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test-3-ceed-basis.py
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test-3-ceed-basis.py
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# Copyright (c) 2017, Lawrence Livermore National Security, LLC. Produced at
# the Lawrence Livermore National Laboratory. LLNL-CODE-734707. All Rights
# reserved. See files LICENSE and NOTICE for details.
#
# This file is part of CEED, a collection of benchmarks, miniapps, software
# libraries and APIs for efficient high-order finite element and spectral
# element discretizations for exascale applications. For more information and
# source code availability see http://github.com/ceed.
#
# The CEED research is supported by the Exascale Computing Project 17-SC-20-SC,
# a collaborative effort of two U.S. Department of Energy organizations (Office
# of Science and the National Nuclear Security Administration) responsible for
# the planning and preparation of a capable exascale ecosystem, including
# software, applications, hardware, advanced system engineering and early
# testbed platforms, in support of the nation's exascale computing imperative.
# @file
# Test Ceed Basis functionality
import os
import math
import libceed
import numpy as np
import buildmats as bm
#-------------------------------------------------------------------------------
# Utilities
#-------------------------------------------------------------------------------
def eval(dim, x):
result, center = 1, 0.1
for d in range(dim):
result *= math.tanh(x[d] - center)
center += 0.1
return result
def feval(x1, x2):
return x1*x1 + x2*x2 + x1*x2 + 1
def dfeval(x1, x2):
return 2*x1 + x2
#-------------------------------------------------------------------------------
# Test creation and distruction of a H1Lagrange basis
#-------------------------------------------------------------------------------
def test_300(ceed_resource, capsys):
ceed = libceed.Ceed(ceed_resource)
b = ceed.BasisTensorH1Lagrange(1, 1, 4, 4, libceed.GAUSS_LOBATTO)
print(b)
del b
b = ceed.BasisTensorH1Lagrange(1, 1, 4, 4, libceed.GAUSS)
print(b)
del b
stdout, stderr = capsys.readouterr()
with open(os.path.abspath("./output/test_300.out")) as output_file:
true_output = output_file.read()
assert stdout == true_output
#-------------------------------------------------------------------------------
# Test QR factorization
#-------------------------------------------------------------------------------
def test_301(ceed_resource, capsys):
ceed = libceed.Ceed(ceed_resource)
qr = np.array([1, -1, 4, 1, 4, -2, 1, 4, 2, 1, -1, 0], dtype="float64")
tau = np.empty(3, dtype="float64")
qr, tau = libceed.Basis.qr_factorization(ceed, qr, tau, 4, 3)
for i in range(len(qr)):
if qr[i] <= 1E-14 and qr[i] >= -1E-14:
qr[i] = 0
print("%12.8f"%qr[i])
for i in range(len(tau)):
if tau[i] <= 1E-14 and tau[i] >= -1E-14:
tau[i] = 0
print("%12.8f"%tau[i])
stdout, stderr = capsys.readouterr()
with open(os.path.abspath("./output/test_301.out")) as output_file:
true_output = output_file.read()
assert stdout == true_output
#-------------------------------------------------------------------------------
# Test Symmetric Schur Decomposition
#-------------------------------------------------------------------------------
