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934 lines
22 KiB
C++
934 lines
22 KiB
C++
/*************************************************************************************
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Grid physics library, www.github.com/paboyle/Grid
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Source file: ./lib/algorithms/iterative/ImplicitlyRestartedLanczos.h
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Copyright (C) 2015
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Author: Peter Boyle <paboyle@ph.ed.ac.uk>
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Author: paboyle <paboyle@ph.ed.ac.uk>
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Author: Chulwoo Jung <chulwoo@bnl.gov>
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This program is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License along
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with this program; if not, write to the Free Software Foundation, Inc.,
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51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
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See the full license in the file "LICENSE" in the top level distribution directory
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*************************************************************************************/
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/* END LEGAL */
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#ifndef GRID_LANC_H
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#define GRID_LANC_H
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#include <string.h> //memset
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#ifdef USE_LAPACK
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#ifdef USE_MKL
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#include<mkl_lapack.h>
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#else
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void LAPACK_dstegr (char *jobz, char *range, int *n, double *d, double *e,
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double *vl, double *vu, int *il, int *iu, double *abstol,
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int *m, double *w, double *z, int *ldz, int *isuppz,
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double *work, int *lwork, int *iwork, int *liwork,
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int *info);
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//#include <lapacke/lapacke.h>
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#endif
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#endif
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#include <Grid/algorithms/densematrix/DenseMatrix.h>
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//#include <Grid/algorithms/iterative/EigenSort.h>
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// eliminate temorary vector in calc()
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#define MEM_SAVE
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namespace Grid
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{
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struct Bisection
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{
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#if 0
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static void get_eig2 (int row_num, std::vector < RealD > &ALPHA,
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std::vector < RealD > &BETA,
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std::vector < RealD > &eig)
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{
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int i, j;
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std::vector < RealD > evec1 (row_num + 3);
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std::vector < RealD > evec2 (row_num + 3);
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RealD eps2;
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ALPHA[1] = 0.;
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BETHA[1] = 0.;
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for (i = 0; i < row_num - 1; i++)
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{
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ALPHA[i + 1] = A[i * (row_num + 1)].real ();
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BETHA[i + 2] = A[i * (row_num + 1) + 1].real ();
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}
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ALPHA[row_num] = A[(row_num - 1) * (row_num + 1)].real ();
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bisec (ALPHA, BETHA, row_num, 1, row_num, 1e-10, 1e-10, evec1, eps2);
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bisec (ALPHA, BETHA, row_num, 1, row_num, 1e-16, 1e-16, evec2, eps2);
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// Do we really need to sort here?
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int begin = 1;
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int end = row_num;
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int swapped = 1;
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while (swapped)
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{
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swapped = 0;
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for (i = begin; i < end; i++)
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{
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if (mag (evec2[i]) > mag (evec2[i + 1]))
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{
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swap (evec2 + i, evec2 + i + 1);
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swapped = 1;
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}
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}
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end--;
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for (i = end - 1; i >= begin; i--)
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{
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if (mag (evec2[i]) > mag (evec2[i + 1]))
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{
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swap (evec2 + i, evec2 + i + 1);
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swapped = 1;
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}
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}
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begin++;
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}
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for (i = 0; i < row_num; i++)
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{
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for (j = 0; j < row_num; j++)
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{
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if (i == j)
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H[i * row_num + j] = evec2[i + 1];
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else
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H[i * row_num + j] = 0.;
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}
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}
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}
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#endif
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static void bisec (std::vector < RealD > &c,
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std::vector < RealD > &b,
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int n,
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int m1,
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int m2,
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RealD eps1,
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RealD relfeh, std::vector < RealD > &x, RealD & eps2)
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{
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std::vector < RealD > wu (n + 2);
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RealD h, q, x1, xu, x0, xmin, xmax;
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int i, a, k;
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b[1] = 0.0;
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xmin = c[n] - fabs (b[n]);
