76 lines
1.7 KiB
Python
76 lines
1.7 KiB
Python
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import copy
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import pprint
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import numpy
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def gaussian_with_pivot(A, b, round = lambda x: x):
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A = numpy.array(A, dtype = numpy.float64)
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b = numpy.array(b, dtype = numpy.float64)
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L = numpy.identity(len(A), dtype = numpy.float64)
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s = numpy.zeros(len(A), dtype = numpy.float64)
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for k in range(len(A)):
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max_a = numpy.absolute(A[k:,k]).argmax()
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A[[k, k + max_a]] = A[[k + max_a, k]]
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b[[k, k + max_a]] = b[[k + max_a, k]]
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s[k] = k + max_a
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for i in range(k + 1, len(A)):
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L[i][k] = round(A[i][k]/A[k][k])
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b[i] = round(b[i] - round(L[i][k] * b[k]))
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for j in range(k + 1, len(A)):
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A[i][j] = round(A[i][j] - round(L[i][k] * A[k][j]))
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A[i][k] = 0
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return A, b, L, s
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def gaussian_no_pivot(A, b, round = lambda x: x):
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A = numpy.array(A, dtype = numpy.float64)
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b = numpy.array(b, dtype = numpy.float64)
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L = numpy.identity(len(A), dtype = numpy.float64)
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for k in range(len(A)):
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for i in range(k + 1, len(A)):
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L[i][k] = round(A[i][k]/A[k][k])
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b[i] = round(b[i] - round(L[i][k] * b[k]))
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for j in range(k + 1, len(A)):
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A[i][j] = round(A[i][j] - round(L[i][k] * A[k][j]))
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A[i][k] = 0
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return A, b, L
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if( __name__ == "__main__"):
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# For Exercise 1
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A = [[10, 1, 0], [15, 2, 1], [5, 0, 1]]
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b = [12, 18, 4]
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pprint.pprint(gaussian_with_pivot(A, b))
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# For Exercise 2
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A = [[7, 1, 1]
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, [10, 1, 1]
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, [1000, 0, 1]]
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b = [10, 13, 1001]
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pprint.pprint(A)
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def round4(x):
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return float("%.4g" % x)
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pprint.pprint(gaussian_with_pivot(A, b, round4))
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pprint.pprint(gaussian_no_pivot(A, b, round4))
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A = numpy.zeros((10, 10))
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for i in range(10):
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if(i - 1 > 0):
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A[i][i - 1] = -1
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A[i][i] = 2
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if(i + 1 < 10):
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A[i][i + 1] = -1
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pprint.pprint(gaussian_no_pivot(A, numpy.ones(10)))
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