def test_304(ceed_resource, capsys):
ceed = libceed.Ceed(ceed_resource)
A = np.array([0.19996678, 0.0745459, -0.07448852, 0.0332866,
0.0745459, 1., 0.16666509, -0.07448852,
-0.07448852, 0.16666509, 1., 0.0745459,
0.0332866, -0.07448852, 0.0745459, 0.19996678], dtype="float64")
lam = libceed.Basis.symmetric_schur_decomposition(ceed, A, 4)
print("Q: ")
for i in range(4):
for j in range(4):
if A[j+4*i] <= 1E-14 and A[j+4*i] >= -1E-14:
A[j+4*i] = 0
print("%12.8f"%A[j+4*i])
print("lambda: ")
for i in range(4):
if lam[i] <= 1E-14 and lam[i] >= -1E-14:
lam[i] = 0
print("%12.8f"%lam[i])
stdout, stderr = capsys.readouterr()
with open(os.path.abspath("./output/test_304.out")) as output_file:
true_output = output_file.read()
assert stdout == true_output
#-------------------------------------------------------------------------------
# Test Simultaneous Diagonalization
#-------------------------------------------------------------------------------
def test_305(ceed_resource, capsys):
ceed = libceed.Ceed(ceed_resource)
M = np.array([0.19996678, 0.0745459, -0.07448852, 0.0332866,
0.0745459, 1., 0.16666509, -0.07448852,
-0.07448852, 0.16666509, 1., 0.0745459,
0.0332866, -0.07448852, 0.0745459, 0.19996678], dtype="float64")
K = np.array([3.03344425, -3.41501767, 0.49824435, -0.11667092,
-3.41501767, 5.83354662, -2.9167733, 0.49824435,
0.49824435, -2.9167733, 5.83354662, -3.41501767,
-0.11667092, 0.49824435, -3.41501767, 3.03344425], dtype="float64")
x, lam = libceed.Basis.simultaneous_diagonalization(ceed, K, M, 4)
print("x: ")
for i in range(4):
for j in range(4):
if x[j+4*i] <= 1E-14 and x[j+4*i] >= -1E-14:
x[j+4*i] = 0
print("%12.8f"%x[j+4*i])
print("lambda: ")
for i in range(4):
if lam[i] <= 1E-14 and lam[i] >= -1E-14:
lam[i] = 0
print("%12.8f"%lam[i])
stdout, stderr = capsys.readouterr()
with open(os.path.abspath("./output/test_305.out")) as output_file:
true_output = output_file.read()
assert stdout == true_output
#-------------------------------------------------------------------------------
# Test GetNumNodes and GetNumQuadraturePoints for basis
#-------------------------------------------------------------------------------
def test_306(ceed_resource):
ceed = libceed.Ceed(ceed_resource)
b = ceed.BasisTensorH1Lagrange( 3, 1, 4, 5, libceed.GAUSS_LOBATTO)
p = libceed.Basis.get_num_nodes(b)
q = libceed.Basis.get_num_quadrature_points(b)
assert p == 64
assert q == 125
#-------------------------------------------------------------------------------
# Test interpolation in multiple dimensions
#-------------------------------------------------------------------------------
def test_313(ceed_resource):
ceed = libceed.Ceed(ceed_resource)
for dim in range(1, 4):
Q = 10
Qdim = Q**dim
Xdim = 2**dim
x = np.empty(Xdim*dim, dtype="float64")
uq = np.empty(Qdim, dtype="float64")
for d in range(dim):
for i in range(Xdim):
x[d*Xdim + i] = 1 if (i % (2**(dim-d))) // (2**(dim-d-1)) else -1
X = ceed.Vector(Xdim*dim)
X.set_array(x, cmode=libceed.USE_POINTER)
Xq = ceed.Vector(Qdim*dim)
Xq.set_value(0)
U = ceed.Vector(Qdim)
U.set_value(0)
Uq = ceed.Vector(Qdim)
bxl = ceed.BasisTensorH1Lagrange(dim, dim, 2, Q, libceed.GAUSS_LOBATTO)
bul = ceed.BasisTensorH1Lagrange(dim, 1, Q, Q, libceed.GAUSS_LOBATTO)
