107 lines
2.7 KiB
Plaintext
107 lines
2.7 KiB
Plaintext
//
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// Gaussian Elimination Estimate
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//
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// FutureBasic 7.0.34 August 2025 R.W
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//
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//--------------------------------------------------
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//
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// Test data array. I wanted it to be base 1 and not zero
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// hence the 99 which is just filler for the zeroeth element
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//
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double a(6,6) = ¬
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{99, 99, 99, 99, 99, 99, 99,¬
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99, 1.00, 0.00, 0.00, 0.00, 0.00, 0.00,¬
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99, 1.00, 0.63, 0.39, 0.25, 0.16, 0.10,¬
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99, 1.00, 1.26, 1.58, 1.98, 2.49, 3.13,¬
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99, 1.00, 1.88, 3.55, 6.70, 12.62, 23.80,¬
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99, 1.00, 2.51, 6.32, 15.88, 39.90, 100.28,¬
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99, 1.00, 3.14, 9.87, 31.01, 97.41, 306.02 }
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double b(6) = ¬
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{99,-0.01, 0.61, 0.91, 0.99, 0.60, 0.02 }
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double x(6)
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double ab(6)
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double ans(6),r(6),bb(6,6), f
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int c, d, g, p1, p2, z
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//
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int row, col
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int j, k, n = 6
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//
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// Pivot n times
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local fn pivot(num as int)
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For p1 = num to n - 1
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For p2 = p1 + 1 To n
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If abs(bb(p1,num)) < abs(bb(p2,num))
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Swap r(p1),r(p2)
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For g = 1 To n
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Swap bb(p1,g),bb(p2,g)
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Next g
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End If
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Next p2
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Next p1
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end fn
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// The 'Gaussian' function takes two matrices,
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// 'a' and 'b', with 'a' square, and it returns
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// the determinant of 'a' and a matrix 'x'
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// such that a * x = b.
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// If 'b' is the identity, then 'x' = inverse of 'a'
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local fn Gaussian(matrix(6,6) as double, rhs(6) as double)
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// copy matrix
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for c = 1 to n
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r(c) = rhs(c)
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for d = 1 to n
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bb(c,d) = matrix(c,d)
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next d
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next c
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// pivot it (hey that's what the task requires
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// don't ask me why. It doesn't
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// improve accuracy with these numbers)
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for k = 1 to n-1
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fn pivot(k)
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for row = k to n-1
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if bb(row + 1, k) == 0 then exit for
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f = bb(k, k) / bb(row+1, k)
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r(row + 1) = r(row + 1) * f - r(k)
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For g = 1 To n
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bb((row + 1), g) = bb((row + 1), g) * f - bb(k,g)
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Next g
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Next row
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Next k
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//back substitute
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For z = n to 1 step -1
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ans(z) = r(z) / bb(z,z)
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For j = n to z + 1 step -1
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ans(z) = ans(z) - (bb(z,j) * ans(j) / bb(z,z))
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Next j
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Next z
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end fn
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window 1,@"Gaussian Elimination"
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print "TEST DATA USED"
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print " ax = transpose b"
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print "[1.00 |0.00 |0.00 | 0.0000 | 0.00 | 0.00] [??] [-0.01]"
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print "[1.00 |0.63 |0.39 | 0.2500 | 0.16 | 0.10] [??] [ 0.61]"
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print "[1.00 |1.26 |1.58 | 1.9800 | 2.49 | 3.13] x [??] = [ 0.91]"
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print "[1.00 |1.88 |3.55 | 6.7000 |12.62 | 23.80] [??] [ 0.99]"
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print "[1.00 |2.51 |6.32 |15.8800 |39.90 |100.28] [??] [ 0.60]"
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print "[1.00 |3.14 |9.87 |31.0100 |97.41 |306.02] [??] [ 0.02]"
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print
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fn Gaussian(a(0,0),b(0))
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print "Solution:"
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print "---------"
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for j = 1 to 6
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print using "###.################";ans(j)
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next j
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HandleEvents
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