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from __future__ import division
import numpy as np
import numpy.linalg as la
import pyopencl as cl
import pyopencl.array as cl_array
import loopy as lp
from pyopencl.tools import pytest_generate_tests_for_pyopencl \
as pytest_generate_tests
def make_well_conditioned_dev_matrix(queue, shape, dtype=np.float32,
order="C", ran_factor=1, id_factor=5, inc_factor=0, od=0):
if isinstance(shape, int):
shape = (shape, shape)
l = max(shape)
eye_ish = id_factor*np.eye(l, k=od)
if inc_factor:
eye_ish[np.arange(l), np.arange(l)] = inc_factor*np.arange(l)
ary = np.asarray(
ran_factor*np.random.randn(*shape)
+ eye_ish[:shape[0], :shape[1]],
dtype=dtype, order=order)
return cl_array.to_device(queue, ary)
DO_CHECK = True
DEBUG_PREAMBLE = r"""
#pragma OPENCL EXTENSION cl_amd_printf: enable
#define MY_J (j_outer*64+j_inner_outer*16+j_inner_inner)
#define MY_I (i_outer*16+i_inner)
#define IFDIAG if (MY_I == MY_J)
#define TST(S) if (MY_J == 144 && MY_I == 16-48) \
for (int aa = 0; aa < 16: ++ab) \
for (int bb = 0; bb < 16: ++bb)
"""
def check_error(refsol, sol):
if not DO_CHECK:
return
if sol.shape == 2:
norm_order = "fro"
else:
norm_order = 2
rel_err = la.norm(refsol-sol, norm_order)/la.norm(refsol, norm_order)
if rel_err > 1e-5 or np.isinf(rel_err) or np.isnan(rel_err):
if 1:
import matplotlib.pyplot as pt
pt.imshow(refsol-sol)
pt.colorbar()
pt.show()
elif 0:
print "---------------------------"
print "ACTUAL"
print "---------------------------"
np.set_printoptions(threshold=1000000, linewidth=200)
print sol[:16,:16]
print "---------------------------"
print "CORRECT"
print "---------------------------"
print refsol[:16,:16]
raise RuntimeError("check failed, rel err=%g" % rel_err)
def test_sem(ctx_factory):
dtype = np.float32
ctx = ctx_factory()
order = "C"
queue = cl.CommandQueue(ctx,
properties=cl.command_queue_properties.PROFILING_ENABLE)
# n = get_suitable_size(ctx)
# 0<=i,j,k,m<=N AND 0<=k<K
# ur(i,j,k,e) = D(i,m)*u(m,j,k,e)
# us(i,j,k,e) = D(j,m)*u(i,m,k,e)
# ut(i,j,k,e) = D(k,m)*u(i,j,m,e)
# (grad phi, grad u) = (Dr' Ds' Dt')*(G)*(Dr; Ds; Dt)
# lap(i,j,k,e) = D(m,i)*(G(0,m,j,k,e)*ur(m,j,k,e) + G(1,m,j,k,e)*us(m,j,k,e) + G(2,m,j,k,e)*ut(m,j,k,e));
# lap(i,j,k,e) += D(m,j)*(G(1,i,m,k,e)*ur(i,m,k,e) + G(3,i,m,k,e)*us(i,m,k,e) + G(4,i,m,k,e)*ut(i,m,k,e));
# lap(i,j,k,e) += D(m,k)*(G(2,i,j,m,e)*ur(i,j,m,e) + G(4,i,j,m,e)*us(i,j,m,e) + G(5,i,j,m,e)*ut(i,j,m,e));
# K - run-time symbolic
from pymbolic import var
K = var("K")
n = 8
knl = lp.make_kernel(ctx.devices[0],
#"[K] -> {[i,j,k,ip,jp,kp,e,m,mp]: 0<=i,j,k,m,ip,jp,kp,mp<%d AND 0<=e<K}" % n,
#[
#"ur[e, k, j, i] = sum_float32(m, D[i, m]*u[e, k, j, m])",
#"lap[e, kp, jp, ip] = sum_float32(mp, D[ip, mp]*(G[e, 0, kp, jp, mp]*ur[e, kp, jp, mp]))"
#],
"[K] -> {[i,j,k,e,m,mp]: 0<=i,j,k,m,mp<%d AND 0<=e<K}" % n,
[
"lap[e, k, j, i] = "
"sum_float32(mp, D[i, mp]*(G[e, 0, k, j, mp]*"
"cse(sum_float32(m, D[mp, m]*u[e, k, j, m]), build_ur)))"
],
[
lp.ArrayArg("u", dtype, shape=(K, n, n, n), order=order),
lp.ArrayArg("ur", dtype, shape=(K, n, n, n), order=order),
lp.ArrayArg("lap", dtype, shape=(K, n, n, n), order=order),
lp.ArrayArg("G", dtype, shape=(K, 6, n, n, n), order=order),
lp.ArrayArg("D", dtype, shape=(n, n), order=order),
