def lstsq(a, b):
"""
Fast least-squares solver, from https://gist.github.com/aldro61/5889795
Returns the least-squares solution to a linear matrix equation.
Solves the equation `a x = b` by computing a vector `x` that
minimizes the Euclidean 2-norm `|| b - a x ||^2`. The equation may
be under-, well-, or over- determined (i.e., the number of
linearly independent rows of `a` can be less than, equal to, or
greater than its number of linearly independent columns). If `a`
is square and of full rank, then `x` (but for round-off error) is
the "exact" solution of the equation.
Parameters
----------
a : (M, N) array_like
"Coefficient" matrix.
b : (M,) array_like
Ordinate or "dependent variable" values.
residuals : bool
Compute the residuals associated with the least-squares solution
Returns
-------
x : (M,) ndarray
Least-squares solution. The shape of `x` depends on the shape of
`b`.
residuals : int
Residuals: ``b - a*x``.
"""
a = np.asarray(a, order='c')
i = dgemm(alpha=1.0, a=a.T, b=a.T, trans_b=True)
x = np.linalg.solve(i, dgemm(alpha=1.0, a=a.T, b=b)).flatten()
return x, np.dot(a, x) - b
def Transient_EIEW(x, alpha_start, alpha, Sn, Sn_inv, omega, wis):
"""
Evaluates the cost function given all parameters.
In here, we used the FORTRAN dgem-functions
instead of @ for efficient matrix multiplication.
"""
N = x.shape[0]
m = alpha.shape[1]
P_alpha_F = alpha_start
cost = omega * np.sum(x)
# cost of clients already entered (only waiting time)
for i in range(1, wis + 1):
cost += (omega - 1) * np.sum(
dgemm(1, P_alpha_F, Sn_inv[0:i * m, 0:i * m]))
F = 1 - np.sum(P_alpha_F)
P_alpha_F = np.hstack((np.matrix(P_alpha_F), alpha * F))
# cost of clients to be scheduled
for i in range(wis + 1, N + wis + 1):
exp_Si = expm(Sn[0:i * m, 0:i * m] * x[i - wis - 1])
cost += float(
dgemv(1, dgemm(1, P_alpha_F, Sn_inv[0:i * m, 0:i * m]),
np.sum(omega * np.eye(i * m) - exp_Si, 1)))
P = dgemm(1, P_alpha_F, exp_Si)
F = 1 - np.sum(P)
P_alpha_F = np.hstack((np.matrix(P), alpha * F))
return cost
def lls_with_blas(x, y, residuals=False):
"""
https://gist.github.com/aldro61/5889795
"""
i = dgemm(alpha=1.0, a=x.T, b=x.T, trans_b=True)
beta = np.linalg.solve(i, dgemm(alpha=1.0, a=x.T, b=y)).flatten()
return beta
def project_whitened_vector(self, vector_instance):
"""
Returns a sheared (non-orthogonal) reconstruction of
``vector_instance``.
Parameters
----------
vector_instance : (n_features,) ndarray
A novel vector.
Returns
-------
sheared_reconstruction : (n_features,) ndarray
A sheared (non-orthogonal) reconstruction of ``vector_instance``
"""
whitened_components = self.whitened_components
weights = dgemm(alpha=1.0,
a=vector_instance.T,
b=whitened_components.T,
trans_a=True)
return dgemm(alpha=1.0,
a=weights.T,
b=whitened_components.T,
trans_a=True,
trans_b=True)
def _llsq_solver_fast(A, y):
""" Return the least-squares solution to a linear matrix equation.
Solves the equation `A x = y` by computing a vector `x` that
minimizes the Euclidean 2-norm `|| b - a x ||^2`. The equation may
be under-, well-, or over- determined (i.e., the number of
linearly independent rows of `A` can be less than, equal to, or
greater than its number of linearly independent columns). If `A`
is square and of full rank, then `x` (but for round-off error) is
the "exact" solution of the equation.
However, if A is rank-deficient, this solver may fail. In that case, use
:func:`_llsq_solver_pinv`.
:param A: (m, d) array like
:param y: (m,) array_like
:returns x: (d,) ndarray, least square solution
"""
if type(A) != np.ndarray or not A.flags['C_CONTIGUOUS']:
warn("Matrix a is not a C-contiguous numpy array. " +
"The solver will create a copy, which will result" +
" in increased memory usage.")
A = np.asarray(A, order='c')
i = dgemm(alpha=1.0, a=A.T, b=A.T, trans_b=True)
x = np.linalg.solve(i, dgemm(alpha=1.0, a=A.T, b=y)).flatten()
return x
def project_out_vectors(self, vectors):
"""
Returns a version of `vectors` where all the basis of the
model have been projected out.
Parameters
----------
vectors : (n_vectors, n_features) ndarray
A matrix of novel vectors.
Returns
-------
projected_out : (n_vectors, n_features) ndarray
A copy of `vectors` with all basis of the model
projected out.
"""
weights = dgemm(alpha=1.0,
a=vectors.T,
b=self.components.T,
trans_a=True)
return (vectors - dgemm(alpha=1.0,
a=weights.T,
b=self.components.T,
trans_a=True,
trans_b=True))
def _solve_matrix(a, b, residuals=False):
i = dgemm(alpha=1.0, a=a.T, b=a.T, trans_b=True)
x = np.linalg.solve(i, dgemm(alpha=1.0, a=a.T, b=b)).flatten()
if residuals:
return x, np.linalg.norm(np.dot(a, x) - b)
else:
return x
def lsq(a, b, residuals=False):
if type(a) != np.ndarray or not a.flags['C_CONTIGUOUS']:
warn('Matrix a is not a C-contiguous numpy array. The solver will create a copy, which will result' + \
' in increased memory usage.')
