def gemm_v1():
'''
Note that all arrays are in Fortran order.
'''
print("Version 1".center(80, '='))
# Prepare arrays for input
A = np.array(np.arange(N**2, dtype=np.float32).reshape(N, N), order='F')
B = np.array(np.arange(N) + 10, dtype=A.dtype, order='F')
D = np.zeros_like(A, order='F')
# NumPy
start = timer()
E = np.dot(A, np.diag(B))
numpy_time = timer() - start
print("Numpy took %f seconds" % numpy_time)
# cuBLAS
blas = Blas()
start = timer()
blas.gemm('N', 'N', N, N, N, 1.0, A, np.diag(B), 1.0, D)
cuda_time = timer() - start
print("CUBLAS took %f seconds" % cuda_time)
diff = np.abs(D - E)
print("Maximum error %f" % np.max(diff))
def gemm_v2():
"""
Let GEMM transpose the input matrices so that they can be in C order,
originally. Note that the output matrix is still in Fortran array.
The string arguments in gemm tells it to apply transformation on the input
matrices.
See argument description in:
http://docs.continuum.io/accelerate/cublas#blas-level-2
"""
print("Version 2".center(80, '='))
# Prepare arrays for input
A = np.array(np.arange(N**2, dtype=np.float32).reshape(N, N))
B = np.array(np.arange(N) + 10, dtype=A.dtype)
D = np.zeros_like(A, order='F')
# NumPy
start = timer()
E = np.dot(A, np.diag(B))
numpy_time = timer() - start
print("Numpy took %f seconds" % numpy_time)
# cuBLAS
blas = Blas()
start = timer()
blas.gemm('T', 'T', N, N, N, 1.0, A, np.diag(B), 1.0, D)
cuda_time = timer() - start
print("CUBLAS took %f seconds" % cuda_time)
diff = np.abs(D - E)
print("Maximum error %f" % np.max(diff))
def gemm_v1():
'''
Note that all arrays are in Fortran order.
'''
print("Version 1".center(80, '='))
# Prepare arrays for input
A = np.array(np.arange(N ** 2, dtype=np.float32).reshape(N, N), order='F')
B = np.array(np.arange(N) + 10, dtype=A.dtype, order='F')
D = np.zeros_like(A, order='F')
# NumPy
start = timer()
E = np.dot(A, np.diag(B))
numpy_time = timer() - start
print("Numpy took %f seconds" % numpy_time)
# cuBLAS
blas = Blas()
start = timer()
blas.gemm('N', 'N', N, N, N, 1.0, A, np.diag(B), 1.0, D)
cuda_time = timer() - start
print("CUBLAS took %f seconds" % cuda_time)
diff = np.abs(D - E)
print("Maximum error %f" % np.max(diff))
def gemm_v2():
"""
Let GEMM transpose the input matrices so that they can be in C order,
originally. Note that the output matrix is still in Fortran array.
The string arguments in gemm tells it to apply transformation on the input
matrices.
See argument description in:
http://docs.continuum.io/accelerate/cublas#blas-level-2
"""
print("Version 2".center(80, '='))
# Prepare arrays for input
A = np.array(np.arange(N ** 2, dtype=np.float32).reshape(N, N))
B = np.array(np.arange(N) + 10, dtype=A.dtype)
D = np.zeros_like(A, order='F')
# NumPy
start = timer()
E = np.dot(A, np.diag(B))
numpy_time = timer() - start
print("Numpy took %f seconds" % numpy_time)
# cuBLAS
blas = Blas()
start = timer()
blas.gemm('T', 'T', N, N, N, 1.0, A, np.diag(B), 1.0, D)
cuda_time = timer() - start
print("CUBLAS took %f seconds" % cuda_time)
diff = np.abs(D - E)
print("Maximum error %f" % np.max(diff))
def __init__(self, int_m, dec_m, device_id=0):
if config['FP_precision'] == 32:
self.fl_pr = np.float32
elif config['FP_precision'] == 64:
self.fl_pr = np.float64
else:
raise Exception(
"CUDASparseContext(): Unknown precision specified.")
