def main():
if (len(sys.argv) != 2):
print "Usage: " + sys.argv[0] + " matrix-name"
sys.exit(0)
# end if
matrixName = sys.argv[1] + ".mtx"
mm = open(sys.argv[1] + '.mm', 'w')
outputName = sys.argv[1] + ".png"
#outputName=sys.argv[1]+ ".pdf"
(n, n, nz, void, fld, symm) = mminfo(matrixName)
A = mmread(matrixName).tocsr().tocoo()
# creating a file in coo format
#print n, n, A.size
mm.write(str(n) + ' ' + str(n) + ' ' + str(A.size) + '\n')
for i in range(A.size):
mm.write(
str(A.row[i]) + ' ' + str(A.col[i]) + ' ' + str(A.data[i]) + '\n')
#print A.row[i]+1, A.col[i]+1 , A.data[i]
# end for
#print repr(A)
#print A.col
#print A.size
# end of creating a file in coo format
#pylab.title("Matrix :" + matrixName, fontsize=22)
pylab.title("Matrix: " + sys.argv[1] + ", n:" + str(n) + ", nz:" +
str(A.size) + '\n',
fontsize=10)
pylab.spy(A, marker='.', markersize=1)
pylab.savefig(outputName, format=None)
def plotDf(x,f,title=None):
""" Quick test routine to display derivative matrices and plot
derivatives of an arbitrary function f(x)
input: x: numpy array of mesh-points
f: function pointer to function to differentiate
"""
# calculate first and second derivative matrices
D1 = setDn(1,x,5)
# D1 = setD(1,x)
D2 = setD(2,x)
#
# print D1
# print D2
# show sparsity pattern of D1
pylab.figure()
pylab.spy(D1)
pylab.title("Sparsity pattern of D1")
# plot a function and it's derivatives
y = f(x)
pylab.figure()
pylab.plot(x,y,x,D1*y,x,D2*y)
pylab.legend(['f','D1*f','D2*f'],loc="best")
if title:
pylab.title(title)
pylab.show()
def plot_possible_hist(mapping, filename, mass_tol, rt_tol):
no_trans = (mapping > 0).sum(1)
mini_hist = []
for i in np.arange(10) + 1:
mini_hist.append((no_trans == i).sum())
print 'mini_hist ' + str(mini_hist)
plt.figure()
plt.subplot(1, 2, 1)
plt.bar(np.arange(10) + 1, mini_hist)
title = 'Binning -- MASS_TOL ' + str(mass_tol) + ', RT_TOL ' + str(rt_tol)
plt.title(title)
plt.subplot(1, 2, 2)
plt.spy(mapping, markersize=1)
plt.title('possible')
plt.suptitle(filename)
plt.show()
def analyse_matrix_and_rhs(filename_matrix, filename_rhs):
# read matrix and rhs from file
mat_object = sio.loadmat(filename_matrix)
matrix = mat_object["matrix"]
rhs_object = sio.loadmat(filename_rhs)
rhs = rhs_object["rhs"]
# size of the matrix
print("Matrix size: " + str(len(rhs)))
print("Number of nonzeros: " + str(matrix.getnnz()) + " (" + str(round(float(matrix.getnnz()) / (len(rhs)**2) * 100.0, 3)) + " %)")
# visualize matrix sparsity pattern
fig = pl.figure()
pl.spy(matrix, markersize=1)
fn_pattern = pythonlab.tempname("png")
pl.savefig(fn_pattern, dpi=60)
pl.close(fig)
# show in console
pythonlab.image(fn_pattern)
def show_spy(socp_vars):
'''Show the sparsity pattern of A and G in
the socp_vars dictionary
'''
import pylab
pylab.figure(1)
pylab.subplot(211)
# print 'A is', socp_vars['A']
if socp_vars['A'] is not None:
pylab.spy(socp_vars['A'], marker='.')
pylab.xlabel('A')
# print 'G is', socp_vars['G']
pylab.subplot(212)
pylab.spy(socp_vars['G'], marker='.')
pylab.xlabel('G')
pylab.show()
def analyse_matrix_and_rhs(filename_matrix, filename_rhs):
# read matrix and rhs from file
mat_object = sio.loadmat(filename_matrix)
matrix = mat_object["matrix"]
rhs_object = sio.loadmat(filename_rhs)
rhs = rhs_object["rhs"]
# size of the matrix
print("Matrix size: " + str(len(rhs)))
print("Number of nonzeros: " + str(matrix.getnnz()) + " (" +
str(round(float(matrix.getnnz()) /
(len(rhs)**2) * 100.0, 3)) + " %)")
# visualize matrix sparsity pattern
fig = pl.figure()
pl.spy(matrix, markersize=1)
fn_pattern = pythonlab.tempname("png")
pl.savefig(fn_pattern, dpi=60)
pl.close(fig)
# show in console
pythonlab.image(fn_pattern)
def plot_clustering(A, l, v, type="spectral"):
fig1 = pylab.figure(1)
x = range(len(v))
pylab.plot(x, v)
if type == "spectral":
pylab.title("v2: $\lambda_2$=%f"%l)
elif type == "modularity":
pylab.title("v1: $\lambda_1$=%f"%l)
else:
pylab.title("v1")
pylab.ylabel("Vector component")
fig1.show()
fig2 = pylab.figure(2)
pylab.plot(x, sorted(v))
if type == "spectral":
pylab.title("v2 sorted: $\lambda_2$=%f"%l)
elif type == "modularity":
pylab.title("v1: $\lambda_1$=%f"%l)
else:
pylab.title("v1")
pylab.ylabel("Vector component")
fig2.show()
sorted_indices = sorted((e, i) for i, e in enumerate(v))
indices = [i for (e, i) in sorted_indices]
fig3 = pylab.figure(3)
pylab.spy(A)
pylab.title("Adjacency Matrix")
fig3.show()
A1 = A[:, indices][indices]
fig4 = pylab.figure(4)
pylab.spy(A1)
pylab.title("Adjacency Matrix Sorted")
fig4.show()
pylab.show()
def spy(L):
import pylab
if isinstance(L, (matrix, spmatrix)):
pylab.spy(matrix(L))
return
n = 0
for (i, j) in L.keys():
if i > n:
n = i
if j > n:
n = j
A = zeros(n+1)
for (i, j) in L.keys():
if isnonzero(L[i,j]):
A[i,j] = 1.0
pylab.spy(matrix(A))
def generate_mm_and_plot(matrixname):
matrixName=matrixname+ ".mtx"
mm = open(matrixname +'.mm', 'w')
outputName=matrixname + ".png"
#outputName=matrixname + ".pdf"
(n,n,nz,void,fld,symm) = mminfo(matrixName)
A = mmread(matrixName).tocsr().tocoo()
