def LLL(l_basis):
ortho = [vector(i) for i in gram_schmidt(l_basis)]
k = 1
n = len(ortho)
while k < n:
for j in range(k - 1, -1, -1):
proj = mu(l_basis[k], ortho[j])
if abs(proj) > 1 / 2:
l_basis[k] = l_basis[k] - l_basis[j] * round(proj)
ortho = gram_schmidt(l_basis)
if ortho[k].dot_product(
ortho[k]) >= (d - mu(l_basis[k], ortho[k - 1])**2) * (
ortho[k - 1].dot_product(ortho[k - 1])):
k += 1
else:
l_basis[k], l_basis[k - 1] = l_basis[k - 1], l_basis[k]
ortho = gram_schmidt(l_basis)
k = max(k - 1, 1)
return l_basis
def qr(mat: np.ndarray):
# (n, m)
Q = gram_schmidt.gram_schmidt(mat)
# (n, k) -> Q.T: (k, n)
R = np.dot(Q.T, mat)
# (k, n) . (n, m): (k, m)
return Q, R
def periodogram(t, x, freq):
"""Returns the Lomb-Scargle periodogram of the data x(t) at frequency freq."""
R = np.zeros((t.size, 2))
R[:, 0] = np.cos(2. * np.pi * freq * t)
R[:, 1] = np.sin(2. * np.pi * freq * t)
Q = gram_schmidt(R)
myperiodogram = np.dot(Q[:, 0], x)**2 + np.dot(Q[:, 1], x)**2
return myperiodogram
def __init__(self, inputs, output, lrmul):
super(MappingBlock, self).__init__()
with torch.no_grad():
self.fc = ln.Linear(inputs, output, lrmul=lrmul)
self.fc.weight.data = self.fc.weight.data.double()
self.fc.weight.data = gram_schmidt(self.fc.weight.data)
self.fc.bias.data = self.fc.bias.data.double()
self.i_fc = ln.Linear(output, inputs, lrmul=lrmul)
self.last_activation = None
self.alpha = 0.2
def tapered_periodogram(t, x, freq, mywindow):
"""Returns the Lomb-Scargle periodogram of the data x(t) at frequency freq."""
R = np.zeros((t.size, 2))
taper = tapering_window(t, t[-1] - t[0], mywindow)
R[:, 0] = taper * np.cos(2. * np.pi * freq * t)
R[:, 1] = taper * np.sin(2. * np.pi * freq * t)
Q = gram_schmidt(R)
myperiodogram = np.dot(Q[:, 0], x)**2 + np.dot(Q[:, 1], x)**2
return myperiodogram
def periodogram_grid_fixed(t, freq):
R = np.zeros((t.size, 2))
R[:, 0] = np.cos(2. * np.pi * freq * t)
R[:, 1] = np.sin(2. * np.pi * freq * t)
Q = gram_schmidt(R)
#mycos2=Q[:,0]
#mysin2=Q[:,1]
#myperiodogram=np.dot(mycos2,x)**2+np.dot(mysin2,x)**2
return Q
def tapered_periodogram_grid_fixed(t,freq,mywindow): R=np.zeros((t.size,2)) taper=tapering_window(t,t[-1]-t[0],mywindow) R[:,0]=taper*np.cos(2.*np.pi*freq*t) R[:,1]=taper*np.sin(2.*np.pi*freq*t) Q=gram_schmidt(R) #mycos2=Q[:,0] #mysin2=Q[:,1] #myperiodogram=np.dot(mycos2,x)**2+np.dot(mysin2,x)**2 return Q
def image_training_pca():
trained = Path(trained_path)
if (trained.is_file()):
print('Loaded {}'.format(trained_path))
return np.loadtxt(trained_path)
#TRAINING SET
images = np.zeros([trnno, areasize])
person = np.zeros([trnno, 1])
imno = 0
per = 0
#Iterate over image person folders
for dire in onlydirs:
#Iterate over image files
for k in range(1, trnperper + 1):
#Pixel matrix
a = plt.imread(mypath + dire + '/{}'.format(k) + '.pgm') / 255.0
#Reshape to vector for insertion in 'images'
images[imno, :] = np.reshape(a, [1, areasize])
person[imno, 0] = dire.split('s')[1]
imno += 1
per += 1
#CARA MEDIA
#Mean for pixel i using 'images' columns
meanimage = np.mean(images, 0)
#resto la media
images = [images[k, :] - meanimage for k in range(images.shape[0])]
A = np.transpose(images)
n, m = A.shape
L = np.dot(images, A)
#A = np.array([[60., 30., 20.], [30., 20., 15.], [20., 15., 12.]])