a = np.asarray(a, order='c')
i = dgemm(alpha=1.0, a=a.T, b=a.T, trans_b=True)
x = np.linalg.solve(i, dgemm(alpha=1.0, a=a.T, b=b)).flatten()
if residuals:
return x, np.linalg.norm(np.dot(a, x) - b)
else:
return x
def g09_calculate_fock(c, s, nbf, e):
# Calculate the Fock matrix
sc_temp = blas.dgemm(1.0, np.array(c), np.array(s), 1.0)
sc = np.asmatrix(sc_temp)
sce = np.matlib.zeros((nbf, nbf))
for i in range(nbf):
sce[i, :] = e[0, i] * sc[i, :]
c_lu, ipiv, info = lapack.dgetrf(c)
ic_lu, info = lapack.dgetri(c_lu, ipiv)
f_temp = blas.dgemm(1.0, np.array(ic_lu), np.array(sce), 1.0)
f = np.asmatrix(f_temp)
return f
def forward(self, X):
# forward propagation through our network
# dot product of X (input) and first set of 3x2 weights
#self.z = np.dot(X, self.W1)
self.z = FD.dgemm(alpha=1.0, a=X.T, b=self.W1.T,
trans_a=True, trans_b=True) # MKL fast dot product
self.z2 = NN.Elu((self.z)) # ACTIVATION FUNCTION
# dot product of hidden layer (z2) and second set of 3x1 weights
#self.z3 = np.dot(self.z2, self.W2)
self.z3 = FD.dgemm(alpha=1.0, a=self.z2.T,
b=self.W2.T, trans_a=True, trans_b=True)
o = expit((self.z3)) # final activation function
return o
def dgemm(a, b, c=None, alpha=1.0, beta=0.0):
# Fortran memory layout so we reorder memory without copying, and then
# form c^T, finally converting to C layout without copying.
if not _is_contiguous(a) or not _is_contiguous(b):
print('WARNING: DGEMM called on non-contiguous data')
m, k = a.shape
n = b.shape[1]
assert k == b.shape[0]
a, ta = _reorder_fortran(a)
b, tb = _reorder_fortran(b)
if c is None:
c = np.zeros((m, n), dtype=np.float64, order='C')
if m == 0 or n == 0 or k == 0:
return c
c, tc = _reorder_fortran(c)
c = blas.dgemm(alpha=alpha,
a=b,
b=a,
c=c,
beta=beta,
trans_a=not tb,
trans_b=not ta)
c, tc = _reorder_c(c)
return c
def polynomial_kernel_matrix(P, Q, c, degree):
"""
Calculate kernel matrix using polynomial kernel.
k(p,q) = (p^{T}q + c)^d
Parameters:
-----------
P : `numpy.ndarray`
(nDataP, nDim) matrix of data. Each row corresponds to a data point.
Q : `numpy.ndarray`
(nDataQ, nDim) matrix of data. Each row corresponds to a data point.
c : `float`
Bias term, c >= 0.
degree : `int`
Degree of the polynomial kernel function.
Returns:
--------
K : `numpy.ndarray`
(nDataP,nDataQ) matrix, the polynomial kernel matrix of the P and Q data matrix.
"""
return ne.evaluate('(c + A)**d', {
'A': dgemm(alpha=1.0, a=P, b=Q, trans_b=True),
'c': c,
'd': degree
})
def xc_scalar_ni(me, sp1, R1, sp2, R2, xc_code, deriv, **kw):
from pyscf.dft.libxc import eval_xc
"""
Computes overlap for an atom pair. The atom pair is given by a pair of species indices
and the coordinates of the atoms.
Args:
sp1,sp2 : specie indices, and
R1,R2 : respective coordinates in Bohr, atomic units
Result:
matrix of orbital overlaps
The procedure uses the numerical integration in coordinate space.
"""
grids = build_3dgrid(me, sp1, R1, sp2, R2, **kw)
rho = dens_libnao(grids.coords, me.sv.nspin)
exc, vxc, fxc, kxc = libxc.eval_xc(xc_code,
rho.T,
spin=me.sv.nspin - 1,
deriv=deriv)
ao1 = ao_eval(me.ao1, R1, sp1, grids.coords)
if deriv == 1:
#print(' vxc[0].shape ', vxc[0].shape)
ao1 = ao1 * grids.weights * vxc[0]
elif deriv == 2:
ao1 = ao1 * grids.weights * fxc[0]
else:
print(' deriv ', deriv)
raise RuntimeError('!deriv!')
ao2 = ao_eval(me.ao2, R2, sp2, grids.coords)
overlaps = blas.dgemm(1.0, ao1, ao2.T)
return overlaps
def matrixMult(A,B):
global initializedMartix
global useNumpy # module based variables
mprint("A",A)
mprint("B",B)
if not initializedMatrix:
matrix_initialize()
if cuda.useCUDA:
return cuda.dot(A,B)
if useNumpy:
return np.dot(A,B)
