def fe_basis_function_figure(d,
target_elm=[1],
N_e=3,
derivative=0,
filename='tmp.pdf',
labels=False):
"""
Draw all basis functions (or their derivative), of degree d,
associated with element target_elm (may be list of elements).
Add a mesh with N_e elements.
"""
nodes, elements = mesh_uniform(N_e, d)
"""
x = 1.1
print locate_element_vectorized(x, elements, nodes)
print locate_element_scalar(x, elements, nodes)
x = 0.1, 0.4, 0.8
print locate_element_vectorized(x, elements, nodes)
"""
if isinstance(target_elm, int):
target_elm = [target_elm] # wrap in list
# Draw the basis functions for element 1
colors = ['r-2', 'b-2', 'g-2', 'y-2', 'k-2', 'c-2']
color_counter = 0
phi_drawn = [] # list of already drawn phi functions
ymin = ymax = 0
for e in target_elm:
for i in elements[e]:
if not i in phi_drawn:
x, y = phi_glob(i, elements, nodes, derivative=derivative)
if x is None and y is None:
return # abort
ymax = max(ymax, max(y))
ymin = min(ymin, min(y))
plt.plot(x, y, colors[color_counter])
color_counter += 1
if color_counter > len(colors) - 1:
color_counter = 0 # restart colors
if labels:
if derivative == 0:
plt.legend(r'\varphi_%d' % i, loc='upper right')
else:
plt.legend(r"\varphi_%d'(x)" % i, loc='upper right')
phi_drawn.append(i)
#plt.axis([nodes[0], nodes[-1], ymin-0.1, ymax+0.1])
plot_fe_mesh(nodes, elements, element_marker=[ymin - 0.1, ymax + 0.1])
plt.plot([0, 0], [0, 0], '-')
plt.axis([nodes[0], nodes[-1], ymin - 0.1, ymax + 0.1])
#plt.axes.set_aspect('')
#plt.daspect([0.2, 1, 1])
#plt.daspactmode('manual')
plt.savefig(filename)
def fe_basis_function_figure(d,
target_elm=[1],
N_e=3,
derivative=0,
filename='tmp.pdf',
labels=False):
"""
Draw all basis functions (or their derivative), of degree d,
associated with element target_elm (may be list of elements).
Add a mesh with N_e elements.
"""
nodes, elements = mesh_uniform(N_e, d)
"""
x = 1.1
print locate_element_vectorized(x, elements, nodes)
print locate_element_scalar(x, elements, nodes)
x = 0.1, 0.4, 0.8
print locate_element_vectorized(x, elements, nodes)
"""
if isinstance(target_elm, int):
target_elm = [target_elm] # wrap in list
# Draw the basis functions for element 1
phi_drawn = [] # list of already drawn phi functions
ymin = ymax = 0
for e in target_elm:
for i in elements[e]:
if not i in phi_drawn:
x, y = phi_glob(i, elements, nodes, derivative=derivative)
if x is None and y is None:
return # abort
ymax = max(ymax, max(y))
ymin = min(ymin, min(y))
plt.plot(x, y, '-')
plt.hold('on')
if labels:
if plt.backend == 'gnuplot':
if derivative == 0:
plt.legend(r'basis func. %d' % i)
else:
plt.legend(r'derivative of basis func. %d' % i)
elif plt.backend == 'matplotlib':
if derivative == 0:
plt.legend(r'\varphi_%d' % i)
else:
plt.legend(r"\varphi_%d'(x)" % i)
phi_drawn.append(i)
plt.axis([nodes[0], nodes[-1], ymin - 0.1, ymax + 0.1])
plot_fe_mesh(nodes, elements, element_marker=[ymin - 0.1, ymax + 0.1])
plt.hold('off')
plt.savefig(filename)
def fe_basis_function_figure(d, target_elm=[1], n_e=3,
derivative=0, filename='tmp.pdf',
labels=False):
"""
Draw all basis functions (or their derivative), of degree d,
associated with element target_elm (may be list of elements).
Add a mesh with n_e elements.
"""
nodes, elements = mesh_uniform(n_e, d)
"""
x = 1.1
print locate_element_vectorized(x, elements, nodes)
print locate_element_scalar(x, elements, nodes)
x = 0.1, 0.4, 0.8
print locate_element_vectorized(x, elements, nodes)
"""
if isinstance(target_elm, int):
target_elm = [target_elm] # wrap in list
# Draw the basis functions for element 1
phi_drawn = [] # list of already drawn phi functions
ymin = ymax = 0
for e in target_elm:
for i in elements[e]:
if not i in phi_drawn:
x, y = phi_glob(i, elements, nodes,
derivative=derivative)
if x is None and y is None:
return # abort
ymax = max(ymax, max(y))
ymin = min(ymin, min(y))
plt.plot(x, y, '-')
plt.hold('on')
if labels:
if plt.backend == 'gnuplot':
if derivative == 0:
plt.legend(r'basis function no. %d' % i)
else:
plt.legend(r'derivative of basis function no. %d' % i)
elif plt.backend == 'matplotlib':
if derivative == 0:
plt.legend(r'\varphi_%d' % i)
else:
plt.legend(r"\varphi_%d'(x)" % i)
phi_drawn.append(i)
plt.axis([nodes[0], nodes[-1], ymin-0.1, ymax+0.1])
plot_fe_mesh(nodes, elements, element_marker=[ymin-0.1, ymax+0.1])
plt.hold('off')
plt.savefig(filename)
plt.savefig('tmp_u_P1_welms.pdf')
plt.show()
if __name__ == '__main__':
import sys
if len(sys.argv) == 1:
print 'Usage: %s phi | pattern | u_sines | u_P1 [num_elements] [d] [uniform | random]' % sys.argv[0]
sys.exit(1)
if sys.argv[1] == 'phi':
draw_basis_functions()
elif sys.argv[1] == 'pattern':
num_elements = int(sys.argv[2])
d = int(sys.argv[3])
uniform = sys.argv[4]
nodes, elements = mesh_uniform(num_elements, d, [0, 1])
num_nodes = len(nodes)
# Shuffle nodes in random order if necessary
if uniform == 'random':
global_node_numbering = range(0, num_nodes)
import random
random.shuffle(global_node_numbering)
for e in range(len(elements)):
for r in range(len(elements[e])):
elements[e][r] = global_node_numbering[elements[e][r]]
draw_sparsity_pattern(elements, num_nodes)
elif sys.argv[1] == 'u_sines':
u_sines()
elif sys.argv[1] == 'u_P1':
u_P1()
plt.savefig('u_example_P1_welms.pdf')
plt.show()
if __name__ == '__main__':
import sys
if len(sys.argv) == 1:
print('Usage: %s phi | u_sines | u_P1 | pattern [num_elements] [d] [uniform | random]' % sys.argv[0])
sys.exit(1)
if sys.argv[1] == 'phi':
draw_basis_functions()
elif sys.argv[1] == 'pattern':
num_elements = int(sys.argv[2])
d = int(sys.argv[3])
uniform = sys.argv[4]
nodes, elements = mesh_uniform(num_elements, d, [0, 1])
num_nodes = len(nodes)
# Shuffle nodes in random order if necessary
if uniform == 'random':
global_node_numbering = list(range(0, num_nodes))
import random
random.shuffle(global_node_numbering)
for e in range(len(elements)):
for r in range(len(elements[e])):
elements[e][r] = global_node_numbering[elements[e][r]]
draw_sparsity_pattern(elements, num_nodes)
elif sys.argv[1] == 'u_sines':
u_sines()
elif sys.argv[1] == 'u_P1':
u_P1()