# creating a file in coo format
#print n, n, A.size
mm.write( str(n) + ' ' + str(n) + ' ' + str(A.size) + '\n')
for i in range(A.size):
mm.write( str(A.row[i])+ ' ' + str(A.col[i])+ ' ' + str(A.data[i])+ '\n')
#print A.row[i]+1, A.col[i]+1 , A.data[i]
# end for
#print repr(A)
#print A.col
#print A.size
# end of creating a file in coo format
#pylab.title("Matrix :" + matrixname, fontsize=22)
pylab.title("Matrix: " + matrixname + ", n:" + str(n) + ", nz:" + str(A.size) + '\n' ,fontsize=10 )
pylab.spy(A,marker='.',markersize=1)
pylab.savefig(outputName,format=None)
# Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public
# License along with CasADi; if not, write to the Free Software
# Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
#
#
#! jacSparsity
#!======================
from casadi import *
from numpy import *
import casadi as c
from pylab import spy, show
#! We construct a simple SX expression
x = SX.sym("x",40)
y = x[:-2]-2*x[1:-1]+x[2:]
#! Let's see what the first 5 entries of y look like
print y[:5]
#! Next, we construct a function
f = SXFunction([x],[y])
f.init()
#! And we visualize the sparsity of the jacobian
spy(f.jacSparsity())
show()
socp_vars = data['socp_vars']
objval = data['objval']
N = data['N']
partition_list = data['partition_list']
# first, solve with ecos
import ecos
sol = ecos.solve(**socp_vars)
ecos_time = sol['info']['timing']['runtime']
# next, solve with dist_ecos
def objective(x):
return socp_vars['c'].dot(x)
if args.show_plot:
pylab.spy(socp_vars['G'], marker='.', alpha=0.2)
pylab.show()
t = time.time()
prox_list, global_indices = form_prox_list(socp_vars, partition_list)
split_time = time.time() - t
result = solve(prox_list, global_indices, parallel=True, max_iters=1000, rho=2)
pri = result['res_pri']
dual = result['res_dual']
if args.show_plot:
pylab.semilogy(range(len(pri)), pri, range(len(dual)), dual)
pylab.legend(['primal', 'dual'])
pylab.show()
# Assemble Helmholtz A = K*scl**2 + kx**2*M A_t = np.zeros((4*(n+1)-3, 4*(n+1)-3)) A_t[0, 0] = 1 A_t[1:n+1, :n+1] = A[1:] A_t[n:2*n+1, n:2*n+1] += A[:] A_t[2*n:3*n+1, 2*n:3*n+1] += A[:] A_t[3*n:4*n, 3*n:4*n+1] += A[:-1] A_t[-1, -1] = 1 f_hat = np.zeros(4*n+1) f_hat[:(n+1)] = np.dot(w*P.T, fj[0]) f_hat[n:2*n+1] += np.dot(w*P.T, fj[1]) f_hat[2*n:3*n+1] += np.dot(w*P.T, fj[2]) f_hat[3*n:4*n+1] += np.dot(w*P.T, fj[3]) f_hat[0] = a f_hat[-1] = b u_hat = np.linalg.solve(A_t, f_hat) uq = np.array([np.dot(P, u_hat[n*i:(i+1)*n+1]) for i in range(4)]) assert np.allclose(uq, uj) plot(xx.flatten(), uq.flatten()) figure() spy(A_t, precision=1e-8) show()
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
# Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public
# License along with CasADi; if not, write to the Free Software
# Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
#
#
#! sparsity_jac
#!======================
from casadi import *
from numpy import *
import casadi as c
from pylab import spy, show
#! We construct a simple SX expression
x = SX.sym("x", 40)
y = x[:-2] - 2 * x[1:-1] + x[2:]
#! Let's see what the first 5 entries of y look like
print(y[:5])
#! Next, we construct a function
f = Function("f", [x], [y])
#! And we visualize the sparsity of the jacobian
spy(f.sparsity_jac(0, 0))
show()
def poisson_solver_nc_ds(filename, mesh_no, flag=0):
mshfile_fullpath = icemcfd_project_folder + filename
part_names, xy_no, xy_fa, xy_cv, noofa, cvofa, faono, faocv, partofa = umesh_reader.read_unstructured_grid(
mshfile_fullpath, node_reordering=True)
# Two slices
x_slice_1 = np.linspace(1.0, 1.5, 51)
y_slice_1 = np.linspace(0.1, 0.4, 51)
x_slice_2 = 1.5 * np.ones(51)
y_slice_2 = np.linspace(0.3, 0.8, 51)
nno = xy_no.shape[0] # No. of nodes
ncv = xy_cv.shape[0] # No. of CVs
nfa = xy_fa.shape[0] # No. of faces
partofa1 = np.array(partofa) # Converting partofa to an array
faono1 = np.array(faono) # Converting faono to an array
cold_bc = np.where(
partofa1 ==
'COLD') # Vectorized approach to find face belonging to part 'COLD'
hot_bc = np.where(
partofa1 ==
'HOT') # Vectorized approach to find face belonging to part 'HOT'
solid = np.where(
partofa1 ==
'SOLID') # Vectorized approach to find face belonging to part 'SOLID'
# Find part to which each node belongs to
partono = []
for j in np.arange(nno):
part_name = partofa1[faono1[j]]
hot_count = np.array(np.where(part_name == 'HOT')).size
cold_count = np.array(np.where(part_name == 'COLD')).size
if cold_count != 0:
partono.append('COLD')
elif hot_count != 0:
partono.append('HOT')
else:
partono.append('SOLID')
partono1 = np.array(partono)
phi = np.zeros(nno) #Full phi
#Temperature for internal nodes
phi_int = np.zeros(
nno - np.unique(noofa[cold_bc]).size -
np.unique(noofa[hot_bc]).size) # Define zero internal nodes
nno_int = phi_int.size # No. of internal nodes
# Initializing values for hot and cold boundary nodes
phi_cold = 300
phi_hot = 500
#Defining boundary values in phi
phi[[np.unique(noofa[cold_bc])]] = phi_cold
phi[[np.unique(noofa[hot_bc])]] = phi_hot
source = -1.