bxl.apply(1, libceed.EVAL_INTERP, X, Xq)
xq = Xq.get_array_read()
for i in range(Qdim):
xx = np.empty(dim, dtype="float64")
for d in range(dim):
xx[d] = xq[d*Qdim + i]
uq[i] = eval(dim, xx)
Xq.restore_array_read()
Uq.set_array(uq, cmode=libceed.USE_POINTER)
# This operation is the identity because the quadrature is collocated
bul.T.apply(1, libceed.EVAL_INTERP, Uq, U)
bxg = ceed.BasisTensorH1Lagrange(dim, dim, 2, Q, libceed.GAUSS)
bug = ceed.BasisTensorH1Lagrange(dim, 1, Q, Q, libceed.GAUSS)
bxg.apply(1, libceed.EVAL_INTERP, X, Xq)
bug.apply(1, libceed.EVAL_INTERP, U, Uq)
xq = Xq.get_array_read()
u = Uq.get_array_read()
for i in range(Qdim):
xx = np.empty(dim, dtype="float64")
for d in range(dim):
xx[d] = xq[d*Qdim + i]
fx = eval(dim, xx)
assert math.fabs(u[i] - fx) < 1E-4
Xq.restore_array_read()
Uq.restore_array_read()
#-------------------------------------------------------------------------------
# Test grad in multiple dimensions
#-------------------------------------------------------------------------------
def test_314(ceed_resource):
ceed = libceed.Ceed(ceed_resource)
for dim in range (1, 4):
P, Q = 8, 10
Pdim = P**dim
Qdim = Q**dim
Xdim = 2**dim
sum1 = sum2 = 0
x = np.empty(Xdim*dim, dtype="float64")
u = np.empty(Pdim, dtype="float64")
for d in range(dim):
for i in range(Xdim):
x[d*Xdim + i] = 1 if (i % (2**(dim-d))) // (2**(dim-d-1)) else -1
X = ceed.Vector(Xdim*dim)
X.set_array(x, cmode=libceed.USE_POINTER)
Xq = ceed.Vector(Pdim*dim)
Xq.set_value(0)
U = ceed.Vector(Pdim)
Uq = ceed.Vector(Qdim*dim)
Uq.set_value(0)
Ones = ceed.Vector(Qdim*dim)
Ones.set_value(1)
Gtposeones = ceed.Vector(Pdim)
Gtposeones.set_value(0)
# Get function values at quadrature points
bxl = ceed.BasisTensorH1Lagrange(dim, dim, 2, P, libceed.GAUSS_LOBATTO)
bxl.apply(1, libceed.EVAL_INTERP, X, Xq)
xq = Xq.get_array_read()
for i in range(Pdim):
xx = np.empty(dim, dtype="float64")
for d in range(dim):
xx[d] = xq[d*Pdim + i]
u[i] = eval(dim, xx)
Xq.restore_array_read()
U.set_array(u, cmode=libceed.USE_POINTER)
# Calculate G u at quadrature points, G' * 1 at dofs
bug = ceed.BasisTensorH1Lagrange(dim, 1, P, Q, libceed.GAUSS)
bug.apply(1, libceed.EVAL_GRAD, U, Uq)
bug.T.apply(1, libceed.EVAL_GRAD, Ones, Gtposeones)
# Check if 1' * G * u = u' * (G' * 1)
gtposeones = Gtposeones.get_array_read()
uq = Uq.get_array_read()
for i in range(Pdim):
sum1 += gtposeones[i]*u[i]
for i in range(dim*Qdim):
sum2 += uq[i]
Gtposeones.restore_array_read()
Uq.restore_array_read()
assert math.fabs(sum1 - sum2) < 1E-10
#-------------------------------------------------------------------------------
# Test integration with a 2D Simplex non-tensor H1 basis
#-------------------------------------------------------------------------------
def test_320(ceed_resource):
ceed = libceed.Ceed(ceed_resource)
P, Q, dim = 6, 4, 2
xr = np.array([0., 0.5, 1., 0., 0.5, 0., 0., 0., 0., 0.5, 0.5, 1.], dtype="float64")
in_array = np.empty(P, dtype="float64")
qref = np.empty(dim*Q, dtype="float64")
qweight = np.empty(Q, dtype="float64")
interp, grad = bm.buildmats(qref, qweight)
b = ceed.BasisH1(libceed.TRIANGLE, 1, P, Q, interp, grad, qref, qweight)
# Interpolate function to quadrature points
for i in range(P):
in_array[i] = feval(xr[0*P+i], xr[1*P+i])
