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 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 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)
