/*
* 最大最大激励化 第 unitdx 个单元
*
*/
double LayerWiseRBMs::maximizeUnit(int layerIdx, int unitIdx, double * unitSample, double argvNorm, int epoch){
int AMnumIn = layers[0]->numVis;
// unitsample 归一化
double curNorm = squareNorm(unitSample, AMnumIn, 1);
cblas_dscal(AMnumIn, argvNorm / curNorm, unitSample, 1);
double maxValue =0;
for(int k=0; k<epoch; k++){
// forward
for(int i=0; i<=layerIdx; i++){
if(i==0)
layers[i]->setInput(unitSample);
else
layers[i]->setInput(layers[i-1]->getOutput());
layers[i]->setBatchSize(1);
layers[i]->runBatch();
}
maxValue = layers[layerIdx]->getOutput()[unitIdx];
//back propagate
for(int i=layerIdx; i>=0; i--){
if(i==layerIdx)
layers[i]->getAMDelta(unitIdx, NULL) ;
else
layers[i]->getAMDelta(-1, layers[i+1]->AMDelta);
}
double lr = 0.01 * cblas_dasum(AMnumIn, unitSample, 1) /
cblas_dasum(AMnumIn, layers[0]->AMDelta, 1);
// update unitSample
cblas_daxpy(AMnumIn, lr, layers[0]->AMDelta, 1, unitSample, 1);
//归一化 unitSample
curNorm = squareNorm(unitSample, AMnumIn, 1);
cblas_dscal(AMnumIn, argvNorm / curNorm, unitSample, 1);
}
return maxValue;
}
Result merge(Result* results) {
Result r1 = results[0];
Result r2 = results[1];
if (r1.C + r1.n * r1.CM == r2.C) { // split n
Result r = {r1.m, 2*r1.n, r1.CM, r1.C};
return r;
} else if (r1.C + r1.m == r2.C) { // split m
Result r = {2*r1.m, r1.n, r1.CM, r1.C};
return r;
} else { // split k
int x;
for (x = 0; x < r1.n; x++) {
cblas_daxpy(r2.m, 1, r2.C + r2.m * x, 1, r1.C + r1.CM * x, 1);
}
free(r2.C);
Result r = {r1.m, r1.n, r1.CM, r1.C};
return r;
}
}
// Calculates p
void cg_solver_calc_p(
const int x,
const int y,
const int z,
const int halo_depth,
const double beta,
double* vec_p,
double* vec_r)
{
int x_inner = x - 2*halo_depth;
#pragma omp parallel for
for(int ii = halo_depth; ii < z-halo_depth; ++ii)
{
for(int jj = halo_depth; jj < y-halo_depth; ++jj)
{
const int offset = ii*x*y + jj*x + halo_depth;
cblas_dscal(x_inner, beta, vec_p + offset, 1);
cblas_daxpy(x_inner, 1.0, vec_r + offset, 1, vec_p + offset, 1);
}
}
}
int main()
{
int n = 10;
int in_x =1;
int in_y =1;
std::vector<double> x(n);
std::vector<double> y(n);
double alpha = 10;
std::fill(x.begin(),x.end(),1.0);
std::fill(y.begin(),y.end(),2.0);
cblas_daxpy( n, alpha, &x[0], in_x, &y[0], in_y);
//Print y
for(int j=0;j<n;j++)
std::cout << y[j] << "\t";
std::cout << std::endl;
}
void Map::process(const double* inputs, double* outputs)
{
if(m_first_source > -1)
{
m_encoders[m_first_source]->process(inputs[m_first_source] * m_gains[m_first_source], m_harmonics_double);
m_widers[m_first_source]->process(m_harmonics_double, outputs);
for(unsigned int i = m_first_source+1; i < m_number_of_sources; i++)
{
if (!m_muted[i])
{
m_encoders[i]->process(inputs[i] * m_gains[i], m_harmonics_double);
m_widers[i]->process(m_harmonics_double, m_harmonics_double);
cblas_daxpy(m_number_of_harmonics, 1.f, m_harmonics_double, 1, outputs, 1);
}
}
}
else
{
for(unsigned int i = 0; i < m_number_of_harmonics; i++)
outputs[i] = 0.;
}
}
int main () {
typedef boost::multi_array<double, 1> vector;
typedef vector::index vector_index;
int N = 100000000;
vector x(boost::extents[N]);
vector y(boost::extents[N]);
vector a(boost::extents[N]);
#pragma omp parallel for
for (vector_index i = 0; i < N; i++) {
x[i] = 1;
y[i] = 1;
a[i] = y[i];
}
cblas_daxpy(N, 1.0, &x[0], 1, &a[0], 1);
std::cout << a[0] << '\n';
return 0;
}
JNIEXPORT void JNICALL Java_edu_berkeley_bid_CBLAS_dmcsrm
(JNIEnv * env, jobject calling_obj, jint M, jint N, jdoubleArray j_A, jint lda,
jdoubleArray j_B, jintArray j_ir, jintArray j_jc, jdoubleArray j_C, jint ldc){
jdouble * A = (*env)->GetPrimitiveArrayCritical(env, j_A, JNI_FALSE);
jdouble * B = (*env)->GetPrimitiveArrayCritical(env, j_B, JNI_FALSE);
jint * ir = (*env)->GetPrimitiveArrayCritical(env, j_ir, JNI_FALSE);
jint * jc = (*env)->GetPrimitiveArrayCritical(env, j_jc, JNI_FALSE);
jdouble * C = (*env)->GetPrimitiveArrayCritical(env, j_C, JNI_FALSE);
int ioff = jc[0];
int i, j, k;
for (i = 0; i < N; i++) {
for (j = jc[i]-ioff; j < jc[i+1]-ioff; j++) {
k = ir[j]-ioff;
cblas_daxpy(M, B[j], A+(i*lda), 1, C+(k*ldc), 1);
}
}
(*env)->ReleasePrimitiveArrayCritical(env, j_C, C, 0);
(*env)->ReleasePrimitiveArrayCritical(env, j_jc, jc, 0);
(*env)->ReleasePrimitiveArrayCritical(env, j_ir, ir, 0);
(*env)->ReleasePrimitiveArrayCritical(env, j_B, B, 0);
(*env)->ReleasePrimitiveArrayCritical(env, j_A, A, 0);
}
CPS_START_NAMESPACE
//--------------------------------------------------------------------
// CVS keywords
//
// $Source: /home/chulwoo/CPS/repo/CVS/cps_only/cps_pp/src/util/dirac_op/d_op_mobius/noarch/mobius_m.C,v $
// $State: Exp $
//
//--------------------------------------------------------------------
//------------------------------------------------------------------
// mobius_m.C
//
// mobius_m is the fermion matrix.
// The in, out fields are defined on the checkerboard lattice
//
//------------------------------------------------------------------
CPS_END_NAMESPACE
#include<util/dwf.h>
#include<util/mobius.h>
#include<util/gjp.h>
#include<util/vector.h>
#include<util/verbose.h>
#include<util/error.h>
#include<util/dirac_op.h>
#include<util/time_cps.h>
#include "blas-subs.h"
CPS_START_NAMESPACE
//4d precond. mobius Dirac op:
// M_5 - kappa_b^2 M4eo M_5^-1 M4oe
void mobius_m(Vector *out,
Matrix *gauge_field,
Vector *in,
Float mass,
Dwf *mobius_lib_arg)
{
//------------------------------------------------------------------
// Initializations
//------------------------------------------------------------------
const int f_size = 24 * mobius_lib_arg->vol_4d * mobius_lib_arg->ls / 2;
const Float kappa_ratio = mobius_lib_arg->mobius_kappa_b/mobius_lib_arg->mobius_kappa_c;
const Float minus_kappa_b_sq = -mobius_lib_arg->mobius_kappa_b * mobius_lib_arg->mobius_kappa_b;
Vector *frm_tmp2 = (Vector *) mobius_lib_arg->frm_tmp2;
//Vector *temp = (Vector *) smalloc(f_size * sizeof(Float));
Float norm;
// out = [ 1 + kappa_b/kappa_c 1/2 dslash_5 - kappa_b^2 Meo M5inv Moe] in
// (dslash_5 uses (1+-g5), not P_R,L, i.e. no factor of 1/2 which is here out front)
// 1. ftmp2 = Meo M5inv Moe in
// 2. out <- in
// 3. out += -kappa_b^2 ftmp2
// 4. out += -kappa_b/kappa_c /2 dslash_5 in
// (done by the dslash_5 with a5_inv = -kappa_b/kappa_c/2 *GJP.MobiusA5Inv() )
//--------------------------------------------------------------
// 1. ftmp2 = Meo M5inv Moe in
//--------------------------------------------------------------
// Apply Dslash O <- E
//------------------------------------------------------------------
time_elapse();
mobius_dslash_4(out, gauge_field, in, 0, 0, mobius_lib_arg, mass);
DEBUG_MOBIUS_DSLASH("mobius_dslash_4 %e\n", time_elapse());
//------------------------------------------------------------------
// Apply M_5^-1 (hopping in 5th dir + diagonal)
//------------------------------------------------------------------
mobius_m5inv(out, mass, 0, mobius_lib_arg);
DEBUG_MOBIUS_DSLASH("mobius_m5inv %e\n", time_elapse());
//------------------------------------------------------------------
// Apply Dslash E <- O
//------------------------------------------------------------------
mobius_dslash_4(frm_tmp2, gauge_field, out, 1, 0, mobius_lib_arg, mass);
DEBUG_MOBIUS_DSLASH("mobius_dslash_4 %e\n", time_elapse());
//------------------------------------------------------------------
// 2. out <- in
//------------------------------------------------------------------
#ifndef USE_BLAS
moveFloat((IFloat*)out, (IFloat*)in, f_size);
#else
cblas_dcopy(f_size, (IFloat*)in, 1, (IFloat*)out, 1);
#endif
DEBUG_MOBIUS_DSLASH("out <- in %e\n", time_elapse());
//------------------------------------------------------------------
// 3. out += -kap2 ftmp2
//------------------------------------------------------------------
#ifndef USE_BLAS
fTimesV1PlusV2((IFloat*)out, minus_kappa_b_sq, (IFloat*)frm_tmp2,
(IFloat *)out, f_size);
#else
cblas_daxpy(f_size, minus_kappa_b_sq, (IFloat*)frm_tmp2,1,
(IFloat *)out, 1);
#endif
DEBUG_MOBIUS_DSLASH("mobius out+= kap2 %e\n", time_elapse());
//------------------------------------------------------------------
// 4. out += kappa_b/kappa_c dslash_5 in
//------------------------------------------------------------------
mobius_kappa_dslash_5_plus(out, in, mass, 0, mobius_lib_arg, kappa_ratio);
DEBUG_MOBIUS_DSLASH("mobius_kappa_dslash_5_plus %e\n", time_elapse());
// Flops count in this function is two AXPY = 4 flops per vector elements
//DiracOp::CGflops += 3*f_size;
}
void plotMerit(double *z, double psi_k, double descentCondition)
{
int incx = 1, incy = 1;
double q_0, q_tk, qp_tk, merit_k;
/* double tmin = 1e-12; */
double tk = 1, aux;
double m1 = 1e-4;
double Nstep = 0;
int i = 0;
FILE *fp;
(*sFphi)(sN, z, sphi_z, 0);
aux = cblas_dnrm2(sN, sphi_z, 1);
/* Computes merit function */
aux = 0.5 * aux * aux;
printf("plot psi_z %e\n", aux);
if (!sPlotMerit)
return;
if (sPlotMerit)
{
/* sPlotMerit=0;*/
strcpy(fileName, "outputLS");
(*sFphi)(sN, z, sphi_z, 0);
q_0 = cblas_dnrm2(sN, sphi_z , incx);
q_0 = 0.5 * q_0 * q_0;
fp = fopen(fileName, "w");
/* sPlotMerit=0;*/
tk = 5e-7;
aux = -tk;
Nstep = 1e4;
for (i = 0; i < 2 * Nstep; i++)
{
cblas_dcopy(sN, z, incx, sz2, incx);
cblas_daxpy(sN , aux , sdir_descent , incx , sz2 , incy);
(*sFphi)(sN, sz2, sphi_z, 0);
q_tk = cblas_dnrm2(sN, sphi_z , incx);
q_tk = 0.5 * q_tk * q_tk;
(*sFjacobianPhi)(sN, sz2, sjacobianPhi_z, 1);
/* Computes the jacobian of the merit function, jacobian_psi = transpose(jacobianPhiMatrix).phiVector */
cblas_dgemv(CblasColMajor,CblasTrans, sN, sN, 1.0, sjacobianPhi_z, sN, sphi_z, incx, 0.0, sgrad_psi_z, incx);
qp_tk = cblas_ddot(sN, sgrad_psi_z, 1, sdir_descent, 1);
merit_k = psi_k + m1 * aux * descentCondition;
fprintf(fp, "%e %.16e %.16e %e\n", aux, q_tk, merit_k, qp_tk);
if (i == Nstep - 1)
aux = 0;
else
aux += tk / Nstep;
}
fclose(fp);
}
}
int lineSearch_Wolfe(double *z, double qp_0)
{
int incx = 1, incy = 1;
double q_0, q_tk, qp_tk;
double tmin = 1e-12;
int maxiter = 100;
int niter = 0;
double tk = 1;
double tg, td;
double m1 = 0.1;
