def __init__(self, usage=None, version=None):
"""
__init__ will create all the necessary information you need to run the code.
It parses the command line to understand all your options.
"""
if not usage:
usage = 'usage: %prog [options] args'
optparse.OptionParser.__init__(self, usage=usage, version=version)
self.add_option("-f", "--file", dest="filename", type='string',
help="gnuplot data filename")
self.add_option("-A", "--matrix_form", dest='MatrixForm', type='string',
default="diagonal",
help="What kind of matrix. Currently only supports diagonal.")
self.add_option("-z", "--size", dest="size", type='int', default=10,
help="Size of matrix.")
self.add_option("-T", "--trials", dest="Trials", type="float", default=1E5,
help="How many independent trials to calculate bias.")
self.add_option("-s", "--sd", dest="sd", type='string', default='0',
help="What noise standard deviations will be used.")
self.add_option("-t", "--tol", dest="Tol", type="float", default=0.1,
help="Accepted tolerance in eigenvalue bias standard deviation.")
self.add_option("-v", "--values", dest="eigenvalues", type="int",
default=1, help="How many eigenvalues calculated.")
self.add_option("-I", "--iterations", dest="I", type="int",
default=10, help="How many Arnoldi Iterations per trial.")
self.add_option("-q", dest="q", type="string",
default="scipy.ones(self.options.size)",
help="Initial q.")
self.add_option("-r", "--run", dest="run", action="store_true", default=False,
help="Perform calculation.")
# Parse command line options
self.options, self.args = self.parse_args()
if string.lower(self.options.MatrixForm) == 'diagonal':
self.A = Matrix.Diagonal(scipy.arange(self.options.size, 0, -1))
elif isinstance(eval(self.options.MatrixForm), scipy.ndarray):
self.A = eval(self.options.MatrixForm)
self.options.size = self.A.shape
else:
raise ValueError, """Only Diagonal matrices or scipy.ndarray objects
import cmath
import time
import scipy
import scipy.linalg
import arnoldiDTM
import NumBias
import Matrix
import gnuplotFile
if __name__ == "__main__":
numby = NumBias.NB(version=str(__version__))
A = Matrix.Diagonal(scipy.arange(numby.options.size, 0, -1))
# Calculate similarDiag matrix
adtm = arnoldiDTM.arnoldiDTM(A, Noise=0.0)
q = scipy.ones(numby.options.size)
adtm.arnoldi(q, numby.options.size)
Q = scipy.array(adtm.Q)
B = scipy.dot(scipy.dot(Q[:-1].transpose(), A), Q[:-1])
# Double-check
print "\n\nDouble-check:"
print "Eigenvalues of A:\n%s\nEigenvalues of B:\n%s\n" % (
scipy.linalg.eigvals(A), scipy.linalg.eigvals(B))
print "A: \n%s" % B
numby.printParameters()
if numby.options.run:
"""This module is meant to complement the Mathematica notes included in
Thesis/Notes. It is a numerical investigation in the bias of the estimated
eigenvalue due to noise."""
import sys
import scipy
import Gnuplot
import arnoldiDTM
import Matrix
if __name__ == "__main__":
M = 2
A = Matrix.Diagonal(scipy.arange(M,0,-1))
I = M+1
q = scipy.zeros(M)
q[0] = 1
Chart = Gnuplot.Gnuplot()
Chart.xlabel('Standard Deviation of Noise')
Chart.ylabel('Mean Eigenvalues')
Means = []
Noises = scipy.arange(1,500,10)
for N in Noises:
eValues = []
for i in xrange(100):
adtm = arnoldiDTM.arnoldiDTM(A, Noise=N, NoiseShape='normal')
Values, Vectors = adtm.arnoldi(q, I)
__version__ = " $Revision: 159 $"
__date__ = "$Date: 2007-09-14 08:07:06 -0600 (Fri, 14 Sep 2007) $"
import scipy.linalg
import Gnuplot
import arnoldiDTM
import Matrix
if __name__ == "__main__":
N = 10
# A = Matrix.DingDong(N)
A = Matrix.Diagonal(scipy.arange(1,N+1))
print A
I = 11 # Arnoldi Iterations
R = 10 # Arnoldi Restarts
q = scipy.random.random(N)
adtm = arnoldiDTM.arnoldiDTM(A)
values, vectors = adtm.arnoldi(q, I)
print "Estimated Eigenvalues: %s" %(values)
realvalues, realvectors = scipy.linalg.eig(A)
realvalues.sort()
print "Real values: %i, Estimated values %i" %(len(realvalues), len(values))
# print "Real Eigenvalues: %s" %(realvalues)
# print "Difference: %s" %(abs(realvalues-values))