def __pow__(self, other):
shape = self.shape
if len(shape) != 2 or shape[0] != shape[1]:
raise TypeError, "matrix is not square"
if type(other) in (type(1), type(1L)):
if other==0:
return matrix(N.identity(shape[0]))
if other<0:
x = self.I
other=-other
else:
x=self
result = x
if other <= 3:
while(other>1):
result=result*x
other=other-1
return result
# binary decomposition to reduce the number of Matrix
# Multiplies for other > 3.
beta = binary_repr(other)
t = len(beta)
Z,q = x.copy(),0
while beta[t-q-1] == '0':
Z *= Z
q += 1
result = Z.copy()
for k in range(q+1,t):
Z *= Z
if beta[t-k-1] == '1':
result *= Z
return result
def __pow__(self, other):
shape = self.shape
if len(shape) != 2 or shape[0] != shape[1]:
raise TypeError, "matrix is not square"
if type(other) in (type(1), type(1L)):
if other==0:
return matrix(N.identity(shape[0]))
if other<0:
x = self.I
other=-other
else:
x=self
result = x
if other <= 3:
while(other>1):
result=result*x
other=other-1
return result
# binary decomposition to reduce the number of Matrix
# Multiplies for other > 3.
beta = binary_repr(other)
t = len(beta)
Z,q = x.copy(),0
while beta[t-q-1] == '0':
Z *= Z
q += 1
result = Z.copy()
for k in range(q+1,t):
Z *= Z
if beta[t-k-1] == '1':
result *= Z
return result
else:
raise TypeError, "exponent must be an integer"
def make(net,name='System',neurons=100,A=[[0]],tau_feedback=0.1):
A=numeric.array(A)
assert len(A.shape)==2
assert A.shape[0]==A.shape[1]
dimensions=A.shape[0]
state=net.make(name,neurons,dimensions)
Ap=A*tau_feedback+numeric.identity(dimensions)
net.connect(state,state,transform=Ap,pstc=tau_feedback)
if net.network.getMetaData("linear") == None:
net.network.setMetaData("linear", HashMap())
linears = net.network.getMetaData("linear")
linear=HashMap(4)
linear.put("name", name)
linear.put("neurons", neurons)
linear.put("A", MU.clone(A))
linear.put("tau_feedback", tau_feedback)
linears.put(name, linear)
if net.network.getMetaData("templates") == None:
net.network.setMetaData("templates", ArrayList())
templates = net.network.getMetaData("templates")
templates.add(name)
if net.network.getMetaData("templateProjections") == None:
net.network.setMetaData("templateProjections", HashMap())
templateproj = net.network.getMetaData("templateProjections")
templateproj.put(name, name)
def make(net, name='System', neurons=100, A=[[0]], tau_feedback=0.1):
A = numeric.array(A)
assert len(A.shape) == 2
assert A.shape[0] == A.shape[1]
dimensions = A.shape[0]
state = net.make(name, neurons, dimensions)
Ap = A * tau_feedback + numeric.identity(dimensions)
net.connect(state, state, transform=Ap, pstc=tau_feedback)
if net.network.getMetaData("linear") == None:
net.network.setMetaData("linear", HashMap())
linears = net.network.getMetaData("linear")
linear = HashMap(4)
linear.put("name", name)
linear.put("neurons", neurons)
linear.put("A", MU.clone(A))
linear.put("tau_feedback", tau_feedback)
linears.put(name, linear)
if net.network.getMetaData("templates") == None:
net.network.setMetaData("templates", ArrayList())
templates = net.network.getMetaData("templates")
templates.add(name)
if net.network.getMetaData("templateProjections") == None:
net.network.setMetaData("templateProjections", HashMap())
templateproj = net.network.getMetaData("templateProjections")
templateproj.put(name, name)
def make(net, name='System', neurons=100, A=[[0]], tau_feedback=0.1):
A = numeric.array(A)
assert len(A.shape) == 2
assert A.shape[0] == A.shape[1]
dimensions = A.shape[0]
state = net.make(name, neurons, dimensions)
Ap = A * tau_feedback + numeric.identity(dimensions)
net.connect(state, state, transform=Ap, pstc=tau_feedback)
def make(net,name='System',neurons=100,A=[[0]],tau_feedback=0.1):
A=numeric.array(A)
assert len(A.shape)==2
assert A.shape[0]==A.shape[1]
dimensions=A.shape[0]
state=net.make(name,neurons,dimensions)
Ap=A*tau_feedback+numeric.identity(dimensions)
net.connect(state,state,transform=Ap,pstc=tau_feedback)
def matrix_power(M,n):
"""Raise a square matrix to the (integer) power n.