double m2 = 0.9;
(*sFphi)(sN, z, sphi_z, 0);
q_0 = cblas_dnrm2(sN, sphi_z , incx);
q_0 = 0.5 * q_0 * q_0;
tg = 0;
td = 10e5;
tk = (tg + td) / 2.0;
while (niter < maxiter || (td - tg) < tmin)
{
niter++;
/*q_tk = 0.5*|| phi(z+tk*d) ||*/
cblas_dcopy(sN, z, incx, sz2, incx);
cblas_daxpy(sN , tk , sdir_descent , incx , sz2 , incy);
(*sFphi)(sN, sz2, sphi_z, 0);
q_tk = cblas_dnrm2(sN, sphi_z , incx);
q_tk = 0.5 * q_tk * q_tk;
(*sFjacobianPhi)(sN, sz2, sjacobianPhi_z, 1);
/* Computes the jacobian of the merit function, jacobian_psi = transpose(jacobianPhiMatrix).phiVector */
cblas_dgemv(CblasColMajor,CblasTrans, sN, sN, 1.0, sjacobianPhi_z, sN, sphi_z, incx, 0.0, sgrad_psi_z, incx);
qp_tk = cblas_ddot(sN, sgrad_psi_z, 1, sdir_descent, 1);
if (qp_tk < m2 * qp_0 && q_tk < q_0 + m1 * tk * qp_0)
{
/*too small*/
if (niter == 1)
break;
tg = tk;
tk = (tg + td) / 2.0;
continue;
}
else if (q_tk > q_0 + m1 * tk * qp_0)
{
/*too big*/
td = tk;
tk = (tg + td) / 2.0;
continue;
}
else
break;
}
cblas_dcopy(sN, sz2, incx, z, incx);
if ((td - tg) <= tmin)
{
printf("NonSmoothNewton2::lineSearchWolfe warning, resulting tk < tmin, linesearch stopped.\n");
return 0;
}
return 1;
}
void caffe_axpy<double>(const int N, const double alpha, const double* X,
double* Y) {
cblas_daxpy(N, alpha, X, 1, Y, 1);
}
void eblas_daxpy_sub(size_t iStart, size_t iStop, double a, const double* x, int incx, double* y, int incy)
{ cblas_daxpy(iStop-iStart, a, x+incx*iStart, incx, y+incy*iStart, incy);
}
void lcp_latin(LinearComplementarityProblem* problem, double *z, double *w, int *info , SolverOptions* options)
{
/* matrix M of the lcp */
double * M = problem->M->matrix0;
/* size of the LCP */
int n = problem->size;
int n2 = n * n;
int i, j, iter1, nrhs;
int info2 = 0;
int itt, it_end;
int incx, incy;
int itermax = options->iparam[0];
double tol = options->dparam[0];
double k_latin = options->dparam[2];
double alpha, beta;
double err1;
double res, errmax;
double *wc, *zc, *kinvden1, *kinvden2, *wt;
double *maxwt, *wnum1, *znum1, *ww, *zz;
double *num1, *kinvnum1, *den1, *den2, *wden1, *zden1;
double *kinvwden1, *kzden1;
double *k, *kinv, *DPO;
// char trans='T', notrans='N', uplo='U', diag='N';
incx = 1;
incy = 1;
/* Recup input */
errmax = tol;
itt = itermax;
/* Initialize output */
options->iparam[1] = 0;
options->dparam[1] = 0.0;
/* Allocations */
ww = (double*) malloc(n * sizeof(double));
zz = (double*) malloc(n * sizeof(double));
wc = (double*) malloc(n * sizeof(double));
zc = (double*) malloc(n * sizeof(double));
znum1 = (double*) malloc(n * sizeof(double));
wnum1 = (double*) malloc(n * sizeof(double));
kinvden1 = (double*) malloc(n * sizeof(double));
kinvden2 = (double*) malloc(n * sizeof(double));
wt = (double*) malloc(n * sizeof(double));
maxwt = (double*) malloc(n * sizeof(double));
num1 = (double*) malloc(n * sizeof(double));
kinvnum1 = (double*) malloc(n * sizeof(double));
den1 = (double*) malloc(n * sizeof(double));
den2 = (double*) malloc(n * sizeof(double));
wden1 = (double*) malloc(n * sizeof(double));
zden1 = (double*) malloc(n * sizeof(double));
kinvwden1 = (double*) malloc(n * sizeof(double));
kzden1 = (double*) malloc(n * sizeof(double));
DPO = (double*) malloc(n2 * sizeof(double));
k = (double*) malloc(n2 * sizeof(double));
kinv = (double*) malloc(n2 * sizeof(double));
/* Initialization */
for (i = 0; i < n2; i++)
{
if (i < n)
{
wc[i] = 0.0;
zc[i] = 0.0;
z[i] = 0.0;
w[i] = 0.0;
znum1[i] = 0.0;
wnum1[i] = 0.0;
kinvden1[i] = 0.0;
kinvden2[i] = 0.0;
wt[i] = 0.0;
maxwt[i] = 0.0;
num1[i] = 0.0;
kinvnum1[i] = 0.0;
den1[i] = 0.0;
den2[i] = 0.0;
}
k[i] = 0.0;
kinv[i] = 0.0;
DPO[i] = 0.0;
}
for (i = 0 ; i < n ; i++)
{
k[i * n + i] = k_latin * M[i * n + i];
if (fabs(k[i * n + i]) < DBL_EPSILON)
{
if (verbose > 0)
{
printf(" Warning nul diagonal term in k matrix \n");
}
free(ww);
free(zz);
free(wc);
free(zc);
free(znum1);
free(wnum1);
free(kinvden1);
free(kinvden2);
free(wt);
free(maxwt);
free(num1);
free(kinvnum1);
free(den1);
free(den2);
free(wden1);
free(zden1);
free(kinvwden1);
free(kzden1);
free(DPO);
free(k);
free(kinv);
*info = 3;
return;
}
else
kinv[i + n * i] = 1.0 / k[i + n * i];
}
for (i = 0; i < n; i++)
for (j = 0; j < n; j++)
DPO[i + n * j] = M[j * n + i] + k[i + n * j];
/* Cholesky */
DPOTRF(LA_UP, n, DPO , n, &info2);
if (info2 != 0)
{
printf(" Matter with Cholesky Factorization \n ");
free(ww);
free(zz);
free(wc);
free(zc);
free(znum1);
free(wnum1);
free(kinvden1);
free(kinvden2);
free(wt);
free(maxwt);
free(num1);
free(kinvnum1);
free(den1);
free(den2);
free(wden1);
free(zden1);
free(kinvwden1);
free(kzden1);
free(DPO);
free(k);
free(kinv);
*info = 2;
return;
}
/* End of Cholesky */
/* Iteration loops */
iter1 = 0;
err1 = 1.;
while ((iter1 < itt) && (err1 > errmax))
{
/* Linear stage (zc,wc) -> (z,w)*/
alpha = 1.;
beta = 1.;
cblas_dgemv(CblasColMajor,CblasTrans, n, n, alpha, k, n, zc, incx, beta, wc, incy);
cblas_dcopy(n, problem->q, incx, znum1, incy);
alpha = -1.;
cblas_dscal(n , alpha , znum1 , incx);
alpha = 1.;
cblas_daxpy(n, alpha, wc, incx, znum1, incy);
nrhs = 1;
DTRTRS(LA_UP, LA_TRANS, LA_NONUNIT, n, nrhs, DPO, n, znum1, n, &info2);
DTRTRS(LA_UP, LA_NOTRANS, LA_NONUNIT, n, nrhs, DPO, n, znum1, n, &info2);
cblas_dcopy(n, znum1, incx, z, incy);
alpha = -1.;
beta = 1.;
cblas_dgemv(CblasColMajor,CblasTrans, n, n, alpha, k, n, z, incx, beta, wc, incy);
cblas_dcopy(n, wc, incx, w, incy);
/* Local Stage */
cblas_dcopy(n, w, incx, wt, incy);
alpha = -1.;
beta = 1.;
cblas_dgemv(CblasColMajor,CblasTrans, n, n, alpha, k, n, z, incx, beta, wt, incy);
for (i = 0; i < n; i++)
{
if (wt[i] > 0.0)
{
wc[i] = wt[i];
zc[i] = 0.0;
}
else
{
wc[i] = 0.0;
zc[i] = -wt[i] / k[i + n * i];
}
}
/* Convergence criterium */
cblas_dcopy(n, w, incx, wnum1, incy);
alpha = -1.;
cblas_daxpy(n, alpha, wc, incx, wnum1, incy);
cblas_dcopy(n, z, incx, znum1, incy);
cblas_daxpy(n, alpha, zc, incx, znum1, incy);
alpha = 1.;
beta = 1.;
cblas_dgemv(CblasColMajor,CblasTrans, n, n, alpha, k, n, znum1, incx, beta, wnum1, incy);
/* wnum1(:) =(w(:)-wc(:))+matmul( k(:,:),(z(:)-zc(:))) */
alpha = 1.;
beta = 0.;
cblas_dgemv(CblasColMajor,CblasTrans, n, n, alpha, kinv, n, wnum1, incx, beta, kinvnum1, incy);
cblas_dcopy(n, z, incx, zz, incy);
cblas_dcopy(n, w, incx, ww, incy);
alpha = 1.;
cblas_daxpy(n, alpha, wc, incx, ww, incy);
cblas_daxpy(n, alpha, zc, incx, zz, incy);
beta = 0.;
alpha = 1.;
cblas_dgemv(CblasColMajor,CblasTrans, n, n, alpha, k, n, zz, incx, beta, kzden1, incy);
beta = 0.;
alpha = 1.;
cblas_dgemv(CblasColMajor,CblasTrans, n, n, alpha, kinv, n, ww, incx, beta, kinvwden1, incy);
lcp_compute_error_only(n, z, w, &err1);
it_end = iter1;
res = err1;
iter1 = iter1 + 1;
options->iparam[1] = it_end;
options->dparam[1] = res;
}
if (isnan(err1) || (err1 > errmax))
{
if (verbose > 0) printf("No convergence of LATIN after %d iterations, the residue is %g\n", iter1, err1);
*info = 1;
}
else
{
if (verbose > 0) printf("Convergence of LATIN after %d iterations, the residue is %g \n", iter1, err1);
*info = 0;
}
free(wc);
free(DPO);
free(k);
free(kinv);
free(zz);
free(ww);
free(zc);
free(znum1);
free(wnum1);
free(kinvden1);
free(kinvden2);
free(wt);
free(maxwt);
free(num1);
free(kinvnum1);
free(den1);
free(den2);
free(wden1);
free(zden1);
free(kinvwden1);
free(kzden1);
}
void get_top_delta(const da *m, const double *y,
const double *x, double *d, const int batch_size){
cblas_dcopy(batch_size * m->n_in, y, 1, d, 1);
cblas_daxpy(batch_size * m->n_in, -1,
x, 1, d, 1);
}
void train_da(da *m, dataset_blas *train_set, dataset_blas *expected_set,
int mini_batch, int n_epcho, char* weight_filename){
int i, j, k, p, q;
int epcho;
double cost, total_cost;
time_t start_time, end_time;
FILE *weight_file;
//weight_file = fopen(weight_filename, "w");
for(epcho = 0; epcho < n_epcho; epcho++){
total_cost = 0.0;
start_time = time(NULL);
for(k = 0; k < train_set->N / mini_batch; k++){
if((k+1) % 500 == 0){
printf("epcho %d batch %d\n", epcho + 1, k + 1);
}
get_hidden_values(m, train_set->input + k * mini_batch * m->n_in, h_out, mini_batch);
get_reconstruct_input(m, h_out, z_out, mini_batch);
get_top_delta(m, z_out, expected_set->input + k * mini_batch * m->n_in, d_high, mini_batch);
get_second_delta(m, h_out, d_high, d_low, mini_batch);
/* modify weight matrix W */
cblas_dgemm(CblasRowMajor, CblasTrans, CblasNoTrans,
m->n_out, m->n_in, mini_batch,
1, d_low, m->n_out,
train_set->input + k * mini_batch * m->n_in, m->n_in,
0, tr1, m->n_in);
cblas_dgemm(CblasRowMajor, CblasTrans, CblasNoTrans,
m->n_out, m->n_in, mini_batch,
1, h_out, m->n_out,
d_high, m->n_in, 0, tr2, m->n_in);
cblas_daxpy(m->n_out * m->n_in, 1, tr1, 1, tr2, 1);
cblas_daxpy(m->n_out * m->n_in, -eta / mini_batch, tr2, 1, m->W, 1);
/* modify bias vector */
cblas_dgemm(CblasRowMajor, CblasTrans, CblasNoTrans,
m->n_out, 1, mini_batch,
1, d_low, m->n_out,
Ivec, 1, 0, tr1, 1);
cblas_daxpy(m->n_out, -eta / mini_batch, tr1, 1, m->b, 1);
cblas_dgemm(CblasRowMajor, CblasTrans, CblasNoTrans,
m->n_in, 1, mini_batch,
1, d_high, m->n_in,
Ivec, 1, 0, tr1, 1);
cblas_daxpy(m->n_in, -eta / mini_batch, tr1, 1, m->c, 1);
for(i = 0; i < mini_batch * m->n_in; i++){
tr1[i] = log(z_out[i]);
}
total_cost -= cblas_ddot(mini_batch * m->n_in, expected_set->input + k * mini_batch * m->n_in, 1,
tr1, 1) / mini_batch;
for(i = 0; i < mini_batch * m->n_in; i++){
tr1[i] = log(1.0 - z_out[i]);
}
cblas_dcopy(mini_batch * m->n_in, Ivec, 1, tr2, 1);
cblas_daxpy(mini_batch * m->n_in, -1, expected_set->input + k * mini_batch * m->n_in,
1, tr2, 1);
total_cost -= cblas_ddot(mini_batch * m->n_in, tr1, 1, tr2, 1) / mini_batch;
}
end_time = time(NULL);
printf("epcho %d cost: %.5lf\ttime: %ds\n", epcho + 1, total_cost / train_set->N * mini_batch, (int)(end_time - start_time));
}
//fclose(weight_file);
}
void bi_conjugate_gradient_sparse(cs *A, double *b, double* x, int n, double itol){
int i,j,iter;
double rho,rho1,alpha,beta,omega;
double r[n], r_t[n];
double z[n], z_t[n];
double q[n], q_t[n], temp_q[n];
double p[n], p_t[n], temp_p[n];
double res[n]; //NA VGEI!
