int main()
{
# include "assoc_legendre_p.ipp"
add_data(assoc_legendre_p);
unsigned data_total = data.size();
screen_data([](const std::vector<double>& v){ return boost::math::legendre_p(v[0], v[1], v[2]); }, [](const std::vector<double>& v){ return v[3]; });
#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES)
screen_data([](const std::vector<double>& v){ return std::tr1::assoc_legendre(v[0], v[1], v[2]); }, [](const std::vector<double>& v){ return v[3]; });
#endif
#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES)
screen_data([](const std::vector<double>& v){ return gsl_sf_legendre_Plm(v[0], v[1], v[2]); }, [](const std::vector<double>& v){ return v[3]; });
#endif
unsigned data_used = data.size();
std::string function = "assoc_legendre[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)";
std::string function_short = "assoc_legendre";
double time;
time = exec_timed_test([](const std::vector<double>& v){ return boost::math::legendre_p(v[0], v[1], v[2]); });
std::cout << time << std::endl;
#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH))
report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name());
#endif
report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name());
//
// Boost again, but with promotion to long double turned off:
//
#if !defined(COMPILER_COMPARISON_TABLES)
if(sizeof(long double) != sizeof(double))
{
time = exec_timed_test([](const std::vector<double>& v){ return boost::math::legendre_p(v[0], v[1], v[2], boost::math::policies::make_policy(boost::math::policies::promote_double<false>())); });
std::cout << time << std::endl;
#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH))
report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>");
#endif
report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>");
}
#endif
#if defined(TEST_LIBSTDCXX) && !defined(COMPILER_COMPARISON_TABLES)
time = exec_timed_test([](const std::vector<double>& v){ return std::tr1::assoc_legendre(v[0], v[1], v[2]); });
std::cout << time << std::endl;
report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "tr1/cmath");
#endif
#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES)
time = exec_timed_test([](const std::vector<double>& v){ return gsl_sf_legendre_Plm(v[0], v[1], v[2]); });
std::cout << time << std::endl;
report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "GSL " GSL_VERSION);
#endif
return 0;
}
/*
* Generate basis transformation matrix for a harmonic oscillator with
* frequency switch: S
*
* rho_t = S * rho_t0 * S'
*
*/
qdpack_operator_t *
basis_transform(qdpack_simulation_t *sim, qdpack_hilbert_space_t *qs, int n, ho_w_func_t ho_w_cb, double t)
{
qdpack_complex z;
qdpack_operator_t *S;
int i, j, ns, mm, ll;
double r, w0, wt, sij;
qdpack_operator_list_t op_list;
ns = qs->nstates[n];
if ((S = qdpack_operator_alloc(qs)) == NULL)
{