if mesh_no == 3:
# For bivariate fit validation
max_nn = np.zeros(nno_int)
A = scysparse.csr_matrix(
(nno_int, nno_int
)) # Thank God that boundary nodes get numbered towards the end!
b = source * np.ones(nno_int)
for i in np.arange(nno_int):
n_nodes = np.unique(
noofa[faono[i]]) # Neighbouring nodes for the collocation point
if mesh_no == 3:
max_nn[i] = n_nodes.size
x_stencil = xy_no[
n_nodes,
0] # X-co-ordinates of neighbouring nodes of ith node. All of them have been taken as stencil
y_stencil = xy_no[
n_nodes,
1] # Y-co-ordinates of neighbouring nodes of ith node. All of them have been taken as stencil
xc = xy_no[i, 0] # X-co-ordinates of centroid
yc = xy_no[i, 1] # Y-co-ordinates of centroid
# Weights for 2nd derivative for all stencil points
weights_dx2 = np.zeros(len(n_nodes))
weights_dy2 = np.zeros(len(n_nodes))
for ino in range(0, len(n_nodes)):
phi_base = np.zeros(len(n_nodes))
phi_base[ino] = 1.0
_, _, weights_dx2[ino] = fit.BiVarPolyFit_X(
xc, yc, x_stencil, y_stencil, phi_base)
_, _, weights_dy2[ino] = fit.BiVarPolyFit_Y(
xc, yc, x_stencil, y_stencil, phi_base)
parts = partono1[n_nodes]
for jj, node in enumerate(n_nodes):
if parts[jj] == 'COLD':
b[i] -= phi_cold * (weights_dx2[jj] + weights_dy2[jj])
elif parts[jj] == 'HOT':
b[i] -= phi_hot * (weights_dx2[jj] + weights_dy2[jj])
else:
A[i, node] += weights_dx2[jj] + weights_dy2[jj]
if mesh_no == 3:
pol_validation(mesh_no, max_nn)
start_time1 = default_timer()
phi_int = splinalg.spsolve(A, b)
end_time1 = default_timer() - start_time1
phi[:nno_int] = phi_int
plot_data.plot_data(
xy_no[:, 0], xy_no[:, 1], phi,
"Mesh " + str(mesh_no) + ": Final Temperature Field Direct Solve.pdf")
plt.spy(A)
plt.savefig(figure_folder + "Mesh " + str(mesh_no) + ": Spy of A.pdf")
plt.close()
slice_1 = griddata(np.vstack(
(xy_no[:, 0].flatten(), xy_no[:, 1].flatten())).T,
np.vstack(phi.flatten()), (x_slice_1, y_slice_1),
method="cubic")
slice_2 = griddata(np.vstack(
(xy_no[:, 0].flatten(), xy_no[:, 1].flatten())).T,
np.vstack(phi.flatten()), (x_slice_2, y_slice_2),
method="cubic")
if flag == 1:
print "The time required for execution of spsolve is: 2.10f" % (
end_time1)
return (A)
else:
return (A, phi, slice_1, slice_2)
def Gradient(filename, mesh_no, flag=0):
mshfile_fullpath = icemcfd_project_folder + filename
part_names, xy_no, xy_fa, xy_cv, noofa, cvofa, faono, faocv, partofa = umesh_reader.read_unstructured_grid(
mshfile_fullpath, node_reordering=True)
nno = xy_no.shape[0] # No. of nodes
ncv = xy_cv.shape[0] # No. of CVs
nfa = xy_fa.shape[0] # No. of faces
partofa1 = np.array(partofa) # Converting partofa to an array
faono1 = np.array(faono) # Converting faono to an array
cold_bc = np.where(
partofa1 ==
'COLD') # Vectorized approach to find face belonging to part 'COLD'
hot_bc = np.where(
partofa1 ==
'HOT') # Vectorized approach to find face belonging to part 'HOT'
solid = np.where(
partofa1 ==
'SOLID') # Vectorized approach to find face belonging to part 'SOLID'
# Find part to which each node belongs to
partono = []
for j in np.arange(nno):
part_name = partofa1[faono1[j]]
hot_count = np.array(np.where(part_name == 'HOT')).size
cold_count = np.array(np.where(part_name == 'COLD')).size
if cold_count != 0:
partono.append('COLD')
elif hot_count != 0:
partono.append('HOT')
else:
partono.append('SOLID')
partono1 = np.array(partono)
Gx_int = scysparse.csr_matrix(
(ncv, ncv)) # Matrix to calculate X-gradient at CVs
Gy_int = scysparse.csr_matrix(
(ncv, ncv)) # Matrix to calculate Y-gradient at CVs
nfa_int = np.size(np.where(partofa1 == 'SOLID'))
Avg_cv2f = scysparse.csr_matrix((nfa_int, ncv))
for i in np.arange(ncv):
neigh_cv = np.unique(
cvofa[faocv[i]]) # Gives neighbouring CVs including the central CV
neigh_cv = np.delete(
neigh_cv, np.where(neigh_cv == i)
) # Find index of central CV and delete that entry from neighbouring CV array
neigh_cv = np.delete(
neigh_cv, np.where(neigh_cv == -1)
) # Find index of boundary CV and delete the -1 entry from neighbouring CV array
dx_ik = (xy_cv[neigh_cv, 0] - xy_cv[i, 0]
) # Stores dx for all neighbouring CVs
dy_ik = (xy_cv[neigh_cv, 1] - xy_cv[i, 1]
) # Stores dy for all neighbouring CVs
w_ik = 1. / np.sqrt(
(dx_ik**2) + (dy_ik**2)) # Array of weights for least-squared fit
a_ik = sum((w_ik * dx_ik)**2)
b_ik = sum(
((w_ik)**2) * dx_ik * dy_ik
) #Co-efficients a_ik, b_ik, c_ik from least-squared fitting algorithm.
