inline void CreateOpenLineList(IntCoord *cpx, IntCoord *cpy, int cpcount) {
int cpi;
llcount = 0;
CalcBSpline(
cpx[0], cpy[0], cpx[0], cpy[0], cpx[0], cpy[0], cpx[1], cpy[1]
);
CalcBSpline(
cpx[0], cpy[0], cpx[0], cpy[0], cpx[1], cpy[1], cpx[2], cpy[2]
);
for (cpi = 1; cpi < cpcount - 2; ++cpi) {
CalcBSpline(
cpx[cpi - 1], cpy[cpi - 1], cpx[cpi], cpy[cpi],
cpx[cpi + 1], cpy[cpi + 1], cpx[cpi + 2], cpy[cpi + 2]
);
}
CalcBSpline(
cpx[cpi - 1], cpy[cpi - 1], cpx[cpi], cpy[cpi],
cpx[cpi + 1], cpy[cpi + 1], cpx[cpi + 1], cpy[cpi + 1]
);
CalcBSpline(
cpx[cpi], cpy[cpi], cpx[cpi + 1], cpy[cpi + 1],
cpx[cpi + 1], cpy[cpi + 1], cpx[cpi + 1], cpy[cpi + 1]
);
}
PetscErrorCode BSSPsi(BSS self, Vec c, Vec xs, Vec ys) {
// yj = sum(i) ci ui(xj)
// PetscErrorCode ierr;
// ierr = BSSChcek(self); CHKERRQ(ierr);
PetscErrorCode ierr;
int nc; VecGetSize(c, &nc);
int nb; BSSGetSize(self, &nb);
int nx; VecGetSize(xs, &nx);
int ny; VecGetSize(ys, &ny);
if(nc != nb) {
SETERRQ(self->comm, 1, "size of c must be same as basis size");
}
if(nx != ny) {
SETERRQ(self->comm, 1, "xs and ys must be same size");
}
Mat f_jx_ib;
ierr = MatCreate(self->comm, &f_jx_ib); CHKERRQ(ierr);
ierr = MatSetSizes(f_jx_ib, PETSC_DECIDE, PETSC_DECIDE, nx, nb); CHKERRQ(ierr);
ierr = MatSetUp(f_jx_ib); CHKERRQ(ierr);
PetscScalar *x_ptr;
VecGetArray(xs, &x_ptr);
PetscReal *x_r_ptr; PetscMalloc1(nx, &x_r_ptr);
for(int ix = 0; ix < nx; ix++)
x_r_ptr[ix] = creal(x_ptr[ix]);
PetscScalar *x_c_ptr; PetscMalloc1(nx, &x_c_ptr);
ierr = CScalingCalc(self->c_scaling, x_r_ptr, nx, NULL, x_c_ptr); CHKERRQ(ierr);
for(int jx = 0; jx < nx; jx++) {
for(int ib = 0; ib < nb; ib++) {
PetscScalar y;
PetscBool zeroq;
ierr = CalcBSpline(self->order, self->ts_r, self->ts_s, self->b_idx_list[ib],
x_r_ptr[jx], x_c_ptr[jx], &y, &zeroq); CHKERRQ(ierr);
if(!zeroq) {
ierr = MatSetValue(f_jx_ib, jx, ib, y, INSERT_VALUES); CHKERRQ(ierr);
}
}
}
MatAssemblyBegin(f_jx_ib, MAT_FINAL_ASSEMBLY);
MatAssemblyEnd(f_jx_ib, MAT_FINAL_ASSEMBLY);
ierr = MatMult(f_jx_ib, c, ys); CHKERRQ(ierr);
MatDestroy(&f_jx_ib);
VecRestoreArray(xs, &x_ptr);
PetscFree(x_r_ptr);
PetscFree(x_c_ptr);
return 0;
}
PetscErrorCode CalcDerivBSpline(int order, PetscReal* ts_r, PetscScalar *ts,
int i, double x_r, PetscScalar x, PetscScalar* y,
PetscBool *zeroq) {
if(order < 1) {
SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE,
"order must be positive integer\n");
}
PetscBool _zeroq;
if(order == 1) {
*y = 0.0;
_zeroq = PETSC_TRUE;
} else {
int k = order;
PetscScalar bs0;
PetscBool zeroq0;
CalcBSpline(k-1, ts_r, ts, i, x_r, x, &bs0, &zeroq0);
PetscScalar bs1;
PetscBool zeroq1;
CalcBSpline(k-1, ts_r, ts, i+1, x_r, x, &bs1, &zeroq1);