For positive integers n, the power is computed by repeated matrix
squarings and matrix multiplications. If n=0, the identity matrix
of the same type as M is returned. If n<0, the inverse is computed
and raised to the exponent.
Parameters
----------
M : array-like
Must be a square array (that is, of dimension two and with
equal sizes).
n : integer
The exponent can be any integer or long integer, positive
negative or zero.
Returns
-------
M to the power n
The return value is a an array the same shape and size as M;
if the exponent was positive or zero then the type of the
elements is the same as those of M. If the exponent was negative
the elements are floating-point.
Raises
------
LinAlgException
If the matrix is not numerically invertible, an exception is raised.
See Also
--------
The matrix() class provides an equivalent function as the exponentiation
operator.
Examples
--------
>>> matrix_power(array([[0,1],[-1,0]]),10)
array([[-1, 0],
[ 0, -1]])
"""
if len(M.shape) != 2 or M.shape[0] != M.shape[1]:
raise ValueError("input must be a square array")
if not issubdtype(type(n),int):
raise TypeError("exponent must be an integer")
from numpy.linalg import inv
if n==0:
M = M.copy()
M[:] = identity(M.shape[0])
return M
elif n<0:
M = inv(M)
n *= -1
result = M
if n <= 3:
for _ in range(n-1):
result=N.dot(result,M)
return result
# binary decomposition to reduce the number of Matrix
# multiplications for n > 3.
beta = binary_repr(n)
Z,q,t = M,0,len(beta)
while beta[t-q-1] == '0':
Z = N.dot(Z,Z)
q += 1
result = Z
for k in range(q+1,t):
Z = N.dot(Z,Z)
if beta[t-k-1] == '1':
result = N.dot(result,Z)
return result
def matrix_power(M,n):
"""
Raise a square matrix to the (integer) power n.
For positive integers n, the power is computed by repeated matrix
squarings and matrix multiplications. If n=0, the identity matrix
of the same type as M is returned. If n<0, the inverse is computed
and raised to the exponent.
Parameters
----------
M : array_like
Must be a square array (that is, of dimension two and with
equal sizes).
n : integer
The exponent can be any integer or long integer, positive
negative or zero.
Returns
-------
M to the power n
The return value is a an array the same shape and size as M;
if the exponent was positive or zero then the type of the
elements is the same as those of M. If the exponent was negative
the elements are floating-point.
Raises
------
LinAlgException
If the matrix is not numerically invertible, an exception is raised.
See Also
--------
The matrix() class provides an equivalent function as the exponentiation
operator.
Examples
--------
>>> np.linalg.matrix_power(np.array([[0,1],[-1,0]]),10)
array([[-1, 0],
[ 0, -1]])
"""
if len(M.shape) != 2 or M.shape[0] != M.shape[1]:
raise ValueError("input must be a square array")
if not issubdtype(type(n),int):
raise TypeError("exponent must be an integer")
from numpy.linalg import inv
if n==0:
M = M.copy()
M[:] = identity(M.shape[0])
return M
elif n<0:
M = inv(M)
n *= -1
result = M
if n <= 3:
for _ in range(n-1):
result=N.dot(result,M)
return result
# binary decomposition to reduce the number of Matrix
# multiplications for n > 3.
beta = binary_repr(n)
Z,q,t = M,0,len(beta)
while beta[t-q-1] == '0':
Z = N.dot(Z,Z)
q += 1
result = Z
for k in range(q+1,t):
Z = N.dot(Z,Z)
if beta[t-k-1] == '1':
result = N.dot(result,Z)
return result
d2_2, d2_2i, d3_3, d3_3i)
# Matrix(), shape()
for data in datas:
m = numeric.Matrix(data)
if m.shape() != (len(data), len(data[0])):
nb_errors += 1
print('error: constructor size: %s' % data)
if m_to_l(m) != data:
nb_errors += 1
print('error: constructor value: %s' % data)
# indentity()
mi1 = numeric.identity(1)
if mi1.shape() != (1, 1):
nb_errors += 1
print('error: identity size')
if m_to_l(mi1) != di1:
nb_errors += 1
print('error: identity value')
mi5 = numeric.identity(5)
if mi5.shape() != (5, 5):
nb_errors += 1
print('error: identity size')
if m_to_l(mi5) != di5:
nb_errors += 1
def main(): # pylint: disable=too-many-locals,too-many-branches,too-many-statements # noqa
# type: () -> None
"""Perform succession of tests."""