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xmax = c[n] + fabs (b[n]);
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for (i = 1; i < n; i++)
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{
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h = fabs (b[i]) + fabs (b[i + 1]);
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if (c[i] + h > xmax)
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xmax = c[i] + h;
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if (c[i] - h < xmin)
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xmin = c[i] - h;
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}
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xmax *= 2.;
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eps2 = relfeh * ((xmin + xmax) > 0.0 ? xmax : -xmin);
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if (eps1 <= 0.0)
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eps1 = eps2;
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eps2 = 0.5 * eps1 + 7.0 * (eps2);
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x0 = xmax;
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for (i = m1; i <= m2; i++)
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{
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x[i] = xmax;
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wu[i] = xmin;
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}
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for (k = m2; k >= m1; k--)
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{
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xu = xmin;
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i = k;
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do
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{
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if (xu < wu[i])
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{
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xu = wu[i];
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i = m1 - 1;
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}
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i--;
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}
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while (i >= m1);
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if (x0 > x[k])
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x0 = x[k];
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while ((x0 - xu) > 2 * relfeh * (fabs (xu) + fabs (x0)) + eps1)
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{
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x1 = (xu + x0) / 2;
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a = 0;
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q = 1.0;
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for (i = 1; i <= n; i++)
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{
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q =
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c[i] - x1 -
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((q != 0.0) ? b[i] * b[i] / q : fabs (b[i]) / relfeh);
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if (q < 0)
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a++;
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}
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// printf("x1=%0.14e a=%d\n",x1,a);
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if (a < k)
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{
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if (a < m1)
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{
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xu = x1;
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wu[m1] = x1;
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}
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else
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{
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xu = x1;
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wu[a + 1] = x1;
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if (x[a] > x1)
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x[a] = x1;
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}
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}
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else
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x0 = x1;
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}
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printf ("x0=%0.14e xu=%0.14e k=%d\n", x0, xu, k);
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x[k] = (x0 + xu) / 2;
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}
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}
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};
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/////////////////////////////////////////////////////////////
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// Implicitly restarted lanczos
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/////////////////////////////////////////////////////////////
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template < class Field > class SimpleLanczos
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{
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const RealD small = 1.0e-16;
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public:
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int lock;
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int get;
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int Niter;
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int converged;
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int Nstop; // Number of evecs checked for convergence
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int Nk; // Number of converged sought
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int Np; // Np -- Number of spare vecs in kryloc space
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int Nm; // Nm -- total number of vectors
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RealD OrthoTime;
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RealD eresid;
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SortEigen < Field > _sort;
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LinearOperatorBase < Field > &_Linop;
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OperatorFunction < Field > &_poly;
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/////////////////////////
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// Constructor
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/////////////////////////
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void init (void)
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{
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};
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void Abort (int ff, DenseVector < RealD > &evals,
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DenseVector < DenseVector < RealD > >&evecs);
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SimpleLanczos (LinearOperatorBase < Field > &Linop, // op
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OperatorFunction < Field > &poly, // polynmial
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int _Nstop, // sought vecs
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int _Nk, // sought vecs
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int _Nm, // spare vecs
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RealD _eresid, // resid in lmdue deficit
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int _Niter): // Max iterations
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_Linop (Linop),
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_poly (poly),
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Nstop (_Nstop), Nk (_Nk), Nm (_Nm), eresid (_eresid), Niter (_Niter)
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{
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Np = Nm - Nk;
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assert (Np > 0);
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};
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/////////////////////////
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// Sanity checked this routine (step) against Saad.