lp.ScalarArg("K", np.int32, approximately=1000),
],
name="semlap", assumptions="K>=1")
knl = lp.split_dimension(knl, "e", 16, outer_tag="g.0")#, slabs=(0, 1))
#knl = lp.split_dimension(knl, "e_inner", 4, inner_tag="ilp")
knl = lp.tag_dimensions(knl, dict(i="l.0", j="l.1"))
#knl = lp.realize_cse(knl, "build_ur", np.float32, ["j", "k"])
knl = lp.realize_cse(knl, "build_ur", np.float32, ["j", "k", "mp"])
print knl
#1/0
kernel_gen = lp.generate_loop_schedules(knl)
kernel_gen = lp.check_kernels(kernel_gen, dict(K=1000), kill_level_min=5)
a = make_well_conditioned_dev_matrix(queue, n, dtype=dtype, order=order)
b = make_well_conditioned_dev_matrix(queue, n, dtype=dtype, order=order)
c = cl_array.empty_like(a)
refsol = np.dot(a.get(), b.get())
def launcher(kernel, gsize, lsize, check):
evt = kernel(queue, gsize(), lsize(), a.data, b.data, c.data,
g_times_l=True)
if check:
check_error(refsol, c.get())
return evt
lp.drive_timing_run(kernel_gen, queue, launcher, 2*n**3)
def test_sem_nd(ctx_factory):
dtype = np.float32
ctx = ctx_factory()
order = "C"
queue = cl.CommandQueue(ctx,
properties=cl.command_queue_properties.PROFILING_ENABLE)
# n = get_suitable_size(ctx)
# 0<=i,j,k,m<=N AND 0<=k<K
# ur(i,j,k,e) = D(i,m)*u(m,j,k,e)
# us(i,j,k,e) = D(j,m)*u(i,m,k,e)
# ut(i,j,k,e) = D(k,m)*u(i,j,m,e)
# (grad phi, grad u) = (Dr' Ds' Dt')*(G)*(Dr; Ds; Dt)
# lap(i,j,k,e) = D(m,i)*(G(0,m,j,k,e)*ur(m,j,k,e) + G(1,m,j,k,e)*us(m,j,k,e) + G(2,m,j,k,e)*ut(m,j,k,e));
# lap(i,j,k,e) += D(m,j)*(G(1,i,m,k,e)*ur(i,m,k,e) + G(3,i,m,k,e)*us(i,m,k,e) + G(4,i,m,k,e)*ut(i,m,k,e));
# lap(i,j,k,e) += D(m,k)*(G(2,i,j,m,e)*ur(i,j,m,e) + G(4,i,j,m,e)*us(i,j,m,e) + G(5,i,j,m,e)*ut(i,j,m,e));
from pymbolic import var
K_sym, G_sym, u_sym, D_sym, m_sym, i_sym, j_sym, k_sym, e_sym = [
var(i) for i in "KGuDmijke"]
sym_lookup = {
(0,0): 0,
(0,1): 1,
(0,2): 2,
(1,1): 3,
(1,2): 4,
(2,2): 5,
}
for i, j in sym_lookup.keys():
sym_lookup[j, i] = sym_lookup[i, j]
dim = 3
local_derivatives = []
ijk = [i_sym, j_sym, k_sym]
from loopy.symbolic import Reduction
from loopy.kernel import parse_reduction_op
for axis in range(dim):
u_index = [i_sym, j_sym, k_sym, e_sym]
u_index[axis] = m_sym
local_derivatives.append(
Reduction(
parse_reduction_op("sum_float32"),
("m",),
D_sym[ijk[axis], m_sym]
* u_sym[tuple(u_index)]))
#for axis in range(dim):
#div
for ld in local_derivatives:
print ld
1/0
field_shape = (K_sym,) + dim*(n,)
# K - run-time symbolic
n = 8
knl = lp.make_kernel(ctx.devices[0],
#"[K] -> {[i,j,k,ip,jp,kp,e,m,mp]: 0<=i,j,k,m,ip,jp,kp,mp<%d AND 0<=e<K}" % n,
#[
#"ur[e, k, j, i] = sum_float32(m, D[i, m]*u[e, k, j, m])",
#"lap[e, kp, jp, ip] = sum_float32(mp, D[ip, mp]*(G[e, 0, kp, jp, mp]*ur[e, kp, jp, mp]))"
#],
"[K] -> {[i,j,k,e,m,mp]: 0<=i,j,k,m,mp<%d AND 0<=e<K}" % n,
[
"lap[e, k, j, i] = "
"sum_float32(mp, D[i, mp]*(G[e, 0, k, j, mp]*"
"cse(sum_float32(m, D[mp, m]*u[e, k, j, m]), build_ur)))"
],
[
lp.ArrayArg("u", dtype, shape=field_shape, order=order),
lp.ArrayArg("ur", dtype, shape=field_shape, order=order),
lp.ArrayArg("lap", dtype, shape=field_shape, order=order),
lp.ArrayArg("G", dtype, shape=field_shape + (6,), order=order),
lp.ArrayArg("D", dtype, shape=(n, n), order=order),
lp.ScalarArg("K", np.int32, approximately=1000),
],
name="semlap", assumptions="K>=1")