if SIMPLEGUICS2PYGAME:
from sys import argv # pylint: disable=import-outside-toplevel
if len(argv) != 2:
print('Test numeric.Matrix ...\n')
else:
print('Test numeric.Matrix ...\n')
nb_errors = 0
dz5_3 = [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0],
[0, 0, 0]] # type: List[List[Union[int, float]]]
dz3_5 = [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0],
[0, 0, 0, 0, 0]] # type: List[List[Union[int, float]]]
di1 = [[1]] # type: List[List[Union[int, float]]]
di5 = [[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0],
[0, 0, 0, 0, 1]] # type: List[List[Union[int, float]]]
d5_3 = [[0, -1, 2], [-3, 4, -5], [6, -7, 8], [-9, 10, -11],
[12, -13, 14]] # type: List[List[Union[int, float]]]
d5_3t = [[0, -3, 6, -9, 12], [-1, 4, -7, 10, -13],
[2, -5, 8, -11, 14]] # type: List[List[Union[int, float]]]
d3_5 = [[0, -1, 2, -3, 4], [-5, 6, -7, 8, -9],
[10, -11, 12, -13, 14]] # type: List[List[Union[int, float]]]
d3_5t = [[0, -5, 10], [-1, 6, -11], [2, -7, 12], [-3, 8, -13],
[4, -9, 14]] # type: List[List[Union[int, float]]]
d2_2 = [[1, 2], [3, 4]] # type: List[List[Union[int, float]]]
d2_2i = [[-2, 1], [1.5, -0.5]] # type: List[List[Union[int, float]]]
d3_3 = [[2, -1, 0], [-1, 2, -1],
[0, -1, 2]] # type: List[List[Union[int, float]]]
d3_3i = [[0.75, 0.5, 0.25], [0.5, 1, 0.5],
[0.25, 0.5, 0.75]] # type: List[List[Union[int, float]]]
datas = (dz5_3, dz3_5, di1, di5, d5_3, d5_3t, d3_5, d3_5t, d2_2, d2_2i,
d3_3, d3_3i
) # type: Tuple[List[List[Union[int, float]]], ...] # noqa
# Matrix(), shape()
for data in datas:
m = numeric.Matrix(data)
if m.shape() != (len(data), len(data[0])):
nb_errors += 1
print('error: constructor size: %s' % data)
if m_to_l(m) != data:
nb_errors += 1
print('error: constructor value: %s' % data)
# indentity()
mi1 = numeric.identity(1)
if mi1.shape() != (1, 1):
nb_errors += 1
print('error: identity size')
if m_to_l(mi1) != di1:
nb_errors += 1
print('error: identity value')
mi5 = numeric.identity(5)
if mi5.shape() != (5, 5):
nb_errors += 1
print('error: identity size')
if m_to_l(mi5) != di5:
nb_errors += 1
print('error: identity value')
# []
for data in datas:
m = numeric.Matrix(data)
for i, row in enumerate(data):
for j in range(len(data[0])):
if m[i, j] != row[j]:
nb_errors += 1
print('error: [%i, %i]: %s' % (i, j, data))
# set []
for data in datas:
m = numeric.Matrix(data)
m2 = numeric.Matrix(data) # pylint: disable=invalid-name
for i in range(len(data)):
for j in range(len(data[0])):
m2[i, j] = 666
if not isinstance(m2[i, j], float) or (m2[i, j] != 666):
nb_errors += 1
print('error: [%i, %i] = 666: %s' % (i, j, data))
print(m2)
m2[i, j] = m[i, j]
if not m_eq(m, m2):
nb_errors += 1
print('error: [%i, %i] = old: %s' % (i, j, data))
print(m2)
# copy()
for data in datas:
m = numeric.Matrix(data)
m2 = m.copy() # pylint: disable=invalid-name
if not m_eq(m, m2):
nb_errors += 1
print('error: [%i, %i] = old: %s' % (i, j, data))
print(m)
print(m2)
m2[0, 0] = 666
if m_eq(m, m2) or (m[0, 0] == 666):
nb_errors += 1
print('error: [%i, %i] = old: %s' % (i, j, data))
print(m)
print(m2)
# getrow()
for data in datas:
m = numeric.Matrix(data)
for i, good_row in enumerate(data):
row = m_to_l(m.getrow(i))[0]
if len(row) != len(data[0]):
