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Matrix.py
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Matrix.py
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from math import *
from Vector import Vector
class Matrix(list):
def __init__(A,B=[]):
A.__Alloc__(B)
for i in range(len(B)):
for j in range(len(B[i])):
A[i][j]=1.0*B[i][j]
def __Alloc__(A,B):
for i in range(len(B)):
A.append([])
for j in range(len(B[i])):
A[i].append(0.0)
def __add__(A,other):
B=Matrix(A)
for i in range(len(other)):
for j in range(len(other[i])):
B[i][j]+=other[i][j]
return B
def __mul__(A,other):
if (other.__class__.__name__=="int"):
other*=1.0
if (other.__class__.__name__=="float"):
B=Matrix()
for i in range( len(A) ):
B.append( [] )
for j in range( len(A[i]) ):
B[i].append( A[i][j]*other )
return B
if (other.__class__.__name__=="Vector"):
v=Vector( len(A) )
for i in range( len(A) ):
v[i]=0.0
for j in range( len(other) ):
v[i]+=A[i][j]*other[j]
return v
print "Matrix:: Invalid second argument type in __mul__:",other.__class__.__name__
#exit()
def __str__(A):
text="["
for i in range( len(A) ):
text+="\n ["
for j in range( len(A[i]) ):
text+=str(A[i][j])
if ( j+1<len(A[i]) ):
text+=","
if (i+1<len(A)):
text+="],"
else:
text+="]\n]"
return text
def Matrix_Column(A,i):
v=Vector()
v.__Alloc__(len(A[i]))
for j in range( len(v) ):
v[j]=A[j][i]
return v
def Matrix_Line(A,i):
v=Vector()
v.__Alloc__(len(A))
for j in range( len(v) ):
v[j]=A[i][j]
return v
def Trace(A):
tr=0.0
for i in range( len(A) ):
tr+=A[i][i]
return tr
def Transpose(A):
AT=Matrix([])
for j in range(len(A[0])):
AT.append( [] )
for i in range(len(A)):
AT[j].append( A[i][j] )
return AT
def MultiplyRow(A,i,c):
for j in range( len(A[i]) ):
A[i][j]*=c
#Do row operation A_j-cA_i
def RowOperation(A,i,j,c):
for k in range( len(A[i]) ):
A[j][k]-=c*A[i][k]
def SwapRows(A,i,j):
if (i==j):
return
for k in range( len(A[i]) ):
tmp=A[i][k]
A[i][k]=A[j][k]
A[j][k]=tmp
def FindPivote(A,n):
large=abs(A[n][n])
pos=n
for i in range(n,len(A)):
if (abs(A[i][n])>large):
large=abs(A[i][n])
pos=i
return i
def GaussForward(self):
#Make a copy in order not to change
A=Matrix(self)
#loop over diagonal elements
det=1.0
for i in range( len(A) ):
ii=A.FindPivote(i)
if (i!=ii):
A.SwapRows(i,ii)
det*=-1.0
c=A[i][i]
det*=c
if (c==0.0):
print "Matrix Singular at position",str(i+1)
return 0.0
A.MultiplyRow(i,1.0/c)
for j in range(i+1,len(A)):
#A_j=A_j-cA_i, c=A_i_j
A.RowOperation(i,j,A[j][i])
return det
def Determinant(A):
return A.GaussForward()
def Discriminant(A):
return (A[0][0]-A[1][1])**2.0+4.0*A[0][1]*A[1][0]
def Eigen_Values(A):
tr=A.Trace()
delta=A.Discriminant()
lambdas=[]
if (delta>=0):
delta=sqrt(delta)
lambdas=[
(tr-delta)*0.5,
(tr+delta)*0.5,
]
return Vector(lambdas)
def Eigen_Vectors2(A,lambdas=[]):
if (not lambdas): lambdas=A.Eigen_Values()
v0=Vector([
lambdas[0]-A[0][0],
A[1][0]
])
if (abs(lambdas[0]-A[0][0])==0.0):
v0=Vector([1.0,0.0])
v0=v0.Normalize()
v1=v0.Transverse2()
return Matrix([
[ v0[0],v1[0] ],
[ v0[1],v1[1] ],
])
def Quadratic_Diagonalize(A,b=None,c=1.0):
if (not ): b=[0.0,0.0]
lambdas=self.Quadratic_Eigen_Values()
D=self.Eigen_Vectors(lambdas)
return [ lambdas,D ]
def Kronecker(i,j):
res=0.0
if (i==j): res=1.0
return res
def I(n):
I=Matrix()
for i in range(n):
I.append([])
for j in range(n):
I[i].append( Kronecker(i,j) )
return I
def Diagonal(v):
D=Matrix()
for i in range(n):
D.append([])
for j in range(n):
D[i].append( v[i]*Kronecker(i,j) )
return D