# If the matrices are in Fortran order then the computations will be faster
# when using dgemm. Otherwise, the function will copy the matrix and that takes time.
if not A.flags['F_CONTIGUOUS']:
AA = A.T
transA = True
else:
AA = A
transA = False
if not B.flags['F_CONTIGUOUS']:
BB = B.T
transB = True
else:
BB = B
transB = False
return dgemm(alpha=1.,a=AA,b=BB,trans_a=transA,trans_b=transB)
def gemm(alpha, A, B, C, beta, MKLProc):
from scipy.linalg.blas import dgemm
from numpy import transpose
import os
os.environ['MKL_NUM_THREADS'] = str(MKLProc)
B = transpose(B)
C = dgemm(alpha, A, B, c=C, beta=beta)
return C
def project_onto_null_space(a,
n,
nt,
lb,
ub,
n_steps_projection,
reactions,
tol=1e-4,
verbose=0):
# Do matrix multuplication
a = dgemm(1.0, n, dgemm(1.0, nt, a)).transpose()[0]
i, accept = 0, True
while any(a < lb - tol) or any(a > ub + tol):
print '[WARNING] Bounds reseted: %d times' % (i + 1)
print '\t lower bound: ', reactions[a < lb - tol]
print '\t upper bound: ', reactions[a > ub + tol]
# Fix bounds violations
lb_violations = a < lb - tol
if any(lb_violations):
a[lb_violations] = lb[lb_violations]
ub_violations = a > ub
if any(ub_violations):
a[ub_violations] = ub[ub_violations]
# Do matrix multiplication
a = dgemm(1.0, n, dgemm(1.0, nt, a)).transpose()[0]
# Verbose
if i > 10:
accept, n_steps_projection = False, max(25,
n_steps_projection - 100)
# Verbose
if verbose > 1:
print '[WARNING] Point discarded! lb: %r, ub: %r' % (
any(lb_violations), any(ub_violations))
break
i += 1
if i == 0:
n_steps_projection = min(25, n_steps_projection + 25)
return accept, n_steps_projection, a.copy()
def main():
lock = int(sys.argv[1])
size_list = [2**i for i in range(8,16)]
no_runs = 10
time_df = pd.DataFrame(columns=["My function (Python)",
"My function (32 Cores Python)",
"matmul (NumPy Python)",
"dgemm (Python)",
"sgemm (Python)"])
for mat_size in size_list:
print(f"Mat size: {mat_size}")
for i in range(no_runs):
print(f"i: {i}")
m1 = np.random.rand(mat_size,mat_size).astype(np.float32)
m2 = np.random.rand(mat_size,mat_size).astype(np.float32)
new_times=[]
time.sleep(10)
if mat_size =< 2048:
my_func_start = time.perf_counter()
m_myfunc = matrix_mult(m1,m2)
my_func_finish = time.perf_counter()
new_times.append(round(my_func_finish-my_func_start,8))
my_func_32cores_start = time.perf_counter()
time_taken, m_myfunc32 = gen_time_results(mat_size,32,m1,m2)
my_func_32cores_finish = time.perf_counter()
new_times.append(round(my_func_32cores_finish-my_func_32cores_start,8))
else:
new_times.append(None)
new_times.append(None)
numpy_start = time.perf_counter()
mn = np.matmul(m1,m2)
numpy_finish = time.perf_counter()
new_times.append(round(numpy_finish-numpy_start,8))
dgemm_start = time.perf_counter()
md = FB.dgemm(alpha=1.0, a=m1, b=m2)
dgemm_finish = time.perf_counter()
new_times.append(round(dgemm_finish-dgemm_start,8))
sgemm_start = time.perf_counter()
ms = FB.sgemm(alpha=1.0, a=m1, b=m2)
sgemm_finish = time.perf_counter()
new_times.append(round(sgemm_finish-sgemm_start,8))
print(new_times)
time_df = time_df.append( pd.DataFrame(columns=["My function (Python)","My function (32 Cores Python)",
"matmul (NumPy_Python)","dgemm (Python)","sgemm (Python)"],index=[mat_size]) )
if lock:
time_df.to_pickle("time_df_libraries_lock.pkl")
else:
time_df.to_pickle("time_df_libraries_no_lock.pkl")
def seidel(adj):
"""
Implements the Seidel algorithm for APSP on unweighted, undirected graphs.
For a given adjacency matrix, returns a like-sized matrix holding the
distances of the shortest paths between nodes.
"""
n = adj.shape[0]
# Prepare our base case to compare against, an n x n matrix that is 0 on the
# diagonal and 1 everywhere else.
base_case = np.ones_like(adj)
np.fill_diagonal(base_case, 0)
# Let Z = A . A
# Using DGEMM directly here instead of np.dot because the latter is 10x slower.
z = dgemm(1, adj, adj)
# Let B be an n x n binary matrix
# where b_ij =
# 1 if it isn't on the diagonal and a_ij = 1 or z_ij > 0
# 0 otherwise
b = np.where(
np.logical_and(
# Not on the diagonal
np.logical_not(np.eye(n)),
np.logical_or(adj == 1, z > 0)),
1,
0)
# If all b_ij not on the diagonal are 1
if (b == base_case).all():
return 2 * b - adj
t = seidel(b)
# Let X = T . A
x = dgemm(1, t, adj)
# Return n x n matrix D
# where d_ij =
# 2*t_ij if x_ij >= t_ij * degree(j)
# 2*t_ij - 1 if x_ij < t_ij * degree(j)
degrees = np.repeat(np.sum(adj, axis=1)[None, :], adj.shape[0], axis=0)
d = np.where(x >= np.multiply(t, degrees), 2 * t, 2 * t - 1)
return d.astype('float32')
def calc_XVX(X, VX):
XVX = np.zeros((VX.shape[1], X.shape[0], VX.shape[2]))
for i in range(XVX.shape[2]):
XVX[:, :, i] = blas.dgemm(1.0, VX[:, :, i], X, trans_a=1, trans_b=1)
return XVX
def project_out_vectors(self, vectors):
"""
Returns a version of `vectors` where all the basis of the
model have been projected out.
Parameters
----------
vectors : (n_vectors, n_features) ndarray
A matrix of novel vectors.
Returns
-------
projected_out : (n_vectors, n_features) ndarray
A copy of `vectors` with all basis of the model
projected out.
"""
weights = dgemm(alpha=1.0, a=vectors.T, b=self.components.T, trans_a=True)
return vectors - dgemm(alpha=1.0, a=weights.T, b=self.components.T, trans_a=True, trans_b=True)
def dgemm(a, b, c=None, alpha=1.0, beta=0.0):
''' Performs dgemm in Fortran memory alignment without copying.
Input matrix should be contiguous (either F or C).
Parameters
----------
a : array
input matrix a
b : array
input matrix b
c : array, optional
output matrix c, if None then it is allocated inside the
function, default None
alpha : float, optional
scalar factor for matrix a
beta : float, optional
scalar factor for matrix c
Returns
-------
c : ndarray
output matrix
'''
#FIXME: this needs testing better - currently this should only be
# used where it has been tested against np.dot specifically for
# that use case!
if (not _is_contiguous(a)) or (not _is_contiguous(b)):
log.warn('DGEMM called on non-contiguous data')
m, k = a.shape
n = b.shape[1]
assert k == b.shape[0]
a, ta = _reorder_fortran(a)
b, tb = _reorder_fortran(b)
if c is None:
c = np.zeros((m, n), dtype=np.float64, order='C')
if m == 0 or n == 0 or k == 0:
return c
c, tc = _reorder_fortran(c)
c = blas.dgemm(alpha=alpha,
a=b,
b=a,
c=c,
beta=beta,
trans_a=not tb,
trans_b=not ta)
c, tc = _reorder_c(c)
return c
def project_whitened_vector(self, vector_instance):
"""
Returns a sheared (non-orthogonal) reconstruction of
``vector_instance``.