nb_errors += 1
print('error: getrow size %i %s %s' % (i, row, good_row))
if row != good_row:
nb_errors += 1
print('error: getrow %i %s %s' % (i, row, good_row))
for j in range(len(data[0])):
if row[j] != good_row[j]:
nb_errors += 1
print('error: getrow != [%i, %i]' % (i, j))
# getcol()
for data in datas:
m = numeric.Matrix(data)
for j in range(len(data[0])):
col = m_to_l(m.getcol(j))[0]
if len(col) != len(data):
nb_errors += 1
print('error: getcol size %i %s %s' % (i, col, data))
for i, row in enumerate(data):
if col[i] != row[j]:
nb_errors += 1
print('error: getcol != [%i, %i]' % (i, j))
# scale(), +, -
# (in CodeSkulptor3 method scale() doesn't exist
# and * is the operator to multiply by a scalar)
for data in datas:
m = numeric.Matrix(data)
adds = numeric.Matrix(data)
if codeskulptor_lib.codeskulptor_version() == 3:
subs = numeric.Matrix(data) * -1
else:
subs = numeric.Matrix(data).scale(-1)
for k in range(1, 10):
if codeskulptor_lib.codeskulptor_version() == 3:
ms = m * k # pylint: disable=invalid-name
else:
ms = m.scale(k) # pylint: disable=invalid-name
if not m_eq(ms, adds):
nb_errors += 1
print('error: scale != +: %i %s' % (k, data))
print(ms)
print(adds)
adds = adds + m
if codeskulptor_lib.codeskulptor_version() == 3:
ms = m * -k # pylint: disable=invalid-name
else:
ms = m.scale(-k) # pylint: disable=invalid-name
if not m_eq(ms, subs):
nb_errors += 1
print('error: scale != -: %i %s' % (k, data))
print(ms)
print(subs)
subs = subs - m
if codeskulptor_lib.codeskulptor_version() != 3:
# *
# (in CodeSkulptor3 * is the operator to multiply by a scalar
# add @ the operator to multiply two matrices)
m = numeric.Matrix(d5_3) * numeric.Matrix(d3_5)
if m_to_l(m) != [[25, -28, 31, -34, 37], [-70, 82, -94, 106, -118],
[115, -136, 157, -178, 199],
[-160, 190, -220, 250, -280],
[205, -244, 283, -322, 361]]:
nb_errors += 1
print('error: (5, 3) * (3, 5)')
print(m)
m = numeric.Matrix(d3_5) * numeric.Matrix(d5_3)
if m_to_l(m) != [[90, -100, 110], [-240, 275, -310], [390, -450, 510]]:
nb_errors += 1
print('error: (3, 5) * (5, 3)')
print(m)
for data in datas:
m = numeric.Matrix(data)
m2 = m * numeric.identity(len(data[0])) # pylint: disable=invalid-name # noqa
if not m_eq(m, m2):
nb_errors += 1
print('error: *: %s' % data)
print(m2)
m2 = numeric.identity(len(data)) * m # pylint: disable=invalid-name # noqa
if not m_eq(m, m2):
nb_errors += 1
print('error: *: %s' % data)
print(m2)
a = numeric.Matrix(d2_2)
b = numeric.Matrix(d2_2i)
if not m_eq(a * b, numeric.identity(2)):
nb_errors += 1
print('error: a * a^(-1)')
print(a * b)
if not m_eq(b * a, numeric.identity(2)):
nb_errors += 1
print('error: a^(-1) * a')
print(b * a)
a = numeric.Matrix(d3_3)
b = numeric.Matrix(d3_3i)
if not m_eq(a * b, numeric.identity(3)):
nb_errors += 1
print('error: a * a^(-1)')
print(a * b)
if not m_eq(b * a, numeric.identity(3)):
nb_errors += 1
print('error: a^(-1) * a')
print(b * a)
# summation()
for k in range(1, 10):
m = numeric.identity(k)
if m.summation() != k:
nb_errors += 1
print('error: sum %i %f' % (k, m.summation()))
m = numeric.Matrix(dz5_3)
if m.summation() != 0:
nb_errors += 1
print('error: sum %f' % m.summation())
m = numeric.Matrix(d5_3)
if m.summation() != 7:
nb_errors += 1
print('error: sum %f' % m.summation())
m = numeric.Matrix(d3_5)
if m.summation() != 7:
nb_errors += 1
print('error: sum %f' % m.summation())
# abs()
m = numeric.Matrix(dz5_3).abs()
if not m_eq(m, numeric.Matrix(dz5_3)):
nb_errors += 1
print('error: abs(0)')
print(m)
for k in range(1, 10):
m = numeric.identity(k).abs()
if not m_eq(m, numeric.identity(k)):
print('error: abs(identity(%i))' % k)
print(m)
m = numeric.Matrix(d5_3).abs()
if m.summation() != 105:
nb_errors += 1
print('error: abs')
print(m)
m = numeric.Matrix(d3_5).abs()
if m.summation() != 105:
nb_errors += 1
print('error: abs')
print(m)
# transpose()
m = numeric.Matrix(dz5_3).transpose()
if not m_eq(m, numeric.Matrix(dz3_5)):
nb_errors += 1
print('error: transpose(0)')
print(m)
for k in range(1, 10):
m = numeric.identity(k).transpose()
if not m_eq(m, numeric.identity(k)):
print('error: transpose(identity(%i))' % k)
print(m)
m = numeric.Matrix(d5_3).transpose()
if not m_eq(m, numeric.Matrix(d5_3t)):
nb_errors += 1
print('error: transpose')
print(numeric.Matrix(d5_3))
print(m)
m = numeric.Matrix(d3_5).transpose()
if not m_eq(m, numeric.Matrix(d3_5t)):
nb_errors += 1
print('error: transpose')
print(numeric.Matrix(d3_5))
print(m)
# inverse()
for k in range(1, 10):
m = numeric.identity(k).inverse()
if not m_eq(m, numeric.identity(k)):
print('error: inverse(identity(%i))' % k)
print(m)
if codeskulptor_lib.codeskulptor_version() == 3:
m = numeric.identity(k) * 5
m = m.inverse()
if not m_eq(m, numeric.identity(k) * (1.0 / 5)):
print('error: inverse(identity(%i)*5)' % k)
print(m)
else:
m = numeric.identity(k).scale(5).inverse()
if not m_eq(m, numeric.identity(k).scale(1.0 / 5)):
print('error: inverse(identity(%i)*5)' % k)
print(m)
m = numeric.identity(k)
m[0, 0] = 0
try:
m = m.inverse()
print('error: not inversible first: %i' % k)
print(m)
except ValueError:
pass
m = numeric.identity(k)
m[k - 1, k - 1] = 0
try:
m = m.inverse()
print('error: not inversible last: %i' % k)
print(m)
except ValueError:
pass
mi = numeric.Matrix(d2_2).inverse() # pylint: disable=invalid-name
if not m_eq(mi, numeric.Matrix(d2_2i), False):
print('error: inverse 1')
print(mi)
print(numeric.Matrix(d2_2i))
mi = numeric.Matrix(d2_2i).inverse() # pylint: disable=invalid-name
if not m_eq(mi, numeric.Matrix(d2_2), False):
print('error: inverse 2')
print(mi)
print(numeric.Matrix(d2_2))
# Result
if nb_errors == 0:
if not SIMPLEGUICS2PYGAME or (len(argv) != 2):
print('Ok')
else:
print('\n%i errors founded' % nb_errors)
exit(nb_errors) # pylint: disable=consider-using-sys-exit
datas = (dz5_3, dz3_5, di1, di5, d5_3, d5_3t, d3_5, d3_5t, d2_2, d2_2i, d3_3,
d3_3i)
# Matrix(), shape()
for data in datas:
m = numeric.Matrix(data)
if m.shape() != (len(data), len(data[0])):
nb_errors += 1
print('error: constructor size: %s' % data)
if m_to_l(m) != data:
nb_errors += 1
print('error: constructor value: %s' % data)
# indentity()
mi1 = numeric.identity(1)
if mi1.shape() != (1, 1):
nb_errors += 1
print('error: identity size')
if m_to_l(mi1) != di1:
nb_errors += 1
print('error: identity value')
mi5 = numeric.identity(5)
if mi5.shape() != (5, 5):
nb_errors += 1
print('error: identity size')
if m_to_l(mi5) != di5:
nb_errors += 1