def lu_fact(matrix):
if(isinstance(matrix, basestring)):
matrix = np.loadtxt(matrix, unpack=False, delimiter=" ")
originalMatrix = matrix
lMatrixQueue = Queue.Queue()
rowIndex = 0
colIndex = 0
while (rowIndex < matrix.shape[0]):
if matrix[rowIndex, colIndex] != 0:
for currentRow in range(rowIndex + 1, matrix.shape[0]):
currentLMatrix = np.identity(matrix.shape[0])
# THIS MAY BE BETTER --> if (matrixA[currentRow, colIndex] > 0 and matrixA[rowIndex, colIndex] > 0) or (matrixA[currentRow, colIndex] < 0 and matrixA[rowIndex, colIndex] < 0):
if (matrix[currentRow, colIndex] > 0 and matrix[rowIndex, colIndex] > 0) or (matrix[currentRow, colIndex] < 0 and matrix[rowIndex, colIndex] < 0):
currentLMatrix[currentRow, :] = currentLMatrix[currentRow, :] - currentLMatrix[rowIndex, :]*(float(matrix[currentRow, colIndex])/float(matrix[rowIndex, colIndex]))
else:
currentLMatrix[currentRow, :] = currentLMatrix[currentRow, :] + currentLMatrix[rowIndex, :]*(float(matrix[currentRow, colIndex])/float(matrix[rowIndex, colIndex]))
matrix = util.multiplyMatrices(currentLMatrix, matrix)
currentLMatrix[currentRow, colIndex] = -currentLMatrix[currentRow, colIndex] #Changing the sign of the item so that we don't need to take the inverse later.
lMatrixQueue.put(currentLMatrix)
rowIndex = rowIndex + 1
colIndex = colIndex + 1
#Form the L matrix
lMatrix = lMatrixQueue.get()
while not lMatrixQueue.empty():
lMatrix = util.multiplyMatrices(lMatrix, lMatrixQueue.get())
#Get error
error = util.matrix_max_norm(util.multiplyMatrices(lMatrix, matrix) - originalMatrix)
#Return
returnList = [lMatrix, matrix, error]
return returnList
def getHarmFlow(matrices):
y, w, grad, gradAdj, curl, curlAdj = matrices
S = np.matmul(curlAdj, curl) - np.matmul(grad, gradAdj)
Dpos = np.diag(w**0.5)
Dneg = np.diag(w**-0.5)
S2 = util.multiplyMatrices([Dpos, S, Dneg])
S2pinv = np.linalg.pinv(S2)
harmFlow = y - util.multiplyMatrices([Dneg, S2pinv, S2, Dpos, y])
return harmFlow
def iter(x0, sigma, m, S, T):
S_inv = inverse_lower_3x3(S)
counter = 1
x_cur = x0
while (counter <= m):
x_prev = x_cur
x_cur = multiplyMatrices(S_inv, multiplyMatrices(T, x_cur) + B)
err = x_cur - x_prev
if math.sqrt(dot_product(err, err)) <= sigma:
return (x0, x_cur, counter)
counter += 1
return None
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"
def solve_househ_b(matrixInput):
if isinstance(matrixInput, basestring):
matrixInput = np.loadtxt(matrixInput, unpack=False, delimiter=" ")
matrixA = matrixInput[:, 0 : matrixInput.shape[1] - 1]
matrixB = np.matrix(matrixInput[:, [matrixInput.shape[1] - 1]])
matrixBCopy = np.copy(matrixB)
matrixACopy = np.copy(matrixA)
qr = qr_fact_househ(matrixACopy)
matrixQCopy = np.copy(qr[0])
matrixRCopy = np.copy(qr[1])
xSolution = solve_b(matrixRCopy, solve_b(matrixQCopy, matrixBCopy))
return [
xSolution,
util.matrix_max_norm(util.multiplyMatrices(matrixA, xSolution) - matrixB),
util.matrix_max_norm(util.multiplyMatrices(qr[0], qr[1]) - matrixA),
]
def solve_lu_b(matrixInput):
if isinstance(matrixInput, basestring):
matrixInput = np.loadtxt(matrixInput, unpack=False, delimiter=" ")
matrixA = matrixInput[:, 0 : matrixInput.shape[1] - 1]
matrixB = np.matrix(matrixInput[:, [matrixInput.shape[1] - 1]])
matrixBCopy = np.copy(matrixB)
matrixACopy = np.copy(matrixA)
lu = lu_fact(matrixACopy)
matrixLCopy = np.copy(lu[0])
matrixUCopy = np.copy(lu[1])
xSolution = solve_b(matrixUCopy, solve_b(matrixLCopy, matrixBCopy))
return [
xSolution,
util.matrix_max_norm(util.multiplyMatrices(matrixA, xSolution) - matrixB),
util.matrix_max_norm(util.multiplyMatrices(lu[0], lu[1]) - matrixA),
]
def getGradFlow(matrices):
y, w, grad, gradAdj, curl, curlAdj = matrices
lapInv = np.linalg.pinv(np.matmul(gradAdj, grad)) # Inv of laplacian
s = util.multiplyMatrices([lapInv, gradAdj, y])
gradFlow = np.matmul(grad, s)
return gradFlow, s
def qr_fact_givens(matrix):
if(isinstance(matrix, basestring)):
matrix = np.loadtxt(matrix, unpack=False, delimiter=" ")
originalMatrix = matrix
diagonalIndex = 0
gMatrixQueue = Queue.Queue()
#while we still have diagonal elements
while (diagonalIndex < matrix.shape[1] - 1):
# X is the pivot
x = matrix[diagonalIndex, diagonalIndex]
for currentIndex in range(diagonalIndex + 1, matrix.shape[0]):
#y is at index below the pivot
y = matrix[currentIndex, diagonalIndex]
if y != 0:
# set cos and sin
cos = x/math.sqrt(x**2 + y**2)
sin = -y/math.sqrt(x**2 + y**2)
matrixG = np.identity(matrix.shape[0])
matrixG[diagonalIndex, diagonalIndex] = cos
matrixG[currentIndex, diagonalIndex] = sin
matrixG[diagonalIndex, currentIndex] = -sin
matrixG[currentIndex, currentIndex] = cos
#add g matrix and update matrix and pivot
gMatrixQueue.put(matrixG.transpose())
matrix = util.multiplyMatrices(matrixG, matrix)
x = matrix[diagonalIndex,diagonalIndex]
diagonalIndex += 1
#Form Q
matrixQ = gMatrixQueue.get()
while not gMatrixQueue.empty():
matrixQ = util.multiplyMatrices(matrixQ, gMatrixQueue.get())
#Get error
error = util.matrix_max_norm(util.multiplyMatrices(matrixQ, matrix) - originalMatrix)
returnList = [matrixQ, matrix, error]
return returnList