Parameters
----------
vector_instance : (n_features,) ndarray
A novel vector.
Returns
-------
sheared_reconstruction : (n_features,) ndarray
A sheared (non-orthogonal) reconstruction of ``vector_instance``
"""
whitened_components = self.whitened_components
weights = dgemm(alpha=1.0, a=vector_instance.T,
b=whitened_components.T, trans_a=True)
return dgemm(alpha=1.0, a=weights.T, b=whitened_components.T,
trans_a=True, trans_b=True)
def linear_least_squares(a, b, residuals=False):
"""
Return the least-squares solution to a linear matrix equation.
Solves the equation `a x = b` by computing a vector `x` that
minimizes the Euclidean 2-norm `|| b - a x ||^2`. The equation may
be under-, well-, or over- determined (i.e., the number of
linearly independent rows of `a` can be less than, equal to, or
greater than its number of linearly independent columns). If `a`
is square and of full rank, then `x` (but for round-off error) is
the "exact" solution of the equation.
Parameters
----------
a : (M, N) array_like
"Coefficient" matrix.
b : (M,) array_like
Ordinate or "dependent variable" values.
residuals : bool
Compute the residuals associated with the least-squares solution
Returns
-------
x : (M,) ndarray
Least-squares solution. The shape of `x` depends on the shape of
`b`.
residuals : int (Optional)
Sums of residuals; squared Euclidean 2-norm for each column in
``b - a*x``.
"""
if type(a) != np.ndarray or not a.flags['C_CONTIGUOUS']:
warn('Matrix a is not a C-contiguous numpy array. The solver will create a copy, which will result' + \
' in increased memory usage.')
a = np.asarray(a, order='c')
i = dgemm(alpha=1.0, a=a.T, b=a.T, trans_b=True)
x = np.linalg.solve(i, dgemm(alpha=1.0, a=a.T, b=b)).flatten()
if residuals:
return x, np.linalg.norm(np.dot(a, x) - b)
else:
return x
def applyBND(mat, **kwargs):
"""Return a BND refinement of a symetric matrix.
If the matrix is not symetric. The calculation for mat+mat.T will be
performanced.
It has comparable speed with the original MATLAB code.
[SUP15] Sun, Hai‐Ping, et al. "Improving accuracy of protein contact
prediction using balanced network deconvolution." Proteins: Structure,
Function, and Bioinformatics (2015)."""
try:
ndim, shape = mat.ndim, mat.shape
except AttributeError:
raise TypeError('Matrix must be a 2D square array')
from numpy import fill_diagonal
from ..Application.math import eigh
from scipy.linalg.blas import dgemm
if ndim != 2 or shape[0] != shape[1]:
raise ValueError('Matrix must be a 2D square array')
if mat.min() != mat.max():
mat = (mat - mat.min()) / (mat.max() - mat.min())
else:
from ..IO.output import printInfo
printInfo("The input matrix is a constant matrix.")
return mat
n = mat.shape[0]
fill_diagonal(mat, 0.)
mat_th = (mat + mat.T) / 2.
# Double symetric eigvector relatively robust representation (RRR)
d, u = eigh(mat_th)
for i in xrange(n):
if d[i] != 0:
d[i] = (-1. + (1 + 4 * d[i] * d[i]) ** .5) / 2. / d[i]
# Double general matrix multiply
mat_new1 = dgemm(alpha=1.0, a=(u * d), b=u, trans_b=True)
# mat_new1 = (u*d).dot(u.T) #old numpy dot,slower
ind_edges = (mat_th > 0) * 1.0
ind_nonedges = (mat_th == 0) * 1.0
m1 = (mat * ind_nonedges).max()
m2 = mat_new1.min()
mat_new2 = (mat_new1 + max(m1 - m2, 0)) * ind_edges + (mat * ind_nonedges)
m1 = mat_new2.min()
m2 = mat_new2.max()
if m1 != m2:
mat_bnd = (mat_new2 - m1) / (m2 - m1)
else:
mat_bnd = mat_new2
return mat_bnd
def compute_metric_gmm(direction, criterion, variables, model_cv, samples, labels, idx):
"""
Function that computes the accuracy of the model_cv using the variables : idx +/- one of variables
Inputs:
direction: 'backward' or 'forward' or 'SFFS'
criterion: criterion function use to discriminate variables
variables: the variable to add or delete to idx
model_cv: the model build with all the variables
samples,labels: the samples/label for testing
idx: the pool of retained variables
Output:
metric: the estimated metric
Used in GMM.forward_selection(), GMM.backward_selection()
"""
# Initialization
metric = sp.zeros(variables.size)
confMatrix = ConfusionMatrix()
# Compute inv of covariance matrix
if len(idx)==0:
logdet = None
Qs = None
scores_t = None
else:
logdet = sp.empty((model_cv.C))
Qs = sp.empty((model_cv.C,len(idx),len(idx)))
scores_t = sp.empty((model_cv.C,samples.shape[0]))
for c in xrange(model_cv.C): # Here -> store Qs and scores_t
vp,Q,rcond = model_cv.decomposition(model_cv.cov[c,idx,:][:,idx])
Qs[c,:,:] = Q/sp.sqrt(vp)
logdet[c] = sp.sum(sp.log(vp))
# Pre compute score
testSamples_c = samples[:,idx] - model_cv.mean[c,idx]
temp = dgemm(1.,Qs[c,:,:].T,testSamples_c,trans_b=True)
scores_t[c,:] = sp.sum(temp**2,axis=0)
for i,var in enumerate(variables):
predLabels = model_cv.predict_gmm_update(direction,samples,logdet,(i,var),Qs,scores_t,featIdx=idx)[0]
confMatrix.compute_confusion_matrix(predLabels,labels)
if criterion=='accuracy':
metric[i] = confMatrix.get_OA()
elif criterion=='F1Mean':
metric[i] = confMatrix.get_F1Mean()
elif criterion=='kappa':