in_vec = ceed.Vector(P)
in_vec.set_array(in_array, cmode=libceed.USE_POINTER)
out_vec = ceed.Vector(Q)
out_vec.set_value(0)
weights_vec = ceed.Vector(Q)
weights_vec.set_value(0)
b.apply(1, libceed.EVAL_INTERP, in_vec, out_vec)
b.apply(1, libceed.EVAL_WEIGHT, libceed.VECTOR_NONE, weights_vec)
# Check values at quadrature points
out_array = out_vec.get_array_read()
weights_array = weights_vec.get_array_read()
sum = 0
for i in range(Q):
sum += out_array[i]*weights_array[i]
assert math.fabs(sum - 17./24.) < 1E-10
out_vec.restore_array_read()
weights_vec.restore_array_read()
#-------------------------------------------------------------------------------
# Test integration with a 2D Simplex non-tensor H1 basis
#-------------------------------------------------------------------------------
def test_322(ceed_resource):
ceed = libceed.Ceed(ceed_resource)
P, Q, dim = 6, 4, 2
xr = np.array([0., 0.5, 1., 0., 0.5, 0., 0., 0., 0., 0.5, 0.5, 1.], dtype="float64")
in_array = np.empty(P, dtype="float64")
qref = np.empty(dim*Q, dtype="float64")
qweight = np.empty(Q, dtype="float64")
interp, grad = bm.buildmats(qref, qweight)
b = ceed.BasisH1(libceed.TRIANGLE, 1, P, Q, interp, grad, qref, qweight)
# Interpolate function to quadrature points
for i in range(P):
in_array[i] = feval(xr[0*P+i], xr[1*P+i])
in_vec = ceed.Vector(P)
in_vec.set_array(in_array, cmode=libceed.USE_POINTER)
out_vec = ceed.Vector(Q)
out_vec.set_value(0)
weights_vec = ceed.Vector(Q)
weights_vec.set_value(0)
b.apply(1, libceed.EVAL_INTERP, in_vec, out_vec)
b.apply(1, libceed.EVAL_WEIGHT, libceed.VECTOR_NONE, weights_vec)
# Check values at quadrature points
out_array = out_vec.get_array_read()
weights_array = weights_vec.get_array_read()
sum = 0
for i in range(Q):
sum += out_array[i]*weights_array[i]
assert math.fabs(sum - 17./24.) < 1E-10
out_vec.restore_array_read()
weights_vec.restore_array_read()
#-------------------------------------------------------------------------------
# Test grad with a 2D Simplex non-tensor H1 basis
#-------------------------------------------------------------------------------
def test_323(ceed_resource):
ceed = libceed.Ceed(ceed_resource)
P, Q, dim = 6, 4, 2
xq = np.array([0.2, 0.6, 1./3., 0.2, 0.2, 0.2, 1./3., 0.6], dtype="float64")
xr = np.array([0., 0.5, 1., 0., 0.5, 0., 0., 0., 0., 0.5, 0.5, 1.], dtype="float64")
in_array = np.empty(P, dtype="float64")
qref = np.empty(dim*Q, dtype="float64")
qweight = np.empty(Q, dtype="float64")
interp, grad = bm.buildmats(qref, qweight)
b = ceed.BasisH1(libceed.TRIANGLE, 1, P, Q, interp, grad, qref, qweight)
# Interpolate function to quadrature points
for i in range(P):
in_array[i] = feval(xr[0*P+i], xr[1*P+i])
in_vec = ceed.Vector(P)
in_vec.set_array(in_array, cmode=libceed.USE_POINTER)
out_vec = ceed.Vector(Q*dim)
out_vec.set_value(0)
b.apply(1, libceed.EVAL_GRAD, in_vec, out_vec)
# Check values at quadrature points
out_array = out_vec.get_array_read()
for i in range(Q):
value = dfeval(xq[0*Q+i], xq[1*Q+i])
assert math.fabs(out_array[0*Q+i] - value) < 1E-10
value = dfeval(xq[1*Q+i], xq[0*Q+i])
assert math.fabs(out_array[1*Q+i] - value) < 1E-10
out_vec.restore_array_read()
#-------------------------------------------------------------------------------