c_ik = sum((w_ik * dy_ik)**2)
det = (a_ik * c_ik) - (b_ik**2)
# Filling out weights for collocation point
Gx_int[i, i] -= sum(((c_ik * ((w_ik)**2) * dx_ik) -
(b_ik * ((w_ik)**2) * dy_ik)) / det)
Gy_int[i, i] -= sum(((a_ik * ((w_ik)**2) * dy_ik) -
(b_ik * ((w_ik)**2) * dx_ik)) / det)
for j, n in enumerate(neigh_cv):
Gx_int[i, n] += ((c_ik * ((w_ik[j])**2) * dx_ik[j]) -
(b_ik * ((w_ik[j])**2) * dy_ik[j])) / det
Gy_int[i, n] += ((a_ik * ((w_ik[j])**2) * dy_ik[j]) -
(b_ik * ((w_ik[j])**2) * dx_ik[j])) / det
for ii in np.arange(nfa_int):
cvs = cvofa[ii]
Avg_cv2f[ii, cvs] = 0.5
Gx = Avg_cv2f * Gx_int
Gy = Avg_cv2f * Gy_int
if flag == 1:
# Validation of gradient evaluation
phi_cv = analytical_f(xy_cv[:, 0], xy_cv[:, 1])
grad_phi_analytical_x = grad_x(xy_fa[:nfa_int, 0], xy_fa[:nfa_int, 1])
grad_phi_analytical_y = grad_y(xy_fa[:nfa_int, 0], xy_fa[:nfa_int, 1])
grad_phi_num_x = Gx * phi_cv
grad_phi_num_y = Gy * phi_cv
plt.quiver(xy_fa[:nfa_int, 0],
xy_fa[:nfa_int, 1],
grad_phi_analytical_x,
grad_phi_analytical_y,
color='b')
plt.quiver(xy_fa[:nfa_int, 0],
xy_fa[:nfa_int, 1],
grad_phi_num_x,
grad_phi_num_y,
color='r')
print "Saving figure: " + figure_folder + "Mesh" + str(
mesh_no) + "Quiver plot for gradient.pdf"
plt.savefig(figure_folder + "Mesh" + str(mesh_no) +
"Quiver_gradient.pdf")
plt.close()
plt.spy(Gx)
plt.savefig(figure_folder + "Mesh " + str(mesh_no) + ": Spy of Gx.pdf")
plt.close()
plt.spy(Gy)
plt.savefig(figure_folder + "Mesh " + str(mesh_no) + ": Spy of Gy.pdf")
plt.close()
return (Gx, Gy)
opti.subject_to(pos[0] == 0) # start at position 0 ...
opti.subject_to(speed[0] == 0) # ... from stand-still
opti.subject_to(pos[-1] == 1) # finish line at position 1
# ---- misc. constraints ----------
opti.subject_to(T >= 0) # Time must be positive
# ---- initial values for solver ---
opti.set_initial(speed, 1)
opti.set_initial(T, 1)
# ---- solve NLP ------
opti.solver("ipopt") # set numerical backend
sol = opti.solve() # actual solve
# ---- post-processing ------
from pylab import plot, step, figure, legend, show, spy
plot(sol.value(speed), label="speed")
plot(sol.value(pos), label="pos")
plot(limit(sol.value(pos)), 'r--', label="speed limit")
step(range(N + 1), sol.value(U), 'k', label="throttle")
legend(loc="upper left")
figure()
spy(sol.value(jacobian(opti.g, opti.x)))
figure()
spy(sol.value(hessian(opti.f + dot(opti.lam_g, opti.g), opti.x)[0]))
show()
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
# Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public
# License along with CasADi; if not, write to the Free Software
# Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
#
#
#! sparsity_jac
#!======================
from casadi import *
from numpy import *
import casadi as c
from pylab import spy, show
#! We construct a simple SX expression
x = SX.sym("x",40)
y = x[:-2]-2*x[1:-1]+x[2:]
#! Let's see what the first 5 entries of y look like
print(y[:5])
#! Next, we construct a function
f = Function("f", [x],[y])
#! And we visualize the sparsity of the jacobian
spy(f.sparsity_jac(0, 0))
show()
opti.subject_to(pos[0]==0) # start at position 0 ...