metric[i] = confMatrix.get_kappa()
return metric
def kronvec_prod(self, x):
"""
Computes K*x where K is a kronecker product matrix and x is a column
vector which is a numpy array
Inputs:
self : (N,M) KronMatrix
x : (M,1) matrix
Outputs:
y : (N,1) matrix
this routine ensures all matricies are in fortran contigous format
before using blas routines
it also takes advantage of matrix symmetry (if sym flag is set)
"""
if x.shape != (self.shape[1], 1):
raise ValueError('x is the wrong shape, must be (%d,1), not %s'\
% (self.shape[1],repr(x.shape)))
y = x
for i, Ki in reversed(list(enumerate(self.K))):
y = np.reshape(y, (self.sshape[i, 1], -1), order='F')
if isinstance(Ki, np.ndarray): # use optimized blas routines
if np.isfortran(Ki):
a = Ki
else:
a = Ki.T
if self.sym:
if np.isfortran(y):
y = blas.dsymm(alpha=1, a=a, b=y, side=0).T
else:
# just switch the order
y = blas.dsymm(alpha=1, a=a, b=y.T, side=1)
else:
if np.isfortran(y):
b = y
else:
b = y.T
y = blas.dgemm(alpha=1,
a=a,
b=b,
trans_a=(not np.isfortran(Ki)),
trans_b=(not np.isfortran(y))).T
else: # use __mul__ routine
y = (Ki * y).T
y = y.reshape((-1, 1), order='F') # reshape to a column vector
return y
def project_onto_null_space(a, n, nt, lb, ub, n_steps_projection, reactions, tol=1e-4, verbose=0):
# Do matrix multuplication
a = dgemm(1.0, n, dgemm(1.0, nt, a)).transpose()[0]
i, accept = 0, True
while any(a < lb - tol) or any(a > ub + tol):
print '[WARNING] Bounds reseted: %d times' % (i+1)
print '\t lower bound: ', reactions[a < lb - tol]
print '\t upper bound: ', reactions[a > ub + tol]
# Fix bounds violations
lb_violations = a < lb - tol
if any(lb_violations):
a[lb_violations] = lb[lb_violations]
ub_violations = a > ub
if any(ub_violations):
a[ub_violations] = ub[ub_violations]
# Do matrix multiplication
a = dgemm(1.0, n, dgemm(1.0, nt, a)).transpose()[0]
# Verbose
if i > 10:
accept, n_steps_projection = False, max(25, n_steps_projection - 100)
# Verbose
if verbose > 1:
print '[WARNING] Point discarded! lb: %r, ub: %r' % (any(lb_violations), any(ub_violations))
break
i += 1
if i == 0:
n_steps_projection = min(25, n_steps_projection + 25)
return accept, n_steps_projection, a.copy()
def project_vectors(self, vectors):
"""
Projects each of the `vectors` onto the model, retrieving
the optimal linear reconstruction weights for each instance.
Parameters
----------
vectors : (n_samples, n_features) ndarray
Returns
-------
weights : (n_samples, n_components) ndarray
The matrix of optimal linear weights
"""
return dgemm(alpha=1.0, a=vectors.T, b=self.components.T, trans_a=True)
def project_vectors(self, vectors):
"""
Projects each of the `vectors` onto the model, retrieving
the optimal linear reconstruction weights for each instance.
Parameters
----------
vectors : (n_samples, n_features) ndarray
Returns
-------
weights : (n_samples, n_components) ndarray
The matrix of optimal linear weights
"""
return dgemm(alpha=1.0, a=vectors.T, b=self.components.T, trans_a=True)
def gen_time_results(mat_size, no_runs):
mat_A = np.random.rand(mat_size, mat_size)
mat_B = np.random.rand(mat_size, mat_size)
time_list_d = []
time_list_s = []
for _ in range(no_runs):
start = time.perf_counter()
result = FB.dgemm(alpha=1, a=mat_A, b=mat_B)
finish = time.perf_counter()
time_taken_d = round(finish - start, 10)
time_list_d.append(time_taken_d)
start = time.perf_counter()
result = FB.sgemm(alpha=1, a=mat_A, b=mat_B)
finish = time.perf_counter()
time_taken_s = round(finish - start, 10)
time_list_s.append(time_taken_s)
return time_list_d, time_list_s
def mytdot(a, b):
if a.flags.c_contiguous:
a_T = False
a = a.T
elif a.flags.f_contiguous:
a_T = True
else:
a_T = True
a = np.asfortranarray(a)
if b.flags.c_contiguous:
b_T = False
b = b.T
elif b.flags.f_contiguous:
b_T = True
else:
b_T = True
b = np.asfortranarray(b)
return bl.dgemm(alpha=1.0, a=b, b=a, trans_a=b_T, trans_b=a_T).T
def single_propagation(self, query, src_net, corr_function=None):
network = self.graphdata.networks[src_net].matrix
names = self.graphdata.networks[src_net].node_names
query_vector = self.generate_query_vector(query, src_net)
initial_score = RWR(query_vector, network)
vectors = initial_score.tolist()
corr_method = self._get_correlation_method(corr_function)
d_vectors = dgemm(alpha=1., a=vectors, b=vectors, trans_a=True)[0][0]
n_paths = 1
corr_score = self.compute_correlation_scores(network,
vectors,
d_vectors,
src_net,
n_paths,
corr_method)
return corr_score
def gaussian_kernel_matrix(P, Q, c):
"""
Calculate kernel matrix using gaussian kernel.
||p-q||^2 = ||p||^2 + ||q||^2 - 2 * p^T * q
k(p,q) = exp(-c*||p-q||^2)
= exp(-c*[||p||^2 + ||q||^2 - 2 * p^T * q])
C: dgemm(alpha=1.0, a=P, b=Q, trans_b=True) double precision
C: sgemm(alpha=1.0, a=P, b=Q, trans_b=True) single precision
C: np.dot(P,Q.T) single precision
P = P.astype(np.float32)
Q = Q.astype(np.float32)
Parameters:
-----------
P : `numpy.ndarray`
(nDataP, nDim) matrix of data. Each row corresponds to a data point.
