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/**********************************************************************
TRAN_Channel_Functions.c:
Routines used in MTRAN_EigenChannel.
Log of TRAN_Channel_Functions.c:
xx/Xxx/2015 Released by M. Kawamura
***********************************************************************/
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <mpi.h>
#include "lapack_prototypes.h"
/* Diagonalize ALbar -> its eigenvector */
/* Then scale it : Albar_{ml} -> ALbar * sqrt(eig_l) */
void TRAN_Calc_Diagonalize(
int n,
dcomplex *evec,
double *eval,
int lscale)
#define evec_ref(i,j) evec[n * (j) + (i)]
{
INTEGER LWORK;
dcomplex *WORK;
double *RWORK;
INTEGER INFO;
int i, j;
double sortmp;
LWORK = 3 * n;
WORK = (dcomplex*)malloc(sizeof(dcomplex)*LWORK);
RWORK = (double*)malloc(sizeof(double)*(3 * n - 2));
F77_NAME(zheev, ZHEEV)("V", "U", &n, evec, &n, eval, WORK, &LWORK, RWORK, &INFO);
/* Re-order eigenvalues & vectors as decreasing order */
i = 1;
for (j = 0; j < n / 2; j++){
sortmp = eval[j];
eval[j] = eval[n - 1 - j];
eval[n - 1 - j] = sortmp;
F77_NAME(zcopy, ZCOPY)(&n, &evec_ref(0, j), &i, WORK, &i);
F77_NAME(zcopy, ZCOPY)(&n, &evec_ref(0, n - 1 - j), &i, &evec_ref(0, j), &i);
F77_NAME(zcopy, ZCOPY)(&n, WORK, &i, &evec_ref(0, n - 1 - j), &i);
} /* for (j = 0; j < n / 2; j++) */
if (INFO != 0){
printf("Zheev error in TRAN_Calc_Diagonalization. info = %d, \n", INFO);
MPI_Abort(MPI_COMM_WORLD, 1);
MPI_Finalize();
exit(0);
}
if (lscale == 1){
for (j = 0; j < n; j++){
for (i = 0; i < n; i++){
evec_ref(i, j).r = evec_ref(i, j).r * sqrt(fabs(eval[j]));
evec_ref(i, j).i = evec_ref(i, j).i * sqrt(fabs(eval[j]));
} /* for (i = 0, i < n; i++) */
} /* for (j = 0; j < n; j++) */
} /* if (lscale == 1) */
free(WORK);
free(RWORK);
} /* TRAN_Calc_Diagonalize */
/* Define thedimention of ortogonal basis space */
int TRAN_Calc_OrtSpace(
int NUM_c,
dcomplex *SCC,
dcomplex *rtS,
dcomplex *rtSinv)
#define Sevec_ref(i,j) Sevec[NUM_c * (j) + (i)]
#define rtS_ref(i,j) rtS[NUM_c * (j) + (i)]
#define rtSinv_ref(i,j) rtSinv[NUM_c * (j) + (i)]
{
int NUM_cs;
double *eval;
dcomplex *Sevec;
int one;
int i, j;
int NUM_c2;
eval = (double*)malloc(sizeof(double)*NUM_c);
Sevec = (dcomplex*)malloc(sizeof(dcomplex)*NUM_c* NUM_c);
one = 1;
NUM_c2 = NUM_c * NUM_c;
F77_NAME(zcopy, ZCOPY)(&NUM_c2, SCC, &one, Sevec, &one);
TRAN_Calc_Diagonalize(NUM_c, Sevec, eval, 0);
NUM_cs = NUM_c;
for (i = 0; i < NUM_c; i++){
if (eval[i] < 0.000001) {
