def sphericalHarmonics(order):
e = EnvironmentMap(50, "LatLong")
sa = e.solidAngles()
cols = ["Mode = {}".format(col) for col in range(-order, order + 1)]
rows = ["Order = {}".format(row) for row in range(order + 1)]
u = np.cos(np.linspace(0, np.pi, 50))
v = np.linspace(0, 2 * np.pi, 100)
ret = []
for n in range(order):
for m in range(-n, n + 1):
s = spharm(n, m, u, v)
ret.append(s * sa)
plt.figure(0)
plt.subplot(order, order * 2 - 1, n * (order * 2 - 1) + m + order)
plt.imshow(ret[-1].real)
plt.gca().axes.get_xaxis().set_visible(False)
plt.gca().axes.get_yaxis().set_visible(False)
# plt.title('n: {}, m: {}'.format(n, m))
plt.figure(1)
plt.subplot(order, order * 2 - 1, n * (order * 2 - 1) + m + order)
plt.imshow(ret[-1].imag)
plt.gca().axes.get_xaxis().set_visible(False)
plt.gca().axes.get_yaxis().set_visible(False)
# plt.title('n: {}, m: {}'.format(n, m))
plt.figure(0)
plt.tight_layout()
# plt.gcf().suptitle("order (m)", fontsize=14)
# plt.gcf().text(0.02, 0.5, 'degree (n)',
# horizontalalignment='center',
# verticalalignment='top', fontsize=14,
# rotation='vertical')
fig = plt.gcf()
fig.set_size_inches(18.5, 5.2)
fig.savefig("real.png", dpi=100, bbox_inches="tight")
plt.figure(1)
plt.tight_layout()
# plt.gcf().suptitle("order (m)", fontsize=14)
# plt.gcf().text(0.02, 0.5, 'degree (n)',
# horizontalalignment='center',
# verticalalignment='top', fontsize=14,
# rotation='vertical')
fig = plt.gcf()
fig.set_size_inches(18.5, 5.2)
fig.savefig("imag.png", dpi=100, bbox_inches="tight")
# plt.show()
return ret
def sphericalHarmonics(order):
e = EnvironmentMap(50, 'LatLong')
sa = e.solidAngles()
cols = ['Mode = {}'.format(col) for col in range(-order, order + 1)]
rows = ['Order = {}'.format(row) for row in range(order + 1)]
u = np.cos(np.linspace(0, np.pi, 50))
v = np.linspace(0, 2 * np.pi, 100)
ret = []
for n in range(order):
for m in range(-n, n + 1):
s = spharm(n, m, u, v)
ret.append(s * sa)
plt.figure(0)
plt.subplot(order, order * 2 - 1, n * (order * 2 - 1) + m + order)
plt.imshow(ret[-1].real)
plt.gca().axes.get_xaxis().set_visible(False)
plt.gca().axes.get_yaxis().set_visible(False)
#plt.title('n: {}, m: {}'.format(n, m))
plt.figure(1)
plt.subplot(order, order * 2 - 1, n * (order * 2 - 1) + m + order)
plt.imshow(ret[-1].imag)
plt.gca().axes.get_xaxis().set_visible(False)
plt.gca().axes.get_yaxis().set_visible(False)
#plt.title('n: {}, m: {}'.format(n, m))
plt.figure(0)
plt.tight_layout()
#plt.gcf().suptitle("order (m)", fontsize=14)
#plt.gcf().text(0.02, 0.5, 'degree (n)',
# horizontalalignment='center',
# verticalalignment='top', fontsize=14,
# rotation='vertical')
fig = plt.gcf()
fig.set_size_inches(18.5, 5.2)
fig.savefig('real.png', dpi=100, bbox_inches='tight')
plt.figure(1)
plt.tight_layout()
#plt.gcf().suptitle("order (m)", fontsize=14)
