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dense_full_overdetermined_lsqr.c
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dense_full_overdetermined_lsqr.c
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#include "mex.h"
#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include <string.h>
#include "config.h"
#ifdef BLAS_UNDERSCORE
#define DGEMV dgemv_
#define DTRSV dtrsv_
#define DNRM2 dnrm2_
#define DDOT ddot_
#define DAXPY daxpy_
#else
#define DGEMV dgemv
#define DTRSV dtrsv
#define DNRM2 dnrm2
#define DDOT ddot
#define DAXPY daxpy
#endif
double DNRM2(long *, double *, long *);
double DDOT(long *, double *, long *, double *, long *);
#define MAX_FULLIT 80
void scale(double *x, int n, double s)
{
int i;
for(i = 0; i < n; i++)
x[i] *= s;
}
void mexFunction(int nargout, mxArray *argout[], int nargin, const mxArray *argin[])
{
double tol;
double *A, *b, *R, *x, *U, *u, *V, *v, *vt, *d, *z;
double beta, alpha, normr, normar, norma;
double c, s, phibar, phi, nn;
double thet, rhot, rho;
double *lsvec, *resvec, *Atr, *r;
long m, n;
long maxit, it, i, k;
long int_zero = 0;
long int_one = 1;
double dbl_one = 1.0;
double dbl_mone = -1.0;
double dbl_zero = 0.0;
A = mxGetPr(argin[0]);
b = mxGetPr(argin[1]);
R = mxIsEmpty(argin[2]) ? NULL : mxGetPr(argin[2]);
tol = mxGetScalar(argin[3]);
maxit = (int)mxGetScalar(argin[4]);
m = mxGetM(argin[0]);
n = mxGetN(argin[0]);
U = malloc(MAX_FULLIT * m * sizeof(double));
u = malloc(m * sizeof(double));
V = malloc(MAX_FULLIT * n * sizeof(double));
v = malloc(n * sizeof(double));
vt = malloc(n * sizeof(double));
d = malloc(n * sizeof(double));
z = malloc(n * sizeof(double));
argout[0] = mxCreateDoubleMatrix(n, 1, mxREAL);
x = mxGetPr(argout[0]);
if (nargout > 2) {
argout[2] = mxCreateDoubleMatrix(maxit+1, 1, mxREAL);
lsvec = mxGetPr(argout[2]);
argout[3] = mxCreateDoubleMatrix(maxit+1, 1, mxREAL);
resvec = mxGetPr(argout[3]);
Atr = malloc(n * sizeof(double));
r = malloc(m * sizeof(double));
memcpy(r, b, m * sizeof(double));
DGEMV("T", &m, &n, &dbl_one, A, &m, r, &int_one, &dbl_zero, Atr, &int_one);
resvec[0] = DNRM2(&m, r, &int_one);
lsvec[0] = DNRM2(&n, Atr, &int_one);
}
memset(x, 0, n * sizeof(double));
memset(d, 0, n * sizeof(double));
memcpy(u, b, m * sizeof(double));
beta = DNRM2(&m, u, &int_one);
normr = beta;
scale(u, m, 1/beta);
memcpy(U, u, m * sizeof(double));
c = 1; s = 0; phibar = beta;
DGEMV("T", &m, &n, &dbl_one, A, &m, u, &int_one, &dbl_zero, v, &int_one);
if (R != NULL)
DTRSV("U", "T", "Not Unit", &n, R, &n, v, &int_one);
alpha = DNRM2(&n, v, &int_one);
scale(v, n, 1/alpha);
memcpy(V, v, n * sizeof(double));
normar = alpha * beta;
norma = 0;
it = 0;
while (it < maxit) {
double malpha = -alpha;
memcpy(z, v, n * sizeof(double));
if (R != NULL)
DTRSV("U", "N", "Not Unit", &n, R, &n, z, &int_one);
DGEMV("N", &m, &n, &dbl_one, A, &m, z, &int_one, &malpha, u, &int_one);
if (it < MAX_FULLIT)
for(k = 0; k <= it; k++) {
double eta = -DDOT(&m, u, &int_one, U + k * m, &int_one);
DAXPY(&m, &eta, U + k * m, &int_one, u, &int_one);
}
beta = DNRM2(&m, u, &int_one);
scale(u, m, 1/beta);
if (it < MAX_FULLIT-1)
memcpy(U + (it + 1) * m, u, m * sizeof(double));
norma = sqrt(norma * norma + alpha * alpha + beta * beta);
thet = - s * alpha;
rhot = c * alpha;
rho = sqrt(rhot * rhot + beta * beta);
c = rhot / rho;
s = - beta / rho;
phi = c * phibar;
phibar = s * phibar;
for (i = 0; i < n; i++) {
d[i] = (z[i] - thet * d[i]) / rho;
x[i] = x[i] + phi * d[i];
}
it++;
if (nargout > 2) {
memcpy(r, b, m * sizeof(double));
DGEMV("N", &m, &n, &dbl_mone, A, &m, x, &int_one, &dbl_one, r, &int_one);
DGEMV("T", &m, &n, &dbl_one, A, &m, r, &int_one, &dbl_zero, Atr, &int_one);
lsvec[it] = DNRM2(&n, Atr, &int_one);
resvec[it] = DNRM2(&m, r, &int_one);
}
normr = fabs(s) * normr;
nn = normar / (normr * norma);
if (nn < tol)
break;
DGEMV("T", &m, &n, &dbl_one, A, &m, u, &int_one, &dbl_zero, vt, &int_one);
if (R != NULL)
DTRSV("U", "T", "Not Unit", &n, R, &n, vt, &int_one);
for (i = 0; i < n; i++)
v[i] = vt[i] - beta * v[i];
if (it < MAX_FULLIT)
for(k = 0; k < it; k++) {
double eta = -DDOT(&n, v, &int_one, V + k * n, &int_one);
DAXPY(&n, &eta, V + k * n, &int_one, v, &int_one);
}
alpha = DNRM2(&n, v, &int_one);
scale(v, n, 1/alpha);
if (it < MAX_FULLIT)
memcpy(V + it * n, v, n * sizeof(double));
normar = alpha * fabs(s * phi);
}
if (nargout > 2){
mxSetM(argout[2] , it + 1);
mxSetM(argout[3] , it + 1);
}
if (nargout > 1)
argout[1] = mxCreateDoubleScalar(it);
if (nn > tol)
mexPrintf("dense_lsqr: did not converge\n");
else
mexPrintf("dense_lsqr: converged at iteration %d\n", it);
free(u);
free(v);
free(vt);
free(d);
free(z);
if (nargout > 2) {
free(Atr);
free(r);
}
}