static void PmlTableGen(int bw,
int m,
double *storeplm,
double *workspace)
{
double *prev, *prevprev, *temp1, *temp2, *temp3, *temp4, *x_i, *eval_args;
int i;
/* double *storeplm_ptr; */
prevprev = workspace;
prev = prevprev + (2*bw);
temp1 = prev + (2*bw);
temp2 = temp1 + (2*bw);
temp3 = temp2 + (2*bw);
temp4 = temp3 + (2*bw);
x_i = temp4 + (2*bw);
eval_args = x_i + (2*bw);
/* storeplm_ptr = storeplm; */
/* get the evaluation nodes */
EvalPts(2*bw,x_i);
ArcCosEvalPts(2*bw,eval_args);
/* set initial values of first two Pmls */
for (i=0; i<2*bw; i++)
prevprev[i] = 0.0;
if (m == 0)
for (i=0; i<2*bw; i++) {
/* prev[i] = 0.5; */
prev[i] = 0.707106781186547 ; /* 1/sqrt(2) */
}
else
Pmm_L2(m, eval_args, 2*bw, prev);
memcpy(storeplm, prev, (size_t) sizeof(double) * 2 * bw);
for(i = 0; i < bw - m - 1; i++)
{
vec_mul(L2_cn(m,m+i),prevprev,temp1,2*bw);
vec_pt_mul(prev, x_i, temp2, 2*bw);
vec_mul(L2_an(m,m+i), temp2, temp3, 2*bw);
vec_add(temp3, temp1, temp4, 2*bw); /* temp4 now contains P(m,m+i+1) */
storeplm += (2 * bw);
memcpy(storeplm, temp4, (size_t) sizeof(double) * 2 * bw);
memcpy(prevprev, prev, (size_t) sizeof(double) * 2 * bw);
memcpy(prev, temp4, (size_t) sizeof(double) * 2 * bw);
}
/* storeplm = storeplm_ptr; */
}
void CosPmlTableGen(int bw,
int m,
double *tablespace,
double *workspace)
{
double *prev, *prevprev, *temp1, *temp2, *temp3, *temp4;
double *x_i, *eval_args;
double *tableptr, *cosres ;
int i, j, k;
/* fftw stuff now */
double fudge ;
fftw_plan p ;
prevprev = workspace;
prev = prevprev + bw;
temp1 = prev + bw;
temp2 = temp1 + bw;
temp3 = temp2 + bw;
temp4 = temp3 + bw;
x_i = temp4 + bw;
eval_args = x_i + bw;
cosres = eval_args + bw;
tableptr = tablespace;
/* make fftw plan */
p = fftw_plan_r2r_1d( bw, temp4, cosres,
FFTW_REDFT10, FFTW_ESTIMATE ) ;
/* main loop */
/* Set the initial number of evaluation points to appropriate
amount */
/* now get the evaluation nodes */
EvalPts(bw,x_i);
ArcCosEvalPts(bw,eval_args);
/* set initial values of first two Pmls */
for (i=0; i<bw; i++)
prevprev[i] = 0.0;
if (m == 0)
for (i=0; i<bw; i++)
prev[i] = 0.707106781186547; /* sqrt(1/2) */
else
Pmm_L2(m, eval_args, bw, prev);
if ( m % 2 ) /* need to divide out sin x */
for (i=0; i<bw; i++)
prev[i] /= sin(eval_args[i]);
/* set k to highest degree coefficient */
if ((m % 2) == 0)
k = m;
else
k = m-1;
/* now compute cosine transform */
memcpy( temp4, prev, sizeof(double) * bw );
fftw_execute( p );
cosres[0] *= 0.707106781186547 ;
fudge = 1. / sqrt(((double) bw ) );
for ( i = 0 ; i < bw ; i ++ )
cosres[i] *= fudge ;
/* store what I've got so far */
for (i=0; i<=k; i+=2)
tableptr[i/2] = cosres[i];
/* update tableptr */