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/////////////////////////
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void RitzMatrix (DenseVector < Field > &evec, int k)
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{
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if (1)
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return;
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GridBase *grid = evec[0]._grid;
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Field w (grid);
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std::cout << GridLogMessage << "RitzMatrix " << std::endl;
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for (int i = 0; i < k; i++)
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{
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_Linop.HermOp (evec[i], w);
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// _poly(_Linop,evec[i],w);
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std::cout << GridLogMessage << "[" << i << "] ";
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for (int j = 0; j < k; j++)
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{
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ComplexD in = innerProduct (evec[j], w);
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if (fabs ((double) i - j) > 1)
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{
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if (abs (in) > 1.0e-9)
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{
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std::cout << GridLogMessage << "oops" << std::endl;
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abort ();
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}
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else
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std::cout << GridLogMessage << " 0 ";
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}
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else
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{
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std::cout << GridLogMessage << " " << in << " ";
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}
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}
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std::cout << GridLogMessage << std::endl;
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}
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}
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void step (DenseVector < RealD > &lmd,
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DenseVector < RealD > &lme,
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Field & last, Field & current, Field & next, uint64_t k)
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{
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if (lmd.size () <= k)
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lmd.resize (k + Nm);
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if (lme.size () <= k)
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lme.resize (k + Nm);
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// _poly(_Linop,current,next ); // 3. wk:=Avk−βkv_{k−1}
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_Linop.HermOp (current, next); // 3. wk:=Avk−βkv_{k−1}
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if (k > 0)
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{
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next -= lme[k - 1] * last;
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}
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// std::cout<<GridLogMessage << "<last|next>" << innerProduct(last,next) <<std::endl;
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ComplexD zalph = innerProduct (current, next); // 4. αk:=(wk,vk)
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RealD alph = real (zalph);
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next = next - alph * current; // 5. wk:=wk−αkvk
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// std::cout<<GridLogMessage << "<current|next>" << innerProduct(current,next) <<std::endl;
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RealD beta = normalise (next); // 6. βk+1 := ∥wk∥2. If βk+1 = 0 then Stop
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// 7. vk+1 := wk/βk+1
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// norm=beta;
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int interval = Nm / 100 + 1;
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if ((k % interval) == 0)
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std::
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cout << GridLogMessage << k << " : alpha = " << zalph << " beta " <<
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beta << std::endl;
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const RealD tiny = 1.0e-20;
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if (beta < tiny)
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{
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std::cout << GridLogMessage << " beta is tiny " << beta << std::
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endl;
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}
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lmd[k] = alph;
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lme[k] = beta;
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}
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void qr_decomp (DenseVector < RealD > &lmd,
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DenseVector < RealD > &lme,
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int Nk,
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int Nm,
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DenseVector < RealD > &Qt, RealD Dsh, int kmin, int kmax)
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{
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int k = kmin - 1;
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RealD x;
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RealD Fden = 1.0 / hypot (lmd[k] - Dsh, lme[k]);
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RealD c = (lmd[k] - Dsh) * Fden;
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RealD s = -lme[k] * Fden;
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RealD tmpa1 = lmd[k];
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RealD tmpa2 = lmd[k + 1];
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RealD tmpb = lme[k];
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lmd[k] = c * c * tmpa1 + s * s * tmpa2 - 2.0 * c * s * tmpb;
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lmd[k + 1] = s * s * tmpa1 + c * c * tmpa2 + 2.0 * c * s * tmpb;
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lme[k] = c * s * (tmpa1 - tmpa2) + (c * c - s * s) * tmpb;
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x = -s * lme[k + 1];
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lme[k + 1] = c * lme[k + 1];
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for (int i = 0; i < Nk; ++i)
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{
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RealD Qtmp1 = Qt[i + Nm * k];
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RealD Qtmp2 = Qt[i + Nm * (k + 1)];
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Qt[i + Nm * k] = c * Qtmp1 - s * Qtmp2;
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Qt[i + Nm * (k + 1)] = s * Qtmp1 + c * Qtmp2;
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}
