def ludcmp_crout(matrix):
"""
Decomposes/factorizes square input matrix into a lower and an
upper matrix using Crout's algorithm WITHOUT pivoting.
NB. It only works for square matrices!!!
"""
ndim = squaredim(matrix, 'ludcmp_crout')
# Copy object instance to new matrix in order for the original instance
# not to be destroyed.
# Create two new square matrices of the same sized as the input matrix:
# one unity matrix (to be the lower matrix), one zero matrix (to be
# the upper matrix)
copymx = deepcopy(matrix)
lower = Matrix()
lower.unity(ndim)
upper = Matrix()
upper.zero(ndim, ndim)
permlist = list(range(0, ndim))
# Perform the necessary manipulations:
for j in range(0, ndim):
iu = 0
while iu <= j:
k = 0
summ = 0.0
while k < iu:
summ += lower[iu][k]*upper[k][j]
k = k + 1
upper[iu][j] = copymx[iu][j] - summ
iu = iu + 1
il = j + 1
while il < ndim:
k = 0
summ = 0.0
while k < j:
summ += lower[il][k]*upper[k][j]
k = k + 1
divisor = float(upper[j][j])
if abs(divisor) < TINY: divisor = fsign(divisor)*TINY
lower[il][j] = (copymx[il][j]-summ) / divisor
il = il + 1
parity = 1.0
return lower, upper, permlist, parity
def ludcmp_crout(matrix):
"""
Decomposes/factorizes square input matrix into a lower and an
upper matrix using Crout's algorithm WITHOUT pivoting.
NB. It only works for square matrices!!!
"""
ndim = squaredim(matrix, 'ludcmp_crout')
# Copy object instance to new matrix in order for the original instance
# not to be destroyed.
# Create two new square matrices of the same sized as the input matrix:
# one unity matrix (to be the lower matrix), one zero matrix (to be
# the upper matrix)
copymx = deepcopy(matrix)
lower = Matrix()
lower.unity(ndim)
upper = Matrix()
upper.zero(ndim, ndim)
permlist = list(range(0, ndim))
# Perform the necessary manipulations:
for j in range(0, ndim):
iu = 0
while iu <= j:
k = 0
summ = 0.0
while k < iu:
summ += lower[iu][k] * upper[k][j]
k = k + 1
upper[iu][j] = copymx[iu][j] - summ
iu = iu + 1
il = j + 1
while il < ndim:
k = 0
summ = 0.0
while k < j:
summ += lower[il][k] * upper[k][j]
k = k + 1
divisor = float(upper[j][j])
if abs(divisor) < TINY: divisor = fsign(divisor) * TINY
lower[il][j] = (copymx[il][j] - summ) / divisor
il = il + 1
parity = 1.0
return lower, upper, permlist, parity
def inverted(matrix, pivoting=True):
"""
Only square matrices can be inverted!
"""
ndim = squaredim(matrix, 'inverted')
# First: LU-decompose matrix to be inverted
if pivoting:
lower, upper, permlist, parity = ludcmp_crout_piv(matrix)
else:
lower, upper, permlist, parity = ludcmp_crout(matrix)
# Create unity matrix
unitymatrix = Matrix()
unitymatrix.unity(ndim)
# Loop over the columns in unity matrix and substitute
# (uses the fact that rows and columns are the same in a unity matrix)
columns = Matrix()
columns.zero(ndim, ndim)
for k in range(0, ndim):
columns[k] = lusubs(lower, upper, unitymatrix[k], permlist)
# preparations below for changing lusubs to handling column vector
# instead of list
#row = Matrix([unitymatrix[k]])
#column = transpose(row)
#columns[k] = lusubs(lower, upper, column, permlist)
#del column
# Transpose matrix to get inverse
newmatrix = ndim * [float('nan')]
for k in range(0,
ndim): # List comprehension is used for the innermost loop
newmatrix[k] = array('d', [row[k] for row in columns])
imatrix = Matrix(newmatrix)
del newmatrix
return imatrix
def inverted(matrix, pivoting=True):
"""
Only square matrices can be inverted!
"""
ndim = squaredim(matrix, 'inverted')
# First: LU-decompose matrix to be inverted
if pivoting:
lower, upper, permlist, parity = ludcmp_crout_piv(matrix)
else:
lower, upper, permlist, parity = ludcmp_crout(matrix)
# Create unity matrix
unitymatrix = Matrix()
unitymatrix.unity(ndim)
# Loop over the columns in unity matrix and substitute
# (uses the fact that rows and columns are the same in a unity matrix)
columns = Matrix()
columns.zero(ndim, ndim)
for k in range(0, ndim):
columns[k] = lusubs(lower, upper, unitymatrix[k], permlist)
# preparations below for changing lusubs to handling column vector
# instead of list
#row = Matrix([unitymatrix[k]])
#column = transpose(row)
#columns[k] = lusubs(lower, upper, column, permlist)
#del column
# Transpose matrix to get inverse
newmatrix = ndim*[float('nan')]
for k in range(0, ndim): # List comprehension is used for the innermost loop
newmatrix[k] = array('d', [row[k] for row in columns])
imatrix = Matrix(newmatrix)
del newmatrix
return imatrix
def corrmatrix(inputmatrix):
"""
Computes the correlation matrix of the input matrix. Each row is assumed
to contain the vector for one parameter.
"""
ndim = len(inputmatrix) # = the number of rows/parameters
# First create unity output matrix
corrmatrix = Matrix()
corrmatrix.unity(ndim)
# Then fill it with correlation coefficients
for k in range(0, ndim):
kp1 = k + 1
for j in range(0, kp1):
if j != k:
#amk,amj,vk,vj,covkj, rhokj = covar(inputmatrix[k], \
# inputmatrix[j])
#corrmatrix[k][j] = corrmatrix[j][k] = rhokj
corrmatrix[k][j] = corrmatrix[j][k] = \
covar(inputmatrix[k], inputmatrix[j])[5] # = rhokj
return corrmatrix
def corrmatrix(inputmatrix):
"""
Computes the correlation matrix of the input matrix. Each row is assumed
to contain the vector for one parameter.
"""
ndim = len(inputmatrix) # = the number of rows/parameters
# First create unity output matrix
corrmatrix = Matrix()
corrmatrix.unity(ndim)
# Then fill it with correlation coefficients
for k in range(0, ndim):
kp1 = k + 1
for j in range(0, kp1):
if j != k:
#amk,amj,vk,vj,covkj, rhokj = covar(inputmatrix[k], \
# inputmatrix[j])
#corrmatrix[k][j] = corrmatrix[j][k] = rhokj
corrmatrix[k][j] = corrmatrix[j][k] = \
covar(inputmatrix[k], inputmatrix[j])[5] # = rhokj
return corrmatrix