opti.subject_to(speed[0]==0) # ... from stand-still
opti.subject_to(pos[-1]==1) # finish line at position 1
# ---- misc. constraints ----------
opti.subject_to(T>=0) # Time must be positive
# ---- initial values for solver ---
opti.set_initial(speed, 1)
opti.set_initial(T, 1)
# ---- solve NLP ------
opti.solver("ipopt") # set numerical backend
sol = opti.solve() # actual solve
# ---- post-processing ------
from pylab import plot, step, figure, legend, show, spy
plot(sol.value(speed),label="speed")
plot(sol.value(pos),label="pos")
plot(limit(sol.value(pos)),'r--',label="speed limit")
step(range(N),sol.value(U),'k',label="throttle")
legend(loc="upper left")
figure()
spy(sol.value(jacobian(opti.g,opti.x)))
figure()
spy(sol.value(hessian(opti.f+dot(opti.lam_g,opti.g),opti.x)[0]))
show()
# HELLO Assembles HELLO matrix. See Trefethen&Bau Exercise 9.3. from pylab import ones, zeros, spy, show bl = ones((8,6)) H = bl.copy() H[0:3,2:4] = zeros((3,2)) H[5:8,2:4] = zeros((3,2)) E = bl.copy() E[2,2:6] = zeros((1,4)) E[5,2:6] = zeros((1,4)) L = bl.copy() L[0:6,2:6] = zeros((6,4)) O = bl.copy() O[2:6,2:4] = zeros((4,2)) HELLO = zeros((15,40)) HELLO[1:9,1:7] = H HELLO[2:10,9:15] = E HELLO[3:11,17:23] = L HELLO[4:12,25:31] = L HELLO[5:13,33:39] = O spy(HELLO,marker='.'); show()
#追跡用画像作成。サイズは適当に。
init_pos = (120,160)
images = create_images((320,320,20), 15, init_pos)
#izipはzip関数のiteration返す版
#zip関数は二つのリストを各リストの要素ごとにタプルにして固めたリストを作る。
#imにseq,pにparticlefilter関数からの値が逐次返ってきている
for image, p in itertools.izip(images, particlefilter(images, init_pos, 8, 100)):
#予測位置、パーティクル、ウェイトを返却
position_center, position_particles, weights_particle = p
#予測フィルタからの結果を取得
#zeros_likeは同じサイズの零行列（配列）を戻す関数
position_overlay = numpy.zeros_like(image)
position_overlay[tuple(position_center)] = 1
#バラ撒いたparticleの場所を取得
particle_overlay = numpy.zeros_like(image)
particle_overlay[tuple(position_particles.T)] = 1
#上書きしていかないで追記する
pylab.hold(False)
#強制再描画。ファイルに吐くときのflash的なもんか？公式サイトにも１行しか説明なし
pylab.draw()
time.sleep(1)
#画像（image）を指定したカラーマップ（cm.gray）で書く
#help(cm)とかすれば他のカラーマップにどういうのがあるのか情報取れる
pylab.imshow(image, cmap = pylab.cm.gray)
#予測フィルタから出てきた物体の位置を青で書く
#markerには's’:四角(default)、'o’:円、‘.’：点、‘,’ ：ピクセルが指定可能
pylab.spy(position_overlay, marker='.', color='b')
#バラ撒いたパーティクルを赤く書く
pylab.spy(particle_overlay, marker=',', color='r')
pylab.show()
# This command-line utility plots the sparsity pattern from a file. To use this
# script, first generate a sparsity pattern file using MocoCasADiSolver's
# optim_write_sparsity property.
#
# Usage:
# python plot_casadi_sparsity.py <prefix>_constraint_Jacobian_sparsity.mtx
#
# In this example, <prefix> is the value of the optim_write_sparsity property.
df = pd.read_csv(sys.argv[1],
skiprows=2,
sep=' ',
names=['row_indices', 'column_indices'])
with open(sys.argv[1]) as f:
# The first line is a comment.
f.readline()
# The second line contains the number of row, columns, and nonzeroes.
line1 = f.readline()
numbers = line1.split(' ')
num_rows = int(numbers[0])
num_cols = int(numbers[1])
spmat = scipy.sparse.coo_matrix(
(np.ones_like(df.index),
(df['row_indices'] - 1, df['column_indices'] - 1)),
shape=(num_rows, num_cols))
pl.spy(spmat, markersize=2, markeredgecolor='k', marker='.')
pl.show()
coef = np.zeros((n_tasks, n_features))
times = np.linspace(0, 2 * np.pi, n_tasks)
for k in range(n_relevant_features):
coef[:, k] = np.sin((1. + rng.randn(1)) * times + 3 * rng.randn(1))
X = rng.randn(n_samples, n_features)
Y = np.dot(X, coef.T) + rng.randn(n_samples, n_tasks)
coef_lasso_ = np.array([Lasso(alpha=0.5).fit(X, y).coef_ for y in Y.T])
coef_multi_task_lasso_ = MultiTaskLasso(alpha=1.).fit(X, Y).coef_
###############################################################################
# Plot support and time series
fig = pl.figure(figsize=(8, 5))
pl.subplot(1, 2, 1)
pl.spy(coef_lasso_)
pl.xlabel('Feature')
pl.ylabel('Time (or Task)')
pl.text(10, 5, 'Lasso')
pl.subplot(1, 2, 2)
pl.spy(coef_multi_task_lasso_)
pl.xlabel('Feature')
pl.ylabel('Time (or Task)')
pl.text(10, 5, 'MultiTaskLasso')
fig.suptitle('Coefficient non-zero location')
feature_to_plot = 0
pl.figure()
pl.plot(coef[:, feature_to_plot], 'k', label='Ground truth')
pl.plot(coef_lasso_[:, feature_to_plot], 'g', label='Lasso')
pl.plot(coef_multi_task_lasso_[:, feature_to_plot],
def preview(message):
"""Diplay message in 3x3 font using pylab."""