#plt.gcf().text(0.02, 0.5, 'degree (n)',
# horizontalalignment='center',
# verticalalignment='top', fontsize=14,
# rotation='vertical')
fig = plt.gcf()
fig.set_size_inches(18.5, 5.2)
fig.savefig('imag.png', dpi=100, bbox_inches='tight')
#plt.show()
return ret
def spharmOCL(im):
assert im.shape[0] * 2 == im.shape[1]
e = EnvironmentMap(im.shape[0], "LatLong")
sa = e.solidAngles().astype("float32")
# plt.imshow(sa)
# plt.show()
# return
depth = max(im.shape)
res_r = np.empty(depth ** 2, dtype="float32")
res_i = np.empty(depth ** 2, dtype="float32")
ctx = cl.create_some_context()
queue = cl.CommandQueue(ctx)
mf = cl.mem_flags
sa_g = cl.Buffer(ctx, mf.READ_ONLY | mf.COPY_HOST_PTR, hostbuf=sa)
im_g = cl.Buffer(ctx, mf.READ_ONLY | mf.COPY_HOST_PTR, hostbuf=im)
res_r_g = cl.Buffer(ctx, mf.READ_WRITE, res_r.nbytes)
res_i_g = cl.Buffer(ctx, mf.READ_WRITE, res_i.nbytes)
prg = cl.Program(
ctx,
"""
void atomic_add_global(volatile global float *source, const float operand);
inline float divfact(uint a, uint b) {
float r = 1.0f;
for (uint i = a + 1; i <= b; ++i) {
r *= i;
}
return 1.0f/r;
}
void atomic_add_global(volatile global float *source, const float operand) {
union {
unsigned int intVal;
float floatVal;
} newVal;
union {
unsigned int intVal;
float floatVal;
} prevVal;
do {
prevVal.floatVal = *source;
newVal.floatVal = prevVal.floatVal + operand;
} while (atomic_cmpxchg((volatile global unsigned int *)source, prevVal.intVal, newVal.intVal) != prevVal.intVal);
}
__kernel void spharm(__global const uchar *im,
const uint height,
const uint width,
const uint depth,
__global const float *sa,
__global float *res_r,
__global float *res_i) {
const uint gidy = get_global_id(0);
const uint gidx = get_global_id(1);
const float this_sa = sa[uint(gidy*width)+gidx];
const float px = convert_float_rte(im[uint(gidy*width)+gidx]);
if (gidx >= width || gidy >= height) {
return;
}
if (gidx != 1 || gidy != 1) return;
float v = (float)gidx / ((float)width - 1.0f) * 2.0f * M_PI;
float u = cos((float)gidy / ((float)height - 1.0f) * M_PI);
//uint nmax = width/2;
uint nmax = depth;
float N, Phi_r_p, Phi_i_p, Phi_r_n, Phi_i_n, P, P_1, P_2;
float fact;
int s_index = 0;
for (uint m = 0; m < nmax; ++m) {
Phi_r_p = cos((float)m*v);
Phi_i_p = sin((float)m*v);
Phi_r_n = cos(-(float)m*v);
Phi_i_n = sin(-(float)m*v);
P_2 = 1.0f;
fact = 1.0f;
for (uint i = 0; i < m; ++i) {
P_2 = -P_2 * fact * sqrt( 1.0f - (u * u) );
fact = fact + 2.0f;
}
if (isnan(P_2) || isinf(P_2)) {
printf("Here 1! nmax: %u\\n", nmax);
printf("P-2: %f, P-1: %f, P: %f\\n", P_2, P_1, P);
return;
}
P_1 = ( 2*m + 1 ) * u * P_2;
if (isnan(P_1) || isinf(P_1)) {
printf("Here 2! nmax: %u\\n", nmax);
printf("P-2: %f, P-1: %f, P: %f\\n", P_2, P_1, P);
return;
}
for (uint n = m; n < nmax; ++n) {
// sqrt(2) ? Is it a normalization term?