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// Givens transformations
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for (int k = kmin; k < kmax - 1; ++k)
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{
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RealD Fden = 1.0 / hypot (x, lme[k - 1]);
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RealD c = lme[k - 1] * Fden;
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RealD s = -x * Fden;
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RealD tmpa1 = lmd[k];
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RealD tmpa2 = lmd[k + 1];
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RealD tmpb = lme[k];
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lmd[k] = c * c * tmpa1 + s * s * tmpa2 - 2.0 * c * s * tmpb;
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lmd[k + 1] = s * s * tmpa1 + c * c * tmpa2 + 2.0 * c * s * tmpb;
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lme[k] = c * s * (tmpa1 - tmpa2) + (c * c - s * s) * tmpb;
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lme[k - 1] = c * lme[k - 1] - s * x;
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if (k != kmax - 2)
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{
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x = -s * lme[k + 1];
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lme[k + 1] = c * lme[k + 1];
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}
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for (int i = 0; i < Nk; ++i)
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{
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RealD Qtmp1 = Qt[i + Nm * k];
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RealD Qtmp2 = Qt[i + Nm * (k + 1)];
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Qt[i + Nm * k] = c * Qtmp1 - s * Qtmp2;
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Qt[i + Nm * (k + 1)] = s * Qtmp1 + c * Qtmp2;
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}
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}
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}
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#ifdef USE_LAPACK
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#ifdef USE_MKL
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#define LAPACK_INT MKL_INT
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#else
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#define LAPACK_INT long long
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#endif
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||
void diagonalize_lapack (DenseVector < RealD > &lmd, DenseVector < RealD > &lme, int N1, // all
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int N2, // get
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GridBase * grid)
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{
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const int size = Nm;
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LAPACK_INT NN = N1;
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double evals_tmp[NN];
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double DD[NN];
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double EE[NN];
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for (int i = 0; i < NN; i++)
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for (int j = i - 1; j <= i + 1; j++)
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if (j < NN && j >= 0)
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{
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if (i == j)
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DD[i] = lmd[i];
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if (i == j)
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evals_tmp[i] = lmd[i];
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if (j == (i - 1))
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EE[j] = lme[j];
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}
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LAPACK_INT evals_found;
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LAPACK_INT lwork =
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((18 * NN) >
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(1 + 4 * NN + NN * NN) ? (18 * NN) : (1 + 4 * NN + NN * NN));
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LAPACK_INT liwork = 3 + NN * 10;
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LAPACK_INT iwork[liwork];
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double work[lwork];
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LAPACK_INT isuppz[2 * NN];
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char jobz = 'N'; // calculate evals only
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char range = 'I'; // calculate il-th to iu-th evals
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// char range = 'A'; // calculate all evals
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char uplo = 'U'; // refer to upper half of original matrix
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char compz = 'I'; // Compute eigenvectors of tridiagonal matrix
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int ifail[NN];
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LAPACK_INT info;
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// int total = QMP_get_number_of_nodes();
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// int node = QMP_get_node_number();
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// GridBase *grid = evec[0]._grid;
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int total = grid->_Nprocessors;
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int node = grid->_processor;
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int interval = (NN / total) + 1;
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double vl = 0.0, vu = 0.0;
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LAPACK_INT il = interval * node + 1, iu = interval * (node + 1);
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if (iu > NN)
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iu = NN;
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double tol = 0.0;
|
||
if (1)
|
||
{
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memset (evals_tmp, 0, sizeof (double) * NN);
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if (il <= NN)
|
||
{
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||
printf ("total=%d node=%d il=%d iu=%d\n", total, node, il, iu);
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||
#ifdef USE_MKL
|
||
dstegr (&jobz, &range, &NN,
|
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#else
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LAPACK_dstegr (&jobz, &range, &NN,
|
||
#endif
|
||
(double *) DD, (double *) EE, &vl, &vu, &il, &iu, // these four are ignored if second parameteris 'A'
|
||
&tol, // tolerance
|
||
&evals_found, evals_tmp, (double *) NULL, &NN,
|
||
isuppz, work, &lwork, iwork, &liwork, &info);
|
||
for (int i = iu - 1; i >= il - 1; i--)
|
||
{
|
||
printf ("node=%d evals_found=%d evals_tmp[%d] = %g\n", node,
|
||
evals_found, i - (il - 1), evals_tmp[i - (il - 1)]);
|
||
evals_tmp[i] = evals_tmp[i - (il - 1)];
|
||
if (il > 1)
|
||
evals_tmp[i - (il - 1)] = 0.;
|
||
}
|
||
}
|
||
{
|
||
grid->GlobalSumVector (evals_tmp, NN);
|
||
}
|
||
}
|
||
// cheating a bit. It is better to sort instead of just reversing it, but the document of the routine says evals are sorted in increasing order. qr gives evals in decreasing order.