tableptr += k/2+1;
/* now generate remaining pmls */
for (i=0; i<bw-m-1; i++)
{
vec_mul(L2_cn(m,m+i),prevprev,temp1,bw);
vec_pt_mul(prev, x_i, temp2, bw);
vec_mul(L2_an(m,m+i), temp2, temp3, bw);
vec_add(temp3, temp1, temp4, bw); /* temp4 now contains P(m,m+i+1) */
/* compute cosine transform */
fftw_execute( p );
cosres[0] *= 0.707106781186547 ;
for ( j = 0 ; j < bw ; j ++ )
cosres[j] *= fudge ;
/* update degree counter */
k++;
/* now put decimated result into table */
if ( i % 2 )
for (j=0; j<=k; j+=2)
tableptr[j/2] = cosres[j];
else
for (j=1; j<=k; j+=2)
tableptr[j/2] = cosres[j];
/* update tableptr */
tableptr += k/2+1;
/* now update Pi and P(i+1) */
memcpy(prevprev, prev, sizeof(double) * bw);
memcpy(prev, temp4, sizeof(double) * bw);
}
fftw_destroy_plan( p );
}
void CosPmlTableGenLim( int bw,
int m,
int lim,
double *tablespace,
double *workspace)
{
double *prev, *prevprev, *temp1, *temp2, *temp3, *temp4;
double *x_i, *eval_args;
double *tableptr, *cosres, *cosworkspace;
int i, j, k;
prevprev = workspace;
prev = prevprev + bw;
temp1 = prev + bw;
temp2 = temp1 + bw;
temp3 = temp2 + bw;
temp4 = temp3 + bw;
x_i = temp4 + bw;
eval_args = x_i + bw;
cosres = eval_args + bw;
cosworkspace = cosres + bw;
tableptr = tablespace;
/* main loop */
/* Set the initial number of evaluation points to appropriate
amount */
/* now get the evaluation nodes */
EvalPts(bw,x_i);
ArcCosEvalPts(bw,eval_args);
/* set initial values of first two Pmls */
for (i=0; i<bw; i++)
prevprev[i] = 0.0;
if (m == 0) {
for (i=0; i<bw; i++) {
prev[i] = 1.0;
}
}
else
Pmm_L2(m, eval_args, bw, prev);
if ((m % 2) == 1) { /* need to divide out sin x */
for (i=0; i<bw; i++)
prev[i] /= sin(eval_args[i]);
}
/* set k to highest degree coefficient */
if ((m % 2) == 0)
k = m;
else
k = m-1;
/* now compute cosine transform */
kFCT(prev, cosres, cosworkspace, bw, bw, 1);
for (i=0; i<=k; i+=2)
tableptr[i/2] = cosres[i];
/* update tableptr */
tableptr += k/2+1;
/* now generate remaining pmls */
for (i = 0 ; i < lim - m - 1 ; i ++) {
vec_mul(L2_cn(m,m+i),prevprev,temp1,bw);
vec_pt_mul(prev, x_i, temp2, bw);
vec_mul(L2_an(m,m+i), temp2, temp3, bw);
vec_add(temp3, temp1, temp4, bw); /* temp4 now contains P(m,m+i+1) */
/* compute cosine transform */
kFCT(temp4, cosres, cosworkspace, bw, bw, 1);
/* update degree counter */
k++;
/* now put decimated result into table */
if ((i % 2) == 1) {
for (j=0; j<=k; j+=2)
tableptr[j/2] = cosres[j];
}
else {
for (j=1; j<=k; j+=2)
tableptr[j/2] = cosres[j];
}
/* update tableptr */
tableptr += k/2+1;
/* now update Pi and P(i+1) */
memcpy(prevprev, prev, sizeof(double) * bw);
memcpy(prev, temp4, sizeof(double) * bw);
}
}