fprintf(stderr, "basis_transform_ho: Failed to allocate basis tranformation matrix (Out of memory?).\n");
}
qdpack_operator_set_zero(S);
w0 = ho_w_cb(0.0, sim);
wt = ho_w_cb(t, sim);
r = 2 * sqrt(w0 * wt) / (wt + w0);
if (r > 1.0)
r = 1.0;
else if (r < -1.0)
r = -1.0;
//printf("DEBUG: basis_transform: r = %f (%f, %f): %f\n", r, w0, wt, t);
for (j = 0; j < ns; j++)
{
for (i = j; i < ns; i++)
{
if ((i == j) || ((i+j)%2 == 0))
{
ll = (i+j)/2;
mm = abs(i-j)/2;
sij = fact_sqrt(MIN(i,j)) / fact_sqrt(MAX(i,j)) * sqrt(r) * gsl_sf_legendre_Plm(ll, mm, r);
//if (wt > w0)
QDPACK_SET_COMPLEX(&z, sij, 0.0);
//else
// QDPACK_SET_COMPLEX(&z, -sij, 0.0);
qdpack_operator_set(S, i, j, z);
if (i != j)
{
sij = pow(-1.0, (j-i)/2.0) * sij;
QDPACK_SET_COMPLEX(&z, sij, 0.0);
qdpack_operator_set(S, j, i, z);
}
}
}
}
if (qs->nsubsys > 1)
{
qdpack_operator_list_init(&op_list);
for (i = 0; i < qs->nsubsys; i++)
{
qdpack_operator_t *M;
qdpack_hilbert_space_t *qs_sub = qdpack_hilbert_space_new();
qdpack_hilbert_space_add(qs_sub, qs->nstates[i]);
M = qdpack_operator_alloc(qs_sub);
if (i != n)
{
operator_unit(M, qs, i);
}
else
{
M = S;
}
qdpack_operator_list_append(&op_list, M);
// XXX: free qs, free M
}
qdpack_operator_tensor(S, qs, &op_list);
qdpack_operator_list_free_entries(&op_list);
}
return S;
}
int main( int argc, const char *argv[] )
{
FILE* fp;
int i,j,k,ii,p,q,x,y,z,u,g,mmm;
int s=0,o=0,v=0;
const int l=137,n=5,r=2,h=17,num=50,m=5;
int lll[h],llll[m],mm[h],cc[10];
double t1[n],t2[n],t3[n],t4[n],t5[n],t6[n],namda[h],bl[h];
double ss[h][h],ssr[h][h],sss[h][h],cs[n],kkk[h];
double uss[h][h][n][n][n],ussr[h][h][n][n][n];
double jc[n][n],jcr[n][n],jjj[n][n][n][h],jj[r][h],jj1[n][n][n][h];
double jjr[n][n][n][h],jjr1[n][n][n][h],pp[h][n],jjjj[h][h][h][h];
const double rr=0.12,pi=3.141592365,aa=0.0288997;
const double a=0.0,b=1.0,c=0.0,d=1.0,e=0.0,f=1.0;
const double node[n]={-0.9061798459,-0.5384693101,0.0,0.5384693101,0.9061798459};
const double w[n]={0.2369268851,0.4786286705,0.5688888889,0.4786286705,0.2369268851};
const double kk[l]={3.142, 4.493, 5.764, 6.283, 6.988, 7.725, 8.183, 9.095, 9.356, 9.425,10.417, 10.513, 10.904, 11.657, 11.705,12.323,12.566, 12.781,12.967,13.698, 13.916, 14.066, 14.207, 15.0335, 15.040, 15.4313,15.515, 15.708,16.1447,16.355,16.641, 16.924, 17.2208, 17.2505,17.648, 17.8386, 18.301,18.3513, 18.689, 18.8496, 18.923, 19.0259, 19.4477, 19.653, 20.1218,20.1825, 20.2039, 20.5402, 20.984, 21.374, 21.4285, 21.5254, 21.6292,21.8539, 21.991, 22.2953, 22.5368, 22.6627, 22.715, 22.9046, 23.3042,23.5195, 23.5913, 23.6933, 23.7978, 23.8865, 24.2628, 24.7276, 24.8438, 24.8732, 24.878, 25.0128, 25.101,25.1327, 25.6029, 25.9557, 25.989, 26.1278, 26.1428, 26.3072, 26.4768, 26.6661, 26.927, 27.0311, 27.1294,27.4013, 27.5058,27.5079, 27.9165, 28.1043, 28.1678, 28.2371, 28.2653,28.2743, 28.6498, 28.6974, 28.8704, 29.1756, 29.3326, 29.3971,29.5346, 29.6426, 29.8116, 29.8828, 29.8893, 30.2173, 30.5251,30.7304, 30.8208, 31.0624, 31.0939, 31.1206, 31.3127, 31.3201, 31.4159, 31.5502, 31.6496, 32.0967, 32.1112, 32.2366, 32.3444, 32.3789, 32.5247, 32.7708, 32.8037, 32.8705, 32.9564, 33.3632, 33.4058, 33.4432, 33.4768, 33.5613, 33.8888,33.9371, 34.1795,34.2654, 34.4705};
