void ClpPdco::matPrecon(double delta, CoinDenseVector<double> &x, CoinDenseVector<double> &y)
{
double *x_elts = x.getElements();
double *y_elts = y.getElements();
matPrecon(delta, x_elts, y_elts);
return;
}
inline double pdxxxmerit(int nlow, int nupp, int *low, int *upp, CoinDenseVector <double> &r1,
CoinDenseVector <double> &r2, CoinDenseVector <double> &rL,
CoinDenseVector <double> &rU, CoinDenseVector <double> &cL,
CoinDenseVector <double> &cU )
{
// Evaluate the merit function for Newton's method.
// It is the 2-norm of the three sets of residuals.
double sum1, sum2;
CoinDenseVector <double> f(6);
f[0] = r1.twoNorm();
f[1] = r2.twoNorm();
sum1 = sum2 = 0.0;
for (int k = 0; k < nlow; k++) {
sum1 += rL[low[k]] * rL[low[k]];
sum2 += cL[low[k]] * cL[low[k]];
}
f[2] = sqrt(sum1);
f[4] = sqrt(sum2);
sum1 = sum2 = 0.0;
for (int k = 0; k < nupp; k++) {
sum1 += rL[upp[k]] * rL[upp[k]];
sum2 += cL[upp[k]] * cL[upp[k]];
}
f[3] = sqrt(sum1);
f[5] = sqrt(sum2);
return f.twoNorm();
}
void ClpPdco::matVecMult( int mode, CoinDenseVector<double> &x, CoinDenseVector<double> &y)
{
double *x_elts = x.getElements();
double *y_elts = y.getElements();
matVecMult( mode, x_elts, y_elts);
return;
}
void ClpLsqr::matVecMult(int mode, CoinDenseVector< double > *x, CoinDenseVector< double > *y)
{
int n = model_->numberColumns();
int m = model_->numberRows();
CoinDenseVector< double > *temp = new CoinDenseVector< double >(n, 0.0);
double *t_elts = temp->getElements();
double *x_elts = x->getElements();
double *y_elts = y->getElements();
ClpPdco *pdcoModel = (ClpPdco *)model_;
if (mode == 1) {
pdcoModel->matVecMult(2, temp, y);
for (int k = 0; k < n; k++)
x_elts[k] += (diag1_[k] * t_elts[k]);
for (int k = 0; k < m; k++)
x_elts[n + k] += (diag2_ * y_elts[k]);
} else {
for (int k = 0; k < n; k++)
t_elts[k] = diag1_[k] * y_elts[k];
pdcoModel->matVecMult(1, x, temp);
for (int k = 0; k < m; k++)
x_elts[k] += diag2_ * y_elts[n + k];
}
delete temp;
return;
}
template <typename T> void
CoinDenseVector<T>::append(const CoinDenseVector<T> & caboose)
{
const int s = nElements_;
const int cs = caboose.getNumElements();
int newsize = s + cs;
resize(newsize);
const T * celem = caboose.getElements();
CoinDisjointCopyN(celem, cs, elements_ + s);
}
inline double pdxxxstep(int nset, int *set, CoinDenseVector <double> &x, CoinDenseVector <double> &dx )
{
// Assumes x > 0.
// Finds the maximum step such that x + step*dx >= 0.
double step = 1e+20;
int n = x.size();
double *x_elts = x.getElements();
double *dx_elts = dx.getElements();
for (int k = 0; k < n; k++)
if (dx_elts[k] < 0)
if ((x_elts[k] / (-dx_elts[k])) < step)
step = x_elts[k] / (-dx_elts[k]);
return step;
}
inline void pdxxxresid1(ClpPdco *model, const int nlow, const int nupp, const int nfix,
int *low, int *upp, int *fix,
CoinDenseVector <double> &b, double *bl, double *bu, double d1, double d2,
CoinDenseVector <double> &grad, CoinDenseVector <double> &rL,
CoinDenseVector <double> &rU, CoinDenseVector <double> &x,
CoinDenseVector <double> &x1, CoinDenseVector <double> &x2,
CoinDenseVector <double> &y, CoinDenseVector <double> &z1,
CoinDenseVector <double> &z2, CoinDenseVector <double> &r1,
CoinDenseVector <double> &r2, double *Pinf, double *Dinf)
{
// Form residuals for the primal and dual equations.