last_R = np.zeros(A.shape)
eig_vec_L = 1
found_eigen = False
while not found_eigen:
Q, R = gram_schmidt(L)
L = np.dot(R, Q)
eig_vec_L = np.dot(eig_vec_L, Q)
found_eigen = cmp_eigen(last_R, R)
last_R = R
eig_vec_C = np.dot(A, eig_vec_L)
for i in range(m):
eig_vec_C[:, i] /= np.linalg.norm(eig_vec_C[:, i])
np.savetxt(trained_path, eig_vec_C, fmt='%s')
return eig_vec_C
def problem():
#Initialize parameters of the problem
m = 15
n = 100
c = 2006.787453080206
#Initilize matrix A and vector b
b = empty(n)
A = empty((n, m))
#Calculate A and b according to the parameters
i = 0
while i < n:
A[i, 0] = 1
A[i, 1] = i / (n - 1)
j = 2
while j < m:
A[i, j] = power(A[i, 1], j)
j = j + 1
b[i] = (1 / c) * exp(sin(4 * A[i, 1]))
i = i + 1
print('Matrix A:')
print(A)
print('\nVector b:')
print(b)
#Calculate x by solving the least squares problem using the normal equations
#NOTE: This won't execute because A is very ill conditioned (det ~= 1E-90)
#ne_x = normal_equations(A, b)
#print(ne_x)
#Calculate x by solving the least squares problem using the Householder tranformations
h_x = householder(A, b)
print('\nValue of x using Householder:')
print(h_x)
#Calculate x by solving the least squares problem using the Gram-Schmidt
gs_x = gram_schmidt(A, b)
print('\nValue of x using Gram-Schmidt:')
print(gs_x)
#Calculate x by solving the least squares problem using the modified Gram-Schmidt
mgs_x = modified_gram_schmidt(A, b)
print('\nValue of x using modified Gram-Schmidt:')
print(mgs_x)
#Calculate x by solving the least squares problem using the SVD decomposition (pseudoinverse)
svd_x = svd(A, b)
print('\nValue of x using the SVD decomposition (pseudoinverse):')
print(svd_x)
def __init__(self, inputs, output, lrmul):
super(MappingBlock, self).__init__()
with torch.no_grad():
self.fc = ln.Linear(inputs, output, lrmul=lrmul)
self.fc.weight.data = self.fc.weight.data.double()
# print("Before", torch.norm(self.fc.weight))
self.fc.weight.data = self.fc.weight.data * 0.9 + gram_schmidt(
self.fc.weight.data) * 0.1
# print("After", torch.norm(self.fc.weight))
self.fc.bias.data = self.fc.bias.data.double()
self.i_fc = ln.Linear(output, inputs, lrmul=lrmul)
self.last_activation = None
self.alpha = 0.2
def main():
"""Script starts here."""
sampling_size = 20000
locations = mu.getlocationofdata()
print(locations.__dict__)
originscsvs = mu.readlistoffiles(locations.originfiles)
filterdcsvs = mu.readlistoffiles(locations.filteredfiles)
m_origin = mu.create_matrix_from_filelist(originscsvs, sampling_size)
m_filtered = mu.create_matrix_from_filelist(filterdcsvs, sampling_size)
q_origin, r_origin = gs.gram_schmidt(m_origin)
print(q_origin.shape, r_origin.shape)
r_filtered = np.dot(q_origin.T, m_filtered)
print("r_filtered:", r_filtered.shape)
print("r_origin:", r_origin.shape)
for colume in r_origin.T:
answer = __find_best_match(colume, r_filtered)
print("found:", answer)
def WOSA_matrix(t, freq, beta, D):
"""Returns the Lomb-Scargle+WOSA periodogram of the data x(t) at frequency freq."""
Q = int(np.floor((t.size - D) / (1. - beta) / float(D))) + 1
weight = np.zeros(t.size)
R = np.zeros((t.size, 2))
M2 = np.zeros((t.size, 2 * Q))
myfact = int((1. - beta) * float(D))
for k in range(Q):
weight[:] = 0.
weight[(k - 1) * myfact:(k - 1) * myfact + D] = 1.
R[:, 0] = weight * np.cos(2. * np.pi * freq * t)
R[:, 1] = weight * np.sin(2. * np.pi * freq * t)
Y = gram_schmidt(R)
M2[:, 2 * k] = Y[:, 0]
M2[:, 2 * k + 1] = Y[:, 1]
M2 /= np.sqrt(float(Q))
return M2
def WOSA_periodogram(t, x, freq, beta, D):
"""Returns the Lomb-Scargle+WOSA periodogram of the data x(t) at frequency freq."""