double eps = 0.000000001;
PetscScalar acc = 0.0;
if(ScalarAbs(bs0) > eps && !zeroq0)
acc += (k-1)/(ts[i+k-1]-ts[i]) * bs0;
if(ScalarAbs(bs1) > eps && !zeroq1)
acc -= (k-1)/(ts[i+k]-ts[i+1]) * bs1;
*y = acc;
_zeroq = (zeroq0 && zeroq1);
}
if(zeroq != NULL)
*zeroq = _zeroq;
return 0;
}
PetscErrorCode BSSBasisPsi(BSS self, int i, PetscReal x, PetscScalar *y) {
PetscErrorCode ierr;
ierr = BSSCheck(self); CHKERRQ(ierr);
PetscScalar z;
PetscReal xs[1] = {x};
PetscScalar Rxs[1];
CScalingCalc(self->c_scaling, xs, 1, NULL, Rxs);
CalcBSpline(self->order,
self->ts_r,
self->ts_s,
self->b_idx_list[i],
xs[0],
Rxs[0],
&z,
NULL);
*y = z;
return 0;
}
int testCalcBSpline() {
PrintTimeStamp(PETSC_COMM_SELF, "calc", NULL);
// see paper
int order = 3;
// overlaped knot points list
double ts_r[10] = {0.0, 0.0, 0.0,
1.0, 2.0, 3.0, 4.0,
5.0, 5.0, 5.0};
PetscScalar ts_s[10];
for(int i = 0; i < 10; i++)
ts_s[i] = ts_r[i];
// non overlaped points list
//double zs[6] = {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
PetscBool zeroq;
PetscScalar y = 777.0;
CalcBSpline(order, ts_r, ts_s, 0, 0.0, 0.0, &y, &zeroq);
ASSERT_DOUBLE_EQ(1.0, y); ASSERT_FALSE(zeroq);
CalcBSpline(order, ts_r, ts_s, 0, 1.0, 1.0, &y, &zeroq);
ASSERT_DOUBLE_EQ(0.0, y); ASSERT_TRUE(zeroq);
CalcBSpline(order, ts_r, ts_s, 6, 4.0, 4.0, &y, &zeroq);
ASSERT_DOUBLE_EQ(0.0, y); ASSERT_TRUE(zeroq);
PetscScalar x = 0.34;
CalcBSpline( order, ts_r, ts_s, 2, x, x, &y, &zeroq);
ASSERT_DOUBLE_EQ(0.5*x*x, y); ASSERT_FALSE(zeroq);
CalcDerivBSpline(order, ts_r, ts_s, 2, x, x, &y, &zeroq);
ASSERT_DOUBLE_EQ(x, y); ASSERT_FALSE(zeroq);
x = 2.44;
CalcBSpline( order, ts_r, ts_s, 2, x, x, &y, &zeroq);
ASSERT_DOUBLE_EQ(0.5*x*x-3*x+4.5, y); ASSERT_FALSE(zeroq);
CalcDerivBSpline(order, ts_r, ts_s, 2, x, x, &y, &zeroq);
ASSERT_DOUBLE_EQ(x-3.0, y); ASSERT_FALSE(zeroq);
x = 3.44;
CalcBSpline( order, ts_r, ts_s, 2, x, x, &y, &zeroq);
ASSERT_DOUBLE_EQ(0.0, y); ASSERT_TRUE(zeroq);
CalcDerivBSpline(order, ts_r, ts_s, 2, x, x, &y, &zeroq);
ASSERT_DOUBLE_EQ(0.0, y); ASSERT_TRUE(zeroq);
return 0;
}
PetscErrorCode CalcBSpline(int k, double* ts_r, PetscScalar* ts,
int i, double x_r, PetscScalar x, PetscScalar* y,
PetscBool *zeroq) {
if(k < 1) {
SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE,
"order must be positive integer\n");
}
PetscBool _zeroq;
if(x_r < ts_r[i] || ts_r[i+k] < x_r) {
*y = 0.0;
if(zeroq != NULL)
*zeroq = PETSC_TRUE;
return 0;
}
if(k == 1) {
if(ts_r[i] <= x_r && x_r < ts_r[i+1]) {
*y = 1.0;
_zeroq = PETSC_FALSE;
} else {
*y = 0.0;
_zeroq = PETSC_TRUE;
}
} else {
PetscScalar ti = ts[i];
PetscScalar ti1 = ts[i+1];
PetscScalar tidm1 = ts[i+k-1];
