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Wolfgang Hottgenroth
2016-08-07 12:24:41 +02:00
commit a1014ed257
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17
.project Normal file
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<?xml version="1.0" encoding="UTF-8"?>
<projectDescription>
<name>RuleOfCramer</name>
<comment></comment>
<projects>
</projects>
<buildSpec>
<buildCommand>
<name>org.python.pydev.PyDevBuilder</name>
<arguments>
</arguments>
</buildCommand>
</buildSpec>
<natures>
<nature>org.python.pydev.pythonNature</nature>
</natures>
</projectDescription>

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.pydevproject Normal file
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<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<?eclipse-pydev version="1.0"?><pydev_project>
<pydev_pathproperty name="org.python.pydev.PROJECT_SOURCE_PATH">
<path>/${PROJECT_DIR_NAME}</path>
</pydev_pathproperty>
<pydev_property name="org.python.pydev.PYTHON_PROJECT_VERSION">python 3.0</pydev_property>
<pydev_property name="org.python.pydev.PYTHON_PROJECT_INTERPRETER">Default</pydev_property>
</pydev_project>

20
generate.py Normal file
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'''
Created on 06.08.2016
@author: wn
'''
import random
order = 10
lowerBound = 0.0
upperBound = 1000.0
matrix = []
for i in range(order+1):
vector = []
for j in range(order):
vector.append(random.uniform(lowerBound, upperBound))
matrix.append(vector)
print(matrix)

120
main.py Normal file
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'''
Created on 06.08.2016
@author: wn
'''
import time
import random
startTime = 0
def log(msg, reset=False):
global startTime
currentTime = time.time()
if reset:
startTime = currentTime
print("%f: %s" % (currentTime - startTime, msg))
def s_permutations(seq):
items = [[]]
for j in seq:
new_items = []
for i, item in enumerate(items):
if i % 2:
# step up
new_items += [item[:i] + [j] + item[i:]
for i in range(len(item) + 1)]
else:
# step down
new_items += [item[:i] + [j] + item[i:]
for i in range(len(item), -1, -1)]
items = new_items
return [(tuple(item), -1 if i % 2 else 1)
for i, item in enumerate(items)]
cachedIndexJ = {}
def det(m):
log("Calculating determinant started")
l = len(m)
indexListI = range(1, l+1)
if l in cachedIndexJ:
indexListJ = cachedIndexJ[l]
log("J for %i taken from cache" % l)
else:
indexListJ = s_permutations(indexListI)
cachedIndexJ[l] = indexListJ
cnt = len(indexListJ)
#print(indexListJ)
log("J for %i generated, %i entries" % (l, cnt))
summ = 0
steps = 0
for indexJ in indexListJ:
sign = indexJ[1]
prod = sign
for indexI in indexListI:
prod *= m[indexI-1][indexJ[0][indexI-1]-1]
steps += 1
summ += prod
log("Calculating determinant done, %i steps" % steps)
return summ
def solve(g):
coeffMatrix = g[:-1]
coeffDet = det(coeffMatrix)
order = len(g)-1
unknowns = []
for i in range(order):
varMatrix = []
for j in range(order):
if (i == j):
varMatrix.append(g[order])
else:
varMatrix.append(g[j])
varDet = det(varMatrix)
var = varDet / coeffDet
unknowns.append(var)
return unknowns
def generate(order, lowerBound, upperBound):
log("Generating system started")
matrix = []
for i in range(order+1):
vector = []
for j in range(order):
vector.append(random.uniform(lowerBound, upperBound))
matrix.append(vector)
log("Generating system done")
return matrix
#g = [[1.0,2.0,10.0], [5.0,3.0,11.0], [7.0,4.0,3.0], [8.0,9.0,13.0]]
#g = [[599.1290806728277, 80.40433203454268, 615.5120772027384], [187.33506822036273, 663.7490700388757, 677.5997857592452], [956.929845461785, 456.8619830134234, 419.21973493934263], [61.824473951393344, 342.8555419523176, 216.32654519677496]]
#g = [[8.019558599768107, 903.9449140455304, 919.612242767639, 753.9105365307668, 59.01030128588536, 920.4023338915356, 202.58884034378954, 431.09289053573997, 339.17491130065537, 313.11544472585905], [317.26651051567023, 727.3387587224795, 152.77343043145507, 408.44599685908923, 155.79032672640025, 425.6401391270683, 864.8657207590146, 298.9063131849389, 430.3786466384899, 425.29127250155807], [865.8564877305874, 669.481784333669, 538.9130960586408, 961.8480073483083, 753.9136870076827, 912.3571914611318, 929.0546428258709, 873.5276061317886, 459.59802608296684, 455.8093236762648], [318.8613025219013, 497.149024070492, 343.8577826382859, 780.6069003672162, 319.67906522418554, 628.3446507753014, 37.526503978800974, 490.48198671795006, 527.0266127960343, 180.8362568347207], [156.8237212311948, 510.1641000612821, 229.2078194439, 637.1024703370609, 972.0604419040393, 571.3909858582223, 184.34543232118418, 479.07607501617986, 382.12667148701297, 150.05251231416116], [297.8478733948842, 981.2792974599201, 271.8121041641507, 990.1956266273802, 645.839991521914, 288.9135934264093, 845.7496599336642, 19.88633912497506, 97.46153065555741, 343.1102890796861], [384.5208626880663, 145.38972551894247, 560.1624430301523, 224.07537517241872, 704.7921876231894, 781.2588369275445, 752.0786768851573, 77.91470589306748, 851.5354388193074, 146.64240712820654], [252.4899031289375, 928.4755757806711, 176.3416092863044, 914.652591937962, 379.5647442648579, 418.6432906860023, 397.44937187401274, 943.8352970973906, 495.8158468453109, 746.6463673774376], [330.80903398935936, 560.2262982840332, 881.0811315973745, 181.77380227358952, 315.50808931102347, 158.5072721277919, 947.7031957044982, 929.3796342482069, 131.55810107335486, 982.8660461523164], [310.9354667285096, 770.115136026887, 334.49254019770905, 236.96386990210726, 918.8431629974137, 893.3379619077041, 431.3668259114833, 285.69624238120986, 64.53926288027478, 799.2392946390154], [20.70259163693389, 306.46447894527165, 420.64284211501723, 37.622373302959474, 336.4417266492545, 247.6600784425259, 215.21800533449152, 426.10683135701044, 783.5055424440518, 817.507304763315]]
for i in range(2, 10+1):
log("Starting ...", reset=True)
g = generate(i, 0.0, 1000.0)
v = solve(g)
log("Solved")
print(i)
print(g)
print(v)
print