const int ll[l]={0, 1, 2, 0, 3, 1, 4, 2, 5, 0, 3, 6, 1, 7, 4, 2, 0, 8, 5, 3, 9, 1, 6, 10, 4, 7, 2, 0, 11, 5, 8, 3, 1, 12, 6, 9, 4, 13, 2, 0, 7, 10, 14, 5, 3, 8, 11, 15, 6, 12, 9, 4, 16, 2, 0, 7, 13, 10, 17, 5, 3, 1, 8, 14, 18, 11, 6, 4, 15, 9, 19, 2, 12, 0, 7, 20, 16, 5, 10, 13, 3, 1, 8, 21, 17, 11, 14, 6, 4, 22, 2, 9, 18, 0, 12, 15, 7, 23, 5, 19, 10, 3, 1,16, 13, 8, 20, 6, 11, 17, 4, 14, 25, 2, 0, 9, 21, 12, 7, 18, 15, 26,5, 22, 3, 10, 1, 13, 19, 27, 8, 16, 23, 6, 11, 4, 2};
#pragma omp parallel
printf("%f\n",kk[136]);
//===============================Gauss Legendre Integrate============================
for ( i=0; i<n; i++)
{
t1[i]=(rr+a)/2.0+(rr+a)*node[i]/2.0;
t2[i]=(rr+c)/2.0+(rr-c)*node[i]/2.0;
t3[i]=(e+f)/2.0+(f-e)*node[i]/2.0;
t4[i]=(b+rr)/2.0+(b-rr)*node[i]/2.0;
t5[i]=(d+rr)/2.0+(d-rr)*node[i]/2.0;
t6[i]=(e+f)/2.0+(f-e)*node[i]/2.0;
/*printf("%d\n",t3[i]);*/
}
//==================================Qutanum Number===================================
for ( i=0; i<m; i++)
{
llll[i]=2*ll[i]+1;
/*printf("%d\n",llll[i]);*/
}
for ( i=0; i<m; i++)
{
for ( j=0; j<llll[i] ; j++)
{
lll[s]=ll[i];
/*printf("%d\n",lll[s]);*/
s=s+1;
}
}
for ( i=0; i<m; i++)
{
mmm=-ll[i];
for ( j=0; j<llll[i]; j++)
{
mm[o]=mmm;
/*printf ("%d\n",mm[o]);*/
mmm=mmm+1;
o=o+1;
}
}
for ( i=0; i<m; i++)
{
for ( j=0; j<llll[i] ; j++)
{
kkk[v]=kk[i];
/*printf ("%f\n",kkk[v]);*/
v=v+1;
}
}
//====================================Radial wave function============================
for ( i=0; i<r; i++)
{
for ( j=0; j<h ; j++)
{
if (lll[j]-pow((-1),i)==-1)
{
jj[i][j]=cos(kkk[j])/kkk[j];
/*printf("%f\n",jj[i][j]);*/
}
else
{
jj[i][j]=gsl_sf_bessel_jl ( lll[j]-pow((-1),i), kkk[j]);
/*printf("%f\n",jj[i][j]);*/
}
}
}
/*printf("%f\n",jj[1][2]);*/
for ( i=0; i<n; i++)
for ( j=0; j<n ; j++)
for ( k=0; k<n; k++)
for ( q=0; q<h; q++)
{
jjr[i][j][k][q]=gsl_sf_bessel_jl(kkk[q]*(sqrt(t1[i]*t1[i]+0.25*t2[j]*t2[j]-t1[i]*t2[j]*t3[k])),lll[q]);
jjr1[i][j][k][q]=gsl_sf_bessel_jl(kkk[q]*(sqrt(t1[i]*t1[i]+0.25*t2[j]*t2[j]+t1[i]*t2[j]*t3[k])),lll[q]);
jjj[i][j][k][q]=gsl_sf_bessel_jl(kkk[q]*(sqrt(t4[i]*t4[i]+0.25*t5[j]*t5[j]-t4[i]*t5[j]*t6[k])),lll[q]);
jj1[i][j][k][q]=gsl_sf_bessel_jl(kkk[q]*(sqrt(t4[i]*t4[i]+0.25*t5[j]*t5[j]+t4[i]*t5[j]*t6[k])),lll[q]);
/*printf("%f\n",jjr[i][j][k][q]);*/
}
//====================================Angular wave function============================
cc[0]=1;
for ( i=1; i<10; i++)
{
cc[i]=cc[i-1]*(i);
/*printf ("%d\n",cc[i]);*/
}
for ( i=0; i<h; i++)
for ( q=0; q<n; q++)
{
if (mm[i]>=0)
{
pp[i][q]=gsl_sf_legendre_Plm (lll[i], mm[i], t3[q]);
/*printf ("%f\n",pp[i][q]);*/
