def stdForm(a, b):
def invert(L): # Inverts lower triangular matrix L
n = len(L)
for j in range(n - 1):
L[j, j] = 1.0 / L[j, j]
for i in range(j + 1, n):
L[i, j] = -np.dot(L[i, j:i], L[j:i, j]) / L[i, i]
L[n - 1, n - 1] = 1.0 / L[n - 1, n - 1]
n = len(a)
L = choleski(b)
invert(L)
h = np.dot(b, np.inner(a, L))
return h, np.transpose(L)
def stdForm(a, b):
def invert(L): # Inverts lower triangular matrix L
n = len(L)
for j in range(n - 1):
L[j, j] = 1.0 / L[j, j]
for i in range(j + 1, n):
L[i, j] = -dot(L[i, j:i], L[j:i, j]) / L[i, i]
L[n - 1, n - 1] = 1.0 / L[n - 1, n - 1]
n = len(a)
L = choleski(b)
invert(L)
h = matrixmultiply(b, matrixmultiply(a, transpose(L)))
return h, transpose(L)
def stdForm(a, b):
def invert(L): # Inverts lower triangular matrix L
n = len(L)
for j in range(n - 1):
L[j, j] = 1.0 / L[j, j]
for i in range(j + 1, n):
L[i, j] = -dot(L[i, j:i], L[j:i, j]) / L[i, i]
L[n - 1, n - 1] = 1.0 / L[n - 1, n - 1]
n = len(a)
L = choleski(b)
invert(L)
h = matrixmultiply(b, matrixmultiply(a, transpose(L)))
return h, transpose(L)
# [ 1.66666667 2.66666667 2.66666667]
#
######################################################
k = np.array([1, 2, 1, 1, 2], np.float64)
W = np.array([2, 1, 2], np.float64)
a = np.zeros((3, 3))
a[0, 0] = k[0] + k[1] + k[2] + k[4]
a[0, 1] = -k[2]
a[0, 2] = -k[4]
a[1, 0] = -k[2]
a[1, 1] = k[2] + k[3]
a[1, 2] = -k[3]
a[2, 0] = -k[4]
a[2, 1] = -k[3]
a[2, 2] = k[3] + k[4]
L = choleski(a)
x = choleskiSol(L, W)
print("Displacements are (in units of W/k):\n\n", x)
print("--------------------------------------------")
## problem2_2_17
######################################################
# 1. Populate a and b below with the values from
# problem 17 on page 82.
#
# Correct Outputs:
# R = 5.0 ohms
# The currents are (in amps):
# [ 2.82926829 1.26829268 4.97560976]
# R = 10.0 ohms
# The currents are (in amps):
#!/usr/bin/python
## example2_8
from numarray import array,matrixmultiply,transpose
from choleski import *
a = array([[ 1.44, -0.36, 5.52, 0.0], \
[-0.36, 10.33, -7.78, 0.0], \
[ 5.52, -7.78, 28.40, 9.0], \
[ 0.0, 0.0, 9.0, 61.0]])
L = choleski(a)
print 'L =\n',L
print '\nCheck: L*L_transpose =\n', \
matrixmultiply(L,transpose(L))
raw_input("\nPress return to exit")
#!/usr/bin/python3
## example2_8 on p. 54
import os
from numpy import linalg,array,dot,transpose
from choleski import *
os.system('clear') # This is handy for clearing the console screen
A = array([[ 1.44, -0.36, 5.52, 0.0], \
[-0.36, 10.33, -7.78, 0.0], \
[ 5.52, -7.78, 28.40, 9.0], \
[ 0.0, 0.0, 9.0, 61.0]])
A_old=A.copy()
L = choleski(A) # original contents of A overwritten
B=dot(L,transpose(L))
print ('A =\n',A_old)
print ('L =\n',L)
print ('\nCheck: L*L_transpose =\n', B)
print('\nError in decomposition = ',linalg.norm(A_old-B))
input("\nPress return to exit")