#======================================================================
# Setup GPU stuff and upload data to it
#======================================================================
try:
from accelerate.cuda.blas import Blas
import accelerate.cuda.sparse as cusparse
from accelerate.cuda import cuda
except ImportError:
raise Exception("kern_CUDA_sparse(): Numbapro CUDA libaries not " +
"installed.\nCan not use GPU.")
cuda.select_device(0)
self.cuda = cuda
self.cusp = cusparse.Sparse()
self.cubl = Blas()
self.set_matrices(int_m, dec_m)
def mscAsianOption(C_P, S0, K, T, r, sigma, M, I):
if C_P == 'C':
par = 1.0
elif C_P == 'P':
par = -1.0
else:
return ("the value can not be calculatable")
prng = rand.PRNG(seed=10000)
prngx = Blas()
dt = T / M
S = np.zeros((M + 1, I))
ArithSum = np.zeros((1, I))
GeoSum = np.ones((1, I))
S[0] = S0
sigma_x = sigma * sqrt(float((M + 1) * (2 * M + 1)) / (6 * M**2))
r_x = float((r - 0.5 * sigma**2) * (M + 1)) / (2 * M) + 0.5 * sigma_x**2
d1 = (log(float(S0) / K) +
(r_x + 0.5 * sigma_x**2) * T) / (sigma_x * sqrt(T))
d2 = d1 - sigma_x * sqrt(T)
S_geoc = par * S0 * exp(r_x * T) * stats.norm.cdf(par * d1)
K_geoc = par * K * stats.norm.cdf(par * d2)
Vgeoc = exp(-r * T) * (S_geoc - K_geoc)
for t in range(1, M + 1):
z = np.empty(I)
prng.normal(z, mean=0, sigma=1)
S[t] = S[t - 1] * np.exp((r - 0.5 * sigma**2) * dt +
sigma * sqrt(dt) * z)
for i in range(1, M, 2):
ArithSum += S[i] + S[i + 1] #ts:time series
GeoSum *= S[i] * S[i + 1]
X = np.maximum(par * ArithSum / M - par * K, 0.0)
Y = np.maximum(par * np.power(GeoSum, 1.0 / M) - par * K, 0.0)
theta = np.cov(X, Y)[0][1] / np.var(Y)
D = exp(-r * T)
Varith = D * prngx.asum(X[0]) / I
Vgeo = D * prngx.asum(Y[0]) / I
# V = Varith+theta*(Vgeoc - Vgeo)
Varray = D * X + theta * (Vgeoc - D * Y)
Vmean = prngx.asum(Varray[0]) / I
Vstd = np.std(Varray)
Vconf = [Vmean - 1.96 * Vstd / sqrt(I), Vmean + 1.96 * Vstd / sqrt(I)]
return Vmean, Vconf, Varith, Vgeo
def mscBasketOption(C_P, S10, S20, K, T, r, sigma1, sigma2, cov, I):
if C_P == 'C':
par = 1.0
elif C_P == 'P':
par = -1.0
else:
return ("the value can not be calculatable")
prng = rand.PRNG(seed=10000)
prngx = Blas()
D = exp(-r * T)
z1 = np.empty(I)
z2 = np.empty(I)
prng.normal(z1, mean=0, sigma=1)
prng.normal(z2, mean=0, sigma=1)
z3 = cov * z1 + sqrt(1 - cov**2) * z2
S1T = S10 * np.exp((r - 0.5 * sigma1**2) * T + sigma1 * sqrt(T) * z1)
S2T = S20 * np.exp((r - 0.5 * sigma2**2) * T + sigma2 * sqrt(T) * z3)
Sa = (S1T + S2T) * 0.5
Sg = np.sqrt(S1T * S2T)
hTa = np.maximum(par * Sa - par * K, 0)
hTg = np.maximum(par * Sg - par * K, 0)
Va = D * prngx.asum(hTa) / I
Vg = D * prngx.asum(hTg) / I
B0 = sqrt(S10 * S20)
Bsigma = 0.5 * sqrt(sigma1**2 + sigma2**2 + 2 * sigma1 * sigma2 * cov)
Bu = r - (sigma1**2 + sigma2**2) / (2 * 2) + 0.5 * Bsigma**2
d1_x_nominator = log(float(B0) / K) + (Bu + 0.5 * Bsigma**2) * T
d1_x = d1_x_nominator / (Bsigma * sqrt(T))
d2_x = d1_x - Bsigma * sqrt(T)
CB_nominator = par * B0 * exp(Bu * T) * stats.norm.cdf(
par * d1_x) - par * K * stats.norm.cdf(par * d2_x)
Vgc = D * CB_nominator
theta = np.cov(hTa, hTg)[0][1] / np.var(hTg)