PetscScalar tid = ts[i+k];
PetscBool zeroq0, zeroq1;
PetscScalar bs0; CalcBSpline(k-1, ts_r, ts, i, x_r, x, &bs0, &zeroq0);
PetscScalar bs1; CalcBSpline(k-1, ts_r, ts, i+1, x_r, x, &bs1, &zeroq1);
_zeroq = PETSC_TRUE;
PetscScalar acc = 0.0;
//if(ScalarAbs(bs0) > 0.000000001 && !zeroq0) {
if(!zeroq0) {
PetscScalar x_minus_ti = x - ti;
if(ScalarAbs(x_minus_ti) > 0.00000000001) {
acc += x_minus_ti / (tidm1 - ti) * bs0;
} else {
zeroq0 = PETSC_TRUE;
}
}
// if(ScalarAbs(bs1) > 0.000000001 && !zeroq1) {
if( !zeroq1) {
if(ScalarAbs(tid-x) > 0.00000000001) {
acc += (tid - x) / (tid - ti1) * bs1;
} else {
zeroq1 = PETSC_TRUE;
}
}
*y = acc;
_zeroq = zeroq1 && zeroq0;
}
if(zeroq != NULL)
*zeroq = _zeroq;
return 0;
}
PetscErrorCode BSSSetUp(BSS self) {
PetscErrorCode ierr;
// check knots are setted
if(!self->set_knots)
SETERRQ(self->comm, 1, "Knots information is not setted. Call BSSSetKnots first.");
// set default scaler
if(self->c_scaling == NULL)
BSSSetCScaling(self, NULL);
// copy ts_r and ts_s
PetscReal *zs; PetscInt num_zs;
BPSGetZs(self->bps, &zs, &num_zs);
for(int i = 0; i < self->order-1; i++) {
self->ts_r[i] = zs[0];
self->ts_r[self->order-1+num_zs+i] = zs[num_zs-1];
}
for(int i = 0; i < num_zs; i++)
self->ts_r[i+self->order-1] = zs[i];
PetscFree(zs);
CScalingCalc(self->c_scaling, self->ts_r, self->num_ts, NULL, self->ts_s);
// for(int i = 0; i < self->num_ts; i++)
// self->ts_s[i] = self->ts_r[i];
// index of basis
for(int ib = 0; ib < self->num_basis; ib++)
self->b_idx_list[ib] = ib + 1;
// each element
for(int ie = 0; ie < self->num_ele; ie++) {
PetscScalar a, b; a = self->bps->zs[ie]; b = self->bps->zs[ie+1];
for(int iq = 0; iq < self->order; iq++) {
PetscReal x_r[1], w_r[1];
PetscScalar x_c[1];
int ix = ie*self->order+iq;
PetscScalar quad_x, quad_w;
LegGauss(self->order, iq, &quad_x, &quad_w);
x_r[0] = creal(quad_x); w_r[0] = creal(quad_w);
x_r[0] = (b+a)/2.0 + (b-a)/2.0 * x_r[0]; w_r[0] = (b-a)/2.0*w_r[0];
CScalingCalc(self->c_scaling, x_r, 1, NULL, x_c);
self->xs[ix] = x_r[0];
self->ws[ix] = w_r[0];
self->xs_s[ix] = x_c[0];
for(int ib = 0; ib < self->num_basis; ib++) {
PetscScalar y;
PetscScalar dy;
PetscReal *ts_r = self->ts_r;
PetscScalar *ts_s = self->ts_s;
int idx = self->b_idx_list[ib];
CalcBSpline( self->order, ts_r, ts_s, idx, x_r[0], x_c[0], &y, NULL);
CalcDerivBSpline(self->order, ts_r, ts_s, idx, x_r[0], x_c[0], &dy, NULL);
int iy = ib*(self->num_ele*self->order) + ie*self->order + iq;
self->vals[iy] = y;
self->derivs[iy] = dy;
}
}
}
int n_xs = self->num_ele * self->order;
ierr = CScalingCalc(self->c_scaling, self->xs, n_xs,
self->qrs, self->Rrs); CHKERRQ(ierr);
self->setup = PETSC_TRUE;
return 0;
}