Q = int(np.floor((t.size - D) / (1. - beta) / float(D))) + 1
#weight=np.zeros(t.size)
R = np.zeros((t.size, 2))
myperiodogram = 0.
myfact = int((1. - beta) * float(D))
for k in range(Q):
#weight[:]=0.
#weight[k*myfact:k*myfact+D]=1.
R[:, 0] = weight * np.cos(2. * np.pi * freq * t)
R[:, 1] = weight * np.sin(2. * np.pi * freq * t)
Y = gram_schmidt(R)
mycos2 = Y[:, 0]
mysin2 = Y[:, 1]
myperiodogram += np.dot(mycos2, x)**2 + np.dot(mysin2, x)**2
myperiodogram /= float(Q)
return myperiodogram
def WOSA_periodogram_grid_fixed(t, freq, beta, D, mywindow):
# !!! D = nombre de points - c'est un nombre entier!
D = int(D)
Q = int(np.floor(float(t.size - D) / (1. - beta) / float(D))) + 1
weight = np.zeros(t.size)
R = np.zeros((t.size, 2))
myfact = int((1. - beta) * float(D))
W = np.zeros((t.size, 2 * Q))
for k in range(Q):
weight[:] = 0.
weight[k * myfact:k * myfact + D] = tapering_window(
t[k * myfact:k * myfact + D],
t[k * myfact + D - 1] - t[k * myfact], mywindow)
R[:, 0] = weight * np.cos(2. * np.pi * freq * t)
R[:, 1] = weight * np.sin(2. * np.pi * freq * t)
Y = gram_schmidt(R)
W[:, 2 * k] = Y[:, 0]
W[:, 2 * k + 1] = Y[:, 1]
#myperiodogram+=np.dot(mycos2,x)**2+np.dot(mysin2,x)**2
#myperiodogram/=float(Q)
return W
def vibrational_analysis(file_name):
nr_atoms = gaussian.get_nr_atoms(file_name)
atom_xyz = gaussian.get_atom_coordinates(file_name, nr_atoms)
atom_mass = gaussian.get_atom_masses(file_name, nr_atoms)
# construct inertia tensor
I = numpy.zeros((3, 3))
for i in range(nr_atoms):
m = atom_mass[i]
x = atom_xyz[i][0]
y = atom_xyz[i][1]
z = atom_xyz[i][2]
I[0][0] += m*(y*y + z*z)
I[1][1] += m*(z*z + x*x)
I[2][2] += m*(x*x + y*y)
I[0][1] -= m*(x*y)
I[1][0] -= m*(x*y)
I[0][2] -= m*(x*z)
I[2][0] -= m*(x*z)
I[1][2] -= m*(y*z)
I[2][1] -= m*(y*z)
# diagonalize
eig, X = numpy.linalg.eig(I)
# minus sign to match gaussian
X *= -1.0
# construct B vectors 1-6
B = numpy.zeros((6, nr_atoms*3))
A = numpy.zeros(3)
k = 0
for i in range(nr_atoms):
m = numpy.sqrt(atom_mass[i])
B[0][k+0] = 1.0
B[1][k+1] = 1.0
B[2][k+2] = 1.0
# B[3][k+1] = -atom_xyz[i][2]
# B[3][k+2] = atom_xyz[i][1]
# B[4][k+0] = atom_xyz[i][2]
# B[4][k+2] = -atom_xyz[i][0]
# B[5][k+0] = -atom_xyz[i][1]
# B[5][k+1] = atom_xyz[i][0]
# k += 3
for j in range(3):
A[j] = atom_xyz[i][0]*X[0][j] + atom_xyz[i][1]*X[1][j] + atom_xyz[i][2]*X[2][j]
for j in range(3):
B[3][k] = (A[1]*X[j][2] - A[2]*X[j][1])
B[4][k] = (A[2]*X[j][0] - A[0]*X[j][2])
B[5][k] = (A[0]*X[j][1] - A[1]*X[j][0])
k += 1
# construct matrix of reciprocal mass square roots
M = numpy.zeros((nr_atoms*3, nr_atoms*3))
k = 0
for iatom in range(nr_atoms):
for ixyz in range(3):
M[k][k] = 1.0/numpy.sqrt(atom_mass[iatom])
k += 1
# orthonormalize vectors
B = gram_schmidt.gram_schmidt(B, 6)
# construct projection matrix
P = numpy.eye(nr_atoms*3) - numpy.array(numpy.mat(numpy.transpose(B))*numpy.mat(B))
# read hessian
H = gaussian.get_hessian(file_name, nr_atoms)
# project out trans-rot
H_proj = numpy.array(numpy.mat(numpy.transpose(P))*(numpy.mat(H)*numpy.mat(P)))
H_mwc = numpy.array(numpy.mat(M)*(numpy.mat(H_proj)*numpy.mat(M)))