}
else
{
pp[i][q]=pow((-1),-mm[i])*cc[lll[i]+mm[i]]/cc[lll[i]-mm[i]]*gsl_sf_legendre_Plm (lll[i], -mm[i], t3[q]);
/*printf ("%f\n",pp[i][q]);*/
}
}
//==========================================Initial===================================
for ( i=0; i<h; i++)
{
bl[i]=sqrt(num*pow(0.5,i));
/*printf ("%f\n",bl[i]);*/
}
//========================================Interaction=================================
for ( i=0; i<n; i++)
for ( j=0; j<n ; j++)
{
jcr[i][j]=0.5*80*(-2)*(2*pi*t1[i]*t2[j])*(2*pi*t1[i]*t2[j]);
jc[i][j]=-0.5*40/3.14*(-2)*(2*pi*t1[i]*t2[j])*(2*pi*t1[i]*t2[j])*pow(t5[j]/rr,-6);
/*printf("%f\n",jc[i][j]);*/
}
//===================================Matrix Element(four)============================
for ( x=0; x<h; x++)
for ( y=0; y<h ; y++)
for ( z=0; z<h; z++)
for ( u=0; u<h; u++)
{
jjjj[x][y][z][u]=jj[1][x]*jj[0][x]*jj[1][y]*jj[0][y]*jj[1][z]*jj[0][z]*jj[1][u]*jj[0][u];
/*printf ("%.10f\n",jjjj[x][y][z][u]);*/
}
for ( x=0; x<h; x++)
for ( y=0; y<h ; y++)
for ( g=0; g<n; g++)
for ( q=0; q<n; q++)
for ( p=0; p<n ; p++)
for ( z=0; z<h; z++)
for ( u=0; u<h; u++)
{
ussr[x][y][p][q][g]=ussr[x][y][p][q][g]+4*jjr[p][q][g][x]*jjr[p][q][g][y]*jjr1[p][q][g][z]*jjr1[p][q][g][u]*bl[z]*bl[u]*pp[x][g]*pp[y][g]*pp[z][g]*pp[u][g]/jjjj[x][y][z][u];
uss[x][y][p][q][g]=uss[x][y][p][q][g]+4*jjj[p][q][g][x]*jjj[p][q][g][y]*jj1[p][q][g][z]*jj1[p][q][g][u]*bl[z]*bl[u]*pp[x][g]*pp[y][g]*pp[z][g]*pp[u][g]/jjjj[x][y][z][u];
/*printf ("%f\n",ussr[x][y][p][q][g]);*/
/*printf ("%f\n",jjr[p][q][g][u]);*/
/*printf ("%f\n",jjr1[p][q][g][x]);*/
/*printf ("%f\n",bl[z]);*/
/*printf ("%f\n",pp[y][g]);*/
/*printf ("%f\n",jj[2][z]);*/
}
//===================================Matrix Element(two)============================
for ( x=0; x<h; x++)
for ( y=0; y<h ; y++)
for ( p=0; p<n; p++)
for ( q=0; q<n; q++)
for ( g=0; g<n; g++)
{
ssr[x][y]=ssr[x][y]+jcr[p][q]*ussr[x][y][p][q][g]*w[p]*w[q]*w[g];
sss[x][y]=sss[x][y]+jc[p][q]*uss[x][y][p][q][g]*w[p]*w[q]*w[g];
/*printf ("%f\n",ussr[0][4][p][q][g]*jcr[p][q]*w[p]*w[q]*w[g]);*/
/*printf ("%.10f\n",jcr[i][j]);*/
/*printf ("%f\n",w[g]);*/
/*printf ("%f\n",sss[x][y]);*/
}
for ( x=0; x<h; x++)
for ( y=0; y<h; y++)
printf("%.8f\n",sss[x][y]);
//======================================Diagnal======================================
for ( x=0; x<h; x++)
for ( y=0; y<h; y++)
{
if ( x==y )
{
ssr[x][y]=ssr[x][y]*(rr-a)/2.0*(rr-c)/2.0*(f-e)/2.0;
sss[x][y]=sss[x][y]*(b-rr)/2.0*(d-rr)/2.0*(f-e)/2.0;
ss[x][y]=sss[x][y]+ssr[x][y]+aa*kkk[y]*kkk[y];
}
if ( x!=y )
{
ssr[x][y]=ssr[x][y]*(rr-a)/2.0*(rr-c)/2.0*(f-e)/2.0;
sss[x][y]=sss[x][y]*(b-rr)/2.0*(d-rr)/2.0*(f-e)/2.0;
ss[x][y]=sss[x][y]+ssr[x][y];
}
}
/*打开文本文件以写入内容*/
fp = fopen("test.txt", "w");
if (!fp)
{
perror("cannot open file");
//exit(-1);
}
/*把二维数组的内容写入文件*/
for (i = 0; i < h; i++)
{
for (j = 0; j < h; j++)
{
fprintf(fp, "%f ", ss[i][j]);
}
fputc('\n', fp);
}
fclose(fp);
return 0;
}