// rL, rU are output, but we input them as full vectors
// initialized (permanently) with any relevant zeros.
// Get some element pointers for efficiency
double *x_elts = x.getElements();
double *r2_elts = r2.getElements();
for (int k = 0; k < nfix; k++)
x_elts[fix[k]] = 0;
r1.clear();
r2.clear();
model->matVecMult( 1, r1, x );
model->matVecMult( 2, r2, y );
for (int k = 0; k < nfix; k++)
r2_elts[fix[k]] = 0;
r1 = b - r1 - d2 * d2 * y;
r2 = grad - r2 - z1; // grad includes d1*d1*x
if (nupp > 0)
r2 = r2 + z2;
for (int k = 0; k < nlow; k++)
rL[low[k]] = bl[low[k]] - x[low[k]] + x1[low[k]];
for (int k = 0; k < nupp; k++)
rU[upp[k]] = - bu[upp[k]] + x[upp[k]] + x2[upp[k]];
double normL = 0.0;
double normU = 0.0;
for (int k = 0; k < nlow; k++)
if (rL[low[k]] > normL) normL = rL[low[k]];
for (int k = 0; k < nupp; k++)
if (rU[upp[k]] > normU) normU = rU[upp[k]];
*Pinf = CoinMax(normL, normU);
*Pinf = CoinMax( r1.infNorm() , *Pinf );
*Dinf = r2.infNorm();
*Pinf = CoinMax( *Pinf, 1e-99 );
*Dinf = CoinMax( *Dinf, 1e-99 );
}
inline void pdxxxresid2(double mu, int nlow, int nupp, int *low, int *upp,
CoinDenseVector <double> &cL, CoinDenseVector <double> &cU,
CoinDenseVector <double> &x1, CoinDenseVector <double> &x2,
CoinDenseVector <double> &z1, CoinDenseVector <double> &z2,
double *center, double *Cinf, double *Cinf0)
{
// Form residuals for the complementarity equations.
// cL, cU are output, but we input them as full vectors
// initialized (permanently) with any relevant zeros.
// Cinf is the complementarity residual for X1 z1 = mu e, etc.
// Cinf0 is the same for mu=0 (i.e., for the original problem).
double maxXz = -1e20;
double minXz = 1e20;
double *x1_elts = x1.getElements();
double *z1_elts = z1.getElements();
double *cL_elts = cL.getElements();
for (int k = 0; k < nlow; k++) {
double x1z1 = x1_elts[low[k]] * z1_elts[low[k]];
cL_elts[low[k]] = mu - x1z1;
if (x1z1 > maxXz) maxXz = x1z1;
if (x1z1 < minXz) minXz = x1z1;
}
double *x2_elts = x2.getElements();
double *z2_elts = z2.getElements();
double *cU_elts = cU.getElements();
for (int k = 0; k < nupp; k++) {
double x2z2 = x2_elts[upp[k]] * z2_elts[upp[k]];
cU_elts[upp[k]] = mu - x2z2;
if (x2z2 > maxXz) maxXz = x2z2;
if (x2z2 < minXz) minXz = x2z2;
}
maxXz = CoinMax( maxXz, 1e-99 );
minXz = CoinMax( minXz, 1e-99 );
*center = maxXz / minXz;
double normL = 0.0;
double normU = 0.0;
for (int k = 0; k < nlow; k++)
if (cL_elts[low[k]] > normL) normL = cL_elts[low[k]];
for (int k = 0; k < nupp; k++)
if (cU_elts[upp[k]] > normU) normU = cU_elts[upp[k]];
*Cinf = CoinMax( normL, normU);
*Cinf0 = maxXz;
}
CoinDenseVector<T>::CoinDenseVector(const CoinDenseVector<T> & rhs):
nElements_(0),
elements_(NULL)
{
setVector(rhs.getNumElements(), rhs.getElements());
}
void ClpLsqr::do_lsqr(CoinDenseVector< double > &b,
double damp, double atol, double btol, double conlim, int itnlim,
bool show, Info info, CoinDenseVector< double > &x, int *istop,
int *itn, Outfo *outfo, bool precon, CoinDenseVector< double > &Pr)
{
/**
Special version of LSQR for use with pdco.m.
It continues with a reduced atol if a pdco-specific test isn't
satisfied with the input atol.