N = sqrt( (float)(2 >> (m == 0)) * (2*n + 1) / (4.0f * M_PI) * (divfact(n - m, n + m)));
P = ( ( ( 2.0f * ((float)n + 2.0f) - 1.0f ) * u * P_1
+ ( - ((float)n + 2.0f) - (float)m + 1.0f ) * P_2 )
/ ( ((float)n + 2.0f) - (float)m ) );
//printf("N: %f, Phi_r_p: %f, Phi_i_p: %f, P_2: %f, sa: %f, px: %f, divfact: %f \\n", N, Phi_r_p, Phi_i_p, P_2, this_sa, px, divfact(n-m, n+m));
//printf("%u: %f, ", s_index, res_r[s_index]);
//printf("P-2: %f, P-1: %f, P: %f\\n", P_2, P_1, P);
//printf("-> %f\\n", (2.0f*((float)n+2.0f) - 1.0f)*u);
//printf("u: %f, n: %f, part1: %f, part2: %f, num: %f, den: %f\\n", u, (float)n, (2.0f*((float)n+2.0f)-1.0f)*u*P_1, (-(n+2.0f) -m + 1)*P_2, (2.0f*((float)n+2.0f)-1.0f)*u*P_1 + (-((float)n+2.0f) -(float)m + 1.0f)*P_2, ((float)n+2.0f)-(float)m);
if (isnan(P) || isinf(P) || isnan(N*Phi_r_n*P_2*this_sa*px)) {
printf("nmax: %u\\n", nmax);
printf("P-2: %f, P-1: %f, P: %f\\n", P_2, P_1, P);
printf("u: %f, n: %f, m: %f, part1: %f, part2: %f, num: %f, den: %f\\n", u, (float)n, (float)m, (2.0f*((float)n+2.0f)-1.0f)*u*P_1, (-(n+2.0f) -m + 1)*P_2, (2.0f*((float)n+2.0f)-1.0f)*u*P_1 + (-((float)n+2.0f) -(float)m + 1.0f)*P_2, ((float)n+2.0f)-(float)m);
return;
}
atomic_add_global(res_r+s_index, N*Phi_r_n*P_2*this_sa*px);
//printf("%f\\n", res_r[s_index]);
atomic_add_global(res_i+s_index, N*Phi_i_n*P_2*this_sa*px);
if (m != 0) {
atomic_add_global(res_r+s_index+1, N*Phi_r_p*P_2*this_sa*px);
atomic_add_global(res_i+s_index+1, N*Phi_i_p*P_2*this_sa*px);
}
s_index += (2 >> (m == 0)); // +1 if m == 0, +2 otherwise
P_2 = P_1;
P_1 = P;
}
}
//printf("Pixel finished!\\n");
}
""",
).build()
global_shape = tuple(map(int, np.ceil(np.array(im.shape) / 64.0) * 64))
prg.spharm(
queue,
global_shape,
(1, 1),
im_g,
np.uint32(im.shape[0]),
np.uint32(im.shape[1]),
np.uint32(10),
sa_g,
res_r_g,
res_i_g,
)
cl.enqueue_copy(queue, res_r, res_r_g)
cl.enqueue_copy(queue, res_i, res_i_g)
print(res_r[:8])
print(res_i[:8])
print(res_r.sum())
print(res_i.sum())
return res_r, res_i
def spharmOCL(im):
assert im.shape[0] * 2 == im.shape[1]
e = EnvironmentMap(im.shape[0], 'LatLong')
sa = e.solidAngles().astype('float32')
#plt.imshow(sa)
#plt.show()
#return
depth = max(im.shape)
res_r = np.empty(depth**2, dtype='float32')
res_i = np.empty(depth**2, dtype='float32')
ctx = cl.create_some_context()
queue = cl.CommandQueue(ctx)
mf = cl.mem_flags
sa_g = cl.Buffer(ctx, mf.READ_ONLY | mf.COPY_HOST_PTR, hostbuf=sa)
im_g = cl.Buffer(ctx, mf.READ_ONLY | mf.COPY_HOST_PTR, hostbuf=im)
res_r_g = cl.Buffer(ctx, mf.READ_WRITE, res_r.nbytes)
res_i_g = cl.Buffer(ctx, mf.READ_WRITE, res_i.nbytes)
prg = cl.Program(
ctx, """
void atomic_add_global(volatile global float *source, const float operand);
inline float divfact(uint a, uint b) {
float r = 1.0f;
for (uint i = a + 1; i <= b; ++i) {
r *= i;
}
return 1.0f/r;
}
void atomic_add_global(volatile global float *source, const float operand) {
union {
unsigned int intVal;
float floatVal;
} newVal;
union {
unsigned int intVal;
float floatVal;
} prevVal;
do {
prevVal.floatVal = *source;
newVal.floatVal = prevVal.floatVal + operand;
} while (atomic_cmpxchg((volatile global unsigned int *)source, prevVal.intVal, newVal.intVal) != prevVal.intVal);
}
__kernel void spharm(__global const uchar *im,
const uint height,
const uint width,
const uint depth,
__global const float *sa,
__global float *res_r,
__global float *res_i) {
const uint gidy = get_global_id(0);
const uint gidx = get_global_id(1);
const float this_sa = sa[uint(gidy*width)+gidx];
const float px = convert_float_rte(im[uint(gidy*width)+gidx]);
if (gidx >= width || gidy >= height) {
return;
}
if (gidx != 1 || gidy != 1) return;
float v = (float)gidx / ((float)width - 1.0f) * 2.0f * M_PI;
float u = cos((float)gidy / ((float)height - 1.0f) * M_PI);
//uint nmax = width/2;
uint nmax = depth;
float N, Phi_r_p, Phi_i_p, Phi_r_n, Phi_i_n, P, P_1, P_2;
float fact;
int s_index = 0;
for (uint m = 0; m < nmax; ++m) {
Phi_r_p = cos((float)m*v);
Phi_i_p = sin((float)m*v);
Phi_r_n = cos(-(float)m*v);
Phi_i_n = sin(-(float)m*v);
P_2 = 1.0f;
fact = 1.0f;
for (uint i = 0; i < m; ++i) {
P_2 = -P_2 * fact * sqrt( 1.0f - (u * u) );
fact = fact + 2.0f;
}
if (isnan(P_2) || isinf(P_2)) {
printf("Here 1! nmax: %u\\n", nmax);
printf("P-2: %f, P-1: %f, P: %f\\n", P_2, P_1, P);
return;
}
P_1 = ( 2*m + 1 ) * u * P_2;
if (isnan(P_1) || isinf(P_1)) {
printf("Here 2! nmax: %u\\n", nmax);
printf("P-2: %f, P-1: %f, P: %f\\n", P_2, P_1, P);
return;
}
for (uint n = m; n < nmax; ++n) {
// sqrt(2) ? Is it a normalization term?