Q : `numpy.ndarray`
(nDataQ, nDim) matrix of data. Each row corresponds to a data point.
c : `int`
Width of the gaussian kernel function.
Returns:
--------
K : `numpy.ndarray`
(nDataP,nDataQ) matrix, the gaussian kernel matrix of the P and Q data matrix.
"""
# Calculate norm
P_norm = np.einsum('ij,ij->i', P, P)
Q_norm = np.einsum('ij,ij->i', Q, Q)
return ne.evaluate(
'exp(-gamma * (A + B - 2*C))', {
'A': P_norm[:, None],
'B': Q_norm[None, :],
'C': dgemm(alpha=1.0, a=P, b=Q, trans_b=True),
'gamma': c
})
finish = time.perf_counter()
time_taken = round(finish - start, 8)
total_time_Numpy += time_taken
#assert mn.all() == ans.all()
print(total_time_Numpy / no_runs)
print("\n")
print("----LAPACK DGEMM----")
for mat_size in mat_sizes:
print(f"Mat size: {mat_size}")
total_time_DGEMM = 0
for _ in range(no_runs):
m1 = np.random.rand(mat_size, mat_size)
m2 = np.random.rand(mat_size, mat_size)
start = time.perf_counter()
md = FB.dgemm(alpha=1, a=m1, b=m2)
finish = time.perf_counter()
time_taken = round(finish - start, 8)
total_time_DGEMM += time_taken
#assert md.all() == ans.all()
print(total_time_DGEMM / no_runs)
print("\n")
print("---- LAPACK SGEMM----")
for mat_size in mat_sizes:
print(f"Mat size: {mat_size}")
total_time_SGEMM = 0
for _ in range(no_runs):
m1 = np.random.rand(mat_size, mat_size)
m2 = np.random.rand(mat_size, mat_size)
start = time.perf_counter()
def _instance_vectors_for_full_weights(self, full_weights):
return dgemm(alpha=1.0, a=full_weights.T, b=self.components.T,
trans_a=True, trans_b=True)
def principal_component_decomposition(X, whiten=False, center=True,
bias=False, inplace=False):
r"""
Apply PCA on the data matrix X. In the case where the data matrix is very
large, it is advisable to set `inplace=True`. However, note this this
destructively edits the data matrix by subtracting the mean inplace.
Parameters
----------
x : (n_samples, n_features) ndarray
Training data
whiten : bool, optional
Normalise the eigenvectors to have unit magnitude
Default: `False`
center : bool, optional
Whether to center the data matrix. If `False`, zero will be subtracted.
Default: `True`
bias : bool, optional
Whether to use a biased estimate of the number of samples. If `False`,
subtracts `1` from the number of samples.
Default: `False`
inplace : bool, optional
Whether to do the mean subtracting inplace or not. This is crucial if
the data matrix is greater than half the available memory size.
Default: `False`
Returns
-------
eigenvectors : (n_components, n_features) ndarray
The eigenvectors of the data matrix
eigenvalues : (n_components,) ndarray
The positive eigenvalues from the data matrix
mean_vector : (n_components,) ndarray
The mean that was subtracted from the dataset
"""
n_samples, n_features = X.shape
if bias:
N = n_samples
else:
N = n_samples - 1.0
if center:
# center data
mean_vector = np.mean(X, axis=0)
else:
mean_vector = np.zeros(n_features)
# This is required if the data matrix is very large!
if inplace:
X -= mean_vector
else:
X = X - mean_vector
if n_features < n_samples:
# compute covariance matrix
# S: n_features x n_features
S = dgemm(alpha=1.0, a=X.T, b=X.T, trans_b=True) / N
# S should be perfectly symmetrical, but numerical error can creep
# in. Enforce symmetry here to avoid creating complex
# eigenvectors from eigendecomposition
S = (S + S.T) / 2.0
# perform eigenvalue decomposition
# eigenvectors: n_features x n_features
# eigenvalues: n_features
eigenvectors, eigenvalues = eigenvalue_decomposition(S)
if whiten:
# whiten eigenvectors
eigenvectors *= np.sqrt(1.0 / eigenvalues)
else:
# n_features > n_samples
# compute covariance matrix
# S: n_samples x n_samples
S = dgemm(alpha=1.0, a=X.T, b=X.T, trans_a=True) / N
# S should be perfectly symmetrical, but numerical error can creep
# in. Enforce symmetry here to avoid creating complex
# eigenvectors from eigendecomposition
S = (S + S.T) / 2.0
# perform eigenvalue decomposition
# eigenvectors: n_samples x n_samples
# eigenvalues: n_samples
eigenvectors, eigenvalues = eigenvalue_decomposition(S)
# compute final eigenvectors
# eigenvectors: n_samples x n_features
if whiten:
w = (N * eigenvalues) ** -1.0
else:
w = np.sqrt(1.0 / (N * eigenvalues))
eigenvectors = w * dgemm(alpha=1.0, a=X.T, b=eigenvectors.T,
trans_b=True)
# transpose eigenvectors
# eigenvectors: n_samples x n_features
eigenvectors = eigenvectors.T
return eigenvectors, eigenvalues, mean_vector
def mean_cov(X): n,p = X.shape m = X.mean(axis=0) cx = X - m S = dgemm(1./(n-1), cx.T, cx.T, trans_a=0, trans_b=1) return cx,m,S.T