*/
// Initialize.
static char term_msg[8][80] = {
"The exact solution is x = 0",
"The residual Ax - b is small enough, given ATOL and BTOL",
"The least squares error is small enough, given ATOL",
"The estimated condition number has exceeded CONLIM",
"The residual Ax - b is small enough, given machine precision",
"The least squares error is small enough, given machine precision",
"The estimated condition number has exceeded machine precision",
"The iteration limit has been reached"
};
// printf("***************** Entering LSQR *************\n");
assert(model_);
char str1[100], str2[100], str3[100], str4[100], head1[100], head2[100];
int n = ncols_; // set m,n from lsqr object
*itn = 0;
*istop = 0;
double ctol = 0;
if (conlim > 0)
ctol = 1 / conlim;
double anorm = 0;
double acond = 0;
double ddnorm = 0;
double xnorm = 0;
double xxnorm = 0;
double z = 0;
double cs2 = -1;
double sn2 = 0;
// Set up the first vectors u and v for the bidiagonalization.
// These satisfy beta*u = b, alfa*v = A'u.
CoinDenseVector< double > u(b);
CoinDenseVector< double > v(n, 0.0);
x.clear();
double alfa = 0;
double beta = u.twoNorm();
if (beta > 0) {
u = (1 / beta) * u;
matVecMult(2, v, u);
if (precon)
v = v * Pr;
alfa = v.twoNorm();
}
if (alfa > 0) {
v.scale(1 / alfa);
}
CoinDenseVector< double > w(v);
double arnorm = alfa * beta;
if (arnorm == 0) {
printf(" %s\n\n", term_msg[0]);
return;
}
double rhobar = alfa;
double phibar = beta;
double bnorm = beta;
double rnorm = beta;
sprintf(head1, " Itn x(1) Function");
sprintf(head2, " Compatible LS Norm A Cond A");
if (show) {
printf(" %s%s\n", head1, head2);
double test1 = 1;
double test2 = alfa / beta;
sprintf(str1, "%6d %12.5e %10.3e", *itn, x[0], rnorm);
sprintf(str2, " %8.1e %8.1e", test1, test2);
printf("%s%s\n", str1, str2);
}
//----------------------------------------------------------------
// Main iteration loop.
//----------------------------------------------------------------
while (*itn < itnlim) {
*itn += 1;
// Perform the next step of the bidiagonalization to obtain the
// next beta, u, alfa, v. These satisfy the relations
// beta*u = a*v - alfa*u,
// alfa*v = A'*u - beta*v.
u.scale((-alfa));
if (precon) {
CoinDenseVector< double > pv(v * Pr);
matVecMult(1, u, pv);
} else {
matVecMult(1, u, v);
}
beta = u.twoNorm();
if (beta > 0) {
u.scale((1 / beta));
anorm = sqrt(anorm * anorm + alfa * alfa + beta * beta + damp * damp);
v.scale((-beta));
CoinDenseVector< double > vv(n);
vv.clear();
matVecMult(2, vv, u);
if (precon)
vv = vv * Pr;
v = v + vv;
alfa = v.twoNorm();
if (alfa > 0)
v.scale((1 / alfa));
}
// Use a plane rotation to eliminate the damping parameter.
// This alters the diagonal (rhobar) of the lower-bidiagonal matrix.
double rhobar1 = sqrt(rhobar * rhobar + damp * damp);
double cs1 = rhobar / rhobar1;
double sn1 = damp / rhobar1;
double psi = sn1 * phibar;
phibar *= cs1;
// Use a plane rotation to eliminate the subdiagonal element (beta)
// of the lower-bidiagonal matrix, giving an upper-bidiagonal matrix.
double rho = sqrt(rhobar1 * rhobar1 + beta * beta);
double cs = rhobar1 / rho;
double sn = beta / rho;
double theta = sn * alfa;
rhobar = -cs * alfa;
double phi = cs * phibar;
phibar = sn * phibar;
double tau = sn * phi;
// Update x and w.
double t1 = phi / rho;
double t2 = -theta / rho;
// dk = ((1/rho)*w);
double w_norm = w.twoNorm();
x = x + t1 * w;
w = v + t2 * w;
ddnorm = ddnorm + (w_norm / rho) * (w_norm / rho);
// if wantvar, var = var + dk.*dk; end
// Use a plane rotation on the right to eliminate the
// super-diagonal element (theta) of the upper-bidiagonal matrix.
