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from math import sqrt | |
import random,time | |
import profile | |
random.seed(1) | |
def bellman_ford(edges): | |
numRows = len(edges) | |
numCols = len(edges[0]) | |
OPT = dict(( (len(edges)-1,x),edges[-1][x]) for x in xrange(len(edges[-1]))) | |
opt = dict(( (len(edges)-1,x),None) for x in xrange(len(edges[-1]))) | |
for y in xrange(numRows-2,-1,-1): | |
for x in xrange(numCols): | |
optNbr = None | |
optPath = [(y,x)] | |
optVal = float("inf") | |
nbrs = [(y+1,x2) for x2 in xrange(x-1,x+2) if x2<numCols and x2>=0 ] | |
for nbr in nbrs: | |
if OPT[nbr] < optVal: | |
optVal = OPT[nbr] | |
optNbr = nbr | |
OPT[(y,x)] = optVal+edges[y][x] | |
opt[(y,x)]=optNbr | |
minKey = min([key for key in OPT if key[0]==0],key=OPT.get) | |
path = [] | |
conductor = minKey | |
while(conductor): | |
path.append(conductor) | |
conductor = opt[conductor] | |
return path,OPT[minKey] | |
def doubleConvolve2DOriginal(matrix,kernel1,kernel2): | |
numRows = len(matrix) | |
numCols = len(matrix[0]) | |
numKernelRows = len(kernel1) | |
numKernelCols = len(kernel1[0]) | |
yradius = (len(kernel1)-1)/2 | |
xradius = (len(kernel1[0])-1)/2 | |
padded = padMatrix(matrix,xradius,yradius) | |
convolvedRows = [] | |
for row in xrange(yradius,numRows+yradius): | |
convolvedRow = [] | |
for col in xrange(xradius,numCols+xradius): | |
totalSum1 = 0 | |
totalSum2 = 0 | |
for kernelRow in xrange(numKernelRows): | |
for kernelCol in xrange(numKernelCols): | |
totalSum1+= kernel1[kernelRow][kernelCol] * padded[row+kernelRow-yradius][col+kernelCol-xradius] | |
totalSum2+= kernel2[kernelRow][kernelCol] * padded[row+kernelRow-yradius][col+kernelCol-xradius] | |
sobeled_pixel = ((totalSum1*totalSum1+totalSum2*totalSum2)**(0.5)) | |
convolvedRow.append(sobeled_pixel) | |
convolvedRows.append(convolvedRow) | |
convolved = [row for row in convolvedRows] | |
del padded | |
return convolved | |
def doubleConvolve2D(matrix,kernel1,kernel2): | |
numRows = len(matrix) | |
numCols = len(matrix[0]) | |
numKernelRows = len(kernel1) | |
numKernelCols = len(kernel1[0]) | |
yradius = (len(kernel1)-1)/2 | |
xradius = (len(kernel1[0])-1)/2 | |
padded = padMatrix(matrix,xradius,yradius) | |
def getPixelInRow(row,xradius,padwidth): | |
while xradius < padwidth: | |
col = xradius | |
xradius += 1 | |
totalSum1 = 0 | |
totalSum2 = 0 | |
for kernelRow in xrange(numKernelRows): | |
for kernelCol in xrange(numKernelCols): | |
totalSum1+= kernel1[kernelRow][kernelCol] * padded[row+kernelRow-yradius][col+kernelCol-xradius] | |
totalSum2+= kernel2[kernelRow][kernelCol] * padded[row+kernelRow-yradius][col+kernelCol-xradius] | |
sobeled_pixel = ((totalSum1*totalSum1+totalSum2*totalSum2)**(0.5)) | |
yield sobeled_pixel | |
def getConvolvedRow(yradius,padheight): | |
while yradius < padheight: | |
row = yradius | |
yradius += 1 | |
# i think ths guy can be converted to a generator comprehension and then it'll get rid | |
# of the last memory overhead, but i don't know how to write the test to ensure equality | |
convolvedRow = [pixel for pixel in getPixelInRow(row,xradius,numCols+xradius)] | |
# the matrix should be still be consumable by iteration, | |
# it just wouldn't exist as a structure with lookups anymore | |
yield convolvedRow | |
convolvedRows = (col for col in getConvolvedRow(yradius,numRows+yradius)) | |
convolved = [row for row in convolvedRows] | |
return convolved | |
def sobel(matrix): | |
xKernel = [[-1,0,1],[-2,0,2],[-1,0,1]] | |
yKernel = [[-1,-2,-1],[0,0,0],[1,2,1]] | |
edges = doubleConvolve2D(matrix,xKernel,yKernel) | |
#assert edges == doubleConvolve2DOriginal(matrix,xKernel,yKernel) | |
return edges | |
def Matrix(numRows,numCols,val=0,rand=False): | |
if not rand: | |
return [ [val for j in xrange(numCols)] for i in range(numRows)] | |
else: | |
return [ [random.randint(0,3) for j in xrange(numCols)] for i in range(numRows)] | |
def padMatrix(matrix,xpad,ypad): | |
padded = [] | |
topRow = [matrix[0][0] for i in xrange(xpad)]+matrix[0]+[matrix[0][-1] for i in range(xpad)] | |
for i in xrange(ypad): | |
padded.append(topRow) | |
for row in matrix: | |
paddedRow = [row[0] for i in xrange(xpad)]+row+[row[-1] for i in range(xpad)] | |
padded.append(paddedRow) | |
bottomRow = [matrix[-1][0] for i in xrange(xpad)]+matrix[-1]+[matrix[-1][-1] for i in range(xpad)] | |
for i in xrange(ypad): | |
padded.append(bottomRow) | |
return padded | |
def bellman_ford_test(): | |
m1 = Matrix(640,480) | |
#m1 = Matrix(160,120) | |
t1 = time.time() | |
#m2 = sobel(m1) | |
profile.runctx("sobel(m1)",globals(),{"m1":m1}) | |
t2 = time.time() | |
#profile.runctx("bellman_ford(m1)",globals(),{"m1":m1}) | |
# bellman_ford(m2) | |
t3 = time.time() | |
print "Sobel:",t2-t1,"s" | |
print "Bellman-Ford:",t3-t2,"s" | |
if __name__=="__main__": | |
bellman_ford_test() | |
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