NUM_cs = i;
break;
} /* if (eval[i] < 0.000001) */
else{
eval[i] = sqrt(eval[i]);
} /* else if (eval[i] > 0.000001) */
} /* for (i = 0; i < NUM_c; i++) */
for (j = 0; j < NUM_cs; j++){
for (i = 0; i < NUM_c; i++){
rtS_ref(i, j).r = Sevec_ref(i, j).r * eval[j];
rtS_ref(i, j).i = Sevec_ref(i, j).i * eval[j];
rtSinv_ref(i, j).r = Sevec_ref(i, j).r / eval[j];
rtSinv_ref(i, j).i = Sevec_ref(i, j).i / eval[j];
} /* for (i = 0; i < NUM_c; i++) */
} /* for (j = 0; j < NUM_cs; j++) */
free(Sevec);
free(eval);
return NUM_cs;
} /* int TRAN_Calc_OrtSpace */
/* i(Sigma Sigma^+) -> Sigma*/
void TRAN_Calc_Linewidth(
int NUM_c,
dcomplex *SigmaL_R,
dcomplex *SigmaR_R)
#define SigmaL_R_ref(i,j) SigmaL_R[NUM_c * (j) + (i)]
#define SigmaR_R_ref(i,j) SigmaR_R[NUM_c * (j) + (i)]
{
int i, j;
double gammar, gammai;
for (j = 0; j < NUM_c; j++){
for (i = 0; i < j; i++){
gammar = - SigmaL_R_ref(i, j).i - SigmaL_R_ref(j, i).i;
gammai = SigmaL_R_ref(i, j).r - SigmaL_R_ref(j, i).r;
SigmaL_R_ref(i, j).r = gammar;
SigmaL_R_ref(i, j).i = gammai;
SigmaL_R_ref(j, i).r = gammar;
SigmaL_R_ref(j, i).i = - gammai;
gammar = -SigmaR_R_ref(i, j).i - SigmaR_R_ref(j, i).i;
gammai = SigmaR_R_ref(i, j).r - SigmaR_R_ref(j, i).r;
SigmaR_R_ref(i, j).r = gammar;
SigmaR_R_ref(i, j).i = gammai;
SigmaR_R_ref(j, i).r = gammar;
SigmaR_R_ref(j, i).i = -gammai;
} /* for (i = 0; i < j; i++) */
SigmaL_R_ref(j, j).r = -2.0 * SigmaL_R_ref(j, j).i;
SigmaL_R_ref(j, j).i = 0.0;
SigmaR_R_ref(j, j).r = -2.0 * SigmaR_R_ref(j, j).i;
SigmaR_R_ref(j, j).i = 0.0;
} /* for (j = 0; j < NUM_c; j++) */
} /* TRAN_Calc_Linewidth */
/* G Gamma_L G^+ -> Sigma_L */
void TRAN_Calc_MatTrans(
int NUM_c,
dcomplex *SigmaL_R,
dcomplex *GC_R,
char* trans1,
char* trans2)
{
dcomplex alpha, beta;
dcomplex *v1;
alpha.r = 1.0; alpha.i = 0.0;
beta.r = 0.0; beta.i = 0.0;
v1 = (dcomplex*)malloc(sizeof(dcomplex)*NUM_c* NUM_c);
F77_NAME(zgemm, ZGEMM)(trans1, "N", &NUM_c, &NUM_c, &NUM_c, &alpha, GC_R, &NUM_c,
SigmaL_R, &NUM_c, &beta, v1, &NUM_c);
F77_NAME(zgemm, ZGEMM)("N", trans2, &NUM_c, &NUM_c, &NUM_c, &alpha, v1, &NUM_c,
GC_R, &NUM_c, &beta, SigmaL_R, &NUM_c);
free(v1);
} /* void TRAN_Calc_MatTran */
/* L\"owdin orthogonalization */
void TRAN_Calc_LowdinOrt(
int NUM_c,
dcomplex *SigmaL_R,
dcomplex *SigmaR_R,
int NUM_cs,
dcomplex *rtS,
dcomplex *rtSinv,
dcomplex *ALbar,
dcomplex *GamRbar)
{
dcomplex alpha, beta;
dcomplex *v1;
alpha.r = 1.0; alpha.i = 0.0;
beta.r = 0.0; beta.i = 0.0;
v1 = (dcomplex*)malloc(sizeof(dcomplex)*NUM_cs* NUM_c);