// Then use the result to estimate norm(x).
double delta = sn2 * rho;
double gambar = -cs2 * rho;
double rhs = phi - delta * z;
double zbar = rhs / gambar;
xnorm = sqrt(xxnorm + zbar * zbar);
double gamma = sqrt(gambar * gambar + theta * theta);
cs2 = gambar / gamma;
sn2 = theta / gamma;
z = rhs / gamma;
xxnorm = xxnorm + z * z;
// Test for convergence.
// First, estimate the condition of the matrix Abar,
// and the norms of rbar and Abar'rbar.
acond = anorm * sqrt(ddnorm);
double res1 = phibar * phibar;
double res2 = res1 + psi * psi;
rnorm = sqrt(res1 + res2);
arnorm = alfa * fabs(tau);
// Now use these norms to estimate certain other quantities,
// some of which will be small near a solution.
double test1 = rnorm / bnorm;
double test2 = arnorm / (anorm * rnorm);
double test3 = 1 / acond;
t1 = test1 / (1 + anorm * xnorm / bnorm);
double rtol = btol + atol * anorm * xnorm / bnorm;
// The following tests guard against extremely small values of
// atol, btol or ctol. (The user may have set any or all of
// the parameters atol, btol, conlim to 0.)
// The effect is equivalent to the normal tests using
// atol = eps, btol = eps, conlim = 1/eps.
if (*itn >= itnlim)
*istop = 7;
if (1 + test3 <= 1)
*istop = 6;
if (1 + test2 <= 1)
*istop = 5;
if (1 + t1 <= 1)
*istop = 4;
// Allow for tolerances set by the user.
if (test3 <= ctol)
*istop = 3;
if (test2 <= atol)
*istop = 2;
if (test1 <= rtol)
*istop = 1;
//-------------------------------------------------------------------
// SPECIAL TEST THAT DEPENDS ON pdco.m.
// Aname in pdco is iw in lsqr.
// dy is x
// Other stuff is in info.
// We allow for diagonal preconditioning in pdDDD3.
//-------------------------------------------------------------------
if (*istop > 0) {
double r3new = arnorm;
double r3ratio = r3new / info.r3norm;
double atolold = atol;
double atolnew = atol;
if (atol > info.atolmin) {
if (r3ratio <= 0.1) { // dy seems good
// Relax
} else if (r3ratio <= 0.5) { // Accept dy but make next one more accurate.
atolnew = atolnew * 0.1;
} else { // Recompute dy more accurately
if (show) {
printf("\n ");
printf(" \n");
printf(" %5.1f%7d%7.3f", log10(atolold), *itn, r3ratio);
}
atol = atol * 0.1;
atolnew = atol;
*istop = 0;
}
outfo->atolold = atolold;
outfo->atolnew = atolnew;
outfo->r3ratio = r3ratio;
}
//-------------------------------------------------------------------
// See if it is time to print something.
//-------------------------------------------------------------------
int prnt = 0;
if (n <= 40)
prnt = 1;
if (*itn <= 10)
prnt = 1;
if (*itn >= itnlim - 10)
prnt = 1;
if (*itn % 10 == 0)
prnt = 1;
if (test3 <= 2 * ctol)
prnt = 1;
if (test2 <= 10 * atol)
prnt = 1;
if (test1 <= 10 * rtol)
prnt = 1;
if (*istop != 0)
prnt = 1;
if (prnt == 1) {
if (show) {
sprintf(str1, " %6d %12.5e %10.3e", *itn, x[0], rnorm);
sprintf(str2, " %8.1e %8.1e", test1, test2);
sprintf(str3, " %8.1e %8.1e", anorm, acond);
printf("%s%s%s\n", str1, str2, str3);
}
}
if (*istop > 0)
break;
}
}
// End of iteration loop.
// Print the stopping condition.
if (show) {
printf("\n LSQR finished\n");
// disp(msg(istop+1,:))
// disp(' ')
printf("%s\n", term_msg[*istop]);
sprintf(str1, "istop =%8d itn =%8d", *istop, *itn);
sprintf(str2, "anorm =%8.1e acond =%8.1e", anorm, acond);
sprintf(str3, "rnorm =%8.1e arnorm =%8.1e", rnorm, arnorm);
sprintf(str4, "bnorm =%8.1e xnorm =%8.1e", bnorm, xnorm);
printf("%s %s\n", str1, str2);
printf("%s %s\n", str3, str4);
}
}