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321 lines
7.5 KiB
C
321 lines
7.5 KiB
C
/* energy.c: Compute energetic properties of quantum systems
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Copyright 2013 Hendrik Weimer
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This file is part of libquantum
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libquantum 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
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by the Free Software Foundation; either version 3 of the License,
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or (at your option) any later version.
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libquantum is distributed in the hope that it will be useful, but
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WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with libquantum; if not, write to the Free Software
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Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
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MA 02110-1301, USA
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*/
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#include <float.h>
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#include <math.h>
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#include <stdlib.h>
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#include <string.h>
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#include "energy.h"
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#include "qureg.h"
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#include "qtime.h"
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#include "complex.h"
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extern void dstevd_(char *jobz, int *n, double *d, double *e, double *z,
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int *ldz, double *work, int *lwork, int *iwork, int *liwork,
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int *info);
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/* Modified Lanczos algorithm that iterates over a series of 2x2
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matrix diagonalzations [E. Dagotto & A. Moreo, Phys. Rev. D 31, 865
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(1985)] */
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double
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quantum_lanczos_modified(quantum_reg H(MAX_UNSIGNED, double), double epsilon,
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quantum_reg *reg)
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{
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double E0=DBL_MAX, Eold=DBL_MAX, E1, E2, t;
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quantum_reg tmp, tmp2;
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int i;
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COMPLEX_FLOAT h01;
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double h00, h11;
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for(i=0; i<reg->size; i++)
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{
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quantum_normalize(reg);
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tmp = quantum_matrix_qureg(H, 0, reg, QUANTUM_RK4_NODELETE);
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h00 = quantum_real(quantum_dot_product(&tmp, reg));
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E0 = h00;
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if(fabs(E0-Eold)<epsilon)
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return E0;
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Eold = E0;
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quantum_copy_qureg(reg, &tmp2);
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quantum_scalar_qureg(-h00, &tmp2);
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quantum_vectoradd_inplace(&tmp, &tmp2);
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quantum_normalize(&tmp);
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quantum_delete_qureg(&tmp2);
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tmp2 = quantum_matrix_qureg(H, 0, &tmp, QUANTUM_RK4_NODELETE);
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h11 = quantum_real(quantum_dot_product(&tmp2, &tmp));
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h01 = quantum_dot_product(&tmp2, reg);
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t = sqrt(h11*h11-2*h00*h11+4*h01*quantum_conj(h01)+h00*h00);
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E1 = -(t-h11-h00)/2.;
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E2 = (t+h11+h00)/2.;
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if(E1<E2)
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{
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quantum_scalar_qureg(-(t-h11+h00)/2./h01, &tmp);
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quantum_vectoradd_inplace(reg, &tmp);
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}
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else
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{
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quantum_scalar_qureg((t+h11-h00)/2./h01, &tmp);
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quantum_vectoradd_inplace(reg, &tmp);
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}
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quantum_delete_qureg(&tmp);
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quantum_delete_qureg(&tmp2);
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}
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quantum_error(QUANTUM_ENOCONVERGE);
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return nan("0");
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}
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/* Standard Lanczos algorithm without reorthogonalization (see, e.g.,
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[E. Dagotto, Rev. Mod. Phys. 66, 763 (1994)]. */
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double
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quantum_lanczos(quantum_reg H(MAX_UNSIGNED, double), double epsilon,
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quantum_reg *reg)
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{
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#ifdef HAVE_LIBLAPACK
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double E0=DBL_MAX, Eold=DBL_MAX, *a, *b, *d, *e, norm, *eig, *work;
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quantum_reg *phi, tmp;
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int n, i, j;
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char jobz = 'V';
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int lwork, *iwork, liwork, info;
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phi = calloc(2, sizeof(quantum_reg));
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a = calloc(2, sizeof(double));
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b = calloc(2, sizeof(double));
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work = malloc(sizeof(double));
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iwork = malloc(sizeof(int));
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eig = malloc(sizeof(double));
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d = malloc(sizeof(double));
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e = malloc(sizeof(double));
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if(!(phi && a && b && work && iwork && eig && d && e))
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quantum_error(QUANTUM_ENOMEM);
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quantum_memman(2*sizeof(quantum_reg)+4*sizeof(double));
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quantum_copy_qureg(reg, &phi[0]);
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quantum_normalize(&phi[0]);
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tmp = quantum_matrix_qureg(H, 0, &phi[0], QUANTUM_RK4_NODELETE);
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a[0] = quantum_dot_product(&tmp, &phi[0]);
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quantum_copy_qureg(&phi[0], &phi[1]);
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quantum_scalar_qureg(-a[0], &phi[1]);
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quantum_vectoradd_inplace(&phi[1], &tmp);
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quantum_delete_qureg(&tmp);
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tmp = quantum_matrix_qureg(H, 0, &phi[1], QUANTUM_RK4_NODELETE);
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norm = quantum_dot_product(&phi[1], &phi[1]);
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a[1] = quantum_dot_product(&tmp, &phi[1]) / norm;
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b[0] = norm / quantum_dot_product(&phi[0], &phi[0]);
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for(n=2; n<reg->size; n++)
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{
