static void calcsteps(void)
/* Used by SET */
{
int i;
for (i=0; i<channelnum; i++)
calcstep(&channels[i]);
}
int mve_presolve(int m, int n, double *A, double *b, int maxiter, double tol,
double *x) {
double t;
double dt, dtc;
double tau0 = 0.995;
double sigma0 = 0.2;
double tau;
double sigma;
double mu;
double bnrm;
double gap;
double rgap;
double total_err;
double prif;
double drif;
double alphap;
double alphad;
double ratio;
char Normal = 'N';
char Transpose = 'T';
double r3;
double one = 1.0;
double none = -1.0;
int oneI = 1;
double zero = 0.0;
int iter, i, j;
int n1 = n + 1;
double *y;
double *tmpmm;
double *tmpnn;
double *tmpm1;
double *tmpm2;
double *B;
double *AtD;
double *AtDe;
double *e_m;
double *s;
double *d;
double *dx;
double *dxc;
double *ds;
double *dsc;
double *dy;
double *dyc;
double *r1;
double *r2;
double *r23;
double *r4;
y = pswarm_malloc(m * sizeof(double));
tmpmm = pswarm_malloc(m * m * sizeof(double));
tmpnn = pswarm_malloc(n * n * sizeof(double));
tmpm1 = pswarm_malloc(m * sizeof(double));
tmpm2 = pswarm_malloc(m * sizeof(double));
B = pswarm_malloc(n1 * n1 * sizeof(double));
AtD = pswarm_malloc(n * m * sizeof(double));
AtDe = pswarm_malloc(n * sizeof(double));
e_m = pswarm_malloc(m * sizeof(double));
s = pswarm_malloc(m * sizeof(double));
d = pswarm_malloc(m * sizeof(double));
dx = pswarm_malloc(n * sizeof(double));
dxc = pswarm_malloc(n * sizeof(double));
ds = pswarm_malloc(m * sizeof(double));
dsc = pswarm_malloc(m * sizeof(double));
dy = pswarm_malloc(m * sizeof(double));
dyc = pswarm_malloc(m * sizeof(double));
r1 = pswarm_malloc(m * sizeof(double));
r2 = pswarm_malloc(n * sizeof(double));
r23 = pswarm_malloc(n1 * sizeof(double));
r4 = pswarm_malloc(m * sizeof(double));
/* initialize */
memset(x, 0, n * sizeof(double));
memset(dx, 0, n * sizeof(double));
memset(dxc, 0, n * sizeof(double));
memset(dy, 0, m * sizeof(double));
memset(dyc, 0, m * sizeof(double));
memset(ds, 0, m * sizeof(double));
memset(dsc, 0, m * sizeof(double));
dt = dtc = 0.0;
bnrm = dnrm2_(&m, b, &oneI);
t = b[0];
for (i = 0; i < m; i++) {
if (t > b[i]) t = b[i];
y[i] = 1.0 / m;
}
t -= 1.0;
for (i = 0; i < m; i++) {
e_m[i] = 1.0;
s[i] = b[i] - t;
}
for (iter = 0; iter < maxiter; iter++) {
memcpy(r1, s, m * sizeof(double));
dgemv_(&Normal, &m, &n, &one, A, &m, x, &oneI, &one, r1,
&oneI); /* r1= s + Ax */
for (i = 0; i < m; i++) { /* r1 = r1 +t;*/
r1[i] += t;
r1[i] = -r1[i];
}
daxpy_(&m, &one, b, &oneI, r1, &oneI); /* r1 = b + r1*/
dgemv_(&Transpose, &m, &n, &none, A, &m, y, &oneI, &zero, r2, &oneI);
r3 = 1.0;
for (i = 0; i < m; i++) r3 -= y[i];
gap = 0.0;
for (i = 0; i < m; i++) {
r4[i] = -s[i] * y[i];
gap -= r4[i];
}
prif = dnrm2_(&m, r1, &oneI) / (1 + bnrm);
memcpy(r23, r2, n * sizeof(double));
r23[n] = r3;
drif = dnrm2_(&n1, r23, &oneI);
rgap = ddot_(&m, b, &oneI, y, &oneI);
rgap = fabs(rgap - t) / (1 + fabs(t));
total_err = rgap;
if (prif > total_err) total_err = prif;
if (drif > total_err) total_err = drif;
if (total_err < tol) {
free(y);
free(tmpmm);
free(tmpnn);
free(tmpm1);
