def qr_fact_househ(matrix):
if isinstance(matrix, basestring):
matrix = np.loadtxt(matrix, unpack=False, delimiter=" ")
originalMatrix = matrix
diagonalIndex = 0
hMatrixQueue = Queue.Queue()
while diagonalIndex < matrix.shape[1] - 1:
# Check to see if there are all zeros below the pivot
allZeros = True
for currentIndex in range(diagonalIndex + 1, matrix.shape[0]):
if matrix[currentIndex, diagonalIndex] != 0:
allZeros = False
# If not all zeros
if allZeros == False:
# Creating the U matrix
matrixU = np.zeros(shape=(matrix.shape[0] - diagonalIndex, 1))
for currentIndex in range(0, matrix.shape[0] - diagonalIndex):
matrixU[currentIndex, 0] = matrix[diagonalIndex + currentIndex, diagonalIndex]
matrixU[0, 0] += util.vector_length(matrixU)
# Creating the H matrix
matrixH = np.identity(matrix.shape[0] - diagonalIndex)
matrixH = matrixH - (2.0 / (util.vector_length(matrixU) ** 2)) * util.multiplyMatrices(
matrixU, matrixU.transpose()
)
matrixHFinal = matrixH
# Putting H matrix in correct size
if matrixH.shape[0] < matrix.shape[0]:
matrixHFinal = np.identity(matrix.shape[0])
for rowIndex in range(diagonalIndex, matrix.shape[0]):
for colIndex in range(diagonalIndex, matrix.shape[1]):
matrixHFinal[rowIndex, colIndex] = matrixH[rowIndex - diagonalIndex, colIndex - diagonalIndex]
# Put H in a queue
hMatrixQueue.put(matrixHFinal)
# Use matrix to form R
matrix = util.multiplyMatrices(matrixHFinal, matrix)
diagonalIndex += 1
# Form Q
matrixQ = hMatrixQueue.get()
while not hMatrixQueue.empty():
matrixQ = util.multiplyMatrices(matrixQ, hMatrixQueue.get())
# Get error
error = util.matrix_max_norm(util.multiplyMatrices(matrixQ, matrix) - originalMatrix)
# Return Q and R
returnList = [matrixQ, matrix, error]
return returnList
def power_method(matrix, ev, error, n, inverse):
if(isinstance(matrix, basestring)):
matrix = np.genfromtxt(matrix, unpack=False, delimiter=" ")
if(isinstance(ev, basestring)):
ev = np.genfromtxt(ev, unpack=False, delimiter=" ")
ev =np.reshape(ev, (ev.shape[0], 1))
if matrix.shape[0] != matrix.shape[0]:
print "matrix must be square"
return
else:
matrixU = ev
matrixW = np.zeros(shape=(ev.shape[0],1))
matrixW[0,0]=1
eValue = 0
for i in range(1, n):
eValueOld = eValue
oldMatrixU = matrixU
matrixU = util.multiplyMatrices(matrix, matrixU)
eValue = np.dot(matrixW.transpose(), matrixU) / np.dot(matrixW.transpose(),oldMatrixU)
if (abs(eValueOld - eValue) < error):
eVector = matrixU / util.vector_length(matrixU)
if (inverse == True):
eValue = 1 / eValue
return [eValue, eVector, i]
return "failure"