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lwork = n*n+4*n+1;
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work = realloc(work, lwork*sizeof(double));
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liwork = 5*n+3;
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iwork = realloc(iwork, lwork*sizeof(int));
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eig = realloc(eig, n*n*sizeof(double));
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d = realloc(d, n*sizeof(double));
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e = realloc(e, n*sizeof(double));
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if(!(work && iwork && eig && d && e))
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quantum_error(QUANTUM_ENOMEM);
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memcpy(d, a, n*sizeof(double));
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for(i=0; i<n; i++)
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e[i] = sqrt(b[i]);
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dstevd_(&jobz, &n, d, e, eig, &n, work, &lwork, iwork, &liwork, &info);
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if(info < 0)
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quantum_error(QUANTUM_ELAPACKARG);
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else if(info > 0)
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quantum_error(QUANTUM_ELAPACKCONV);
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E0 = d[0];
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if(fabs(E0-Eold) < epsilon)
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break;
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Eold = E0;
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phi = realloc(phi, (n+1)*sizeof(quantum_reg));
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a = realloc(a, (n+1)*sizeof(double));
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b = realloc(b, (n+1)*sizeof(double));
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if(!(phi && a && b))
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quantum_error(QUANTUM_ENOMEM);
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quantum_memman(sizeof(quantum_reg)+2*sizeof(double));
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quantum_copy_qureg(&phi[n-1], &phi[n]);
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quantum_scalar_qureg(-a[n-1], &phi[n]);
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quantum_vectoradd_inplace(&phi[n], &tmp);
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quantum_delete_qureg(&tmp);
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quantum_copy_qureg(&phi[n-2], &tmp);
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quantum_scalar_qureg(-b[n-2], &tmp);
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quantum_vectoradd_inplace(&phi[n], &tmp);
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/* printf("%i %f\n", n, quantum_prob(quantum_dot_product(&phi[n],
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&phi[0]))); */
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quantum_delete_qureg(&tmp);
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tmp = quantum_matrix_qureg(H, 0, &phi[n], QUANTUM_RK4_NODELETE);
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norm = quantum_dot_product(&phi[n], &phi[n]);
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a[n] = quantum_dot_product(&tmp, &phi[n]) / norm;
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b[n-1] = norm / quantum_dot_product(&phi[n-1], &phi[n-1]);
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}
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if(n == reg->size)
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{
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quantum_error(QUANTUM_ENOCONVERGE);
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return nan("0");
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}
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for(i=0; i<n; i++)
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quantum_normalize(&phi[i]);
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for(i=0; i<reg->size; i++)
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{
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reg->amplitude[i] = 0;
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for(j=0; j<n; j++)
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reg->amplitude[i] += eig[j]*phi[j].amplitude[i];
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}
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quantum_delete_qureg(&tmp);
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for(i=0; i<n; i++)
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quantum_delete_qureg(&phi[i]);
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free(phi);
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free(a);
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free(b);
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free(d);
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free(e);
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free(eig);
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free(work);
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free(iwork);
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return E0;
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#else
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quantum_error(QUANTUM_ENOLAPACK);
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#endif /* HAVE_LIBLAPACK */
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}
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/* Imaginary time evolution algorithm */
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double
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quantum_imaginary_time(quantum_reg H(MAX_UNSIGNED, double), double epsilon,
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double dt, quantum_reg *reg)
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{
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double E0=DBL_MAX, Eold=DBL_MAX;
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quantum_reg reg2;
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int i;
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for(i=0; i<reg->size; i++)
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{
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quantum_rk4(reg, 0, dt, H, QUANTUM_RK4_IMAGINARY | QUANTUM_RK4_NODELETE);
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reg2 = quantum_matrix_qureg(H, 0, reg, QUANTUM_RK4_NODELETE);
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E0 = quantum_real(quantum_dot_product(®2, reg));
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quantum_delete_qureg(®2);
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if(fabs(Eold-E0)<epsilon)
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break;
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Eold = E0;
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}
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if(i == reg->size)
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{
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quantum_error(QUANTUM_ENOCONVERGE);
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return nan("0");
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}
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else
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return E0;
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}
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/* Wrapper around the various solver functions */
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double
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quantum_groundstate(quantum_reg *reg, double epsilon,
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quantum_reg H(MAX_UNSIGNED, double), int solver,
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double stepsize)
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{
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switch(solver)
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{
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case QUANTUM_SOLVER_LANCZOS:
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return quantum_lanczos(H, epsilon, reg);
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case QUANTUM_SOLVER_LANCZOS_MODIFIED:
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return quantum_lanczos_modified(H, epsilon, reg);
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case QUANTUM_SOLVER_IMAGINARY_TIME:
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return quantum_imaginary_time(H, epsilon, stepsize, reg);
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default:
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quantum_error(QUANTUM_ENOSOLVER);
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return nan("0");
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}
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}
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