freq, L = numpy.linalg.eig(H_mwc)
C = numpy.array(numpy.transpose(L)*numpy.mat(M))
reduced_mass = numpy.zeros(nr_atoms*3 - 6)
for m in range(nr_atoms*3 - 6):
reduced_mass[m] = 1.0/numpy.dot(C[m], C[m])
T = gaussian.get_dipole_derv(file_name, nr_atoms)
dip_derv = numpy.array(numpy.mat(C)*numpy.mat(numpy.transpose(T)))
I = numpy.zeros(nr_atoms*3 - 6)
freq_cm = numpy.zeros(nr_atoms*3 - 6)
for m in range(nr_atoms*3 - 6):
I[m] = conf.au_to_kmmol*numpy.dot(dip_derv[m], dip_derv[m])
freq_cm[m] = conf.hartree_to_cm*numpy.sqrt(abs(freq[m])/conf.amu_to_au)
C_normalized = numpy.zeros((nr_atoms*3 - 6, nr_atoms, 3))
for m in range(nr_atoms*3 - 6):
k = 0
for iatom in range(nr_atoms):
for ixyz in range(3):
C_normalized[m][iatom][ixyz] = C[m][k]*reduced_mass[m]**0.5
k += 1
sort_list = []
for m in range(nr_atoms*3 - 6):
sort_list.append([freq_cm[m], m])
sort_list.sort()
freq_cm_sorted = numpy.zeros(nr_atoms*3 - 6)
I_sorted = numpy.zeros(nr_atoms*3 - 6)
reduced_mass_sorted = numpy.zeros(nr_atoms*3 - 6)
C_normalized_sorted = numpy.zeros((nr_atoms*3 - 6, nr_atoms, 3))
dip_derv_sorted = numpy.zeros((nr_atoms*3 - 6, 3))
k = 0
for s in sort_list:
m = s[1]
freq_cm_sorted[k] = freq_cm[m]
I_sorted[k] = I[m]
reduced_mass_sorted[k] = reduced_mass[m]
C_normalized_sorted[k] = C_normalized[m]
dip_derv_sorted[k] = dip_derv[m]
k += 1
return freq_cm_sorted, I_sorted, reduced_mass_sorted, C_normalized_sorted, dip_derv_sorted
for j in range(3):
B[3][k] = (A[1] * X[j][2] - A[2] * X[j][1])
B[4][k] = (A[2] * X[j][0] - A[0] * X[j][2])
B[5][k] = (A[0] * X[j][1] - A[1] * X[j][0])
k += 1
# construct matrix of reciprocal mass square roots
M = numpy.zeros((nr_atoms * 3, nr_atoms * 3))
k = 0
for iatom in range(nr_atoms):
for ixyz in range(3):
M[k][k] = 1.0 / numpy.sqrt(atom_mass[iatom])
k += 1
# orthonormalize vectors
B = gram_schmidt.gram_schmidt(B, 6)
# construct projection matrix
P = numpy.eye(nr_atoms * 3) - numpy.array(
numpy.mat(numpy.transpose(B)) * numpy.mat(B))
# read hessian
H = numpy.zeros((nr_atoms * 3, nr_atoms * 3))
for line in open('molecular_hessian', 'r').readlines():
i = int(line.split()[0])
j = int(line.split()[1])
f = float(line.split()[2])
H[i][j] = f
# symmetrize it fully
for i in range(nr_atoms * 3):
for j in range(3):
B[3][k] = (A[1]*X[j][2] - A[2]*X[j][1])
B[4][k] = (A[2]*X[j][0] - A[0]*X[j][2])
B[5][k] = (A[0]*X[j][1] - A[1]*X[j][0])
k += 1
# construct matrix of reciprocal mass square roots
M = numpy.zeros((nr_atoms*3, nr_atoms*3))
k = 0
for iatom in range(nr_atoms):
for ixyz in range(3):
M[k][k] = 1.0/numpy.sqrt(atom_mass[iatom])
k += 1
# orthonormalize vectors
B = gram_schmidt.gram_schmidt(B, 6)
# construct projection matrix
P = numpy.eye(nr_atoms*3) - numpy.array(numpy.mat(numpy.transpose(B))*numpy.mat(B))
# read hessian
H = numpy.zeros((nr_atoms*3, nr_atoms*3))
for line in open('molecular_hessian', 'r').readlines():
i = int(line.split()[0])
j = int(line.split()[1])
f = float(line.split()[2])
H[i][j] = f
# symmetrize it fully
for i in range(nr_atoms*3):
for j in range(nr_atoms*3):
