115 lines
4.3 KiB
Nim
115 lines
4.3 KiB
Nim
from random import initRand, rand
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from nwo/utils import `...`
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from mmath/rational import newRational, Rational, one, zero, abs, `>`, `<`, `==`, `*`, `+`, `-`, `/`, `/=`, `+=`, `sqrt`
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from mmath/hmatrix import det, lu, from_pivot, newHMatrix, HMatrix, lu_det, invert, identity,
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clone, tril, triu, lu_solve, `*`, `-`, `+`, `+=`, `-=`, `==`, norm2, transpose, lup, squared_norm2
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from mmath/hvector import buildHVector, newHVector, `-`, abs, norm
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import unittest
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suite "Nim linear algebra library":
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let test_matrix = newHMatrix[float32](3, 3, [1.0f32, 2f32, 3f32, 4f32, 5f32, 6f32, 8f32, 7f32, 9f32])
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test "+":
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let mtx1 = newHMatrix[int8](3, 3, [1i8,2,3,4,5,6,7,8,9])
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let mtx2 = newHMatrix[int8](3, 3, [-1i8,-2,-3,-4,-5,-6,-7,-8,-9])
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check(mtx1 + mtx2 == newHMatrix[int8](3,3))
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test "-":
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let mtx = newHMatrix[int8](3, 3, [1i8,2,3,4,5,6,7,8,9])
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check(mtx - mtx == newHMatrix[int8](3, 3))
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test "+=":
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var mtx = newHMatrix[int8](3, 3, [1i8,2,3,4,5,6,7,8,9])
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mtx += mtx
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check(mtx == newHMatrix[int8](3, 3, [2i8,4,6,8,10,12,14,16,18]))
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test "-=":
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var mtx = newHMatrix[int8](3, 3, [1i8,2,3,4,5,6,7,8,9])
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mtx -= mtx
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check(mtx == newHMatrix[int8](3, 3))
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test "*":
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block:
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let mtx = newHMatrix[int8](3, 3, [1i8,2,3,4,5,6,8,7,9])
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let res = mtx * buildHVector[int8](1i8, 2, 3)
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check(res == buildHVector[int8](14i8, 32, 49))
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block:
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let mtx = newHMatrix[int](2, 5, [1,4,8,2,5,7,3,6,9,0])
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let res = mtx * mtx.transpose()
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check(res == newHMatrix[int](2, 2, [110,85,85,175]))
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block:
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let mtx = newHMatrix[int](2, 5, [1,4,8,2,5,7,3,6,9,0])
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let res = mtx.transpose() * mtx
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check(res == newHMatrix[int](5, 5, [
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50, 25, 50, 65, 5,
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25, 25, 50, 35, 20,
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50, 50, 100, 70, 40,
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65, 35, 70, 85, 10,
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5, 20, 40, 10, 25]))
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test "Determinant":
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check(test_matrix.det() == -9f32)
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test "LU Determinant":
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check(test_matrix.lu_det() == -9f32)
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test "Inverse":
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let err = test_matrix * test_matrix.invert() - identity[float32](3)
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check(err.norm2() < 1e-5)
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test "LU decomposition":
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var rng = initRand(101325)
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var arr : array[0..(25 - 1), Rational[int64]]
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for i in 0..<arr.len:
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arr[i] = newRational(rng.rand(-20..20).int64, 20.int64)
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let mtx = newHMatrix[Rational[int64]](5, 5, arr)
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var lu = mtx.clone()
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let pivot = lu.lup()
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let l = lu.tril(Rational[int64].one)
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let u = lu.triu()
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let err = pivot * mtx - (l * u)
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check(err.squared_norm2() == Rational[int64].zero)
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test "Linear system solve":
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var rng = initRand(101325)
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var arr : array[0..(100 * 100 - 1), float64]
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for i in 0..<arr.len:
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arr[i] = rng.rand(-100f32..100f32)
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var mtx = newHMatrix[float64](100, 100, arr)
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var lu = mtx.clone()
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let pivot = lu.lup()
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var b = newHVector[float64](100, 0.0f)
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for i in 0...len(b):
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b[i] = float64(rng.rand(b.len))
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let x = lu.lu_solve(b, pivot)
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let error = (mtx * x) - b
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check(error.norm() < 1e-5)
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test "triu":
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let mtx = newHMatrix[int8](3, 3, [1i8,2,3,4,5,6,7,8,9])
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block:
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let upper = mtx.triu()
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check(upper == newHMatrix[int8](3, 3, [1i8,2,3,0,5,6,0,0,9]))
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block:
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let upper = mtx.triu(1)
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check(upper == newHMatrix[int8](3, 3, [1i8,2,3,0,1,6,0,0,1]))
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test "tril":
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let mtx = newHMatrix[uint](3, 3, [1u,2,3,4,5,6,7,8,9])
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block:
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let lower = mtx.tril()
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check(lower == newHMatrix[uint](3, 3, [1u,0,0,4,5,0,7,8,9]))
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block:
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let lower = mtx.tril(1)
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check(lower == newHMatrix[uint](3, 3, [1u,0,0,4,1,0,7,8,1]))
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test "transpose":
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block:
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let mtx = newHMatrix[int](3, 3, [1, 2, 3, 4, 5, 6, 8, 7, 9])
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let xpose = newHMatrix[int](3, 3, [1,4,8,2,5,7,3,6,9])
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check(mtx.transpose() == xpose)
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block:
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let mtx = newHMatrix[int](2, 5, [1,4,8,2,5,7,3,6,9,0])
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let xpose = newHMatrix[int](5, 2, [1,7,4,3,8,6,2,9,5,0])
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check(mtx.transpose() == xpose) |