array = fontify.convert(message)
pylab.spy(array)
pylab.show()
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
# Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public
# License along with CasADi; if not, write to the Free Software
# Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
#
#
#! sparsity_jac
#!======================
from casadi import *
from numpy import *
import casadi as c
from pylab import spy, show
#! We construct a simple SX expression
x = SX.sym("x", 40)
y = x[:-2] - 2 * x[1:-1] + x[2:]
#! Let's see what the first 5 entries of y look like
print y[:5]
#! Next, we construct a function
f = Function("f", [x], [y])
#! And we visualize the sparsity of the jacobian
spy(f.sparsity_jac())
show()
def Divergence_val(filename, mesh_no):
mshfile_fullpath = icemcfd_project_folder + filename
part_names, xy_no, xy_fa, xy_cv, noofa, cvofa, faono, faocv, partofa = umesh_reader.read_unstructured_grid(
mshfile_fullpath, node_reordering=True)
nno = xy_no.shape[0] # No. of nodes
ncv = xy_cv.shape[0] # No. of CVs
nfa = xy_fa.shape[0] # No. of faces
partofa1 = np.array(partofa) # Converting partofa to an array
faono1 = np.array(faono) # Converting faono to an array
cold_bc = np.where(
partofa1 ==
'COLD') # Vectorized approach to find face belonging to part 'COLD'
hot_bc = np.where(
partofa1 ==
'HOT') # Vectorized approach to find face belonging to part 'HOT'
solid = np.where(
partofa1 ==
'SOLID') # Vectorized approach to find face belonging to part 'SOLID'
# Find part to which each node belongs to
partono = []
for j in np.arange(nno):
part_name = partofa1[faono1[j]]
hot_count = np.array(np.where(part_name == 'HOT')).size
cold_count = np.array(np.where(part_name == 'COLD')).size
if cold_count != 0:
partono.append('COLD')
elif hot_count != 0:
partono.append('HOT')
else:
partono.append('SOLID')
partono1 = np.array(partono)
nfa_int = np.size(np.where(partofa1 == 'SOLID'))
# Divergence operator
Dx_f2cv = scysparse.csr_matrix(
(ncv, nfa_int), dtype="float64") #Creating x part of operator
Dy_f2cv = scysparse.csr_matrix(
(ncv, nfa_int), dtype="float64") #Creating y part of operator
q_bc = np.zeros(ncv)
u_bc = np.zeros(nfa)
v_bc = np.zeros(nfa)
u = (xy_fa[:, 1]) * (xy_fa[:, 0]**2) #x-component of velocity
v = -(xy_fa[:, 0]) * (xy_fa[:, 1]**2) #y-component of velocity
for l in np.arange(nfa):
if partofa1[l] != 'SOLID':
u_bc[l] = u[l]
v_bc[l] = v[l]
NORMAL = [] #blank normal array to be filled up
AREA = np.zeros(ncv)
#Pre-processing and finding normals over all CVs
for i in np.arange(ncv):
nocv = noofa[faocv[i]] # Nodal pairs for each face of the CV
face_co = xy_fa[faocv[i]] # Face centroids of each face of CV
check_vecs = face_co - xy_cv[i] #Vectors from CV centre to face centre
par_x = xy_no[nocv[:, 1], 0] - xy_no[
nocv[:, 0],
0] #x-component of vector parallel to face. Convention, 2nd point - 1st point in nocv
par_y = xy_no[nocv[:, 1], 1] - xy_no[
nocv[:, 0],
1] #y-component of vector parallel to face. Convention, 2nd point - 1st point in nocv
normal_fa = np.c_[
-par_y,
par_x] #Defining normal vector to faces. Convention, normal is 90* clock-wise.
dir_check = normal_fa[:,
0] * check_vecs[:,
0] + normal_fa[:,
1] * check_vecs[:,
1] # Checks if normal_fa is aligned in the same direction as check_vecs.
normal_fa[np.where(dir_check < 0)] = -normal_fa[np.where(
dir_check < 0
)] # Flips sign of components in normal_fa where the dot product i.e. dir_check is negative
NORMAL.append(normal_fa) # Spits out all normals indexed by Cvs
#Calculating areas of CV assuming rectangles or triangles
if np.size(faocv[i]) == 3:
area_cv = np.abs(0.5 * ((par_x[0] * par_y[1]) -
(par_x[1] * par_y[0])))
AREA[i] = area_cv
if np.size(faocv[i]) == 4:
area_cv = max(
np.abs((par_x[0] * par_y[1]) - (par_x[1] * par_y[0])),
np.abs((par_x[0] * par_y[2]) - (par_x[2] * par_y[0])))
AREA[i] = area_cv
for j in np.arange(ncv):
normal = NORMAL[j] # Normals of the CV
#Works as there are utmost 4 nodes right now. Dont know how slow it will be for higher order element shapes
for ii, nn in enumerate(faocv[j]):
if partofa1[nn] == 'SOLID':
Dx_f2cv[j, nn] += normal[ii, 0] / AREA[j]
Dy_f2cv[j, nn] += normal[ii, 1] / AREA[j]
else:
q_bc[j] += u_bc[nn] * normal[
ii, 0] / AREA[j] + v_bc[nn] * normal[ii, 1] / AREA[j]
DIVERGENCE = (Dx_f2cv.dot(u[:nfa_int])) + (Dy_f2cv.dot(v[:nfa_int])) + q_bc
e_RMS = np.sqrt(np.average(DIVERGENCE**2))
plot_data.plot_data(
xy_cv[:, 0], xy_cv[:, 1], DIVERGENCE,
"Mesh " + str(mesh_no) + "Flooded_Contour_of_Divergence.pdf")
plt.spy(Dx_f2cv)
plt.savefig(figure_folder + "Mesh " + str(mesh_no) + ": Spy of Dx.pdf")
plt.close()
plt.spy(Dy_f2cv)
plt.savefig(figure_folder + "Mesh " + str(mesh_no) + ": Spy of Dy.pdf")
plt.close()
return (Dx_f2cv, Dy_f2cv, q_bc, e_RMS)
def calcSolution(ax,bx,ay,by,mx,my,show_matrix,show_result):
hx = (bx-ax)/mx
hy = (by-ay)/my
alpha = hx/hy
x = np.linspace(ax,bx,mx+2) # grid points x including boundaries
y = np.linspace(ay,by,my+2) # grid points y including boundaries
X,Y = np.meshgrid(x,y) # 2d arrays of x,y values
X = X.T # transpose so that X(i,j),Y(i,j) are
Y = Y.T # coordinates of (i,j) point
Xint = X[1:-1,1:-1] # interior points
Yint = Y[1:-1,1:-1]
rhs = f(Xint,Yint) # evaluate f at interior points for right hand side
# rhs is modified below for boundary conditions.
# set boundary conditions around edges of usoln array:
usoln = np.zeros(X.shape)
usoln[:,0] = u_exact(x,ay)
usoln[:,-1] = u_exact(x,by)
usoln[0,:] = u_exact(ax,y)
usoln[-1,:] = u_exact(bx,y)
# adjust the rhs to include boundary terms:
rhs[:,0] -= usoln[1:-1,0] / hy**2
rhs[:,-1] -= usoln[1:-1,-1] / hy**2
rhs[0,:] -= usoln[0,1:-1] / hx**2
rhs[-1,:] -= usoln[-1,1:-1] / hx**2
# convert the 2d grid function rhs into a column vector for rhs of system:
F = rhs.reshape((mx*my,1))
# form matrix A:
Ix = sp.eye(mx,mx)
Iy = sp.eye(my,my)
ex = np.ones(mx)
ey = np.ones(my)
T = sp.spdiags([alpha*ey,-2*(alpha+1/alpha)*ey,alpha*ey],[-1,0,1],my,my)
S = sp.spdiags([1/alpha*ex,1/alpha*ex],[-1,1],mx,mx)
A = (sp.kron(Ix,T) + sp.kron(S,Iy)) / (hx*hy)
A = A.tocsr()
show_matrix = True
if (show_matrix):
pylab.figure()
pylab.spy(A,marker='.')