def predict_gmm_update(self, direction, testSamples, logdet, newFeat, Qs,scores_t,featIdx):
"""
Function that predict the label for testSamples using the learned model (with an update method of the inverse of covariance matrix)
Inputs:
direction: 'backward' or 'forward'
testSamples: the samples to be classified
invCov: inverte of covariance matrix of already selected features
newFeat: couple (index,feature) to add or delete
featIdx: indices of features to use for classification
Outputs:
predLabels: the class
scores: the decision value for each class
"""
# Get machine precision
eps = sp.finfo(sp.float64).eps
# Get information from the data
nbTestSpl = testSamples.shape[0] # Number of testing samples
scores = sp.empty((nbTestSpl,self.C))
# New set of features
if direction=='forward':
id_t = list(featIdx)
id_t.append(newFeat[1])
elif direction=='backward':
id_t = list(featIdx)
# Start the prediction for each class
for c in xrange(self.C):
testSamples_c = testSamples[:,id_t] - self.mean[c,id_t]
if len(id_t)==1:
scores[:,c] = sp.sum(testSamples_c*testSamples_c,axis=1)/self.cov[c,id_t,id_t] + sp.log(self.cov[c,id_t,id_t]) - self.logprop[c]
else:
if direction=='forward':
temp = dgemm(1.0,Qs[c,:,:].T,self.cov[c,newFeat[1],:][featIdx].T)
alpha = self.cov[c,newFeat[1],newFeat[1]] - sp.sum(temp**2)
if alpha < eps:
alpha = eps
logdet_update = sp.log(alpha) + logdet[c]
row_feat = sp.empty((len(id_t)))
row_feat[:len(featIdx)] = dgemm(-1/alpha,Qs[c,:,:],temp).flatten()
row_feat[-1] = 1/alpha
cst_feat = alpha * (sp.dot(row_feat,testSamples_c.T)**2)
elif direction=='backward':
alpha = 1/invCov[c,newFeat[0],newFeat[0]]
if alpha < eps:
alpha = eps
logdet_update = - sp.log(alpha) + logdet[c]
row_feat = invCov[c,newFeat[0],:]
cst_feat = - alpha * (sp.dot(row_feat,testSamples_c.T)**2)
cst = logdet_update - self.logprop[c] # Pre compute the constant term
# temp = sp.dot(testSamples_c,invCov[c,:,:][:,:]) # Here -> symmetric dot product
scores[:,c] = scores_t[c,:] + cst_feat + cst
del temp
del testSamples_c
# Assign the label to the minimum value of scores
predLabels = sp.argmin(scores,1)+1
return predLabels,scores
def principal_component_decomposition(X, whiten=False, center=True,
bias=False):
r"""
Apply PCA on the data matrix X.
Parameters
----------
x : (n_samples, n_features) ndarray
Training data
Returns
-------
eigenvectors : (n_components, n_features) ndarray
eigenvalues : (n_components,) ndarray
"""
n_samples, n_features = X.shape
if bias:
N = n_samples
else:
N = n_samples - 1
if center:
# center data
mean_vector = np.mean(X, axis=0)
else:
mean_vector = np.zeros(n_features)
X -= mean_vector
if n_features < n_samples:
# compute covariance matrix
# S: n_features x n_features
S = dgemm(alpha=1.0, a=X.T, b=X.T, trans_b=True) / N
# S should be perfectly symmetrical, but numerical error can creep
# in. Enforce symmetry here to avoid creating complex
# eigenvectors from eigendecomposition
S = (S + S.T) / 2
# perform eigenvalue decomposition
# eigenvectors: n_features x n_features
# eigenvalues: n_features
eigenvectors, eigenvalues = eigenvalue_decomposition(S)
if whiten:
# whiten eigenvectors
eigenvectors *= eigenvalues ** -0.5
else:
# n_features > n_samples
# compute covariance matrix
# S: n_samples x n_samples
S = dgemm(alpha=1.0, a=X.T, b=X.T, trans_a=True) / N
# S should be perfectly symmetrical, but numerical error can creep
# in. Enforce symmetry here to avoid creating complex
# eigenvectors from eigendecomposition
S = (S + S.T) / 2
# perform eigenvalue decomposition
# eigenvectors: n_samples x n_samples
# eigenvalues: n_samples
eigenvectors, eigenvalues = eigenvalue_decomposition(S)
aux = 2
if whiten:
# will cause eigenvectors to be whiten
aux = 1
# compute final eigenvectors
# eigenvectors: n_samples x n_features
w = (N * eigenvalues) ** (-1 / aux)
eigenvectors = w * dgemm(alpha=1.0, a=X.T, b=eigenvectors.T,
trans_b=True)
# transpose eigenvectors
# eigenvectors: n_samples x n_features
eigenvectors = eigenvectors.T
return eigenvectors, eigenvalues, mean_vector
def calculate(self, theta, data, sparse):
'''
Calculates the cost function of a Sparse network for a given data using
feedforward and backpropagation algorithms.
Parameters
----------
theta : Theta
Theta values of the Sparse network.
data : numpy.ndarray
Training data.
sparse : Sparse
Sparse network.
Returns
-------
cost_function : float
Value of the cost function.
total_partials : numpy.ndarray
Matrix containing theta and bias values.