double precond[n];
//Initializations
memset(precond, 0, n*sizeof(double));
memset(r, 0, n*sizeof(double));
memset(r_t, 0, n*sizeof(double));
memset(z, 0, n*sizeof(double));
memset(z_t, 0, n*sizeof(double));
memset(q, 0, n*sizeof(double));
memset(q_t, 0, n*sizeof(double));
memset(temp_q, 0, n*sizeof(double));
memset(p, 0, n*sizeof(double));
memset(p_t, 0, n*sizeof(double));
memset(temp_p, 0, n*sizeof(double));
memset(res, 0, n*sizeof(double));
/* Preconditioner */
double max;
int pp;
for(j = 0; j < n; ++j){
for(pp = A->p[j], max = fabs(A->x[pp]); pp < A->p[j+1]; pp++)
if(fabs(A->x[pp]) > max) //vriskei to diagonio stoixeio
max = fabs(A->x[pp]);
precond[j] = 1/max;
}
cs *AT = cs_transpose (A, 1) ;
cblas_dcopy (n, x, 1, res, 1);
//r=b-Ax
cblas_dcopy (n, b, 1, r, 1);
memset(p, 0, n*sizeof(double));
cs_gaxpy (A, x, p);
for(i=0;i<n;i++){
r[i]=r[i]-p[i];
}
cblas_dcopy (n, r, 1, r_t, 1);
double r_norm = cblas_dnrm2 (n, r, 1);
double b_norm = cblas_dnrm2 (n, b, 1);
if(!b_norm)
b_norm = 1;
iter = 0;
while( r_norm/b_norm > itol && iter < n ){
iter++;
cblas_dcopy (n, r, 1, z, 1); //gia na min allaksei o r
cblas_dcopy (n, r_t, 1, z_t, 1); //gia na min allaksei o r_t
for(i=0;i<n;i++){
z[i]=precond[i]*z[i];
z_t[i]=precond[i]*z_t[i];
}
rho = cblas_ddot (n, z, 1, r_t, 1);
if (fpclassify(fabs(rho)) == FP_ZERO){
printf("RHO aborting Bi-CG due to EPS...\n");
exit(42);
}
if (iter == 1){
cblas_dcopy (n, z, 1, p, 1);
cblas_dcopy (n, z_t, 1, p_t, 1);
}
else{
//p = z + beta*p;
beta = rho/rho1;
cblas_dscal (n, beta, p, 1); //rescale p by beta
cblas_dscal (n, beta, p_t, 1); //rescale p_t by beta
cblas_daxpy (n, 1, z, 1, p, 1); //p = 1*z + p
cblas_daxpy (n, 1, z_t, 1, p_t, 1); //p_t = 1*z_t + p_t
}
rho1 = rho;
//q = Ap
//q_t = trans(A)*p_t
memset(q, 0, n*sizeof(double));
cs_gaxpy (A, p, q);
memset(q_t, 0, n*sizeof(double));
cs_gaxpy(AT, p_t, q_t);
omega = cblas_ddot (n, p_t, 1, q, 1);
if (fpclassify(fabs(omega)) == FP_ZERO){
printf("OMEGA aborting Bi-CG due to EPS...\n");
exit(42);
}
alpha = rho/omega;
//x = x + aplha*p;
cblas_dcopy (n, p, 1, temp_p, 1);
cblas_dscal (n, alpha, temp_p, 1);//rescale by aplha
cblas_daxpy (n, 1, temp_p, 1, res, 1);// sum x = 1*x + temp_p
//R = R - aplha*Q;
cblas_dcopy (n, q, 1, temp_q, 1);
cblas_dscal (n, -alpha, temp_q, 1);//rescale by -aplha
cblas_daxpy (n, 1, temp_q, 1, r, 1);// sum r = 1*r - temp_p
//~r=~r-alpha*~q
cblas_dcopy (n, q_t, 1, temp_q, 1);
cblas_dscal (n, -alpha, temp_q, 1);//rescale by -aplha
cblas_daxpy (n, 1, temp_q, 1, r_t, 1);// sum r = 1*r - temp_p
r_norm = cblas_dnrm2 (n, r, 1); //next step
}
cblas_dcopy (n, res, 1, x, 1);
cs_spfree(AT);
}
/* Ref: Weiss, Algorithm 11 CGS
* INPUT
* n : dimension of the problem
* b [n] : r-h-s vector
* atimes (int n, static double *x, double *b, void *param) :
* calc matrix-vector product A.x = b.
* atimes_param : parameters for atimes().
* it : struct iter. following entries are used
* it->max = kend : max of iteration
* it->eps = eps : criteria for |r^2|/|b^2|
* OUTPUT
* returned value : 0 == success, otherwise (-1) == failed
* x [n] : solution
* it->niter : # of iteration
* it->res2 : |r^2| / |b^2|
*/
int
cgs (int n, const double *b, double *x,
void (*atimes) (int, const double *, double *, void *),
void *atimes_param,
struct iter *it)
{
#ifndef HAVE_CBLAS_H
# ifdef HAVE_BLAS_H
/* use Fortran BLAS routines */
int i_1 = 1;
double d_m1 = -1.0;
double d_2 = 2.0;
# endif // !HAVE_BLAS_H
#endif // !HAVE_CBLAS_H
int ret = -1;
double eps2 = it->eps * it->eps;
int itmax = it->max;
double *r = (double *)malloc (sizeof (double) * n);
double *r0 = (double *)malloc (sizeof (double) * n);
double *p = (double *)malloc (sizeof (double) * n);
double *u = (double *)malloc (sizeof (double) * n);
double *ap = (double *)malloc (sizeof (double) * n);
double *q = (double *)malloc (sizeof (double) * n);
double *t = (double *)malloc (sizeof (double) * n);
CHECK_MALLOC (r, "cgs");
CHECK_MALLOC (r0, "cgs");
CHECK_MALLOC (p, "cgs");
CHECK_MALLOC (u, "cgs");
CHECK_MALLOC (ap, "cgs");
CHECK_MALLOC (q, "cgs");
CHECK_MALLOC (t, "cgs");
double r0ap;
double rho, rho1;
double delta;
double beta;
double res2 = 0.0;
#ifdef HAVE_CBLAS_H
/**
* ATLAS version
*/
double b2 = cblas_ddot (n, b, 1, b, 1); // (b,b)
eps2 *= b2;
// initial residue
atimes (n, x, r, atimes_param); // r = A.x
cblas_daxpy (n, -1.0, b, 1, r, 1); // r = A.x - b
cblas_dcopy (n, r, 1, r0, 1); // r0* = r
cblas_dcopy (n, r, 1, p, 1); // p = r
cblas_dcopy (n, r, 1, u, 1); // u = r
rho = cblas_ddot (n, r0, 1, r, 1); // rho = (r0*, r)
int i;
for (i = 0; i < itmax; i ++)
{
atimes (n, p, ap, atimes_param); // ap = A.p
r0ap = cblas_ddot (n, r0, 1, ap, 1); // r0ap = (r0*, A.p)
delta = - rho / r0ap;
cblas_dcopy (n, u, 1, q, 1); // q = u
cblas_dscal (n, 2.0, q, 1); // q = 2 u
cblas_daxpy (n, delta, ap, 1, q, 1); // q = 2 u + delta A.p
atimes (n, q, t, atimes_param); // t = A.q
cblas_daxpy (n, delta, t, 1, r, 1); // r = r + delta t
cblas_daxpy (n, delta, q, 1, x, 1); // x = x + delta q
res2 = cblas_ddot (n, r, 1, r, 1);
if (it->debug == 2)
{
fprintf (it->out, "libiter-cgs %d %e\n", i, res2 / b2);
}
if (res2 <= eps2)
{
ret = 0; // success
break;
}
rho1 = cblas_ddot (n, r0, 1, r, 1); // rho = (r0*, r)
beta = rho1 / rho;
rho = rho1;
// here t is not used so that this is used for working area.
double *qu = t;
cblas_dcopy (n, q, 1, qu, 1); // qu = q
cblas_daxpy (n, -1.0, u, 1, qu, 1); // qu = q - u
cblas_dcopy (n, r, 1, u, 1); // u = r
cblas_daxpy (n, beta, qu, 1, u, 1); // u = r + beta (q - u)
cblas_daxpy (n, beta, p, 1, qu, 1); // qu = q - u + beta * p
cblas_dcopy (n, u, 1, p, 1); // p = u
cblas_daxpy (n, beta, qu, 1, p, 1); // p = u + beta (q - u + b * p)
}
#else // !HAVE_CBLAS_H
# ifdef HAVE_BLAS_H
/**
* BLAS version
*/
double b2 = ddot_ (&n, b, &i_1, b, &i_1); // (b,b)
eps2 *= b2;
// initial residue
atimes (n, x, r, atimes_param); // r = A.x
daxpy_ (&n, &d_m1, b, &i_1, r, &i_1); // r = A.x - b
dcopy_ (&n, r, &i_1, r0, &i_1); // r0* = r
dcopy_ (&n, r, &i_1, p, &i_1); // p = r
dcopy_ (&n, r, &i_1, u, &i_1); // u = r
rho = ddot_ (&n, r0, &i_1, r, &i_1); // rho = (r0*, r)
int i;
for (i = 0; i < itmax; i ++)
{
atimes (n, p, ap, atimes_param); // ap = A.p
r0ap = ddot_ (&n, r0, &i_1, ap, &i_1); // r0ap = (r0*, A.p)
delta = - rho / r0ap;
dcopy_ (&n, u, &i_1, q, &i_1); // q = u
dscal_ (&n, &d_2, q, &i_1); // q = 2 u
daxpy_ (&n, &delta, ap, &i_1, q, &i_1); // q = 2 u + delta A.p
atimes (n, q, t, atimes_param); // t = A.q
daxpy_ (&n, &delta, t, &i_1, r, &i_1); // r = r + delta t
daxpy_ (&n, &delta, q, &i_1, x, &i_1); // x = x + delta q
res2 = ddot_ (&n, r, &i_1, r, &i_1);
if (it->debug == 2)
{
fprintf (it->out, "libiter-cgs %d %e\n", i, res2 / b2);
}
if (res2 <= eps2)
{
ret = 0; // success
break;
}
rho1 = ddot_ (&n, r0, &i_1, r, &i_1); // rho = (r0*, r)
beta = rho1 / rho;
rho = rho1;
// here t is not used so that this is used for working area.
double *qu = t;
dcopy_ (&n, q, &i_1, qu, &i_1); // qu = q
daxpy_ (&n, &d_m1, u, &i_1, qu, &i_1); // qu = q - u
dcopy_ (&n, r, &i_1, u, &i_1); // u = r
daxpy_ (&n, &beta, qu, &i_1, u, &i_1); // u = r + beta (q - u)
daxpy_ (&n, &beta, p, &i_1, qu, &i_1); // qu = q - u + beta * p
dcopy_ (&n, u, &i_1, p, &i_1); // p = u
daxpy_ (&n, &beta, qu, &i_1, p, &i_1); // p = u + beta (q - u + b * p)
}
# else // !HAVE_BLAS_H
/**
* local BLAS version
*/
double b2 = my_ddot (n, b, 1, b, 1); // (b,b)
eps2 *= b2;
// initial residue
atimes (n, x, r, atimes_param); // r = A.x
my_daxpy (n, -1.0, b, 1, r, 1); // r = A.x - b
my_dcopy (n, r, 1, r0, 1); // r0* = r
my_dcopy (n, r, 1, p, 1); // p = r
my_dcopy (n, r, 1, u, 1); // u = r
rho = my_ddot (n, r0, 1, r, 1); // rho = (r0*, r)
int i;
for (i = 0; i < itmax; i ++)
{
atimes (n, p, ap, atimes_param); // ap = A.p
r0ap = my_ddot (n, r0, 1, ap, 1); // r0ap = (r0*, A.p)
delta = - rho / r0ap;
my_dcopy (n, u, 1, q, 1); // q = u
my_dscal (n, 2.0, q, 1); // q = 2 u
my_daxpy (n, delta, ap, 1, q, 1); // q = 2 u + delta A.p
atimes (n, q, t, atimes_param); // t = A.q
my_daxpy (n, delta, t, 1, r, 1); // r = r + delta t
my_daxpy (n, delta, q, 1, x, 1); // x = x + delta q
res2 = my_ddot (n, r, 1, r, 1);
if (it->debug == 2)
{
fprintf (it->out, "libiter-cgs %d %e\n", i, res2 / b2);
}
if (res2 <= eps2)
{
ret = 0; // success
break;
}
rho1 = my_ddot (n, r0, 1, r, 1); // rho = (r0*, r)
beta = rho1 / rho;
rho = rho1;
// here t is not used so that this is used for working area.