|
||
}
|
||
#undef LAPACK_INT
|
||
#endif
|
||
|
||
|
||
void diagonalize (DenseVector < RealD > &lmd,
|
||
DenseVector < RealD > &lme,
|
||
int N2, int N1, GridBase * grid)
|
||
{
|
||
|
||
#ifdef USE_LAPACK
|
||
const int check_lapack = 0; // just use lapack if 0, check against lapack if 1
|
||
|
||
if (!check_lapack)
|
||
return diagonalize_lapack (lmd, lme, N2, N1, grid);
|
||
|
||
// diagonalize_lapack(lmd2,lme2,Nm2,Nm,Qt,grid);
|
||
#endif
|
||
}
|
||
|
||
#if 1
|
||
static RealD normalise (Field & v)
|
||
{
|
||
RealD nn = norm2 (v);
|
||
nn = sqrt (nn);
|
||
v = v * (1.0 / nn);
|
||
return nn;
|
||
}
|
||
|
||
void orthogonalize (Field & w, DenseVector < Field > &evec, int k)
|
||
{
|
||
double t0 = -usecond () / 1e6;
|
||
typedef typename Field::scalar_type MyComplex;
|
||
MyComplex ip;
|
||
|
||
if (0)
|
||
{
|
||
for (int j = 0; j < k; ++j)
|
||
{
|
||
normalise (evec[j]);
|
||
for (int i = 0; i < j; i++)
|
||
{
|
||
ip = innerProduct (evec[i], evec[j]); // are the evecs normalised? ; this assumes so.
|
||
evec[j] = evec[j] - ip * evec[i];
|
||
}
|
||
}
|
||
}
|
||
|
||
for (int j = 0; j < k; ++j)
|
||
{
|
||
ip = innerProduct (evec[j], w); // are the evecs normalised? ; this assumes so.
|
||
w = w - ip * evec[j];
|
||
}
|
||
normalise (w);
|
||
t0 += usecond () / 1e6;
|
||
OrthoTime += t0;
|
||
}
|
||
|
||
void setUnit_Qt (int Nm, DenseVector < RealD > &Qt)
|
||
{
|
||
for (int i = 0; i < Qt.size (); ++i)
|
||
Qt[i] = 0.0;
|
||
for (int k = 0; k < Nm; ++k)
|
||
Qt[k + k * Nm] = 1.0;
|
||
}
|
||
|
||
|
||
void calc (DenseVector < RealD > &eval, const Field & src, int &Nconv)
|
||
{
|
||
|
||
GridBase *grid = src._grid;
|
||
// assert(grid == src._grid);
|
||
|
||
std::
|
||
cout << GridLogMessage << " -- Nk = " << Nk << " Np = " << Np << std::
|
||
endl;
|
||
std::cout << GridLogMessage << " -- Nm = " << Nm << std::endl;
|
||
std::cout << GridLogMessage << " -- size of eval = " << eval.
|
||
size () << std::endl;
|
||
|
||
// assert(c.size() && Nm == eval.size());
|
||
|
||
DenseVector < RealD > lme (Nm);
|
||
DenseVector < RealD > lmd (Nm);
|
||
|
||
|
||
Field current (grid);
|
||
Field last (grid);
|
||
Field next (grid);
|
||
|
||
Nconv = 0;
|
||
|
||
RealD beta_k;
|
||
|
||
// Set initial vector
|
||
// (uniform vector) Why not src??
