def testLTSolve(self):
for m, s in self.data:
L = ni.lower_tri_sp(m, m, s)
b = ni.vect(ni.np.arange(m, dtype=ni.np.float64))
x = cppsparse.dvec(b)
L.ltsolve(x)
self.verifySolve(L, b, True, x)
def testLTSolve(self):
for m, s in self.data:
L = ni.lower_tri_sp(m, m, s)
b = ni.vect(ni.np.arange(m, dtype=ni.np.float64))
x = cppsparse.dvec(b)
L.ltsolve(x)
self.verifySolve(L, b, True, x)
def qr_left(A):
"Computes a left-looking QR factorization of A with M >= N"
import numpy as np
from cppsparse import dhouse, dvec
m,n = A.shape
V = np.zeros((m, n))
B = np.zeros(n);
R = np.zeros((m, n))
for i in range(n):
x = A[:, i].copy();
for k in range(i):
v = V[k::, k]
beta = B[k]
x[k::] = apply_q(v, beta, x[k::])
xt = dvec(x[i::])
norm, beta = dhouse(xt)
V[i::,i] = np.array(xt)
B[i] = beta
R[:i,i] = x[:i]
R[i,i] = norm
Q = compute_q(V, B)
return Q, R
def qr_left(A):
"Computes a left-looking QR factorization of A with M >= N"
import numpy as np
from cppsparse import dhouse, dvec
m, n = A.shape
V = np.zeros((m, n))
B = np.zeros(n)
R = np.zeros((m, n))
for i in range(n):
x = A[:, i].copy()
for k in range(i):
v = V[k::, k]
beta = B[k]
x[k::] = apply_q(v, beta, x[k::])
xt = dvec(x[i::])
norm, beta = dhouse(xt)
V[i::, i] = np.array(xt)
B[i] = beta
R[:i, i] = x[:i]
R[i, i] = norm
Q = compute_q(V, B)
return Q, R
def testUTSolve(self):
for m, s in self.data:
U = ni.upper_tri_sp(m, m, s)
b = ni.vect(ni.np.arange(m, dtype=ni.np.float64))
x = cppsparse.dvec(b)
U.utsolve(x)
self.verifySolve(U, b, True, x)
def testUTSolve(self):
for m, s in self.data:
U = ni.upper_tri_sp(m, m, s)
b = ni.vect(ni.np.arange(m, dtype=ni.np.float64))
x = cppsparse.dvec(b)
U.utsolve(x)
self.verifySolve(U, b, True, x)
def householder(x):
from cppsparse import dhouse, dvec
import numpy
xtemp = dvec(x)
norm, beta = dhouse(xtemp)
v = numpy.array(xtemp)
v.shape = len(x), 1
print(v)
return numpy.identity(len(x)) - beta * numpy.dot(v, v.transpose())
def householder(x):
from cppsparse import dhouse, dvec
import numpy
xtemp = dvec(x);
norm, beta = dhouse(xtemp)
v = numpy.array(xtemp)
v.shape = len(x),1
print(v)
return numpy.identity(len(x)) - beta * numpy.dot(v, v.transpose())
def vect(n):
v = None
if n.dtype == np.float64:
v = c.dvec()
for elem in n:
v.push_back(float(elem))
elif n.dtype == np.int32 or n.dtype == np.int64:
v = c.ivec()
for elem in n:
v.push_back(int(elem))
else:
raise RuntimeError("Array must be float or integer")
return v
def vect(n):
v = None
if n.dtype == np.float64:
v = c.dvec();
for elem in n:
v.push_back(float(elem))
elif n.dtype == np.int32 or n.dtype == np.int64:
v = c.ivec()
for elem in n:
v.push_back(int(elem))
else:
raise RuntimeError("Array must be float or integer")
return v
def verifySolve(self, A, b, trans, xAct):
m = A.n_rows()
res = cppsparse.dvec(m, 0.0);
if trans:
normA = A.norm(cppsparse.NORM_INF)
A.gatxpy(xAct, res)
else:
normA = A.norm(cppsparse.NORM_ONE)
A.gaxpy(xAct, res)
normRes = numpy.linalg.norm(ni.nvec(b) - ni.nvec(res), numpy.inf)
self.assertTrue(normRes/(numpy.finfo('double').eps * normA * m) < 100,
'Residual norm = %f'%(normRes/(numpy.finfo('double').eps * normA * m)))
def verifySolve(self, A, b, trans, xAct):