double *qu = t;
my_dcopy (n, q, 1, qu, 1); // qu = q
my_daxpy (n, -1.0, u, 1, qu, 1); // qu = q - u
my_dcopy (n, r, 1, u, 1); // u = r
my_daxpy (n, beta, qu, 1, u, 1); // u = r + beta (q - u)
my_daxpy (n, beta, p, 1, qu, 1); // qu = q - u + beta * p
my_dcopy (n, u, 1, p, 1); // p = u
my_daxpy (n, beta, qu, 1, p, 1); // p = u + beta (q - u + b * p)
}
# endif // !HAVE_BLAS_H
#endif // !HAVE_CBLAS_H
free (r);
free (r0);
free (p);
free (u);
free (ap);
free (q);
free (t);
if (it->debug == 1)
{
fprintf (it->out, "libiter-cgs it= %d res^2= %e\n", i, res2);
}
it->niter = i;
it->res2 = res2 / b2;
return (ret);
}
void caffe_cpu_xpasv<double>(const int M, const int N, const double alpha,
double* X, const double* a, const double* b) {
for (int i = 0; i < M; ++i) {
cblas_daxpy(N, alpha * a[i], b, 1, X + i * N, 1);
}
}
void FrictionContact2D_latin(FrictionContactProblem* problem , double *reaction , double *velocity , int *info, SolverOptions* options)
{
int nc = problem->numberOfContacts;
assert(nc>0);
double * vec = problem->M->matrix0;
double *qq = problem->q;
double * mu = problem->mu;
int info77 = 0;
int i, j, kk, iter1, ino, ddl, nrhs;
int info2 = 0;
int n = 2 * nc;
size_t idim, nbno;
int incx = 1, incy = 1;
size_t taille, taillet, taillen, itt;
int *ddln;
int *ddlt, *vectnt;
assert(n>0);
double errmax, alpha, beta, maxa, k_latin;
double aa, nt, wn, tc, zc0;
double err1, num11, err0;
double den11, den22, knz0, ktz0, *ktz, *wf;
double *wc, *zc, *wt, *maxwt, *wnum1, *znum1;
double *zt, *maxzt;
double *kn, *kt;
// char trans='T', diag='N';
// char uplo='U', notrans='N';
double *k, *DPO, *kf, *kninv;
double *kinvwden1, *kzden1, *kfinv, *knz, *wtnc;
/* Recup input */
itt = options->iparam[0];
errmax = options->dparam[0];
k_latin = options->dparam[2];
/* Initialize output */
options->iparam[1] = 0;
options->dparam[1] = 0.0;
/* Allocations */
k = (double*) malloc(n * n * sizeof(double));
DPO = (double*) malloc(n * n * sizeof(double));
kf = (double*) malloc(n * n * sizeof(double));
kfinv = (double*) malloc(n * n * sizeof(double));
kninv = (double*) malloc(nc * nc * sizeof(double));
kn = (double*) malloc(nc * nc * sizeof(double));
kt = (double*) malloc(nc * nc * sizeof(double));
kinvwden1 = (double*) malloc(n * sizeof(double));
kzden1 = (double*) malloc(n * sizeof(double));
wc = (double*) malloc(n * sizeof(double));
zc = (double*) malloc(n * sizeof(double));
znum1 = (double*) malloc(n * sizeof(double));
wnum1 = (double*) malloc(n * sizeof(double));
wt = (double*) malloc(n * sizeof(double));
maxzt = (double*) malloc(n * sizeof(double));
knz = (double*) malloc(nc * sizeof(double));
wtnc = (double*) malloc(nc * sizeof(double));
ktz = (double*) malloc(nc * sizeof(double));
wf = (double*) malloc(nc * sizeof(double));
maxwt = (double*) malloc(nc * sizeof(double));
zt = (double*) malloc(nc * sizeof(double));
vectnt = (int*) malloc(n * sizeof(int));
ddln = (int*) malloc(nc * sizeof(int));
ddlt = (int*) malloc(nc * sizeof(int));
/* Initialization */
for (i = 0; i < n * n; i++)
{
k[i] = 0.;
kf[i] = 0.;
kfinv[i] = 0.;
if (i < nc * nc)
{
kn[i] = 0.0;
kt[i] = 0.0;
kninv[i] = 0.0;
if (i < n)
{
wc[i] = 0.0;
zc[i] = 0.;
reaction[i] = 0.;
velocity[i] = 0.;
znum1[i] = 0.;
wnum1[i] = 0.;
wt[i] = 0.;
maxzt[i] = 0.;
if (i < nc)
{
maxwt[i] = 0.;
zt[i] = 0.;
knz[i] = 0.;
ktz[i] = 0.;
wf[i] = 0.;
wtnc[i] = 0.;
}
}
}
}
for (i = 0; i < n; i++)
{
if (fabs(vec[i * n + i]) < DBL_EPSILON)
{
if (verbose > 0)
printf("\n Warning nul diagonal term in M matrix \n");
free(k);
free(DPO);
free(kf);
free(kfinv);
free(kninv);
free(kn);
free(kt);
free(kinvwden1);
free(kzden1);
free(wc);
free(zc);
free(znum1);
free(wnum1);
free(wt);
free(maxzt);
free(knz);
free(wtnc);
free(ktz);
free(wf);
free(maxwt);
free(zt);
free(vectnt);
free(ddln);
free(ddlt);
*info = 3;
return;
}
else
{
k[i + n * i] = k_latin / vec[i * n + i];
vectnt[i] = i + 1;
}
}
for (i = 0; i < nc; i++)
{
ddln[i] = vectnt[2 * i];
if (i != 0) ddlt[i] = vectnt[2 * i - 1];
else ddlt[i] = 0;
}
for (i = 0; i < nc; i++)
{
kn[i + nc * i] = k[ddln[i] + n * ddln[i]];
kt[i + nc * i] = k[ddlt[i] + n * ddlt[i]];
}
taillen = sizeof(ddln) / sizeof(ddln[0]);
taillet = sizeof(ddlt) / sizeof(ddlt[0]);
idim = 1 + taillen / taillet;
taille = 0;
for (i = 0; i < n; i++)
taille = sizeof(qq[i]) + taille;
taille = taille / sizeof(qq[0]);
nbno = taille / idim;
for (i = 0; i < nc; i++)
{
kf[ddln[i] + n * ddln[i]] = kn[i + nc * i];
kf[ddlt[i] + n * ddlt[i]] = kt[i + nc * i];
}
for (i = 0; i < n; i++)
{
kfinv[i + n * i] = 1. / kf[i + n * i];
if (i < nc)
kninv[i + nc * i] = 1. / kt[i + nc * i];
}
for (i = 0; i < n; i++)
for (j = 0; j < n; j++)
DPO[i + n * j] = vec[j * n + i] + kfinv[i + n * j];
DPOTRF(LA_UP, n, DPO , n, &info2);
if (info2 != 0)
{
if (verbose > 0)
printf("\n Matter with Cholesky factorization \n");
free(k);
free(DPO);
free(kf);
free(kfinv);
free(kninv);
free(kn);
free(kt);
free(kinvwden1);
free(kzden1);
free(wc);
free(zc);
free(znum1);
free(wnum1);
free(wt);
free(maxzt);
free(knz);
free(wtnc);
free(ktz);
free(wf);
free(maxwt);
free(zt);
free(vectnt);
free(ddln);
free(ddlt);
*info = 2;
return;
}
/* Iteration loops */
iter1 = 0;
err1 = 1.;
while ((iter1 < itt) && (err1 > errmax))
{
/* Linear stage (zc,wc) -> (z,w) */
alpha = 1.;
beta = 1.;
cblas_dgemv(CblasColMajor,CblasNoTrans, n, n, alpha, kfinv, n, zc, incx, beta, wc, incy);
cblas_dcopy(n, qq, incx, znum1, incy);
alpha = -1.;
cblas_dscal(n , alpha , znum1 , incx);
alpha = 1.;
cblas_daxpy(n, alpha, wc, incx, znum1, incy);
nrhs = 1;
DTRTRS(LA_UP, LA_TRANS, LA_NONUNIT, n, nrhs, DPO, n, znum1, n, &info77);
DTRTRS(LA_UP, LA_NOTRANS, LA_NONUNIT, n, nrhs, DPO, n, znum1, n, &info77);
cblas_dcopy(n, znum1, incx, reaction, incy);
alpha = -1.;
beta = 1.;
cblas_dgemv(CblasColMajor,CblasNoTrans, n, n, alpha, kfinv, n, reaction, incx, beta, wc, incy);
cblas_dcopy(n, wc, incx, velocity, incy);
/* Local stage (z,w)->(zc,wc) */
for (i = 0; i < n; i++)
{
zc[i] = 0.;
wc[i] = 0.0;
}
/* Normal party */
for (i = 0; i < nc; i++)
{
knz0 = 0.;
for (kk = 0; kk < nc; kk++)
{
knz[i] = kt[i + nc * kk] * velocity[ddlt[kk]] + knz0;
knz0 = knz[i];
}
zt[i] = reaction[ddlt[i]] - knz[i];
if (zt[i] > 0.0)
{
zc[ddlt[i]] = zt[i];
maxzt[i] = 0.0;
}
else
{
zc[ddlt[i]] = 0.0;
maxzt[i] = -zt[i];
}
}
for (i = 0; i < nc; i++)
{
zc0 = 0.;
ktz0 = 0.;
for (j = 0; j < nc; j++)
{
wc[ddlt[i]] = kninv[i + nc * j] * maxzt[j] + zc0;
zc0 = wc[ddlt[i]];
ktz[i] = kn[i + nc * j] * velocity[ddln[j]] + ktz0;
ktz0 = ktz[i];
}
wf[i] = reaction[ddln[i]] - ktz[i];
}
/* Loop other nodes */
for (ino = 0; ino < nbno; ino++)
{
ddl = ddln[ino];
nt = fabs(wf[ino]);
/* Tangential vector */
if (nt < 1.e-8) tc = 0.;
else tc = wf[ino] / nt;
/* Tangentiel component */
wn = zc[ddlt[ino]];
aa = nt - mu[ino] * wn;
if (aa > 0.0)
{
maxa = aa;
}
else
{
maxa = 0.0;
}
wc[ddl] = (maxa / (-1 * kn[ino + nc * ino])) * tc;
aa = -nt + mu[ino] * wn;
if (aa > 0.0)
{
maxa = aa;
}
else
{
maxa = 0.0;
}
zc[ddl] = (mu[ino] * wn - maxa) * tc;
}
/* Convergence criterium */
cblas_dcopy(n, reaction, incx, znum1, incy);
alpha = -1.;
cblas_daxpy(n, alpha, zc, incx, znum1, incy);
cblas_dcopy(n, velocity, incx, wnum1, incy);
cblas_daxpy(n, alpha, wc, incx, wnum1, incy);
alpha = 1.;
beta = 1.;
cblas_dgemv(CblasColMajor,CblasNoTrans, n, n, alpha, kf, n, wnum1, incx, beta, znum1, incy);
num11 = 0.;
alpha = 1.;
beta = 0.;
cblas_dgemv(CblasColMajor,CblasNoTrans, n, n, alpha, kfinv, n, znum1, incx, beta, wnum1, incy);
num11 = cblas_ddot(n, wnum1, incx, znum1, incy);
cblas_dcopy(n, reaction, incx, znum1, incy);
alpha = 1.;
beta = 1.;
cblas_dgemv(CblasColMajor,CblasNoTrans, n, n, alpha, kf, n, velocity, incx, beta, znum1, incy);
alpha = 1.;
beta = 0.;
cblas_dgemv(CblasColMajor,CblasNoTrans, n, n, alpha, kfinv, n, znum1, incx, beta, wnum1, incy);
den11 = cblas_ddot(n, wnum1, incx, znum1, incy);
cblas_dcopy(n, zc, incx, znum1, incy);
alpha = 1.;
beta = 1.;
cblas_dgemv(CblasColMajor,CblasNoTrans, n, n, alpha, kf, n, wc, incx, beta, znum1, incy);
alpha = 1.;
beta = 0.;
cblas_dgemv(CblasColMajor,CblasNoTrans, n, n, alpha, kfinv, n, znum1, incx, beta, wnum1, incy);
den22 = cblas_ddot(n, znum1, incx, wnum1, incy);
err0 = num11 / (den11 + den22);
err1 = sqrt(err0);
options->iparam[1] = iter1;
options->dparam[1] = err1;
iter1 = iter1 + 1;
}
if (err1 > errmax)
{
if (verbose > 0)
printf("No convergence after %d iterations, the residue is %g\n", iter1, err1);
*info = 1;
}
else
{
if (verbose > 0)
printf("Convergence after %d iterations, the residue is %g \n", iter1, err1);
*info = 0;
}
free(k);
free(DPO);
free(kf);
free(kfinv);
free(kninv);
free(kn);
free(kt);
free(kinvwden1);
free(kzden1);
free(wc);
free(zc);
free(znum1);
free(wnum1);
free(wt);
free(maxzt);
free(knz);
free(wtnc);
free(ktz);
free(wf);
free(maxwt);
free(zt);
free(vectnt);
free(ddln);
free(ddlt);
}
int _globalLineSearchSparseGP(
GlobalFrictionContactProblem *problem,
AlartCurnierFun3x3Ptr computeACFun3x3,
double *solution,
double *direction,
double *mu,
double *rho,
double *F,
double *psi,
CSparseMatrix *J,
double *tmp,
double alpha[1],
unsigned int maxiter_ls)
{
double inf = 1e10;
double alphamin = 1e-16;
double alphamax = inf;
double m1 = 0.01, m2 = 0.99;
unsigned int n = (unsigned)NM_triplet(problem->M)->m;
unsigned int m = problem->H->size1;
unsigned int problem_size = n+2*m;
// Computation of q(t) and q'(t) for t =0
double q0 = 0.5 * cblas_ddot(problem_size, psi, 1, psi, 1);
// tmp <- J * direction
cblas_dscal(problem_size, 0., tmp, 1);
cs_gaxpy(J, direction, tmp);
double dqdt0 = cblas_ddot(problem_size, psi, 1, tmp, 1);
DEBUG_PRINTF("dqdt0=%e\n",dqdt0);
DEBUG_PRINTF("q0=%e\n",q0);
for(unsigned int iter = 0; iter < maxiter_ls; ++iter)
{
// tmp <- alpha*direction+solution
cblas_dcopy(problem_size, solution, 1, tmp, 1);
cblas_daxpy(problem_size, alpha[0], direction, 1, tmp, 1);
ACPsi(
problem,
computeACFun3x3,
tmp, /* v */
tmp+problem->M->size0+problem->H->size1, /* P */
tmp+problem->M->size0, /* U */
rho, psi);
double q = 0.5 * cblas_ddot(problem_size, psi, 1, psi, 1);
assert(q >= 0);
double slope = (q - q0) / alpha[0];
int C1 = (slope >= m2 * dqdt0);
int C2 = (slope <= m1 * dqdt0);
DEBUG_PRINTF("C1=%i\t C2=%i\n",C1,C2);
if(C1 && C2)
{
numerics_printf_verbose(1, "---- GFC3D - NSN_AC - global line search success. Number of ls iteration = %i alpha = %.10e, q = %.10e",
iter,
alpha[0], q);
return 0;
}
else if(!C1)
{
alphamin = alpha[0];
}
else
{
// not(C2)
alphamax = alpha[0];
}
if(alpha[0] < inf)
{
alpha[0] = 0.5 * (alphamin + alphamax);
}
else
{
alpha[0] = alphamin;
}
}
numerics_printf_verbose(1,"---- GFC3D - NSN_AC - global line search unsuccessful. Max number of ls iteration reached = %i with alpha = %.10e",
maxiter_ls, alpha[0]);
return -1;
}