free(tmpm2);
free(B);
free(AtD);
free(AtDe);
free(e_m);
free(s);
free(d);
free(dx);
free(dxc);
free(ds);
free(dsc);
free(dy);
free(dyc);
free(r1);
free(r2);
free(r23);
free(r4);
return 0; /* sucess */
}
if (dt > (1e+3) * bnrm || t > (1e+6) * bnrm) {
free(y);
free(tmpmm);
free(tmpnn);
free(tmpm1);
free(tmpm2);
free(B);
free(AtD);
free(AtDe);
free(e_m);
free(s);
free(d);
free(dx);
free(dxc);
free(ds);
free(dsc);
free(dy);
free(dyc);
free(r1);
free(r2);
free(r23);
free(r4);
return 1; /* unbounded ? */
}
for (i = 0; i < m; i++) {
d[i] = 5.0e+15;
if (d[i] > y[i] / s[i]) d[i] = y[i] / s[i];
}
memset(tmpmm, 0, m * m * sizeof(double));
for (i = 0; i < m; i++) tmpmm[i * m + i] = d[i];
dgemm_(&Transpose, &Normal, &n, &m, &m, &one, A, &m, tmpmm, &m, &zero, AtD,
&n);
dgemv_(&Normal, &n, &m, &one, AtD, &n, e_m, &oneI, &zero, AtDe, &oneI);
/* construct B matrix */
dgemm_(&Normal, &Normal, &n, &n, &m, &one, AtD, &n, A, &m, &zero, tmpnn,
&n);
for (i = 0; i < n; i++) {
B[i * (n + 1) + n] = B[i + n * (n + 1)] = AtDe[i];
for (j = 0; j < n; j++) {
B[i + j * (n + 1)] = tmpnn[i + j * n];
}
}
B[n + n * (n + 1)] = d[0];
for (i = 1; i < m; i++) B[n + n * (n + 1)] += d[i];
for (i = 0; i < n + 1; i++) B[i * (n + 1) + i] += 1e-14;
/* dpotrf_(&Upper, &n1, B, &n1, &info); No Cholesky decomposition */
calcstep(m, n, A, B, s, y, r1, r2, r3, r4, dx, ds, &dt, dy);
alphap = -1.0;
alphad = -1.0;
for (i = 0; i < m; i++) {
if (alphap > ds[i] / s[i]) alphap = ds[i] / s[i];
if (alphad > dy[i] / y[i]) alphad = dy[i] / y[i];
}
alphad = -1.0 / alphad;
alphap = -1.0 / alphap;
memcpy(tmpm1, s, m * sizeof(double));
daxpy_(&m, &alphap, ds, &oneI, tmpm1, &oneI);
memcpy(tmpm2, y, m * sizeof(double));
daxpy_(&m, &alphad, dy, &oneI, tmpm2, &oneI);
ratio = ddot_(&m, tmpm1, &oneI, &tmpm2, &oneI) / gap;
sigma = sigma0;
if (sigma > ratio * ratio) sigma = ratio * ratio;
mu = sigma * gap / m;
memset(r1, 0, m * sizeof(double));
memset(r2, 0, n * sizeof(double));
r3 = 0.0;
for (i = 0; i < m; i++) r4[i] = mu - ds[i] * dy[i];
calcstep(m, n, A, B, s, y, r1, r2, r3, r4, dxc, dsc, &dtc, dyc);
daxpy_(&n, &one, dxc, &oneI, dx, &oneI);
daxpy_(&m, &one, dsc, &oneI, ds, &oneI);
daxpy_(&m, &one, dyc, &oneI, dy, &oneI);
dt += dtc;
alphap = -0.5;
alphad = -0.5;
for (i = 0; i < m; i++) {
if (alphap > ds[i] / s[i]) alphap = ds[i] / s[i];
if (alphad > dy[i] / y[i]) alphad = dy[i] / y[i];
}
alphap = -1.0 / alphap;
alphad = -1.0 / alphad;
tau = tau0;
if (tau < 1 - gap / m) tau = 1 - gap / m;
if (tau * alphap < 1) {
alphap = tau * alphap;
} else {
alphap = 1.0;
}
if (tau * alphad < 1) {
alphad = tau * alphad;
} else {
alphad = 1.0;
}
daxpy_(&n, &alphap, dx, &oneI, x, &oneI);
daxpy_(&m, &alphap, ds, &oneI, s, &oneI);
t += alphap * dt;
daxpy_(&m, &alphad, dy, &oneI, y, &oneI);
}
free(y);
free(tmpmm);
free(tmpnn);
free(tmpm1);
free(tmpm2);
free(B);
free(AtD);
free(AtDe);
free(e_m);
free(s);
free(d);
free(dx);
free(dxc);
free(ds);
free(dsc);
free(dy);
free(dyc);
free(r1);
free(r2);
free(r23);
free(r4);
if (t < 1e-16) return 2; /* no volume */
return 0;
}