# V = Va + theta*(Vgc - Vg)
Varray = D * hTa + theta * (Vgc - D * hTg)
Vmean = prngx.asum(Varray) / I
Vstd = np.std(Varray)
Vconf = [Vmean - 1.96 * Vstd / sqrt(I), Vmean + 1.96 * Vstd / sqrt(I)]
return Vmean, Vconf, Va, Vg, Vgc
def simple(data, covfct, u, N=0, nugget=0):
# calculate the matrices K, and k
K, k, P = kmatrices(data, covfct, u, N)
print len(K)
# calculate the kriging weights
weights = Blas().gemv('N', len(K), len(K), 1.0, K, K, 0.0, P)
weights = np.array(weights)
# calculate k' * K * k for
# the kriging variance
kvar = k.T * weights
# mean of the variable
mu = np.mean(data[:, 2])
# calculate the residuals
residuals = P[:, 2] - mu
# calculate the estimation
estimation = np.dot(weights.T, residuals) + mu
# calculate the sill and the
# kriging standard deviation
sill = np.var(data[:, 2])
kvar = float(sill + nugget - kvar)
kstd = np.sqrt(kvar)
return float(estimation), kstd
def gemm(A, B, dD):
N = A.shape[0] # square matrices
'''
Note that all arrays are in Fortran order.
'''
# cuBLAS
blas = Blas()
start = timer()
blas.gemm('N', 'N', N, N, N, 1.0, A, B, 1.0, dD)
cuda_time = timer() - start
D = dD.copy_to_host()
print("CUBLAS took %f seconds" % cuda_time)
diff = np.abs(D - E)
print("Maximum error %f" % np.max(diff))
return D
class CUDASparseContext(object):
def __init__(self, int_m, dec_m, device_id=0):
if config['FP_precision'] == 32:
self.fl_pr = np.float32
elif config['FP_precision'] == 64:
self.fl_pr = np.float64
else:
raise Exception(
"CUDASparseContext(): Unknown precision specified.")
#======================================================================
# Setup GPU stuff and upload data to it
#======================================================================
try:
from accelerate.cuda.blas import Blas
import accelerate.cuda.sparse as cusparse
from accelerate.cuda import cuda
except ImportError:
raise Exception("kern_CUDA_sparse(): Numbapro CUDA libaries not " +
"installed.\nCan not use GPU.")
cuda.select_device(0)
self.cuda = cuda
self.cusp = cusparse.Sparse()
self.cubl = Blas()
self.set_matrices(int_m, dec_m)
def set_matrices(self, int_m, dec_m):
import accelerate.cuda.sparse as cusparse
from accelerate.cuda import cuda
self.m, self.n = int_m.shape
self.int_m_nnz = int_m.nnz
self.int_m_csrValA = cuda.to_device(int_m.data.astype(self.fl_pr))
self.int_m_csrRowPtrA = cuda.to_device(int_m.indptr)
self.int_m_csrColIndA = cuda.to_device(int_m.indices)
self.dec_m_nnz = dec_m.nnz
self.dec_m_csrValA = cuda.to_device(dec_m.data.astype(self.fl_pr))
self.dec_m_csrRowPtrA = cuda.to_device(dec_m.indptr)
self.dec_m_csrColIndA = cuda.to_device(dec_m.indices)
self.descr = self.cusp.matdescr()
self.descr.indexbase = cusparse.CUSPARSE_INDEX_BASE_ZERO
self.cu_delta_phi = self.cuda.device_array_like(
np.zeros(self.m, dtype=self.fl_pr))
print np.zeros(self.m, dtype=self.fl_pr).shape
def set_phi(self, phi):
self.cu_curr_phi = self.cuda.to_device(phi.astype(self.fl_pr))
def get_phi(self):
return self.cu_curr_phi.copy_to_host()
def do_step(self, rho_inv, dX):
self.cusp.csrmv(trans='N',
m=self.m,
n=self.n,
nnz=self.int_m_nnz,
descr=self.descr,
alpha=self.fl_pr(1.0),
csrVal=self.int_m_csrValA,
csrRowPtr=self.int_m_csrRowPtrA,
