def normalizeData(data, meanOnly = False):
"""
normalize data by subtracting mean and dividing by sd per COLUMN
@param data: an array
@param meanOnly: if True subtract mean only; otherwise divide by sd too
@return: (an array with the same dimension as data, mean, stds, the transformer)
"""
# compute the new data
m = mean(data, axis=0)
res = data - m
if meanOnly:
stds = 1
else:
stds = sqrt(var(data, axis=0))
stds[stds==0] = 1 # to avoid dividing by 0
res /= stds
# figure out the transformer
def foo(givenData):
assert givenData.shape[1]==data.shape[1], "Only arrays of %d columns are handled." % data.shape[1]
return (givenData - m)/stds
return res, m, stds, foo
def symMatrix(numRows, numCols, letter):
A = matrix(SR, numRows, numCols)
for i in range(0, numRows):
for j in range(0, numCols):
A[i, j] = var("%s%d%d" % (letter, i, j))
return A
def symVector(numRows, letter):
"""Creates a column vector where each element is a unique symbol
"""
n = len(str(numRows))
format = '%s%0' + str(n) + 'd'
A = matrix(SR, numRows, 1)
for i in range(0, numRows):
A[i, 0] = var(format % (letter, i))
return A
def symMatrix( numRows , numCols , letter ):
"""Creates a matrix where each element is a unique symbol
"""
A = matrix(SR,numRows,numCols)
for i in range(0,numRows):
for j in range(0,numCols):
A[i,j] = var('%s%d%d' % (letter,i,j) )
return A
def symVector( numRows , letter ):
"""Creates a column vector where each element is a unique symbol
"""
n = len(str(numRows))
format = '%s%0'+str(n)+'d'
A = matrix(SR,numRows,1)
for i in range(0,numRows):
A[i,0] = var(format % (letter,i) )
return A
def symMatrix(numRows, numCols, letter):
"""Creates a matrix where each element is a unique symbol
"""
n = max(len(str(numRows)), len(str(numCols)))
format = '%s%0' + str(n) + 'd' + '%0' + str(n) + 'd'
A = matrix(SR, numRows, numCols)
for i in range(0, numRows):
for j in range(0, numCols):
A[i, j] = var(format % (letter, i, j))
return A
def evolve(p, m):
for j in range(200):
for i in range(len(p.chromos)):
sums = computeSums(m, p.chromos[i].genes[0], p.chromos[i].genes[1])
if len(sums) == 1:
p.chromos[i].fitness = 0.1
else:
# if var(sums) == 0.0:
# print('Solution:')
# print(sums)
# return
p.chromos[i].fitness = (1/(var(sums) + 0.0001)) #+ (len(sums)/(numR*numC))
if j%10 == 0:
best = p.getBestIndividuals()
sums = computeSums(m, best[0].genes[0], best[0].genes[1])
print("best")
print(sums)
print(var(sums))
print(best[0].fitness)
p.newGeneration()
def symMatrix( numRows , numCols , letter ):
"""Creates a matrix where each element is a unique symbol
"""
n = max(len(str(numRows)),len(str(numCols)))
format = '%s%0'+str(n)+'d'+'%0'+str(n)+'d'
A = matrix(SR,numRows,numCols)
for i in range(0,numRows):
for j in range(0,numCols):
A[i,j] = var(format % (letter,i,j) )
return A
def normalizeData(data, meanOnly = False):
"""
normalize data by subtracting mean and dividing by sd per COLUMN
Parameters:
- data: an array
- meanOnly: if True subtract mean only; otherwise divide by sd too
Returns: an array with the same dimension as data
"""
if meanOnly:
return data-mean(data,axis=0)
else:
stds = sqrt(var(data, axis=0))
stds[stds==0] = 1 # to avoid dividing by 0
return (data - mean(data, axis=0))/stds
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# Expands out symbolic equations for solving the linear system and polynomials in Nister's paper
# The script should be run using sage by typing "sage nister5.py"
#
# Works with Sage Version 5.2
from numpy.core.fromnumeric import var
from numpy.linalg.linalg import det
from sage.all import *
from utilsymbolic import *
x,y,z = var('x','y','z')
X = symMatrix( 3, 3 , 'X')
Y = symMatrix( 3, 3 , 'Y')
Z = symMatrix( 3, 3 , 'Z')
W = symMatrix( 3, 3 , 'W')
E = x*X + y*Y + z*Z + 1*W
EE = E*E.T
eq1=det(E)
eq2=EE*E-0.5*EE.trace()*E
eqs = (eq1,eq2[0,0],eq2[0,1],eq2[0,2],eq2[1,0],eq2[1,1],eq2[1,2],eq2[2,0],eq2[2,1],eq2[2,2])
keysA = ('x^3','y^3','x^2*y','x*y^2','x^2*z','x^2','y^2*z','y^2','x*y*z','x*y')
include = [removeFirst(w, bestVar) for w in include]
output = bestVar + "*( "
if bestVar[0].isdigit():
output += simplifyExpanded(reconstruct(include))
else:
output += reconstruct(include)
output += " )"
if len(exclude):
output += " + " + simplifyExpanded(reconstruct(exclude))
return output
x, y, z = var("x", "y", "z")
X = symMatrix(3, 3, "X")
Y = symMatrix(3, 3, "Y")
Z = symMatrix(3, 3, "Z")
W = symMatrix(3, 3, "W")
E = x * X + y * Y + z * Z + 1 * W
EE = E * E.T
eq1 = det(E)
eq2 = EE * E - 0.5 * EE.trace() * E
eqs = (eq1, eq2[0, 0], eq2[0, 1], eq2[0, 2], eq2[1, 0], eq2[1, 1], eq2[1, 2], eq2[2, 0], eq2[2, 1], eq2[2, 2])
keysA = ("x^3", "y^3", "x^2*y", "x*y^2", "x^2*z", "x^2", "y^2*z", "y^2", "x*y*z", "x*y")