# Solve the linear system:
tic = time.time()
uvec = spsolve(A, F)
toc = time.time()
# reshape vector solution uvec as a grid function and
# insert this interior solution into usoln for plotting purposes:
# (recall boundary conditions in usoln are already set)
usoln[1:-1, 1:-1] = uvec.reshape( (mx,my) )
show_result = True
if show_result:
# plot results:
pylab.figure()
ax = Axes3D(pylab.gcf())
ax.plot_surface(X,Y,usoln, rstride=1, cstride=1, cmap=pylab.cm.jet)
ax.set_xlabel('x')
ax.set_ylabel('y')
ax.set_zlabel('u')
#pylab.axis([a, b, a, b])
#pylab.daspect([1 1 1])
pylab.title('Surface plot of computed solution')
pylab.show(block=False)
# form matrix A:
I = np.eye(m, m)
e = np.ones(m)
Tcol = np.zeros((m, ))
Tcol[:2] = [-4, 1]
T = toeplitz(Tcol)
Scol = np.zeros((m, ))
Scol[:2] = [0, 1]
S = toeplitz(Scol)
A = (np.kron(I, T) + np.kron(S, I)) / h**2
show_matrix = False
if (show_matrix):
pylab.spy(A, marker='.')
pylab.show()
# Solve the linear system:
uvec = solve(A, F)
# reshape vector solution uvec as a grid function and
# insert this interior solution into usoln for plotting purposes:
# (recall boundary conditions in usoln are already set)
usoln[1:-1, 1:-1] = uvec.reshape((m, m))
# using Linf norm of spectral solution good to 10 significant digits
umax_true = 0.07367135328
umax = usoln.max()
# Assemble Helmholtz A = K * scl**2 + kx**2 * M A_t = np.zeros((4 * (n + 1) - 3, 4 * (n + 1) - 3)) A_t[0, 0] = 1 A_t[1:n + 1, :n + 1] = A[1:] A_t[n:2 * n + 1, n:2 * n + 1] += A[:] A_t[2 * n:3 * n + 1, 2 * n:3 * n + 1] += A[:] A_t[3 * n:4 * n, 3 * n:4 * n + 1] += A[:-1] A_t[-1, -1] = 1 f_hat = np.zeros(4 * n + 1) f_hat[:(n + 1)] = np.dot(w * P.T, fj[0]) f_hat[n:2 * n + 1] += np.dot(w * P.T, fj[1]) f_hat[2 * n:3 * n + 1] += np.dot(w * P.T, fj[2]) f_hat[3 * n:4 * n + 1] += np.dot(w * P.T, fj[3]) f_hat[0] = a f_hat[-1] = b u_hat = np.linalg.solve(A_t, f_hat) uq = np.array([np.dot(P, u_hat[n * i:(i + 1) * n + 1]) for i in range(4)]) assert np.allclose(uq, uj) plot(xx.flatten(), uq.flatten()) figure() spy(A_t, precision=1e-8) show()
# Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public
# License along with CasADi; if not, write to the Free Software
# Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
#
#
#! jacSparsity
#!======================
from casadi import *
from numpy import *
import casadi as c
from pylab import spy, show
#! We construct a simple SX expression
x = ssym("x",40)
y = x[:-2]-2*x[1:-1]+x[2:]
#! Let's see what the first 5 entries of y look like
print y[:5]
#! Next, we construct a function
f = SXFunction([x],[y])
f.init()
#! And we visualize the sparsity of the jacobian
spy(f.jacSparsity())
show()
coef = np.zeros((n_tasks, n_features))
times = np.linspace(0, 2 * np.pi, n_tasks)
for k in range(n_relevant_features):
coef[:, k] = np.sin((1.0 + rng.randn(1)) * times + 3 * rng.randn(1))
X = rng.randn(n_samples, n_features)
Y = np.dot(X, coef.T) + rng.randn(n_samples, n_tasks)
coef_lasso_ = np.array([Lasso(alpha=0.5).fit(X, y).coef_ for y in Y.T])
coef_multi_task_lasso_ = MultiTaskLasso(alpha=1.0).fit(X, Y).coef_
###############################################################################
# Plot support and time series
fig = pl.figure(figsize=(8, 5))
pl.subplot(1, 2, 1)
pl.spy(coef_lasso_)
pl.xlabel("Feature")
pl.ylabel("Time (or Task)")
pl.text(10, 5, "Lasso")
pl.subplot(1, 2, 2)
pl.spy(coef_multi_task_lasso_)
pl.xlabel("Feature")
pl.ylabel("Time (or Task)")
pl.text(10, 5, "MultiTaskLasso")
fig.suptitle("Coefficient non-zero location")
feature_to_plot = 0
pl.figure()
pl.plot(coef[:, feature_to_plot], "k", label="Ground truth")
pl.plot(coef_lasso_[:, feature_to_plot], "g", label="Lasso")
pl.plot(coef_multi_task_lasso_[:, feature_to_plot], "r", label="MultiTaskLasso")
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
# Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public
# License along with CasADi; if not, write to the Free Software
# Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
#
#
#! sparsity_jac
#!======================
from casadi import *
from numpy import *
import casadi as c
from pylab import spy, show
#! We construct a simple SX expression
x = SX.sym("x",40)
y = x[:-2]-2*x[1:-1]+x[2:]
#! Let's see what the first 5 entries of y look like
print(y[:5])
#! Next, we construct a function
f = Function("f", [x],[y])
#! And we visualize the sparsity of the jacobian
spy(f.sparsity_jac())
show()
def preview(message):
"""Diplay message in 3x3 font using pylab."""
