def qr_fact_givens(matA):
original = matA.copy()
n = len(matA) # n is # of cols and rows
rot_list = [] # keep track of all rotation matrices for calculation of Q
temp = zeros(n) # weird error happens if I don't do this
matA = temp + matA # weird error happens if I don't do this
for i in range(0, n): # for each col
for j in range(i + 1, n): # for each row
if matA[j, i] != 0: # if entry not already 0
rot_matrix = build_rot_mat(
n, j, i, matA[i, i], matA[j, i]
) # build rotation matrix using pivot and target entry
rot_list.append(rot_matrix) # add rotation matrix to list
matA = matrixMult(rot_matrix, matA) # update matrix to approach R
rot_list.reverse() # reverse order of rotation matrices for multiplication
qMat = rot_list[0].transpose() # transpose first rotation matrix
for k in range(1, len(rot_list)): # for each rotation matrix
qMat = matrixMult(rot_list[k].transpose(), qMat) # multiply every rotation matrix transposed together
derived_A = matrixMult(qMat, matA) # begin error calculation, compute Q*R
derived_A = derived_A - original # compute QR - A
current_max = 0 # find norm by finding largest abs val of entries
for col in range(0, n): # for each col
for row in range(0, n): # for each row
if abs(derived_A[row, col]) > current_max: # if current abs val entry is bigger than max
current_max = abs(derived_A[row, col]) # update
return [qMat, matA, current_max] # return Q and R
def lu_fact(matA):
original = matA.copy()
n = len(matA) # n is # of rows and cols
i_matA = identity(n, float) # i_matA will be transformed into L via all row operations that create U
for col in range(0, n): # for each col
i = 0 # initialize i
for i in range(col, n): # for each row
if matA[i, col] != 0: # find pivot
break
if matA[i, col] != 0:
for k in range(col + 1, n): # for each entry beneath pivot
if matA[k, col] != 0: # if entry not already 0
multiple = matA[k, col] / matA[i, col] # find multiple for eliminating entry
i_matA[k, col] = multiple # set corresponding i_matA entry to construct L
for c in range(0, n): # for each entry along row, we want to apply same operation
matA[k, c] = matA[k, c] - (
matA[i, c] * multiple
) # eliminate entry by multiplying pivot by multiple and subtracting
derived_A = matrixMult(i_matA, matA) # begin error calculation, compute L*U
derived_A = derived_A - original # compute LU - A
current_max = 0 # find norm by finding largest abs val of entries
for col in range(0, n): # for each col
for row in range(0, n): # for each row
if abs(derived_A[row, col]) > current_max: # if current abs val entry is bigger than max
current_max = abs(derived_A[row, col]) # update
return [i_matA, matA, current_max] # return L, U, and error