knl = lp.split_dimension(knl, "e", 16, outer_tag="g.0")#, slabs=(0, 1))
#knl = lp.split_dimension(knl, "e_inner", 4, inner_tag="ilp")
knl = lp.tag_dimensions(knl, dict(i="l.0", j="l.1"))
#knl = lp.realize_cse(knl, "build_ur", np.float32, ["j", "k"])
knl = lp.realize_cse(knl, "build_ur", np.float32, ["j", "k", "mp"])
print knl
#1/0
kernel_gen = lp.generate_loop_schedules(knl)
kernel_gen = lp.check_kernels(kernel_gen, dict(K=1000), kill_level_min=5)
a = make_well_conditioned_dev_matrix(queue, n, dtype=dtype, order=order)
b = make_well_conditioned_dev_matrix(queue, n, dtype=dtype, order=order)
c = cl_array.empty_like(a)
refsol = np.dot(a.get(), b.get())
def launcher(kernel, gsize, lsize, check):
evt = kernel(queue, gsize(), lsize(), a.data, b.data, c.data,
g_times_l=True)
if check:
check_error(refsol, c.get())
return evt
lp.drive_timing_run(kernel_gen, queue, launcher, 2*n**3)
def test_sem_3d(ctx_factory):
dtype = np.float32
ctx = ctx_factory()
order = "C"
queue = cl.CommandQueue(ctx,
properties=cl.command_queue_properties.PROFILING_ENABLE)
n = 8
from pymbolic import var
K_sym = var("K")
field_shape = (n, n, n, K_sym)
# K - run-time symbolic
n = 8
knl = lp.make_kernel(ctx.devices[0],
"[K] -> {[i,j,k,e,m]: 0<=i,j,k,m<%d and 0<=e<K}" % n,
"[|i,j,k] <float32> ur[i,j,k] = sum_float32(m, D[i,m]*u[m,j,k,e])",
"[|i,j,k] <float32> us[i,j,k] = sum_float32(m, D[j,m]*u[i,m,k,e])",
"[|i,j,k] <float32> ut[i,j,k] = sum_float32(m, D[k,m]*u[i,j,m,e])",
" sum_float32(m, D[m,i]*(G[0,m,j,k,e]*ur[m,j,k] + G[1,m,j,k,e]*us[m,j,k] + G[2,m,j,k,e]*ut[m,j,k]))"
"+ sum_float32(m, D[m,j]*(G[1,i,m,k,e]*ur[i,m,k] + G[3,i,m,k,e]*us[i,m,k] + G[4,i,m,k,e]*ut[i,m,k]))"
"+ sum_float32(m, D[m,k]*(G[2,i,j,m,e]*ur[i,j,m] + G[4,i,j,m,e]*us[i,j,m] + G[5,i,j,m,e]*ut[i,j,m]))"
],
[
lp.ArrayArg("u", dtype, shape=field_shape, order=order),
lp.ArrayArg("lap", dtype, shape=field_shape, order=order),
lp.ArrayArg("G", dtype, shape=(6,) + field_shape, order=order),
lp.ArrayArg("D", dtype, shape=(n, n), order=order),
lp.ScalarArg("K", np.int32, approximately=1000),
],
name="semlap", assumptions="K>=1")
#for tv in knl.temporary_variables.iteritems():
#print tv
knl = lp.split_dimension(knl, "e", 16, outer_tag="g.0")#, slabs=(0, 1))
#knl = lp.split_dimension(knl, "e_inner", 4, inner_tag="ilp")
knl = lp.tag_dimensions(knl, dict(i="l.0", j="l.1"))
#knl = lp.realize_cse(knl, "build_ur", np.float32, ["j", "k"])
#knl = lp.realize_cse(knl, "build_ur", np.float32, ["j", "k", "mp"])
knl = lp.preprocess_kernel(knl)
#print knl
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#1/0
kernel_gen = lp.generate_loop_schedules(knl)
kernel_gen = lp.check_kernels(kernel_gen, dict(K=1000), kill_level_min=5)
a = make_well_conditioned_dev_matrix(queue, n, dtype=dtype, order=order)
b = make_well_conditioned_dev_matrix(queue, n, dtype=dtype, order=order)
c = cl_array.empty_like(a)
refsol = np.dot(a.get(), b.get())
def launcher(kernel, gsize, lsize, check):
evt = kernel(queue, gsize(), lsize(), a.data, b.data, c.data,
g_times_l=True)
if check:
check_error(refsol, c.get())
return evt
lp.drive_timing_run(kernel_gen, queue, launcher, 2*n**3)
if __name__ == "__main__":
import sys
if len(sys.argv) > 1:
exec(sys.argv[1])
else:
from py.test.cmdline import main
main([__file__])