void fc3d_ProjectedGradientOnCylinder(FrictionContactProblem* problem, double *reaction, double *velocity, int* info, SolverOptions* options)
{
/* int and double parameters */
int* iparam = options->iparam;
double* dparam = options->dparam;
/* Number of contacts */
int nc = problem->numberOfContacts;
double* q = problem->q;
NumericsMatrix* M = problem->M;
/* Dimension of the problem */
int n = 3 * nc;
/* Maximum number of iterations */
int itermax = iparam[0];
/* Tolerance */
double tolerance = dparam[0];
/***** Projected Gradient iterations *****/
int j, iter = 0; /* Current iteration number */
double error = 1.; /* Current error */
int hasNotConverged = 1;
int contact; /* Number of the current row of blocks in M */
int nLocal = 3;
dparam[0] = dparam[2]; // set the tolerance for the local solver
double * velocitytmp = (double *)malloc(n * sizeof(double));
double rho = 0.0;
int isVariable = 0;
double rhoinit, rhomin;
if (dparam[3] > 0.0)
{
rho = dparam[3];
}
else
{
/* Variable step in fixed*/
isVariable = 1;
printf("Variable step (line search) in Projected Gradient iterations\n");
rhoinit = dparam[3];
rhomin = dparam[4];
}
double * reactionold;
double * direction;
if (isVariable)
{
reactionold = (double *)malloc(n * sizeof(double));
direction = (double *)malloc(n * sizeof(double));
}
double alpha = 1.0;
double beta = 1.0;
/* double minusrho = -1.0*rho; */
if (!isVariable)
{
while ((iter < itermax) && (hasNotConverged > 0))
{
++iter;
cblas_dcopy(n , q , 1 , velocitytmp, 1);
prodNumericsMatrix(n, n, alpha, M, reaction, beta, velocitytmp);
// projection for each contact
cblas_daxpy(n, -1.0, velocitytmp, 1, reaction , 1);
for (contact = 0 ; contact < nc ; ++contact)
projectionOnCylinder(&reaction[ contact * nLocal],
options->dWork[contact]);
#ifdef VERBOSE_DEBUG
printf("reaction before LS\n");
for (contact = 0 ; contact < nc ; ++contact)
{
for (j = 0; j < 3; j++)
printf("reaction[%i] = %le\t", 3 * contact + j, reaction[3 * contact + j]);
printf("\n");
}
printf("velocitytmp before LS\n");
for (contact = 0 ; contact < nc ; ++contact)
{
for (j = 0; j < 3; j++)
printf("velocitytmp[%i] = %le\t", 3 * contact + j, velocitytmp[3 * contact + j]);
printf("\n");
}
#endif
/* **** Criterium convergence **** */
fc3d_Tresca_compute_error(problem, reaction , velocity, tolerance, options, &error);
if (options->callback)
{
options->callback->collectStatsIteration(options->callback->env, nc * 3,
reaction, velocity,
error, NULL);
}
if (verbose > 0)
printf("----------------------------------- FC3D - Projected Gradient On Cylinder (PGoC) - Iteration %i rho = %14.7e \tError = %14.7e\n", iter, rho, error);
if (error < tolerance) hasNotConverged = 0;
*info = hasNotConverged;
}
}
else
{
rho = rhoinit;
cblas_dcopy(n , q , 1 , velocitytmp, 1);
prodNumericsMatrix(n, n, 1.0, M, reaction, 1.0, velocitytmp);
cblas_daxpy(n, rho, velocitytmp, 1, reaction, 1);
for (contact = 0 ; contact < nc ; ++contact)
projectionOnCylinder(&reaction[contact * nLocal],
options->dWork[contact]);
cblas_dcopy(n , q , 1 , velocitytmp, 1);
prodNumericsMatrix(n, n, 1.0, M, reaction, 1.0, velocitytmp);
double oldcriterion = cblas_ddot(n, reaction, 1, velocitytmp, 1);
#ifdef VERBOSE_DEBUG
printf("oldcriterion =%le \n", oldcriterion);
#endif
while ((iter < itermax) && (hasNotConverged > 0))
{
++iter;
// store the old reaction
cblas_dcopy(n , reaction , 1 , reactionold , 1);
// compute the direction
cblas_dcopy(n , q , 1 , velocitytmp, 1);
prodNumericsMatrix(n, n, 1.0, M, reaction, 1.0, velocitytmp);
cblas_dcopy(n, velocitytmp, 1, direction, 1);
// start line search
j = 0;
if (rho <= 100 * rhoinit) rho = 10.0 * rho;
double newcriterion = 1e24;
do
{
cblas_dcopy(n , reactionold , 1 , reaction , 1);
cblas_daxpy(n, rho, direction, 1, reaction , 1) ;
#ifdef VERBOSE_DEBUG
printf("LS iteration %i step 0 \n", j);
printf("rho = %le \n", rho);
for (contact = 0 ; contact < nc ; ++contact)
{
for (int k = 0; k < 3; k++)
printf("reaction[%i] = %le\t",
3 * contact + k, reaction[3 * contact + k]);
printf("\n");
}
#endif
for (contact = 0 ; contact < nc ; ++contact)
projectionOnCylinder(&reaction[contact * nLocal],
options->dWork[contact]);
/* printf("options->dWork[%i] = %le\n",contact, options->dWork[contact] );} */
#ifdef VERBOSE_DEBUG
printf("LS iteration %i step 1 after projection\n", j);
for (contact = 0 ; contact < nc ; ++contact)
{
for (int k = 0; k < 3; k++)
printf("reaction[%i] = %le\t",
3 * contact + k, reaction[3 * contact + k]);
printf("\n");
}
#endif
cblas_dcopy(n , q , 1 , velocitytmp, 1);
prodNumericsMatrix(n, n, 1.0, M, reaction, 1.0, velocitytmp);
#ifdef VERBOSE_DEBUG
printf("LS iteration %i step 3 \n", j);
for (contact = 0 ; contact < nc ; ++contact)
{
for (int k = 0; k < 3; k++)
printf("velocitytmp[%i] = %le\t", 3 * contact + k, velocitytmp[3 * contact + k]);
printf("\n");
}
#endif
newcriterion = cblas_ddot(n, reaction, 1, velocitytmp, 1);
#ifdef VERBOSE_DEBUG
printf("LS iteration %i newcriterion =%le\n", j, newcriterion);
#endif
if (rho > rhomin)
{
rho = rhomin;
break;
}
rho = 0.5 * rho;
}
while (newcriterion > oldcriterion &&
++j <= options->iparam[2]);
oldcriterion = newcriterion;
/* **** Criterium convergence **** */
fc3d_Tresca_compute_error(problem, reaction , velocity, tolerance, options, &error);
if (verbose > 0)
printf("----------------------------------- FC3D - Projected Gradient On Cylinder (PGoC) - Iteration %i rho = %14.7e \tError = %14.7e\n", iter, rho, error);
if (error < tolerance) hasNotConverged = 0;
*info = hasNotConverged;
}
}
printf("----------------------------------- FC3D - Projected Gradient On Cylinder (PGoC)- #Iteration %i Final Residual = %14.7e\n", iter, error);
dparam[0] = tolerance;
dparam[1] = error;
free(velocitytmp);
if (isVariable)
{
free(reactionold);
free(direction);
}
}
void variationalInequality_ExtraGradient(VariationalInequality* problem, double *x, double *w, int* info, SolverOptions* options)
{
/* /\* int and double parameters *\/ */
int* iparam = options->iparam;
double* dparam = options->dparam;
/* Number of contacts */
int n = problem->size;
/* Maximum number of iterations */
int itermax = iparam[0];
/* Tolerance */
double tolerance = dparam[0];
/***** Fixed point iterations *****/
int iter = 0; /* Current iteration number */
double error = 1.; /* Current error */
int hasNotConverged = 1;
dparam[0] = dparam[2]; // set the tolerance for the local solver
double * xtmp = (double *)malloc(n * sizeof(double));
double * wtmp = (double *)malloc(n * sizeof(double));
double rho = 0.0, rho_k =0.0;
int isVariable = 0;
if (dparam[3] > 0.0)
{
rho = dparam[3];
if (verbose > 0)
{
printf("----------------------------------- VI - Extra Gradient (EG) - Fixed stepsize with rho = %14.7e \n", rho);
}
}
else
{
/* Variable step in iterations*/
isVariable = 1;
rho = -dparam[3];
if (verbose > 0)
{
printf("----------------------------------- VI - Extra Gradient (EG) - Variable stepsize with starting rho = %14.7e \n", rho);
}
}
/* Variable for Line_search */
int success =0;
double error_k, light_error_sum =0.0;
int ls_iter = 0;
int ls_itermax = 10;
double tau=dparam[4], tauinv=dparam[5], L= dparam[6], Lmin = dparam[7];
double a1=0.0, a2=0.0;
double * x_k =0;
double * w_k =0;
if (isVariable)
{
x_k = (double *)malloc(n * sizeof(double));
w_k = (double *)malloc(n * sizeof(double));
}
//isVariable=0;
if (!isVariable)
{
/* double minusrho = -1.0*rho; */
while ((iter < itermax) && (hasNotConverged > 0))
{
++iter;
/* xtmp <- x */
cblas_dcopy(n , x , 1 , xtmp, 1);
/* wtmp <- F(xtmp) */
problem->F(problem, n, xtmp,wtmp);
/* xtmp <- xtmp - F(xtmp) */
cblas_daxpy(n, -1.0, wtmp , 1, xtmp , 1) ;
/* wtmp <- ProjectionOnX(xtmp) */
problem->ProjectionOnX(problem,xtmp,wtmp);
/* x <- x - wtmp */
cblas_daxpy(n, -1.0, wtmp , 1, x , 1) ;
/* x <- ProjectionOnX(x) */
cblas_dcopy(n , xtmp , 1 , x, 1);
problem->ProjectionOnX(problem,xtmp,x);
/* problem->F(problem,x,w); */
/* cblas_daxpy(n, -1.0, w , 1, x , 1) ; */
/* cblas_dcopy(n , x , 1 , xtmp, 1); */
/* problem->ProjectionOnX(problem,xtmp,x); */
/* **** Criterium convergence **** */
if (options->iparam[SICONOS_VI_ERROR_EVALUATION] == SICONOS_VI_ERROR_EVALUATION_FULL )
{
variationalInequality_computeError(problem, x , w, tolerance, options, &error);
}
else if (options->iparam[SICONOS_VI_ERROR_EVALUATION] == SICONOS_VI_ERROR_EVALUATION_LIGHT )
{
cblas_dcopy(n, xtmp, 1,x , 1) ;
cblas_daxpy(n, -1.0, x_k , 1, xtmp , 1) ;
light_error_sum = cblas_dnrm2(n,xtmp,1);
double norm_x= cblas_dnrm2(n,x,1);
if (fabs(norm_x) > DBL_EPSILON)
light_error_sum /= norm_x;
error=light_error_sum;
}
if (options->callback)
{
options->callback->collectStatsIteration(options->callback->env, n,
x, w,
error, NULL);
}
if (verbose > 0)
{
printf("----------------------------------- VI - Extra Gradient (EG) - Iteration %i rho = %14.7e \tError = %14.7e\n", iter, rho, error);
}
if (error < tolerance) hasNotConverged = 0;
*info = hasNotConverged;
}
}
if (isVariable)
{
if (iparam[1]==0)/* Armijo rule with Khotbotov ratio (default) */
{
while ((iter < itermax) && (hasNotConverged > 0))
{
++iter;
/* Store the error */
error_k = error;
/* x_k <-- x store the x at the beginning of the iteration */
cblas_dcopy(n , x , 1 , x_k, 1);
problem->F(problem, n, x, w_k);
ls_iter = 0 ;
success =0;
rho_k=rho / tau;
while (!success && (ls_iter < ls_itermax))
{
/* if (iparam[3] && ls_iter !=0) rho_k = rho_k * tau * min(1.0,a2/(rho_k*a1)); */
/* else */ rho_k = rho_k * tau ;
/* x <- x_k for the std approach*/
if (iparam[2]==0) cblas_dcopy(n, x_k, 1, x , 1) ;
/* x <- x - rho_k* w_k */
cblas_daxpy(n, -rho_k, w_k , 1, x , 1) ;
/* xtmp <- ProjectionOnX(x) */
problem->ProjectionOnX(problem,x,xtmp);
problem->F(problem,n,xtmp,w);
DEBUG_EXPR_WE( for (int i =0; i< 5 ; i++) { printf("xtmp[%i]=%12.8e\t",i,xtmp[i]);
printf("w[%i]=F[%i]=%12.8e\n",i,i,w[i]);});
/* velocitytmp <- velocity */
/* cblas_dcopy(n, w, 1, wtmp , 1) ; */
/* velocity <- velocity - velocity_k */
cblas_daxpy(n, -1.0, w_k , 1, w , 1) ;
/* a1 = ||w - w_k|| */
a1 = cblas_dnrm2(n, w, 1);
DEBUG_PRINTF("a1 = %12.8e\n", a1);
/* xtmp <- x */
cblas_dcopy(n, xtmp, 1,x , 1) ;
/* xtmp <- x - x_k */
cblas_daxpy(n, -1.0, x_k , 1, xtmp , 1) ;
/* a2 = || x - x_k || */
a2 = cblas_dnrm2(n, xtmp, 1) ;
DEBUG_PRINTF("a2 = %12.8e\n", a2);
DEBUG_PRINTF("test rho_k*a1 < L * a2 = %e < %e\n", rho_k*a1 , L * a2 ) ;
success = (rho_k*a1 < L * a2)?1:0;
/* printf("rho_k = %12.8e\t", rho_k); */
/* printf("a1 = %12.8e\t", a1); */
/* printf("a2 = %12.8e\t", a2); */
/* printf("norm x = %12.8e\t",cblas_dnrm2(n, x, 1) ); */
/* printf("success = %i\n", success); */
ls_iter++;
}
/* velocitytmp <- q */
/* cblas_dcopy(n , q , 1 , velocitytmp, 1); */
/* prodNumericsMatrix(n, n, alpha, M, reaction, beta, velocitytmp); */
problem->F(problem, n, x,wtmp);
/* x <- x - rho_k* wtmp */
