i]);
if (y[k] == 0)
continue;
for (i = k+1; i < d; i++)
y[i] -= y[k] * u[i*d+k];
}
/* solve Ux=y */
for (k = d; k > 0; k--) {
s = y[k-1];
for (i = k; i < d; i++)
s -= u[(k-1)*d+i] * x[i];
x[k-1] = s / u[(k-1)*d+(k-1)];
}
}
template<typename T> void minv(T *ainv, const T *a, unsigned int d)
{
T *u, *y;
unsigned int *p;
unsigned int k;
u = alloca(d * d * sizeof(u[0]));
p = alloca((d-1) * sizeof(p[0]));
mlufact(u, p, a, d);
for (k = 0; k < d; k++) {
y = &ainv[k*d];
memset(y, 0, d * sizeof(y[0]));
y[k] = T(1);
mlusolve(y, y, u, p, d);
}
mtranspose(ainv, ainv, d, d);
}
/*
* Gauss-Seidel iterative solver
*/
/*
* This routine calculates A*c=b iteratively, using the Gauss-Seidel iteration method
*/
template<typename T> void mgaussseidel(const complex<T> *a, const complex<T> *b, complex<T> *c, unsigned int d, unsigned int iter)
{
complex<T> *adiag;
unsigned int i, j, k;
complex<T> s;
adiag = alloca(d*sizeof(adiag[0]));
/* initial vector */
for (i = 1; i < d; i++)
c[i] = T(0);
c[0] = T(1);
/* check for diagonal */
for (i = 0; i < d; i++) {
if (a[i*d+i] == T(0)) {
ostringstream os;
os << "mgaussseidel: matrix diagonal zero a[" << i << "][" << i << "]=" << a[i*d+i] << "\n";
throw matrix_exception(os.str());
}
adiag[i] = T(1) / a[i*d+i];
}
/* iteration */
for (i = 0; i < iter; i++) {
for (j = 0; j < d; j++) {
s = b[j];
for (k = 0; k < j; k++)
s -= a[j*d+k] * c[k];
for (k = j+1; k < d; k++)
s -= a[j*d+k] * c[k];
c[j] = s * adiag[j];
}
}
}
#endif /* _MAT_H */
Reference in a new issue View git blame Copy permalink