def qr_gs_inverse(A: matrix):
B = matrix(A.size1, A.size2)
I = matrix(A.size1, A.size2)
e_i = vector(I.size1)
c = vector(I.size1)
for ii in range(I.size1):
for jj in range(I.size2):
if ii == jj:
I[ii, jj] = 1
else:
I[ii, jj] = 0
for ii in range(A.size1):
for jj in range(A.size1):
e_i[jj] = matrix.get(I, jj, ii)
c = qr_gs_solve(A, e_i)
for jj in range(A.size2):
B[jj, ii] = vector.get(c, jj)
return B
def outer(a: vector, b: vector):
A = matrix(a.size, b.size)
for ii in range(a.size):
for jj in range(b.size):
A[ii,jj] = a[ii] * b[jj]
return A
def qr_gs_decomp(A: matrix):
n = A.size1
m = A.size2
Q = matrix(n, m)
R = matrix(m, m)
A_new = mt_copy(A)
for ii in range(m): #iteration over columns
R[ii, ii] = matrix.dot_prod(A_new.get_col(ii),
A_new.get_col(ii))**(1. / 2)
for jj in range(n): #iteration over rows
Q[jj, ii] = A_new[jj, ii] / R[ii, ii]
for kk in range(ii + 1, m):
R[ii, kk] = matrix.dot_prod(Q.get_col(ii), A_new.get_col(kk))
for ll in range(n):
A_new[ll, kk] = A_new[ll, kk] - Q[ll, ii] * R[ii, kk]
return Q, R
import numpy as np
import qr_decomp
from eigen import *
from matrix_codes import matrix, trans, matrix_mult
import random
from vector_codes import vector, mt_vt_mult
n = 3
A = matrix(n, n)
N = matrix(n, n)
for ii in range(0, n):
A[ii, ii] = np.random.random()
N[ii, ii] = np.random.random()
for jj in range(ii, n):
A[ii, jj] = np.random.random()
A[jj, ii] = A[ii, jj]
N[ii, jj] = np.random.random()
N[jj, ii] = N[ii, jj]
NtN = matrix_mult(trans(N), N)
for ii in range(NtN.size1):
N[ii, ii] = NtN[ii, ii] #Make N real positive definite
print("Printing matrix A")
matrix.printing(A)
print("\n\nPrinting matrix N")
matrix.printing(N)
import numpy as np
import qr_decomp
from matrix_codes import matrix, trans, matrix_mult
import random
from vector_codes import vector, mt_vt_mult
n = 5
m = 3
A = matrix(n, m)
for ii in range(0, n):
for jj in range(0, m):
A[ii, jj] = np.random.random()
print("\n----------Part A.1----------\n")
print("\nTesting decomposition:\n")
Q, R = qr_decomp.qr_gs_decomp(A)
print("My Q matrix: \n")
matrix.printing(Q)
print("My R matrix: \n")
matrix.printing(R)
print("My QTQ matrix: \n")
QT = trans(Q)
QTQ = matrix_mult(QT, Q)
matrix.printing(QTQ)