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class DetCalcThread(threading.Thread):
def __init__(self, name, m):
threading.Thread.__init__(self, name = name)
self.m = m
self.setDaemon(True)
print("Thread %s created" % self.name)
def run(self):
print("Thread %s started" % self.name)
self.d = self.det(self.m)
print("Thread %s done" % self.name)
def getValue(self):
return self.d
def det(self, m):
print("Start building permutations for thread %s" % self.name)
indexListI = range(1, len(m)+1)
indexListJ = s_permutations(indexListI)
print("Permutations for thread %s ready" % self.name)
summ = 0
for indexJ in indexListJ:
sign = indexJ[1]
prod = sign
for indexI in indexListI:
prod *= m[indexI-1][indexJ[0][indexI-1]-1]
print("Thread %s stepped" % self.name)
summ += prod
return summ
def threadedSolve(g):
coeffMatrix = g[:-1]
coeffThread = DetCalcThread('coeff', coeffMatrix)
coeffThread.start()
order = len(g) - 1
varThreads = []
for i in range(order):
varMatrix = []
for j in range(order):
if (i == j):
varMatrix.append(g[order])
else:
varMatrix.append(g[j])
detCalcThread = DetCalcThread("%i" % i, varMatrix)
detCalcThread.start()
varThreads.append(detCalcThread)
coeffThread.join()
coeffDet = coeffThread.getValue()
unknowns = []
for varThread in varThreads:
varThread.join()
varDet = varThread.getValue()
var = varDet / coeffDet
unknowns.append(var)
return unknowns