/* Transform A_L into orthogonal basis space with S^{1/2}*/
F77_NAME(zgemm, ZGEMM)("C", "N", &NUM_cs, &NUM_c, &NUM_c, &alpha, rtS, &NUM_c,
SigmaL_R, &NUM_c, &beta, v1, &NUM_cs);
F77_NAME(zgemm, ZGEMM)("N", "N", &NUM_cs, &NUM_cs, &NUM_c, &alpha, v1, &NUM_cs,
rtS, &NUM_c, &beta, ALbar, &NUM_cs);
/* Transform Gamma_R int orthogonal basis space wit S^{-1/2} */
F77_NAME(zgemm, ZGEMM)("C", "N", &NUM_cs, &NUM_c, &NUM_c, &alpha, rtSinv, &NUM_c,
SigmaR_R, &NUM_c, &beta, v1, &NUM_cs);
F77_NAME(zgemm, ZGEMM)("N", "N", &NUM_cs, &NUM_cs, &NUM_c, &alpha, v1, &NUM_cs,
rtSinv, &NUM_c, &beta, GamRbar, &NUM_cs);
free(v1);
} /* void TRAN_Calc_LowdinOrt */
/* Transform eigenchannel into non-orthogonal basis space */
void TRAN_Calc_ChannelLCAO(
int NUM_c,
int NUM_cs,
dcomplex *rtSinv,
dcomplex *ALbar,
dcomplex *GamRbar,
double *eval,
dcomplex *GC_R,
int TRAN_Channel_Num,
dcomplex **EChannel,
double *eigentrans)
#define GC_R_ref(i,j) GC_R[NUM_c * (j) + (i)]
{
int i, j;
dcomplex alpha, beta;
dcomplex *v1;
double ecabs;
dcomplex ecphase, ec0;
alpha.r = 1.0; alpha.i = 0.0;
beta.r = 0.0; beta.i = 0.0;
v1 = (dcomplex*)malloc(sizeof(dcomplex)*NUM_cs* NUM_cs);
F77_NAME(zgemm, ZGEMM)("N", "N", &NUM_cs, &NUM_cs, &NUM_cs, &alpha, ALbar, &NUM_cs,
GamRbar, &NUM_cs, &beta, v1, &NUM_cs);
F77_NAME(zgemm, ZGEMM)("N", "N", &NUM_c, &NUM_cs, &NUM_cs, &alpha, rtSinv, &NUM_c,
v1, &NUM_cs, &beta, GC_R, &NUM_c);
/* Adjust phase in each eigenchannel */
for (j = 0; j < NUM_cs; j++){
ecphase.r = 0.0;
ecphase.i = 0.0;
for (i = 0; i < NUM_c; i++){
if (GC_R_ref(i, j).i > 0.0){
ecphase.r += GC_R_ref(i, j).r;
ecphase.i += GC_R_ref(i, j).i;
}
else{
ecphase.r -= GC_R_ref(i, j).r;
ecphase.i -= GC_R_ref(i, j).i;
}
}
ecabs = sqrt(ecphase.r * ecphase.r + ecphase.i * ecphase.i);
ecphase.r /= ecabs;
ecphase.i /= ecabs;
for (i = 0; i < NUM_c; i++){
ec0.r = GC_R_ref(i, j).r;
ec0.i = GC_R_ref(i, j).i;
GC_R_ref(i, j).r = ec0.r * ecphase.r + ec0.i * ecphase.i;
GC_R_ref(i, j).i = - ec0.r * ecphase.i + ec0.i * ecphase.r;
}
}
/* Fill Trancated dimentions with 0 */
for (j = NUM_cs; j < NUM_c; j++){
eval[j] = 0.0;
for (i = 0; i < NUM_c; i++){
GC_R_ref(i, j).r = 0.0;
GC_R_ref(i, j).i = 0.0;
}
}
/* Store for cube output */
for (j = 0; j < TRAN_Channel_Num; j++){
eigentrans[j] = eval[j];
for (i = 0; i < NUM_c; i++){
EChannel[j][i].r = GC_R_ref(i, j).r;
EChannel[j][i].i = GC_R_ref(i, j).i;
}
}
free(v1);
} /* void TRAN_Calc_ChannelLCAO */
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