cblas_daxpy(n, -rho_k, wtmp , 1, x , 1) ;
/* wtmp <- ProjectionOnX(xtmp) */
cblas_dcopy(n , x , 1 , xtmp, 1);
problem->ProjectionOnX(problem,xtmp,x);
DEBUG_EXPR_WE( for (int i =0; i< 5 ; i++)
{
printf("x[%i]=%12.8e\t",i,x[i]); printf("w[%i]=F[%i]=%12.8e\n",i,i,w[i]);
}
);
/* **** Criterium convergence **** */
if (options->iparam[SICONOS_VI_ERROR_EVALUATION] == SICONOS_VI_ERROR_EVALUATION_FULL )
{
variationalInequality_computeError(problem, x , w, tolerance, options, &error);
}
else if (options->iparam[SICONOS_VI_ERROR_EVALUATION] == SICONOS_VI_ERROR_EVALUATION_LIGHT )
{
cblas_dcopy(n, xtmp, 1,x , 1) ;
cblas_daxpy(n, -1.0, x_k , 1, xtmp , 1) ;
light_error_sum = cblas_dnrm2(n,xtmp,1);
double norm_x= cblas_dnrm2(n,x,1);
if (fabs(norm_x) > DBL_EPSILON)
light_error_sum /= norm_x;
error=light_error_sum;
}
DEBUG_PRINTF("error = %12.8e\t error_k = %12.8e\n",error,error_k);
/*Update rho*/
if ((rho_k*a1 < Lmin * a2) && (error < error_k))
{
rho =rho_k*tauinv;
}
else
rho =rho_k;
if (verbose > 0)
{
printf("----------------------------------- VI - Extra Gradient (EG) - Iteration %i rho = %14.7e \tError = %14.7e\n", iter, rho, error);
}
if (error < tolerance) hasNotConverged = 0;
*info = hasNotConverged;
}
}// end iparam[1]==0
/* Linesearch */
int linesearch2_Armijo(int n, double *z, double psi_k, double descentCondition)
{
/* IN :
psi_k (merit function for current iteration)
jacobian_psi_k (jacobian of the merit function)
dk: descent direction
OUT: tk, z
*/
double m1 = 0.1;
double tk = 1;
double tkl, tkr, tkaux;
int incx = 1, incy = 1;
double merit, merit_k;
double tmin = 1e-14;
double qp_tk;
/* cblas_dcopy(sN, z, incx,sz2,incx);*/
/* z1 = z0 + dir */
/* cblas_daxpy(n , 1.0 , sdir_descent , incx , z , incy );*/
tk = 3.25;
while (tk > tmin)
{
/* Computes merit function = 1/2*norm(phi(z_{k+1}))^2 */
cblas_dcopy(sN, z, incx, sz2, incx);
cblas_daxpy(n , tk , sdir_descent , incx , sz2 , incy);
(*sFphi)(n, sz2, sphi_z, 0);
merit = cblas_dnrm2(n, sphi_z , incx);
merit = 0.5 * merit * merit;
merit_k = psi_k + m1 * tk * descentCondition;
if (merit < merit_k)
{
tkl = 0;
tkr = tk;
/*calcul merit'(tk)*/
(*sFjacobianPhi)(sN, sz2, sjacobianPhi_z, 1);
/* Computes the jacobian of the merit function, jacobian_psi = transpose(jacobianPhiMatrix).phiVector */
cblas_dgemv(CblasColMajor,CblasTrans, sN, sN, 1.0, sjacobianPhi_z, sN, sphi_z, incx, 0.0, sgrad_psi_zaux, incx);
qp_tk = cblas_ddot(sN, sgrad_psi_zaux, 1, sdir_descent, 1);
if (qp_tk > 0)
{
while (fabs(tkl - tkr) > tmin)
{
tkaux = 0.5 * (tkl + tkr);
cblas_dcopy(sN, z, incx, sz2, incx);
cblas_daxpy(n , tkaux , sdir_descent , incx , sz2 , incy);
/*calcul merit'(tk)*/
(*sFphi)(n, sz2, sphi_z, 0);
(*sFjacobianPhi)(sN, sz2, sjacobianPhi_z, 1);
/* Computes the jacobian of the merit function, jacobian_psi = transpose(jacobianPhiMatrix).phiVector */
cblas_dgemv(CblasColMajor,CblasTrans, sN, sN, 1.0, sjacobianPhi_z, sN, sphi_z, incx, 0.0, sgrad_psi_zaux, incx);
qp_tk = cblas_ddot(sN, sgrad_psi_zaux, 1, sdir_descent, 1);
if (qp_tk > 0)
{
tkr = tkaux;
}
else
{
tkl = tkaux;
}
}
}
/* printf("merit = %e, merit_k=%e,tk= %e,tkaux=%e \n",merit,merit_k,tk,tkaux);*/
cblas_dcopy(sN, sz2, incx, z, incx);
break;
}
tk = tk * 0.5;
}
if (tk <= tmin)
{
cblas_dcopy(sN, sz2, incx, z, incx);
printf("NonSmoothNewton::linesearch2_Armijo warning, resulting tk=%e < tmin, linesearch stopped.\n", tk);
return 0;
}
return 1;
}
double search_Armijo_standalone(int n, double* theta, double preRHS, search_data* ls_data)
{
assert(ls_data->alpha0 > 0.0);
assert(ls_data->alpha0 > ls_data->alpha_min);
double alpha = ls_data->alpha0;
double theta_iter = *theta, theta_ref = *theta;
double* z = ls_data->z;
double* zc = ls_data->zc;
double* F = ls_data->F;
double* F_merit = ls_data->F_merit;
double* desc_dir = ls_data->desc_dir;
void* data = ls_data->data;
bool arcsearch = ls_data->searchtype == ARCSEARCH;
void* set = ls_data->set;
double RHS;
armijo_extra_params* aep = (armijo_extra_params*) ls_data->extra_params;
assert(aep);
preRHS *= aep->gamma;
while (alpha >= ls_data->alpha_min)
{
DEBUG_PRINTF("search_Armijo :: alpha %g, ls_data->alpha_min %g \n", alpha, ls_data->alpha_min);
// desc_dir contains the direction d
cblas_dcopy(n, z, 1, zc, 1);
cblas_daxpy(n, alpha, desc_dir, 1, zc, 1); // z + alpha*d --> z
if (arcsearch)
{
project_on_set(n, zc, set);
/* we use F as a work vector here */
cblas_dcopy(n, z, 1, F, 1);
cblas_daxpy(n, -1.0, zc, 1, F, 1); /* F = z(0) - z(alpha) */
/* warning desc_dir = -JacMerit !*/
double dotprod = cblas_ddot(n, desc_dir, 1, F, 1);
if (dotprod > 0.0)
RHS = ls_data->sigma*dotprod;
else
RHS = -alpha*ls_data->sigma*theta_ref;
}
else
{
RHS = alpha*preRHS;
}
// compute new F_merit
ls_data->compute_F(data, zc, F);
ls_data->compute_F_merit(data, zc, F, F_merit);
DEBUG_PRINT("z ");
DEBUG_EXPR_WE(for (unsigned int i = 0; i < n; ++i)
{ DEBUG_PRINTF("% 2.2e ", zc[i]) }
DEBUG_PRINT("\n"));
DEBUG_PRINT("F ");
DEBUG_EXPR_WE(for (unsigned int i = 0; i < n; ++i)
{ DEBUG_PRINTF("% 2.2e ", F[i]) }
DEBUG_PRINT("\n"));
DEBUG_PRINT("F_merit ");
DEBUG_EXPR_WE(for (unsigned int i = 0; i < n; ++i)
{ DEBUG_PRINTF("% 2.2e ", F_merit[i]) }
DEBUG_PRINT("\n"));
theta_iter = 0.5 * cblas_ddot(n, F_merit, 1, F_merit, 1);
DEBUG_PRINTF("search_Armijo :: alpha %g\n", alpha);
DEBUG_PRINTF("search_Armijo :: theta_iter %.*e ; theta_ref %.*e \n", DECIMAL_DIG, theta_iter, DECIMAL_DIG, theta_ref);
// acceptance test
if (theta_iter <= theta_ref + RHS)
{
if (verbose > 1)
printf("search_Armijo :: alpha %g\n", alpha);
break;
}
else
{
// alpha too large, decrease it
alpha /= 2.0;
}
}
*theta = theta_iter;
return alpha;
}
int nonSmoothNewtonNeigh(int n, double* z, NewtonFunctionPtr* phi, NewtonFunctionPtr* jacobianPhi, int* iparam, double* dparam)
{
int itermax = iparam[0]; // maximum number of iterations allowed
int iterMaxWithSameZ = itermax / 4;
int niter = 0; // current iteration number
double tolerance = dparam[0];
/* double coef; */
sFphi = phi;
sFjacobianPhi = jacobianPhi;
// verbose=1;
if (verbose > 0)
{
printf(" ============= Starting of Newton process =============\n");
printf(" - tolerance: %14.7e\n - maximum number of iterations: %i\n", tolerance, itermax);
}
int incx = 1;
/* int n2 = n*n; */
int infoDGESV;
/** merit function and its jacobian */
double psi_z;
/** The algorithm is alg 4.1 of the paper of Kanzow and Kleinmichel, "A new class of semismooth Newton-type methods
for nonlinear complementarity problems", in Computational Optimization and Applications, 11, 227-251 (1998).
We try to keep the same notations
*/
double rho = 1e-8;
double descentCondition, criterion, norm_jacobian_psi_z, normPhi_z;
double p = 2.1;
double terminationCriterion = 1;
double norm;
int findNewZ, i, j, NbLookingForANewZ;
/* int naux=0; */
double aux = 0;
/* double aux1=0; */
int ii;
int resls = 1;
/* char c; */
/* double * oldz; */
/* oldz=(double*)malloc(n*sizeof(double));*/
NbLookingForANewZ = 0;
/** Iterations ... */
while ((niter < itermax) && (terminationCriterion > tolerance))
{
scmp++;
++niter;
/** Computes phi and its jacobian */
if (sZsol)
{
for (ii = 0; ii < sN; ii++)
szzaux[ii] = sZsol[ii] - z[ii];
printf("dist zzsol %.32e.\n", cblas_dnrm2(n, szzaux, 1));
}
(*sFphi)(n, z, sphi_z, 0);
(*sFjacobianPhi)(n, z, sjacobianPhi_z, 1);
/* Computes the jacobian of the merit function, jacobian_psi = transpose(jacobianPhiMatrix).phiVector */
cblas_dgemv(CblasColMajor,CblasTrans, n, n, 1.0, sjacobianPhi_z, n, sphi_z, incx, 0.0, sgrad_psi_z, incx);
norm_jacobian_psi_z = cblas_dnrm2(n, sgrad_psi_z, 1);
/* Computes norm2(phi) */
normPhi_z = cblas_dnrm2(n, sphi_z, 1);
/* Computes merit function */
psi_z = 0.5 * normPhi_z * normPhi_z;
if (normPhi_z < tolerance)
{
/*it is the solution*/
terminationCriterion = tolerance / 2.0;
break;
}
if (verbose > 0)
{
printf("Non Smooth Newton, iteration number %i, norm grad psi= %14.7e , psi = %14.7e, normPhi = %e .\n", niter, norm_jacobian_psi_z, psi_z, normPhi_z);
printf(" -----------------------------------------------------------------------\n");
}
NbLookingForANewZ++;
if (niter > 2)
{
if (10 * norm_jacobian_psi_z < tolerance || !resls || NbLookingForANewZ > iterMaxWithSameZ)
{
NbLookingForANewZ = 0;
resls = 1;
/* if (NbLookingForANewZ % 10 ==1 && 0){
printf("Try NonMonotomnelineSearch\n");
cblas_dcopy(n,sgrad_psi_z,1,sdir_descent,1);
cblas_dscal( n , -1.0 ,sdir_descent,incx);
NonMonotomnelineSearch( z, phi, 10);
continue;
}
*/
/* FOR DEBUG ONLY*/
if (sZsol)
{
printf("begin plot prev dir\n");
plotMerit(z, 0, 0);
printf("end\n");
/* gets(&c);*/
(*sFphi)(n, sZsol, szaux, 0);
printf("value psi(zsol)=%e\n", cblas_dnrm2(n, szaux, 1));
cblas_dcopy(n, sZsol, incx, szaux, incx);
cblas_daxpy(n , -1 , z , 1 , szaux , 1);
printf("dist to sol %e \n", cblas_dnrm2(n, szaux, 1));
for (ii = 0; ii < n; ii++)
sdir_descent[ii] = sZsol[ii] - z[ii];
aux = norm;
norm = 1;
printf("begin plot zzsol dir\n");
plotMerit(z, 0, 0);
printf("end\n");
/* gets(&c);*/
norm = aux;
}
printf("looking for a new Z...\n");
/*may be a local minimal*/
/*find a gradiant going out of this cul-de-sac.*/
norm = n / 2;
findNewZ = 0;
for (j = 0; j < 20; j++)
{
for (i = 0; i < n; i++)
{
if (sZsol)
{
/* FOR DEBUG ONLY*/
(*sFphi)(n, sZsol, sphi_zaux, 0);
norm = cblas_dnrm2(n, sphi_zaux, 1);
printf("Norm of the sol %e.\n", norm);
for (ii = 0; ii < n; ii++)
sdir_descent[ii] = sZsol[ii] - z[ii];
norm = 1;
}
else
{
for (ii = 0; ii < n; ii++)
{
sdir_descent[ii] = 1.0 * rand();
}
cblas_dscal(n, 1 / cblas_dnrm2(n, sdir_descent, 1), sdir_descent, incx);
cblas_dscal(n, norm, sdir_descent, incx);
}
cblas_dcopy(n, z, incx, szaux, incx);
// cblas_dscal(n,0.0,zaux,incx);
/* zaux = z + dir */
cblas_daxpy(n , norm , sdir_descent , 1 , szaux , 1);
/* Computes the jacobian of the merit function, jacobian_psi_zaux = transpose(jacobianPhi_zaux).phi_zaux */
(*sFphi)(n, szaux, sphi_zaux, 0);
(*sFjacobianPhi)(n, szaux, sjacobianPhi_zaux, 1);
/* FOR DEBUG ONLY*/
if (sZsol)
{
aux = cblas_dnrm2(n, sphi_zaux, 1);
printf("Norm of the sol is now %e.\n", aux);
for (ii = 0; ii < n; ii++)
printf("zsol %e zaux %e \n", sZsol[ii], szaux[ii]);
}
cblas_dgemv(CblasColMajor, CblasTrans, n, n, 1.0, sjacobianPhi_zaux, n, sphi_zaux, incx, 0.0, sgrad_psi_zaux, incx);
cblas_dcopy(n, szaux, 1, szzaux, 1);
cblas_daxpy(n , -1 , z , incx , szzaux , incx);
/*zzaux must be a descente direction.*/
/*ie jacobian_psi_zaux.zzaux <0
printf("jacobian_psi_zaux : \n");*/
/*cblas_dcopy(n,sdir,incx,sdir_descent,incx);
plotMerit(z, phi);*/
aux = cblas_ddot(n, sgrad_psi_zaux, 1, szzaux, 1);
/* aux1 = cblas_dnrm2(n,szzaux,1);
aux1 = cblas_dnrm2(n,sgrad_psi_zaux,1);*/
aux = aux / (cblas_dnrm2(n, szzaux, 1) * cblas_dnrm2(n, sgrad_psi_zaux, 1));
/* printf("aux: %e\n",aux);*/
if (aux < 0.1 * (j + 1))
{
//zaux is the new point.