'''
th1, th2, b1, b2 = wrap_matrices(sparse, theta)
num_samples = data.shape[0]
# layer 1
a1 = data
# layer 2
bias2 = np.dot(np.ones((num_samples, 1)), b1.T)
z2 = np.dot(th1, data.T).T + bias2
a2 = sigmoid(z2)
# layer 3
bias3 = np.dot(np.ones((num_samples, 1)), b2.T)
z3 = np.dot(th2, a2.T).T + bias3
a3 = sigmoid(z3)
### feedforward cost ###
reg = np.sum(np.power(th1, 2)) + np.sum(np.power(th2, 2))
norm = np.power(a3 - data, 2)
Jnn = 0.5 * np.sum(norm) / num_samples + 0.5 * sparse.lamb * reg
rhoest = np.sum(a2, axis=0) / num_samples
kl = self.__compute_kl(sparse.rho, rhoest)
cost_function = Jnn + sparse.beta * np.sum(kl)
### Backpropagation ##
sum2 = sparse.beta * (-sparse.rho / rhoest + (1.0 - sparse.rho) /
(1.0 - rhoest))
delta3 = (-(data - a3) * a3 * (1 - a3)).T
sum1 = dgemm(alpha=1.0, a=th2.T, b=delta3, trans_b=False)
sum2 = sum2[:, np.newaxis]
delta2 = np.add(sum1, sum2) * a2.T * (1 - a2.T)
partial_j1 = np.dot(delta2, a1)
partial_j2 = np.dot(delta3, a2)
partial_b1 = delta2.sum(axis=1)
partial_b2 = delta3.sum(axis=1)
total_partials = [
1.0 / num_samples * partial_j1 + sparse.lamb * th1,
1.0 / num_samples * partial_j2 + sparse.lamb * th2,
1.0 / num_samples * partial_b1, 1.0 / num_samples * partial_b2
]
return cost_function, unwrap_matrices(total_partials)
# suppliers or licensors in any way.
#
#*******************************************************************************
# Content:
# dgemm example
#*******************************************************************************
import numpy as np
import scipy.linalg.blas as slb
import time
M = 10000
N = 10000
matrix_list = [1024, 2048, 4096, 8192, 10000]
for K in matrix_list:
a = np.array(np.random.random((M, K)), dtype=np.double, order='F')
b = np.array(np.random.random((K, N)), dtype=np.double, order='F')
A = np.matrix(a, dtype=np.double, copy=False)
B = np.matrix(b, dtype=np.double, copy=False)
start = time.time()
C = slb.dgemm(1.0, a=A, b=B)
end = time.time()
texec = end - start
print('M x N x K == ', M, N, K, '.. Scipy Execution Time == ', texec,
'sec')
NITER = 30 A_array = random((N,N)) B_array = random((N,N)) C_array = zeros((N,N)) start = time.time() for it in range(NITER): C_array = dot(A_array,B_array) stop = time.time() print"Time for 2d array dot product is:", (stop - start)/NITER A_mat = matrix(A_array) B_mat = matrix(B_array) C_mat = matrix(C_array) start = time.time() for it in range(NITER): C_mat = A_mat*B_mat stop = time.time() print "Time for Matrix multiplication is:", (stop-start)/NITER alpha = 1 start = time.time() for it in range(NITER): C_array = dgemm(alpha, A_array, B_array) stop = time.time() print "Time for dgemm is:", (stop-start)/NITER
#env = os.environ
if len(sys.argv) >= 2:
K = int(sys.argv[1])
M = K
N = K
ITER = 1
else:
print "usage: python numpy_dgemm.py MATRIX_DIMENSION"
sys.exit()
a1 = np.array(np.random.random((M, K)), dtype=np.double, order='C', copy=False)
a2 = np.array(np.random.random((K, N)), dtype=np.double, order='C', copy=False)
m1 = np.matrix(a1, dtype=np.double, copy=False)
m2 = np.matrix(a2, dtype=np.double, copy=False)
t_start = time.time()
for i in range(ITER):
#mf2 = np.dot(m1, m2)
#print "%d: dot(m1, m2)" % i
mf2 = sp.dgemm(alpha=1.0, a=m1, b=m2)
t_end = time.time()
#print "= = = PYTHON NUMPY MKL = = ="
#print
print "dgemm(%dx%d, %dx%d), %d iterations" % (M, K, K, N, ITER)
print "dot(m1, m2): %f sec" % (t_end - t_start)
def compute_cov(xj,mean,ni):
"""
"""
Xc = xj-mean
cov = dgemm(1.0/(ni-1),Xc,Xc,trans_a=True,trans_b=False) # dsyrk could have been used -> but then triangular matrix must be handled everywhere
return cov
def calculate(self, theta, data, sparse):
'''
Calculates the cost function of a Sparse network for a given data using
feedforward and backpropagation algorithms.
Parameters
----------
theta : Theta
Theta values of the Sparse network.
data : numpy.ndarray
Training data.
sparse : Sparse
Sparse network.
Returns
-------
cost_function : float
Value of the cost function.
total_partials : numpy.ndarray
Matrix containing theta and bias values.
'''
th1, th2, b1, b2 = wrap_matrices(sparse, theta)
num_samples = data.shape[0]
# layer 1
a1 = data
# layer 2
bias2 = np.dot(np.ones((num_samples,1)),b1.T)
z2 = np.dot(th1, data.T).T + bias2
a2 = sigmoid(z2)
# layer 3
bias3 = np.dot(np.ones((num_samples,1)),b2.T)
z3 = np.dot(th2, a2.T).T + bias3
a3 = sigmoid(z3)
### feedforward cost ###
reg = np.sum(np.power(th1, 2)) + np.sum(np.power(th2, 2))
norm = np.power(a3 - data, 2)
Jnn = 0.5 * np.sum(norm) / num_samples + 0.5 * sparse.lamb * reg
rhoest = np.sum(a2, axis=0) / num_samples
kl = self.__compute_kl(sparse.rho, rhoest)
cost_function = Jnn + sparse.beta * np.sum(kl)
### Backpropagation ##
sum2 = sparse.beta * (-sparse.rho / rhoest + (1.0 - sparse.rho) / (1.0 - rhoest))
delta3 = (-(data - a3) * a3 * (1 - a3)).T
sum1 = dgemm(alpha=1.0, a=th2.T, b=delta3, trans_b=False)
sum2 = sum2[:,np.newaxis]
delta2 = np.add(sum1,sum2)* a2.T * (1 - a2.T)
partial_j1 = np.dot(delta2, a1)
partial_j2 = np.dot(delta3, a2)
partial_b1 = delta2.sum(axis=1)
partial_b2 = delta3.sum(axis=1)
total_partials = [1.0 / num_samples * partial_j1 + sparse.lamb * th1, 1.0 / num_samples * partial_j2 + sparse.lamb * th2, 1.0 / num_samples * partial_b1, 1.0 / num_samples * partial_b2]
return cost_function, unwrap_matrices(total_partials)