void DynamicProgrammingQ2(double *Q1, double *T1, double *Q2, double *T2, int m1, int n1, int n2,
double *tv1, double *tv2, int n1v, int n2v, double *G, double *T, double *size, double lam1){
int *idxv1 = 0;
int *idxv2 = 0;
double *E = 0; /* E[ntv1*j+i] = cost of best path to (tv1[i],tv2[j]) */
int *P = 0; /* P[ntv1*j+i] = predecessor of (tv1[i],tv2[j]) along best path */
idxv1=(int*)malloc((n1v)*sizeof(int));
idxv2=(int*)malloc((n2v)*sizeof(int));
E=(double*)malloc((n1v)*(n2v)*sizeof(double));
P=(int*)calloc((n1v)*(n2v),sizeof(int));
/* dp_costs() needs indexes for gridpoints precomputed */
dp_all_indexes( T1, n1, tv1, n1v, idxv1 );
dp_all_indexes( T2, n2, tv2, n2v, idxv2 );
/* Compute cost of best path from (0,0) to every other grid point */
dp_costs( Q1, T1, n1, Q2, T2, n2,
m1, tv1, idxv1, n1v, tv2, idxv2, n2v, E, P, lam1 );
/* Reconstruct best path from (0,0) to (1,1) */
*size = dp_build_gamma( P, tv1, n1v, tv2, n2v, G, T );
// free allocated memory
free(idxv1); free(idxv2); free(E); free(P);
}
static void test_dp_edge_weight_basic2()
{
/* Q1 and Q2 are column-major arrays! */
double Q1[2*3] =
{
1,1,
1,1,
1,1
};
double T1[]={0,1.0/3.0,2.0/3.0,1};
double Q2[2*4] =
{
1,-1,
-1,1,
1,-1,
-1,1
};
double T2[]={0,.25,.5,.75,1};
double tv1[]={0,1.0/3.0,2.0/3.0,1};
double tv2[]={0,0.5,1};
int idxv1[4];
int idxv2[3];
double W[144]; /* edge weight matrix */
double E[12]; /* DP cost matrix */
int P[12]; /* DP predecessor matrix */
double G[4]; /* gamma function values */
double T[4]; /* gamma parameter values */
double retval;
double Eexp[] = {
0.0, 1e9, 1e9, 1e9,
1e9, 5.0/3.0, 7.0/3.0, 3,
1e9, 8.0/3.0, 10.0/3.0, 4.0
};
int nsamps1 = sizeof(T1) / sizeof(double);
int nsamps2 = sizeof(T2) / sizeof(double);
int ntv1 = sizeof(tv1) / sizeof(double);
int ntv2 = sizeof(tv2) / sizeof(double);
int dim = 2;
int Gnsamps;
int i;
dp_all_indexes(T1,nsamps1,tv1,ntv1,idxv1);
dp_all_indexes(T2,nsamps2,tv2,ntv2,idxv2);
retval = dp_costs( Q1, T1, nsamps1, Q2, T2, nsamps2,
dim, tv1, idxv1, ntv1, tv2, idxv2, ntv2, E, P );
CU_ASSERT_DOUBLE_EQUAL( retval, E[ntv1*ntv2-1], 1e-3 );
for ( i=0; i<ntv1*ntv2; ++i )
{
CU_ASSERT_DOUBLE_EQUAL( E[i], Eexp[i], 1e-3 );
}
dp_all_edge_weights (
Q1, T1, nsamps1, Q2, T2, nsamps2,
dim, tv1, idxv1, ntv1, tv2, idxv2, ntv2, W );
Gnsamps = dp_build_gamma(P,tv1,ntv1,tv2,ntv2,G,T);
printf( "Gamma: " );
for ( i=0; i<Gnsamps; ++i )
{
printf( "(%0.3f,%0.3f)", T[i], G[i] );
}
printf( "\n" );
}
static void test_dp_edge_weight_basic1()
{
double T1[] = { 0.0, 1.0/6.0, 0.5, 4.0/6.0, 5.0/6.0, 1.0 };
double Q1[] = { 1.0, -1.0, 1.0, -1.0, 1.0 };
double T2[] = { 0.0, 2.0/6.0, 5.0/6.0, 1.0 };
double Q2[] = { -1.0, 1.0, -1.0 };
double tv1[] = { 0.0, 0.25, 0.5, 0.75, 1.0 };
double tv2[] = { 0.0, 0.25, 0.5, 0.75, 1.0 };
int nsamps1 = sizeof(T1) / sizeof(double);
int nsamps2 = sizeof(T2) / sizeof(double);
int ntv1 = sizeof(tv1) / sizeof(double);
int ntv2 = sizeof(tv2) / sizeof(double);
int dim = 1;
double W[ntv2*ntv1*ntv2*ntv1]; /* edge weight matrix */
double E[ntv2*ntv1]; /* DP cost matrix */
int P[ntv2*ntv1]; /* DP predecessor matrix */
int idxv1b[ntv1];
int idxv2b[ntv2];
double G[ntv1]; /* gamma function values */
double T[ntv1]; /* gamma parameter values */
int npts;
double a[] = { 0.25, 0.75, 0.0, 0.0, 0.25, 1.0/6.0 };
double b[] = { 0.75, 1.0, 0.75, 0.25, 0.5, 0.5 };
double c[] = { 0.25, 0.25, 0.0, 0.0, 0.0, 1.0/6.0 };
double d[] = { 0.5, 1.0, 0.25, 0.25, 0.25, 5.0/6.0 };
double expected[] = { 0.51430, 0.90377, 0.90377, 0.66667, 0.0, 1.4714 };
int ncases = sizeof(expected) / sizeof(double);
int idxv1a, idxv2a;
double actual;
int i;
for ( i=0; i<ncases; ++i )
{
/* Can't use dp_all_indexes() for this because a and c are
* not sorted in ascending order */
idxv1a = dp_lookup(T1,nsamps1,a[i]);
idxv2a = dp_lookup(T2,nsamps2,c[i]);
actual = dp_edge_weight (
Q1, T1, nsamps1,
Q2, T2, nsamps2,
dim, a[i], b[i], c[i], d[i], idxv1a, idxv2a );
CU_ASSERT_DOUBLE_EQUAL( actual, expected[i], 0.0001 );
if ( fabs(actual - expected[i]) > 0.0001 )
{
printf( "\nCase %d: expected %0.5f but got %0.5f\n", i, expected[i], actual );
}
}
dp_all_indexes(T1,nsamps1,tv1,ntv1,idxv1b);
dp_all_indexes(T2,nsamps2,tv2,ntv2,idxv2b);
dp_all_edge_weights(Q1,T1,6,Q2,T2,4,1,tv1,idxv1b,ntv1,tv2,idxv2b,ntv2,W);
dp_costs(Q1,T1,6,Q2,T2,4,1,tv1,idxv1b,ntv1,tv2,idxv2b,ntv2,E,P);
npts = dp_build_gamma( P, tv1, ntv1, tv2, ntv2, G, T );
printf( "gamma:\n" );
for ( i=0; i<npts; ++i )
{
printf( "(%0.2f,%0.2f)\n", T[i], G[i] );
}
}