findNewZ = 1;
cblas_dcopy(n, szaux, incx, z, incx);
break;
}
}
if (findNewZ)
break;
if (j == 10)
{
norm = n / 2;
}
else if (j > 10)
norm = -2 * norm;
else
norm = -norm / 2.0;
}
if (! findNewZ)
{
printf("failed to find a new z\n");
/* exit(1);*/
continue;
}
else
continue;
}
}
/* Stops if the termination criterion is satisfied */
terminationCriterion = norm_jacobian_psi_z;
/* if(terminationCriterion < tolerance){
break;
}*/
/* Search direction calculation
Find a solution dk of jacobianPhiMatrix.d = -phiVector.
dk is saved in phiVector.
*/
cblas_dscal(n , -1.0 , sphi_z, incx);
DGESV(n, 1, sjacobianPhi_z, n, sipiv, sphi_z, n, &infoDGESV);
if (infoDGESV)
{
printf("DGEV error %d.\n", infoDGESV);
}
cblas_dcopy(n, sphi_z, 1, sdir_descent, 1);
criterion = cblas_dnrm2(n, sdir_descent, 1);
/* printf("norm dir descent %e\n",criterion);*/
/*printf("begin plot descent dir\n");
plotMerit(z, phi);
printf("end\n");
gets(&c);*/
/*printf("begin plot zzsol dir\n");
plotMeritToZsol(z,phi);
printf("end\n");
gets(&c);*/
/*
norm = cblas_dnrm2(n,sdir_descent,1);
printf("norm desc %e \n",norm);
cblas_dscal( n , 1/norm , sdir_descent, 1);
*/
/* descentCondition = jacobian_psi.dk */
descentCondition = cblas_ddot(n, sgrad_psi_z, 1, sdir_descent, 1);
/* Criterion to be satisfied: error < -rho*norm(dk)^p */
criterion = -rho * pow(criterion, p);
/* printf("ddddddd %d\n",scmp);
if (scmp>100){
displayMat(sjacobianPhi_z,n,n,n);
exit(1);
}*/
// if ((infoDGESV != 0 || descentCondition > criterion) && 0)
// {
// printf("no a desc dir, get grad psy\n");
/* dk = - jacobian_psi (remind that dk is saved in phi_z) */
// cblas_dcopy(n, sgrad_psi_z, 1, sdir_descent, 1);
// cblas_dscal(n , -1.0 , sdir_descent, incx);
/*DEBUG ONLY*/
/*printf("begin plot new descent dir\n");
plotMerit(z);
printf("end\n");
gets(&c);*/
// }
/* coef=fabs(norm_jacobian_psi_z*norm_jacobian_psi_z/descentCondition);
if (coef <1){
cblas_dscal(n,coef,sdir_descent,incx);
printf("coef %e norm dir descent is now %e\n",coef,cblas_dnrm2(n,sdir_descent,1));
}*/
/* Step-3 Line search: computes z_k+1 */
/*linesearch_Armijo(n,z,sdir_descent,psi_z, descentCondition, phi);*/
/* if (niter == 10){
printf("begin plot new descent dir\n");
plotMerit(z);
printf("end\n");
gets(&c);
}*/
/* memcpy(oldz,z,n*sizeof(double));*/
resls = linesearch2_Armijo(n, z, psi_z, descentCondition);
if (!resls && niter > 1)
{
/* displayMat(sjacobianPhi_z,n,n,n);
printf("begin plot new descent dir\n");
plotMerit(oldz,psi_z, descentCondition);
printf("end\n");
gets(&c);*/
}
/* lineSearch_Wolfe(z, descentCondition, phi,jacobianPhi);*/
/* if (niter>3){
printf("angle between prev dir %e.\n",acos(cblas_ddot(n, sdir_descent, 1, sPrevDirDescent, 1)/(cblas_dnrm2(n,sdir_descent,1)*cblas_dnrm2(n,sPrevDirDescent,1))));
}*/
cblas_dcopy(n, sdir_descent, 1, sPrevDirDescent, 1);
/* for (j=20;j<32;j++){
if (z[j]<0)
z[j]=0;
}*/
/* if( 1 || verbose>0)
{
printf("Non Smooth Newton, iteration number %i, error grad equal to %14.7e , psi value is %14.7e .\n",niter, terminationCriterion,psi_z);
printf(" -----------------------------------------------------------------------\n");
}*/
}
/* Total number of iterations */
iparam[1] = niter;
/* Final error */
dparam[1] = terminationCriterion;
/** Free memory*/
if (verbose > 0)
{
if (dparam[1] > tolerance)
printf("Non Smooth Newton warning: no convergence after %i iterations\n" , niter);
else
printf("Non Smooth Newton: convergence after %i iterations\n" , niter);
printf(" The residue is : %e \n", dparam[1]);
}
/* free(oldz);*/
if (dparam[1] > tolerance)
return 1;
else return 0;
}
void My_daxpy(gsl_vector* y, const gsl_vector* x, double alpha)
{
cblas_daxpy(y->size, alpha, x->data, x->stride, y->data, y->stride);
}
/* Ref: Weiss, Algorithm 12 BiCGSTAB
* INPUT
* n : dimension of the problem
* b [n] : r-h-s vector
* atimes (int n, static double *x, double *b, void *param) :
* calc matrix-vector product A.x = b.
* atimes_param : parameters for atimes().
* it : struct iter. following entries are used
* it->max = kend : max of iteration
* it->eps = eps : criteria for |r^2|/|b^2|
* OUTPUT
* returned value : 0 == success, otherwise (-1) == failed
* x [n] : solution
* it->niter : # of iteration
* it->res2 : |r^2| / |b^2|
*/
int
bicgstab (int n, const double *b, double *x,
void (*atimes) (int, const double *, double *, void *),
void *atimes_param,
struct iter *it)
{
#ifndef HAVE_CBLAS_H
# ifdef HAVE_BLAS_H
/* use Fortran BLAS routines */
int i_1 = 1;
double d_1 = 1.0;
double d_m1 = -1.0;
# endif // !HAVE_BLAS_H
#endif // !HAVE_CBLAS_H
int ret = -1;
double eps2 = it->eps * it->eps;
int itmax = it->max;
double *r = (double *)malloc (sizeof (double) * n);
double *rs = (double *)malloc (sizeof (double) * n);
double *p = (double *)malloc (sizeof (double) * n);
double *ap = (double *)malloc (sizeof (double) * n);
double *s = (double *)malloc (sizeof (double) * n);
double *t = (double *)malloc (sizeof (double) * n);
CHECK_MALLOC (r, "bicgstab");
CHECK_MALLOC (rs, "bicgstab");
CHECK_MALLOC (p, "bicgstab");
CHECK_MALLOC (ap, "bicgstab");
CHECK_MALLOC (s, "bicgstab");
CHECK_MALLOC (t, "bicgstab");
double rsap; // (r*, A.p)
double st;
double t2;
double rho, rho1;
double delta;
double gamma;
double beta;
double res2 = 0.0;
#ifdef HAVE_CBLAS_H
/**
* ATLAS version
*/
double b2 = cblas_ddot (n, b, 1, b, 1); // (b,b)
eps2 *= b2;
atimes (n, x, r, atimes_param); // r = A.x ...
cblas_daxpy (n, -1.0, b, 1, r, 1); // - b
cblas_dcopy (n, r, 1, rs, 1); // r* = r
cblas_dcopy (n, r, 1, p, 1); // p = r
rho = cblas_ddot (n, rs, 1, r, 1); // rho = (r*, r)
int i;
for (i = 0; i < itmax; i ++)
{
atimes (n, p, ap, atimes_param); // ap = A.p
rsap = cblas_ddot (n, rs, 1, ap, 1); // rsap = (r*, A.p)
delta = - rho / rsap;
cblas_dcopy (n, r, 1, s, 1); // s = r ...
cblas_daxpy (n, delta, ap, 1, s, 1); // + delta A.p
atimes (n, s, t, atimes_param); // t = A.s
st = cblas_ddot (n, s, 1, t, 1); // st = (s, t)
t2 = cblas_ddot (n, t, 1, t, 1); // t2 = (t, t)
gamma = - st / t2;
cblas_dcopy (n, s, 1, r, 1); // r = s ...
cblas_daxpy (n, gamma, t, 1, r, 1); // + gamma t
cblas_daxpy (n, delta, p, 1, x, 1); // x = x + delta p...
cblas_daxpy (n, gamma, s, 1, x, 1); // + gamma s
res2 = cblas_ddot (n, r, 1, r, 1);
if (it->debug == 2)
{
fprintf (it->out,
"libiter-bicgstab(cblas) %d %e\n",
i, res2 / b2);
}
if (res2 <= eps2)
{
ret = 0; // success
break;
}
rho1 = cblas_ddot (n, rs, 1, r, 1); // rho = (r*, r)
beta = rho1 / rho * delta / gamma;
rho = rho1;
cblas_daxpy (n, gamma, ap, 1, p, 1); // p = p + gamma A.p
cblas_dscal (n, beta, p, 1); // p = beta (p + gamma A.p)
cblas_daxpy (n, 1.0, r, 1, p, 1); // p = r + beta(p + gamma A.p)
}
#else // !HAVE_CBLAS_H
# ifdef HAVE_BLAS_H
/**
* BLAS version
*/
double b2 = ddot_ (&n, b, &i_1, b, &i_1); // (b,b)
eps2 *= b2;
atimes (n, x, r, atimes_param); // r = A.x ...
daxpy_ (&n, &d_m1, b, &i_1, r, &i_1); // - b
dcopy_ (&n, r, &i_1, rs, &i_1); // r* = r
dcopy_ (&n, r, &i_1, p, &i_1); // p = r
rho = ddot_ (&n, rs, &i_1, r, &i_1); // rho = (r*, r)
int i;
for (i = 0; i < itmax; i ++)
{
atimes (n, p, ap, atimes_param); // ap = A.p
rsap = ddot_ (&n, rs, &i_1, ap, &i_1); // rsap = (r*, A.p)
delta = - rho / rsap;
dcopy_ (&n, r, &i_1, s, &i_1); // s = r ...
daxpy_ (&n, &delta, ap, &i_1, s, &i_1); // + delta A.p
atimes (n, s, t, atimes_param); // t = A.s
st = ddot_ (&n, s, &i_1, t, &i_1); // st = (s, t)
t2 = ddot_ (&n, t, &i_1, t, &i_1); // t2 = (t, t)
gamma = - st / t2;
dcopy_ (&n, s, &i_1, r, &i_1); // r = s ...
daxpy_ (&n, &gamma, t, &i_1, r, &i_1); // + gamma t
daxpy_ (&n, &delta, p, &i_1, x, &i_1); // x = x + delta p...
daxpy_ (&n, &gamma, s, &i_1, x, &i_1); // + gamma s
res2 = ddot_ (&n, r, &i_1, r, &i_1);
if (it->debug == 2)
{
fprintf (it->out,
"libiter-bicgstab(blas) %d %e\n",
i, res2 / b2);
}
if (res2 <= eps2)
{
ret = 0; // success
break;
}
if (res2 > 1.0e20)
{
// already too big residual
break;
}
rho1 = ddot_ (&n, rs, &i_1, r, &i_1); // rho = (r*, r)
beta = rho1 / rho * delta / gamma;
rho = rho1;
daxpy_ (&n, &gamma, ap, &i_1, p, &i_1); // p = p + gamma A.p
dscal_ (&n, &beta, p, &i_1); // p = beta (p + gamma A.p)
daxpy_ (&n, &d_1, r, &i_1, p, &i_1); // p = r + beta(p + gamma A.p)
}
# else // !HAVE_BLAS_H
/**
* local BLAS version
*/
double b2 = my_ddot (n, b, 1, b, 1); // (b,b)
eps2 *= b2;
atimes (n, x, r, atimes_param); // r = A.x ...
my_daxpy (n, -1.0, b, 1, r, 1); // - b
my_dcopy (n, r, 1, rs, 1); // r* = r
my_dcopy (n, r, 1, p, 1); // p = r
rho = my_ddot (n, rs, 1, r, 1); // rho = (r*, r)
int i;
for (i = 0; i < itmax; i ++)
{
atimes (n, p, ap, atimes_param); // ap = A.p
rsap = my_ddot (n, rs, 1, ap, 1); // rsap = (r*, A.p)
delta = - rho / rsap;
my_dcopy (n, r, 1, s, 1); // s = r ...
