def LU(a): #LU decomposition
n = len(a)
l = mh.MatrixMake(n, n) #MatrixMake(a,b) creates empty Matrix axb
u = mh.MatrixMake(n, n)
for i in range(n): #Doolittle's way of computing
l[i][i] = 1
for j in range(i, n):
u[i][j] = a[i][j] - Sigma(lambda k: l[i][k] * u[k][j], 0, i - 1)
for j in range(i + 1, n):
l[j][i] = (a[j][i] -
Sigma(lambda k: l[j][k] * u[k][i], 0, i - 1)) / u[i][i]
return l, u
def __mul__(self, w):
if len(w) - 1:
n = len(w)
matrix = handler.MatrixMake(n - 1, n)
vector = handler.MatrixMake(n, 1)
for i in range(1, n):
matrix[i - 1][i] = i
vector[i][0] = w[i]
# handler.MatrixPrint(matrix)
self.size = (n - 1, n)
handler.MatrixPrint(vector, "pętla")
handler.MatrixPrint(w.getVector(), "metoda")
return handler.MatrixMulti(matrix, vector)
else:
return [[0]]
def LLt(a): #Cholesky
n = len(a)
l = mh.MatrixMake(n, n)
for i in range(n):
l[i][i] = mh.math.sqrt(a[i][i] - Sigma(lambda k: l[i][k]**2, 0, i - 1))
for j in range(i, n):
l[j][i] = (a[j][i] -
Sigma(lambda k: l[j][k] * l[i][k], 0, i - 1)) / l[i][i]
return l
def fill(c, hp
): #fill fills hp matrix with identity matrix and two zeroed matrices
h = mh.MatrixMake(c, c)
for i in range(c - len(hp)):
h[i][i] = 1
for i in range(len(hp)):
for j in range(len(hp)):
h[i + c - len(hp)][j + c - len(hp)] = hp[i][j]
return h
def __init__(self, vals=0, size=('auto', 'auto')):
if hasattr(vals, '__iter__'):
if hasattr(vals[0], '__iter__'):
self.__size = (len(vals), len(vals[0]))
else:
self.size = (1, len(vals))
self.__vals = vals.copy()
else:
self.__size = size
if size != ('auto', 'auto'):
self.__vals = handler.MatrixMake(size[0], size[1])
def SVD(a):
aat = mh.MatrixMulti(a, mh.MatrixTrans(a))
ata = mh.MatrixMulti(mh.MatrixTrans(a), a)
mh.MatrixPrint(aat, "aat")
mh.MatrixPrint(ata, "ata")
eigenvalues_aat = list(map(lambda x: round(x, ndigits=6), Francis(aat)))
singularvalues_aat = list(map(sqrt, eigenvalues_aat))
mh.MatrixPrint([eigenvalues_aat], "eigen aat")
mh.MatrixPrint([singularvalues_aat], "singular aat")
eigenvalues_ata = list(map(lambda x: round(x, ndigits=6), Francis(ata)))
singularvalues_ata = list(map(sqrt, eigenvalues_ata))
mh.MatrixPrint([eigenvalues_ata], "eigen ata")
mh.MatrixPrint([singularvalues_ata], "singular ata")
S = mh.MatrixMake(len(a), len(a[0]))
for i in range(min(len(a), len(a[0]))):
S[i][i] = singularvalues_aat[i]
mh.MatrixPrint(S, msg="Σ")