|
||
// evec[0] = 1.0;
|
||
current = src;
|
||
std::cout << GridLogMessage << "norm2(src)= " << norm2 (src) << std::
|
||
endl;
|
||
normalise (current);
|
||
std::
|
||
cout << GridLogMessage << "norm2(evec[0])= " << norm2 (current) <<
|
||
std::endl;
|
||
|
||
// Initial Nk steps
|
||
OrthoTime = 0.;
|
||
double t0 = usecond () / 1e6;
|
||
RealD norm; // sqrt norm of last vector
|
||
|
||
uint64_t iter = 0;
|
||
|
||
bool initted = false;
|
||
std::vector < RealD > low (Nstop * 10);
|
||
std::vector < RealD > high (Nstop * 10);
|
||
RealD cont = 0.;
|
||
while (1) {
|
||
cont = 0.;
|
||
std::vector < RealD > lme2 (Nm);
|
||
std::vector < RealD > lmd2 (Nm);
|
||
for (uint64_t k = 0; k < Nm; ++k, iter++) {
|
||
step (lmd, lme, last, current, next, iter);
|
||
last = current;
|
||
current = next;
|
||
}
|
||
double t1 = usecond () / 1e6;
|
||
std::cout << GridLogMessage << "IRL::Initial steps: " << t1 -
|
||
t0 << "seconds" << std::endl;
|
||
t0 = t1;
|
||
std::
|
||
cout << GridLogMessage << "IRL::Initial steps:OrthoTime " <<
|
||
OrthoTime << "seconds" << std::endl;
|
||
|
||
// getting eigenvalues
|
||
lmd2.resize (iter + 2);
|
||
lme2.resize (iter + 2);
|
||
for (uint64_t k = 0; k < iter; ++k) {
|
||
lmd2[k + 1] = lmd[k];
|
||
lme2[k + 2] = lme[k];
|
||
}
|
||
t1 = usecond () / 1e6;
|
||
std::cout << GridLogMessage << "IRL:: copy: " << t1 -
|
||
t0 << "seconds" << std::endl;
|
||
t0 = t1;
|
||
{
|
||
int total = grid->_Nprocessors;
|
||
int node = grid->_processor;
|
||
int interval = (Nstop / total) + 1;
|
||
int iu = (iter + 1) - (interval * node + 1);
|
||
int il = (iter + 1) - (interval * (node + 1));
|
||
std::vector < RealD > eval2 (iter + 3);
|
||
RealD eps2;
|
||
Bisection::bisec (lmd2, lme2, iter, il, iu, 1e-16, 1e-10, eval2,
|
||
eps2);
|
||
// diagonalize(eval2,lme2,iter,Nk,grid);
|
||
RealD diff = 0.;
|
||
for (int i = il; i <= iu; i++) {
|
||
if (initted)
|
||
diff =
|
||
fabs (eval2[i] - high[iu-i]) / (fabs (eval2[i]) +
|
||
fabs (high[iu-i]));
|
||
if (initted && (diff > eresid))
|
||
cont = 1.;
|
||
if (initted)
|
||
printf ("eval[%d]=%0.14e %0.14e, %0.14e\n", i, eval2[i],
|
||
high[iu-i], diff);
|
||
high[iu-i] = eval2[i];
|
||
}
|
||
il = (interval * node + 1);
|
||
iu = (interval * (node + 1));
|
||
Bisection::bisec (lmd2, lme2, iter, il, iu, 1e-16, 1e-10, eval2,
|
||
eps2);
|
||
for (int i = il; i <= iu; i++) {
|
||
if (initted)
|
||
diff =
|
||
fabs (eval2[i] - low[i]) / (fabs (eval2[i]) +
|
||
fabs (low[i]));
|
||
if (initted && (diff > eresid))
|
||
cont = 1.;
|
||
if (initted)
|
||
printf ("eval[%d]=%0.14e %0.14e, %0.14e\n", i, eval2[i],
|
||
low[i], diff);
|
||
low[i] = eval2[i];
|
||
}
|
||
t1 = usecond () / 1e6;
|
||
std::cout << GridLogMessage << "IRL:: diagonalize: " << t1 -
|
||
t0 << "seconds" << std::endl;
|
||
t0 = t1;
|
||
}
|
||
|
||
for (uint64_t k = 0; k < Nk; ++k) {
|
||
// eval[k] = eval2[k];
|
||
}
|
||
if (initted)
|
||
{
|
||
grid->GlobalSumVector (&cont, 1);
|
||
if (cont < 1.) return;
|
||
}
|
||
initted = true;
|
||
}
|
||
|
||
}
|
||
|
||
|
||
|
||
|
||
|
||
|
||
/**
|
||
There is some matrix Q such that for any vector y
|
||
Q.e_1 = y and Q is unitary.