N = sqrt( (float)(2 >> (m == 0)) * (2*n + 1) / (4.0f * M_PI) * (divfact(n - m, n + m)));
P = ( ( ( 2.0f * ((float)n + 2.0f) - 1.0f ) * u * P_1
+ ( - ((float)n + 2.0f) - (float)m + 1.0f ) * P_2 )
/ ( ((float)n + 2.0f) - (float)m ) );
//printf("N: %f, Phi_r_p: %f, Phi_i_p: %f, P_2: %f, sa: %f, px: %f, divfact: %f \\n", N, Phi_r_p, Phi_i_p, P_2, this_sa, px, divfact(n-m, n+m));
//printf("%u: %f, ", s_index, res_r[s_index]);
//printf("P-2: %f, P-1: %f, P: %f\\n", P_2, P_1, P);
//printf("-> %f\\n", (2.0f*((float)n+2.0f) - 1.0f)*u);
//printf("u: %f, n: %f, part1: %f, part2: %f, num: %f, den: %f\\n", u, (float)n, (2.0f*((float)n+2.0f)-1.0f)*u*P_1, (-(n+2.0f) -m + 1)*P_2, (2.0f*((float)n+2.0f)-1.0f)*u*P_1 + (-((float)n+2.0f) -(float)m + 1.0f)*P_2, ((float)n+2.0f)-(float)m);
if (isnan(P) || isinf(P) || isnan(N*Phi_r_n*P_2*this_sa*px)) {
printf("nmax: %u\\n", nmax);
printf("P-2: %f, P-1: %f, P: %f\\n", P_2, P_1, P);
printf("u: %f, n: %f, m: %f, part1: %f, part2: %f, num: %f, den: %f\\n", u, (float)n, (float)m, (2.0f*((float)n+2.0f)-1.0f)*u*P_1, (-(n+2.0f) -m + 1)*P_2, (2.0f*((float)n+2.0f)-1.0f)*u*P_1 + (-((float)n+2.0f) -(float)m + 1.0f)*P_2, ((float)n+2.0f)-(float)m);
return;
}
atomic_add_global(res_r+s_index, N*Phi_r_n*P_2*this_sa*px);
//printf("%f\\n", res_r[s_index]);
atomic_add_global(res_i+s_index, N*Phi_i_n*P_2*this_sa*px);
if (m != 0) {
atomic_add_global(res_r+s_index+1, N*Phi_r_p*P_2*this_sa*px);
atomic_add_global(res_i+s_index+1, N*Phi_i_p*P_2*this_sa*px);
}
s_index += (2 >> (m == 0)); // +1 if m == 0, +2 otherwise
P_2 = P_1;
P_1 = P;
}
}
//printf("Pixel finished!\\n");
}
""").build()
global_shape = tuple(map(int, np.ceil(np.array(im.shape) / 64.0) * 64))
prg.spharm(queue, global_shape, (1, 1), im_g, np.uint32(im.shape[0]),
np.uint32(im.shape[1]), np.uint32(10), sa_g, res_r_g, res_i_g)
cl.enqueue_copy(queue, res_r, res_r_g)
cl.enqueue_copy(queue, res_i, res_i_g)
print(res_r[:8])
print(res_i[:8])
print(res_r.sum())
print(res_i.sum())
return res_r, res_i
