def qr_fact_househ(matrixA):
m = matrixA.shape[0]
n = matrixA.shape[1]
#get Householder vector for first column of A
H = make_h(matrixA.T[0])
Q = H
for i in range(n):
result = np.dot(Q, matrixA)
result = result.T
col = result[i, i:]
smaller_matrix = make_h(col)
height_1 = len(col)
I = np.eye(n)
#reverse all the H and V entries in matrix
reverse = np.flipud(np.fliplr(smaller_matrix))
#want to insert smaller_matrix into H2 (matrix of zeros)
for r in range(reverse.shape[0]):
for c in range(reverse.shape[1]):
I[I.shape[0] - r - 1, I.shape[1] - c - 1] = reverse[r, c]
Q = mult(I, Q)
R = mult(Q, matrixA)
errorMatrix = np.dot(Q, R) - A
error = find_max(errorMatrix)
x = solve_qr_b(Q, R, b)
return Q.T, R, error, x
def qr_fact_givens(matrixA):
Q = np.eye(matrixA.shape[0])
R = matrixA
for y in range(matrixA.shape[1]):
for num in range(matrixA.shape[0]):
if y is num:
pivot = (num, y)
if y < num:
identity = np.eye(matrixA.shape[0])
cosX, sinX = make_givens(R, pivot, (num, y))
identity[num][num] = cosX
identity[y][y] = cosX
identity[y][num] = sinX
identity[num][y] = -sinX
R = mult(identity, R)
Q = Q.dot(identity.T)
#error value of ||QR - A||
errorValue = 0
errorMatrix = mult(Q,R) - A
for i in range(errorMatrix.shape[0]):
for j in range(errorMatrix.shape[1]):
if (errorValue < errorMatrix[i, j]):
errorValue = errorMatrix[i, j]
x = solve_qr_b(Q, R, b)
return Q, R, errorValue, x