|
||
**/
|
||
template < class T >
|
||
static T orthQ (DenseMatrix < T > &Q, DenseVector < T > y)
|
||
{
|
||
int N = y.size (); //Matrix Size
|
||
Fill (Q, 0.0);
|
||
T tau;
|
||
for (int i = 0; i < N; i++)
|
||
{
|
||
Q[i][0] = y[i];
|
||
}
|
||
T sig = conj (y[0]) * y[0];
|
||
T tau0 = fabs (sqrt (sig));
|
||
|
||
for (int j = 1; j < N; j++)
|
||
{
|
||
sig += conj (y[j]) * y[j];
|
||
tau = abs (sqrt (sig));
|
||
|
||
if (abs (tau0) > 0.0)
|
||
{
|
||
|
||
T gam = conj ((y[j] / tau) / tau0);
|
||
for (int k = 0; k <= j - 1; k++)
|
||
{
|
||
Q[k][j] = -gam * y[k];
|
||
}
|
||
Q[j][j] = tau0 / tau;
|
||
}
|
||
else
|
||
{
|
||
Q[j - 1][j] = 1.0;
|
||
}
|
||
tau0 = tau;
|
||
}
|
||
return tau;
|
||
}
|
||
|
||
/**
|
||
There is some matrix Q such that for any vector y
|
||
Q.e_k = y and Q is unitary.
|
||
**/
|
||
template < class T >
|
||
static T orthU (DenseMatrix < T > &Q, DenseVector < T > y)
|
||
{
|
||
T tau = orthQ (Q, y);
|
||
SL (Q);
|
||
return tau;
|
||
}
|
||
|
||
|
||
/**
|
||
Wind up with a matrix with the first con rows untouched
|
||
|
||
say con = 2
|
||
Q is such that Qdag H Q has {x, x, val, 0, 0, 0, 0, ...} as 1st colum
|
||
and the matrix is upper hessenberg
|
||
and with f and Q appropriately modidied with Q is the arnoldi factorization
|
||
|
||
**/
|
||
|
||
template < class T > static void Lock (DenseMatrix < T > &H, ///Hess mtx
|
||
DenseMatrix < T > &Q, ///Lock Transform
|
||
T val, ///value to be locked
|
||
int con, ///number already locked
|
||
RealD small, int dfg, bool herm)
|
||
{
|
||
//ForceTridiagonal(H);
|
||
|
||
int M = H.dim;
|
||
DenseVector < T > vec;
|
||
Resize (vec, M - con);
|
||
|
||
DenseMatrix < T > AH;
|
||
Resize (AH, M - con, M - con);
|
||
AH = GetSubMtx (H, con, M, con, M);
|
||
|
||
DenseMatrix < T > QQ;
|
||
Resize (QQ, M - con, M - con);
|
||
|
||
Unity (Q);
|
||
Unity (QQ);
|
||
|
||
DenseVector < T > evals;
|
||
Resize (evals, M - con);
|
||
DenseMatrix < T > evecs;
|
||
Resize (evecs, M - con, M - con);
|
||
|
||
Wilkinson < T > (AH, evals, evecs, small);
|
||
|
||
int k = 0;
|
||
RealD cold = abs (val - evals[k]);
|
||
for (int i = 1; i < M - con; i++)
|
||
{
|
||
RealD cnew = abs (val - evals[i]);
|
||
if (cnew < cold)
|
||
{
|
||
k = i;
|
||
cold = cnew;
|
||
}
|
||
}
|
||
vec = evecs[k];
|
||
|
||
ComplexD tau;
|
||
orthQ (QQ, vec);
|
||
//orthQM(QQ,AH,vec);
|
||
|