m = A.n_rows()
res = cppsparse.dvec(m, 0.0)
if trans:
normA = A.norm(cppsparse.NORM_INF)
A.gatxpy(xAct, res)
else:
normA = A.norm(cppsparse.NORM_ONE)
A.gaxpy(xAct, res)
normRes = numpy.linalg.norm(ni.nvec(b) - ni.nvec(res), numpy.inf)
self.assertTrue(
normRes / (numpy.finfo('double').eps * normA * m) < 100,
'Residual norm = %f' % (normRes /
(numpy.finfo('double').eps * normA * m)))
def qr_right(a):
"Computes a right-looking QR factorization of A with M >= N"
import numpy as np
from cppsparse import dhouse, dvec
m, n = a.shape
V = np.zeros((m, n))
B = np.zeros(n)
R = a.copy()
for i in range(n):
x = dvec(R[i::, i])
norm, beta = dhouse(x)
x = np.array(x)
V[i::, i] = x
B[i] = beta
x.shape = x.size, 1
R[i::, i::] = R[i::, i::] - beta * np.dot(x, np.dot(x.T, R[i::, i::]))
return compute_q(V, B), np.triu(R)
def qr_right(a):
"Computes a right-looking QR factorization of A with M >= N"
import numpy as np
from cppsparse import dhouse, dvec
m,n = a.shape
V = np.zeros((m, n))
B = np.zeros(n);
R = a.copy();
for i in range(n):
x = dvec(R[i::, i]);
norm, beta = dhouse(x)
x = np.array(x)
V[i::,i] = x
B[i] = beta
x.shape = x.size,1
R[i::,i::] = R[i::, i::] - beta * np.dot(x, np.dot(x.T, R[i::, i::]))
return compute_q(V, B), np.triu(R)
lower_tri = c.dtrp(5, 5)
full_sym = c.dtrp(5, 5)
upper_tri = c.dtrp(5, 5)
for col in range(5):
for row in range(col, 5):
lower_tri.push_back(row, col, float(row + col * 5.0))
full_sym.push_back(row, col, float(row + col * 5.0))
upper_tri.push_back(col, row, float(row + col * 5.0))
if row != col:
full_sym.push_back(col, row, float(row + col * 5.0))
lower_tri = c.dcsc(lower_tri)
upper_tri = c.dcsc(upper_tri)
full_sym = c.dcsc(full_sym)
x = c.dvec(range(5))
y = c.dvec(5)
lower_tri.sym_gaxpy(x, y, c.LOWER_TRIANGULAR)
print(nvec(y))
y = c.dvec(5)
upper_tri.sym_gaxpy(x, y, c.UPPER_TRIANGULAR)
print(nvec(y))
y = c.dvec(5)
full_sym.gaxpy(x, y)
print(nvec(y))
import cppsparse as c
x = c.dtrp("data.txt")
print(x)
row = c.ivec(5)
print(row.size())
col = c.ivec(5)
nnz = c.dvec(25)
for i in range(5):
row[i] = i
col[i] = i
for i in range(25):
nnz[i] = i
x.push_back(row, col, nnz)
print(x)
import cppsparse as c
x = c.dtrp("fem.dat")
y = c.dcsc(x)
y.sum_duplicates()
m = y.n_rows()
n = y.n_cols()
print m, n
cs = c.dvec(n, 2.0)
rs = c.dvec(m, 3.0)
print(y.find())
y.scale(rs, cs)
print(y.find())
import cppsparse as c
x = c.dtrp("fem.dat")
y = c.dcsc(x)
y.sum_duplicates()
m = y.n_rows()
n = y.n_cols()
print m, n
cs = c.dvec(n, 2.0)
rs = c.dvec(m, 3.0)
print (y.find())
y.scale(rs, cs)
print (y.find())
upper_tri = c.dtrp(5, 5)
for col in range(5):
for row in range(col, 5):
lower_tri.push_back(row, col, float(row + col * 5.0))
full_sym.push_back (row, col, float(row + col * 5.0))
upper_tri.push_back (col, row, float(row + col * 5.0))
if row != col:
full_sym.push_back (col, row, float(row + col * 5.0))
lower_tri = c.dcsc(lower_tri)
upper_tri = c.dcsc(upper_tri)
full_sym = c.dcsc(full_sym)
x = c.dvec(range(5))
y = c.dvec(5)
lower_tri.sym_gaxpy(x, y, c.LOWER_TRIANGULAR)
print(nvec(y))
y = c.dvec(5)
upper_tri.sym_gaxpy(x, y, c.UPPER_TRIANGULAR)
print(nvec(y))
y = c.dvec(5)
full_sym.gaxpy(x, y)
print(nvec(y))