array = fontify.convert(message)
pylab.spy(array)
pylab.show()
def calcSolution(m, show_matrix, show_result):
a = 0.0
b = 1.0
h = (b - a) / (m + 1)
x = np.linspace(a, b, m + 2) # grid points x including boundaries
y = np.linspace(a, b, m + 2) # grid points y including boundaries
X, Y = np.meshgrid(x, y) # 2d arrays of x,y values
X = X.T # transpose so that X(i,j),Y(i,j) are
Y = Y.T # coordinates of (i,j) point
Xint = X[1:-1, 1:-1] # interior points
Yint = Y[1:-1, 1:-1]
rhs = f(Xint, Yint) # evaluate f at interior points for right hand side
# rhs is modified below for boundary conditions.
# set boundary conditions around edges of usoln array:
usoln = np.zeros(X.shape)
usoln[:, 0] = u_exact(x, a)
usoln[:, -1] = u_exact(x, b)
usoln[0, :] = u_exact(a, y)
usoln[-1, :] = u_exact(b, y)
# adjust the rhs to include boundary terms:
rhs[:, 0] -= usoln[1:-1, 0] / h**2
rhs[:, -1] -= usoln[1:-1, -1] / h**2
rhs[0, :] -= usoln[0, 1:-1] / h**2
rhs[-1, :] -= usoln[-1, 1:-1] / h**2
# convert the 2d grid function rhs into a column vector for rhs of system:
F = rhs.reshape((m * m, 1))
# form matrix A:
I = sp.eye(m, m)
e = np.ones(m)
T = sp.spdiags([e, -4. * e, e], [-1, 0, 1], m, m)
S = sp.spdiags([e, e], [-1, 1], m, m)
A = (sp.kron(I, T) + sp.kron(S, I)) / h**2
A = A.tocsr()
if show_matrix:
pylab.figure()
pylab.spy(A, marker='.')
# Solve the linear system:
tic = time.time()
uvec = spsolve(A, F)
toc = time.time()
# reshape vector solution uvec as a grid function and
# insert this interior solution into usoln for plotting purposes:
# (recall boundary conditions in usoln are already set)
usoln[1:-1, 1:-1] = uvec.reshape((m, m))
# Find errors
abs_err = grid_norm2(usoln - u_exact(X, Y), h)
rel_err = abs_err / grid_norm2(usoln, h)
print "m = {0}".format(m)
print "Absolute error = {0:10.3e}, relative error = {1:10.3e}".format(
abs_err, rel_err)
print 'Elapsed Time = {0} s'.format(toc - tic)
if show_result:
# plot results:
pylab.figure()
ax = Axes3D(pylab.gcf())
ax.plot_surface(X, Y, usoln, rstride=1, cstride=1, cmap=pylab.cm.jet)
ax.set_xlabel('x')
ax.set_ylabel('y')
ax.set_zlabel('u')
#pylab.axis([a, b, a, b])
#pylab.daspect([1 1 1])
pylab.title('Surface plot of computed solution')
pylab.show(block=False)
return [abs_err, rel_err]
# distance_from_center = np.sqrt(np.power(Xc-Lx/2.,2.0)+np.power(Yc-Ly/2.,2.0))
# j_obstacle,i_obstacle = np.where(distance_from_center<obstacle_radius)
# pressureCells_Mask[j_obstacle,i_obstacle] = False
# number of actual pressure cells
Np = len(np.where(pressureCells_Mask==True)[0])
q = np.ones((Np,1))
# a more advanced option is to separately create the divergence and gradient operators
DivGrad = spatial_operators.create_DivGrad_operator(Dxc,Dyc,Xc,Yc,pressureCells_Mask,boundary_conditions="Homogeneous Dirichlet")
# DivGrad = spatial_operators.create_DivGrad_operator(Dxc,Dyc,Xc,Yc,pressureCells_Mask)
Divx = spatial_operators.Divx_operator(Dxc,Xc,pressureCells_Mask,boundary_conditions="Homogeneous Dirichlet")
# Divx = spatial_operators.Divx_operator(Dxc,Xc,pressureCells_Mask,boundary_conditions="Homogeneous Neumann")
# if boundary_conditions are not specified, it defaults to "Homogeneous Neumann"
plt.spy(DivGrad)
# plt.title('Spy plot for Homogeneous Neumann')
# plt.savefig('Spy plot for Homogeneous Neumann.png')
plt.show()
print(DivGrad.shape)
############# Successive over relaxation ##################
def fcn_q(Xc,Yc,n,Re):
fcn_q = np.sin(2*np.pi*n*Yc)*(2*np.pi*n*np.cos(2*np.pi*n*Xc)+(8*n**2*np.pi**2/Re)*(np.sin(2*np.pi*n*Xc)))
return fcn_q
fc = []
for i in range(Nxc):
for j in range(Nyc):
fc.append(fcn_q(x_u[i],y_v[j],n,Re))
fc = np.array(fc)
socp_vars = data['socp_vars']
objval = data['objval']
N = data['N']
partition_list = data['partition_list']
# first, solve with ecos
import ecos
sol = ecos.solve(**socp_vars)
ecos_time = sol['info']['timing']['runtime']
# next, solve with dist_ecos
def objective(x):
return socp_vars['c'].dot(x)
if args.show_plot:
pylab.spy(socp_vars['G'], marker='.', alpha=0.2)
pylab.show()
t = time.time()
prox_list, global_indices = form_prox_list(socp_vars, partition_list)
split_time = time.time() - t
result = solve(prox_list,
global_indices,
parallel=True,
max_iters=1000,
rho=2)
pri = result['res_pri']
dual = result['res_dual']