||
AH = Hermitian (QQ) * AH;
|
||
AH = AH * QQ;
|
||
|
||
for (int i = con; i < M; i++)
|
||
{
|
||
for (int j = con; j < M; j++)
|
||
{
|
||
Q[i][j] = QQ[i - con][j - con];
|
||
H[i][j] = AH[i - con][j - con];
|
||
}
|
||
}
|
||
|
||
for (int j = M - 1; j > con + 2; j--)
|
||
{
|
||
|
||
DenseMatrix < T > U;
|
||
Resize (U, j - 1 - con, j - 1 - con);
|
||
DenseVector < T > z;
|
||
Resize (z, j - 1 - con);
|
||
T nm = norm (z);
|
||
for (int k = con + 0; k < j - 1; k++)
|
||
{
|
||
z[k - con] = conj (H (j, k + 1));
|
||
}
|
||
normalise (z);
|
||
|
||
RealD tmp = 0;
|
||
for (int i = 0; i < z.size () - 1; i++)
|
||
{
|
||
tmp = tmp + abs (z[i]);
|
||
}
|
||
|
||
if (tmp < small / ((RealD) z.size () - 1.0))
|
||
{
|
||
continue;
|
||
}
|
||
|
||
tau = orthU (U, z);
|
||
|
||
DenseMatrix < T > Hb;
|
||
Resize (Hb, j - 1 - con, M);
|
||
|
||
for (int a = 0; a < M; a++)
|
||
{
|
||
for (int b = 0; b < j - 1 - con; b++)
|
||
{
|
||
T sum = 0;
|
||
for (int c = 0; c < j - 1 - con; c++)
|
||
{
|
||
sum += H[a][con + 1 + c] * U[c][b];
|
||
} //sum += H(a,con+1+c)*U(c,b);}
|
||
Hb[b][a] = sum;
|
||
}
|
||
}
|
||
|
||
for (int k = con + 1; k < j; k++)
|
||
{
|
||
for (int l = 0; l < M; l++)
|
||
{
|
||
H[l][k] = Hb[k - 1 - con][l];
|
||
}
|
||
} //H(Hb[k-1-con][l] , l,k);}}
|
||
|
||
DenseMatrix < T > Qb;
|
||
Resize (Qb, M, M);
|
||
|
||
for (int a = 0; a < M; a++)
|
||
{
|
||
for (int b = 0; b < j - 1 - con; b++)
|
||
{
|
||
T sum = 0;
|
||
for (int c = 0; c < j - 1 - con; c++)
|
||
{
|
||
sum += Q[a][con + 1 + c] * U[c][b];
|
||
} //sum += Q(a,con+1+c)*U(c,b);}
|
||
Qb[b][a] = sum;
|
||
}
|
||
}
|
||
|
||
for (int k = con + 1; k < j; k++)
|
||
{
|
||
for (int l = 0; l < M; l++)
|
||
{
|
||
Q[l][k] = Qb[k - 1 - con][l];
|
||
}
|
||
} //Q(Qb[k-1-con][l] , l,k);}}
|
||
|
||
DenseMatrix < T > Hc;
|
||
Resize (Hc, M, M);
|
||
|
||
for (int a = 0; a < j - 1 - con; a++)
|
||
{
|
||
for (int b = 0; b < M; b++)
|
||
{
|
||
T sum = 0;
|
||
for (int c = 0; c < j - 1 - con; c++)
|
||
{
|
||
sum += conj (U[c][a]) * H[con + 1 + c][b];
|
||
} //sum += conj( U(c,a) )*H(con+1+c,b);}
|
||
Hc[b][a] = sum;
|
||
}
|
||
}
|
||
|
||
for (int k = 0; k < M; k++)
|
||
{
|
||
for (int l = con + 1; l < j; l++)
|
||
{
|
||
H[l][k] = Hc[k][l - 1 - con];
|
||
}
|
||
} //H(Hc[k][l-1-con] , l,k);}}
|
||
|
||
}
|
||
}
|
||
#endif
|
||
|
||
|
||
};
|
||
|
||
}
|
||
#endif
|