csrColInd=self.int_m_csrColIndA,
x=self.cu_curr_phi,
beta=self.fl_pr(0.0),
y=self.cu_delta_phi)
# print np.sum(cu_curr_phi.copy_to_host())
self.cusp.csrmv(trans='N',
m=self.m,
n=self.n,
nnz=self.dec_m_nnz,
descr=self.descr,
alpha=self.fl_pr(rho_inv),
csrVal=self.dec_m_csrValA,
csrRowPtr=self.dec_m_csrRowPtrA,
csrColInd=self.dec_m_csrColIndA,
x=self.cu_curr_phi,
beta=self.fl_pr(1.0),
y=self.cu_delta_phi)
self.cubl.axpy(alpha=self.fl_pr(dX),
x=self.cu_delta_phi,
y=self.cu_curr_phi)
def kern_CUDA_dense(nsteps,
dX,
rho_inv,
int_m,
dec_m,
phi,
grid_idcs,
mu_egrid=None,
mu_dEdX=None,
mu_lidx_nsp=None,
prog_bar=None):
"""`NVIDIA CUDA cuBLAS <https://developer.nvidia.com/cublas>`_ implementation
of forward-euler integration.
Function requires a working :mod:`numbapro` installation. It is typically slower
compared to :func:`kern_MKL_sparse` but it depends on your hardware.
Args:
nsteps (int): number of integration steps
dX (numpy.array[nsteps]): vector of step-sizes :math:`\\Delta X_i` in g/cm**2
rho_inv (numpy.array[nsteps]): vector of density values :math:`\\frac{1}{\\rho(X_i)}`
int_m (numpy.array): interaction matrix :eq:`int_matrix` in dense or sparse representation
dec_m (numpy.array): decay matrix :eq:`dec_matrix` in dense or sparse representation
phi (numpy.array): initial state vector :math:`\\Phi(X_0)`
prog_bar (object,optional): handle to :class:`ProgressBar` object
Returns:
numpy.array: state vector :math:`\\Phi(X_{nsteps})` after integration
"""
fl_pr = None
if config['FP_precision'] == 32:
fl_pr = np.float32
elif config['FP_precision'] == 64:
fl_pr = np.float64
else:
raise Exception("kern_CUDA_dense(): Unknown precision specified.")
# if config['enable_muon_energyloss']:
# raise NotImplementedError('kern_CUDA_dense(): ' +
# 'Energy loss not imlemented for this solver.')
if config['enable_muon_energy_loss']:
raise NotImplementedError(
'kern_CUDA_dense(): ' +
'Energy loss not imlemented for this solver.')
#=======================================================================
# Setup GPU stuff and upload data to it
#=======================================================================
try:
from accelerate.cuda.blas import Blas
from accelerate.cuda import cuda
except ImportError:
raise Exception("kern_CUDA_dense(): Numbapro CUDA libaries not " +
"installed.\nCan not use GPU.")
cubl = Blas()
m, n = int_m.shape
stream = cuda.stream()
cu_int_m = cuda.to_device(int_m.astype(fl_pr), stream)
cu_dec_m = cuda.to_device(dec_m.astype(fl_pr), stream)
cu_curr_phi = cuda.to_device(phi.astype(fl_pr), stream)
cu_delta_phi = cuda.device_array(phi.shape, dtype=fl_pr)
from time import time
start = time()
for step in xrange(nsteps):
if prog_bar:
prog_bar.update(step)
cubl.gemv(trans='N',
m=m,
n=n,
alpha=fl_pr(1.0),
A=cu_int_m,
x=cu_curr_phi,
beta=fl_pr(0.0),
y=cu_delta_phi)
cubl.gemv(trans='N',
m=m,
n=n,
alpha=fl_pr(rho_inv[step]),
A=cu_dec_m,
x=cu_curr_phi,
beta=fl_pr(1.0),
y=cu_delta_phi)
cubl.axpy(alpha=fl_pr(dX[step]), x=cu_delta_phi, y=cu_curr_phi)
print "Performance: {0:6.2f}ms/iteration".format(1e3 * (time() - start) /
float(nsteps))
return cu_curr_phi.copy_to_host(), []