my_daxpy (n, delta, ap, 1, s, 1); // + delta A.p
atimes (n, s, t, atimes_param); // t = A.s
st = my_ddot (n, s, 1, t, 1); // st = (s, t)
t2 = my_ddot (n, t, 1, t, 1); // t2 = (t, t)
gamma = - st / t2;
my_dcopy (n, s, 1, r, 1); // r = s ...
my_daxpy (n, gamma, t, 1, r, 1); // + gamma t
my_daxpy (n, delta, p, 1, x, 1); // x = x + delta p...
my_daxpy (n, gamma, s, 1, x, 1); // + gamma s
res2 = my_ddot (n, r, 1, r, 1);
if (it->debug == 2)
{
fprintf (it->out,
"libiter-bicgstab(myblas) %d %e\n",
i, res2 / b2);
}
if (res2 <= eps2)
{
ret = 0; // success
break;
}
rho1 = my_ddot (n, rs, 1, r, 1); // rho = (r*, r)
beta = rho1 / rho * delta / gamma;
rho = rho1;
my_daxpy (n, gamma, ap, 1, p, 1); // p = p + gamma A.p
my_dscal (n, beta, p, 1); // p = beta (p + gamma A.p)
my_daxpy (n, 1.0, r, 1, p, 1); // p = r + beta(p + gamma A.p)
}
# endif // !HAVE_BLAS_H
#endif // !HAVE_CBLAS_H
free (r);
free (rs);
free (p);
free (ap);
free (s);
free (t);
if (it->debug == 1)
{
fprintf (it->out, "libiter-bicgstab %d %e\n", i, res2 / b2);
}
it->niter = i;
it->res2 = res2 / b2;
return (ret);
}
void variationalInequality_FixedPointProjection(VariationalInequality* problem, double *x, double *w, int* info, SolverOptions* options)
{
/* /\* int and double parameters *\/ */
int* iparam = options->iparam;
double* dparam = options->dparam;
/* Number of contacts */
int n = problem->size;
/* Maximum number of iterations */
int itermax = iparam[0];
/* Tolerance */
double tolerance = dparam[0];
/***** Fixed point iterations *****/
int iter = 0; /* Current iteration number */
double error = 1.; /* Current error */
int hasNotConverged = 1;
double * xtmp = (double *)malloc(n * sizeof(double));
double * wtmp = (double *)malloc(n * sizeof(double));
double rho = 0.0, rho_k =0.0;
int isVariable = 0;
if (dparam[3] > 0.0)
{
rho = dparam[3];
if (verbose > 0)
{
printf("----------------------------------- VI - Fixed Point Projection (FPP) - Fixed stepsize with rho = %14.7e \n", rho);
}
}
else
{
/* Variable step in iterations*/
isVariable = 1;
rho = -dparam[3];
if (verbose > 0)
{
printf("----------------------------------- VI - Fixed Point Projection (FPP) - Variable stepsize with starting rho = %14.7e \n", rho);
}
}
/* Variable for Line_search */
int success =0;
double error_k;
int ls_iter = 0;
int ls_itermax = 10;
double tau=dparam[4], tauinv=dparam[5], L= dparam[6], Lmin = dparam[7];
DEBUG_PRINTF("tau=%g, tauinv=%g, L= %g, Lmin = %g",dparam[4], dparam[5], dparam[6], dparam[7] ) ;
double a1=0.0, a2=0.0;
double * x_k = NULL;
double * w_k = NULL;
if (isVariable)
{
x_k = (double *)malloc(n * sizeof(double));
w_k = (double *)malloc(n * sizeof(double));
}
//isVariable=0;
if (!isVariable)
{
/* double minusrho = -1.0*rho; */
while ((iter < itermax) && (hasNotConverged > 0))
{
++iter;
problem->F(problem,n,x,w);
cblas_daxpy(n, -1.0, w , 1, x , 1) ;
cblas_dcopy(n , x , 1 , xtmp, 1);
problem->ProjectionOnX(problem,xtmp,x);
/* **** Criterium convergence **** */
variationalInequality_computeError(problem, x , w, tolerance, options, &error);
if (options->callback)
{
options->callback->collectStatsIteration(options->callback->env, n,
x, w,
error, NULL);
}
if (verbose > 0)
{
printf("----------------------------------- VI - Fixed Point Projection (FPP) - Iteration %i rho = %14.7e \tError = %14.7e\n", iter, rho, error);
}
if (error < tolerance) hasNotConverged = 0;
*info = hasNotConverged;
}
}
else if (isVariable)
{
if (iparam[1]==0) /* Armijo rule with Khotbotov ratio (default) */
{
DEBUG_PRINT("Variable step size method with Armijo rule with Khotbotov ratio (default) \n");
while ((iter < itermax) && (hasNotConverged > 0))
{
++iter;
/* Store the error */
error_k = error;
/* x_k <-- x store the x at the beginning of the iteration */
cblas_dcopy(n , x , 1 , x_k, 1);
/* compute w_k =F(x_k) */
problem->F(problem,n,x,w_k);
ls_iter = 0 ;
success =0;
rho_k=rho / tau;
while (!success && (ls_iter < ls_itermax))
{
/* if (iparam[3] && ls_iter !=0) rho_k = rho_k * tau * min(1.0,a2/(rho_k*a1)); */
/* else */ rho_k = rho_k * tau ;
/* x <- x_k for the std approach*/
if (iparam[2]==0) cblas_dcopy(n, x_k, 1, x , 1) ;
/* x <- x - rho_k* w_k */
cblas_daxpy(n, -rho_k, w_k , 1, x , 1) ;
/* xtmp <- ProjectionOnX(x) */
problem->ProjectionOnX(problem,x,xtmp);
problem->F(problem,n,xtmp,w);
DEBUG_EXPR_WE( for (int i =0; i< 5 ; i++) { printf("xtmp[%i]=%12.8e\t",i,xtmp[i]);
printf("w[%i]=F[%i]=%12.8e\n",i,i,w[i]);});
/* velocitytmp <- velocity */
/* cblas_dcopy(n, w, 1, wtmp , 1) ; */
/* velocity <- velocity - velocity_k */
cblas_daxpy(n, -1.0, w_k , 1, w , 1) ;
/* a1 = ||w - w_k|| */
a1 = cblas_dnrm2(n, w, 1);
DEBUG_PRINTF("a1 = %12.8e\n", a1);
/* xtmp <- x */
cblas_dcopy(n, xtmp, 1,x , 1) ;
/* xtmp <- x - x_k */
cblas_daxpy(n, -1.0, x_k , 1, xtmp , 1) ;
/* a2 = || x - x_k || */
a2 = cblas_dnrm2(n, xtmp, 1) ;
DEBUG_PRINTF("a2 = %12.8e\n", a2);
DEBUG_PRINTF("test rho_k*a1 < L * a2 = %e < %e\n", rho_k*a1 , L * a2 ) ;
success = (rho_k*a1 < L * a2)?1:0;
/* printf("rho_k = %12.8e\t", rho_k); */
/* printf("a1 = %12.8e\t", a1); */
/* printf("a2 = %12.8e\t", a2); */
/* printf("norm x = %12.8e\t",cblas_dnrm2(n, x, 1) ); */
/* printf("success = %i\n", success); */
ls_iter++;
}
/* problem->F(problem,x,w); */
DEBUG_EXPR_WE( for (int i =0; i< 5 ; i++) { printf("x[%i]=%12.8e\t",i,x[i]);
printf("w[%i]=F[%i]=%12.8e\n",i,i,w[i]);});
/* **** Criterium convergence **** */
variationalInequality_computeError(problem, x , w, tolerance, options, &error);
DEBUG_EXPR_WE(
if ((error < error_k))
{
printf("(error < error_k) is satisfied\n");
};
);
void lanczos(double *F, double *Es, double *L, int n_eigs, int n_patch,
int LANCZOS_ITR)
{
double *b;
double b_norm;
double *z;
double *alpha, *beta;
double *q;
int i;
double *eigvec; // eigenvectors
// generate random b with norm 1.
srand((unsigned int)time(NULL));
b = (double *)malloc(n_patch * sizeof(double));
for (i = 0; i < n_patch; i++)
b[i] = rand();
b_norm = norm2(b, n_patch);
for (i = 0; i < n_patch; i++)
b[i] /= b_norm;
alpha = (double *)malloc( (LANCZOS_ITR + 1) * sizeof(double) );
beta = (double *)malloc( (LANCZOS_ITR + 1) * sizeof(double) );
beta[0] = 0.0; // beta_0 <- 0
z = (double *)malloc( n_patch * sizeof(double));
q = (double *)malloc( n_patch * (LANCZOS_ITR + 2) * sizeof(double) );
memset(&q[0], 0, n_patch * sizeof(double)); // q_0 <- 0
memcpy(&q[n_patch], b, n_patch * sizeof(double)); // q_1 <- b
for (i = 1; i <= LANCZOS_ITR; i++) {
// z = L * Q(:, i)
cblas_dsymv(CblasColMajor, CblasLower, n_patch, 1.0, L,
n_patch, &q[i * n_patch], 1, 0.0, z, 1);
// alpha(i) = Q(:, i)' * z;
alpha[i] = cblas_ddot(n_patch, &q[i * n_patch], 1, z, 1);
// z = z - alpha(i) * Q(:, i)
cblas_daxpy(n_patch, -alpha[i], &q[i * n_patch], 1, z, 1);
// z = z - beta(i - 1) * Q(:, i - 1);
cblas_daxpy(n_patch, -beta[i - 1], &q[(i - 1) * n_patch], 1, z, 1);
// beta(i) = norm(z, 2);
beta[i] = cblas_dnrm2(n_patch, z, 1);
// Q(:, i + 1) = z / beta(i);
divide_copy(&q[(i + 1) * n_patch], z, n_patch, beta[i]);
}
// compute approximate eigensystem
eigvec = (double *)malloc(LANCZOS_ITR * LANCZOS_ITR * sizeof(double));
LAPACKE_dstedc(LAPACK_COL_MAJOR, 'I', LANCZOS_ITR, &alpha[1], &beta[1],
eigvec, LANCZOS_ITR);
// copy specified number of eigenvalues
memcpy(Es, &alpha[1], n_eigs * sizeof(double));
// V = Q(:, 1:k) * U
cblas_dgemm(CblasColMajor, CblasNoTrans, CblasNoTrans, n_patch,
LANCZOS_ITR, LANCZOS_ITR, 1.0, &q[n_patch], n_patch, eigvec,
LANCZOS_ITR, 0.0, L, n_patch);
// copy the corresponding eigenvectors
memcpy(F, L, n_patch * n_eigs * sizeof(double));
free(b);
free(z);
free(alpha);
free(beta);
free(q);
free(eigvec);
}
void conjugate_gradient_sparse(cs *A, double *b, double* x, int n, double itol)
{
int i,j;
int iter;
double rho,rho1,alpha,beta,omega;
double r[n];
double z[n];
double q[n], temp_q[n];
double p[n], temp_p[n];
double res[n];
double precond[n]; //Preconditioner
memset(precond, 0, n*sizeof(double));
memset(r, 0, n*sizeof(double));
memset(z, 0, n*sizeof(double));
memset(q, 0, n*sizeof(double));
memset(temp_q, 0, n*sizeof(double));
memset(p, 0, n*sizeof(double));
memset(temp_p, 0, n*sizeof(double));
/* Preconditioner */
double max;
int pp;
for(j = 0; j < n; ++j){
for(pp = A->p[j], max = fabs(A->x[pp]); pp < A->p[j+1]; pp++)
if(fabs(A->x[pp]) > max) //vriskei to diagonio stoixeio
max = fabs(A->x[pp]);
precond[j] = 1/max;
}
cblas_dcopy (n, x, 1, res, 1);
//r=b-Ax
cblas_dcopy (n, b, 1, r, 1);
memset(p, 0, n*sizeof(double));
cs_gaxpy (A, x, p);
for(i=0;i<n;i++){
r[i]=r[i]-p[i];
}
double r_norm = cblas_dnrm2 (n, r, 1);
double b_norm = cblas_dnrm2 (n, b, 1);
if(!b_norm)
b_norm = 1;
iter = 0;
while( r_norm/b_norm > itol && iter < n )
{
iter++;
cblas_dcopy (n, r, 1, z, 1); //gia na min allaksei o r
for(i=0;i<n;i++){
z[i]=precond[i]*z[i];
}
rho = cblas_ddot (n, z, 1, r, 1);
if (fpclassify(fabs(rho)) == FP_ZERO){
printf("RHO aborting CG due to EPS...\n");
exit(42);
}
if (iter == 1){
cblas_dcopy (n, z, 1, p, 1);
}
else{
beta = rho/rho1;
//p = z + beta*p;
cblas_dscal (n, beta, p, 1); //rescale
cblas_daxpy (n, 1, z, 1, p, 1); //p = 1*z + p
}
rho1 = rho;
//q = Ap
memset(q, 0, n*sizeof(double));
cs_gaxpy (A, p, q);
omega = cblas_ddot (n, p, 1, q, 1);
if (fpclassify(fabs(omega)) == FP_ZERO){
printf("OMEGA aborting CG due to EPS...\n");
exit(42);
}
alpha = rho/omega;
//x = x + aplha*p;
cblas_dcopy (n, p, 1, temp_p, 1);
cblas_dscal (n, alpha, temp_p, 1);//rescale by alpha
cblas_daxpy (n, 1, temp_p, 1, res, 1);// sum x = 1*x + temp_p
//r = r - aplha*q;
cblas_dcopy (n, q, 1, temp_q, 1);
cblas_dscal (n, -alpha, temp_q, 1);//rescale by alpha
cblas_daxpy (n, 1, temp_q, 1, r, 1);// sum r = 1*r - temp_p
//next step
r_norm = cblas_dnrm2 (n, r, 1);
}
cblas_dcopy (n, res, 1, x, 1);
}
