added rational numbers

tests/test_hmatrix.nim

@@ -1,7 +1,8 @@
 from random import initRand, rand
 from nwo/utils import `...`
+from mmath/rational import newRational, Rational, one, zero, abs, `>`, `<`, `==`, `*`, `+`, `-`, `/`, `/=`, `+=`, `sqrt`
 from mmath/hmatrix import det, lu, from_pivot, newHMatrix, HMatrix, lu_det, invert, identity,
-    clone, tril, triu, lu_solve, `*`, `-`, `+`, `+=`, `-=`, `==`, norm2, transpose, lup
+    clone, tril, triu, lu_solve, `*`, `-`, `+`, `+=`, `-=`, `==`, norm2, transpose, lup, squared_norm2
 from mmath/hvector import buildHVector, newHVector, `-`, abs, norm
 import unittest
 
@@ -58,16 +59,16 @@ suite "Nim linear algebra library":
 
     test "LU decomposition":
         var rng = initRand(101325)
-        var arr : array[0..(25 - 1), float32]
+        var arr : array[0..(25 - 1), Rational[int64]]
         for i in 0..<arr.len:
-            arr[i] = rng.rand(-4f32..4f32)    
-        let mtx = newHMatrix[float32](5, 5, arr)
+            arr[i] = newRational(rng.rand(-20..20).int64, 20.int64)
+        let mtx = newHMatrix[Rational[int64]](5, 5, arr)
         var lu = mtx.clone()        
         let pivot = lu.lup()
-        let l = lu.tril(1.0)
+        let l = lu.tril(Rational[int64].one)
         let u = lu.triu()
         let err = pivot * mtx - (l * u)
-        check(err.norm2() < 1e-5)
+        check(err.squared_norm2() == Rational[int64].zero)
 
     test "Linear system solve":
         var rng = initRand(101325)

tests/test_rational.nim

@@ -0,0 +1,96 @@
+import unittest
+from mmath/rational import newRational, `+`, `-`, `*`, `/`, `$`, simplify, gcd, pow, mcm, `==`, `cmp`, `<`, `>`, `<=`, `>=`, abs
+
+suite "Nim rational numbers":
+
+    test "gcd":
+        let a = 14
+        let b = 21
+        check 7 == gcd(a, b)
+
+    test "mcm":
+        let a = 14
+        let b = 21
+        check 42 == mcm(a, b)
+
+    test "pow":
+        check 625 == pow(5, 4)
+
+    test "==":
+        let r1 = newRational(1, 3)
+        let r2 = newRational(5, 15)        
+        let r3 = newRational(35, 105)
+        check r1 == r2
+        check r1 == r3
+        check r2 == r3
+
+    test "+":
+        let r1 = newRational(1, 3)
+        let r2 = newRational(2, 3)
+        let r3 = r1 + r2
+        check r3 == newRational(1)
+
+    test "-":
+        let r1 = newRational(1, 3)
+        let r2 = newRational(2, 3)
+        let r3 = r1 - r2
+        check r3 == newRational(-1, 3)
+
+    test "*":
+        let r1 = newRational(1, 3)
+        let r2 = newRational(2, 3)
+        let r3 = r1 * r2
+        check r3 == newRational(2, 9)
+
+    test "/":
+        let r1 = newRational(1, 3)
+        let r2 = newRational(2, 3)
+        let r3 = r1 / r2
+        check r3 == newRational(1, 2)
+
+    test "simplify":
+        var r1 = newRational(65, 169)
+        check r1 == newRational(5, 13)
+        r1.simplify()
+        check r1.num == 5
+        check r1.den == 13
+
+    test "pow":
+        let r1 = newRational(65, 169)
+        let r2 = r1.pow(2)
+        check r2 == newRational(25, 169)
+
+    test "cmp":
+        let r1 = newRational(65, 169)
+        let r2 = newRational(5, 13)
+        let r3 = newRational(6, 13)
+        check r1 < r3
+        check r3 > r1
+        check r1 <= r3
+        check r1 <= r2
+        check r3 >= r1
+        check r2 >= r1
+        check r2 == r1
+
+    test "abs":
+        let r1 = newRational(-65, -169)
+        let r2 = newRational(65, -169)
+        check r1 == r1.abs()
+        check r1 == r2.abs()
+        check r1 != r2
+
+    test "i64":
+        let p1 = 32452867i64
+        let p2 = 49979687i64
+        let p3 = 15485867i64
+        let r1 = newRational(p3, p1 * p2)
+        let r2 = newRational(p2, p1 * p3)
+        var r3 = newRational(p2, p2 * p3)
+        check newRational(1i64, p3) == r3
+        r3.simplify()
+        check r3.num == 1i64
+        check r3.den == p3
+        expect(OverflowDefect):
+            discard r1 / r2
+        expect(OverflowDefect):
+            discard r1 + r2

tests/test_smatrix.nim

@@ -2,9 +2,10 @@ from random import initRand, rand
 from nwo/utils import `...`
 from mmath/smatrix import det, lu, lup, lu_det, lup, det, from_pivot, invert, identity, 
     newSMatrix, SMatrix, clone, tril, triu, lu_solve, `$`, `*`, `-`, `+`, `-=`, `+=`, `==`, `*`, norm2, newSMatrixFromArray,
-    gauss_jordan_high, gauss_jordan_low, transpose
+    gauss_jordan_high, gauss_jordan_low, transpose, squared_norm2
 from mmath/svector import buildSVector, `-`, abs, norm, Svector
 from mmath/pivot import SingularMatrixError
+from mmath/rational import newRational, Rational, one, zero, abs, `>`, `<`, `==`, `*`, `+`, `-`, `/`, `/=`, `+=`, `sqrt`
 import unittest
 
 suite "Nim linear algebra library":
@@ -58,19 +59,19 @@ suite "Nim linear algebra library":
     test "Inverse":
         let err = test_matrix * test_matrix.invert() - identity[3, float32]()
         check(err.norm2() < 1e-5)
-
+    
     test "LU decomposition":
         var rng = initRand(101325)
-        var arr : array[0..(25 - 1), float32]
+        var arr : array[0..(25 - 1), Rational[int64]]
         for i in 0..<arr.len:
-            arr[i] = rng.rand(-4f32..4f32)    
-        let mtx = newSMatrixFromArray[5, 5, float32](arr)
-        var lu = mtx.clone()        
+            arr[i] = newRational(rng.rand(-20..20).int64, 20.int64)
+        let mtx = newSMatrixFromArray[5, 5, Rational[int64]](arr)
+        var lu = mtx.clone()
         let pivot = lu.lup()
-        let l = lu.tril(1.0)
+        let l = lu.tril(Rational[int64].one)
         let u = lu.triu()
         let err = pivot * mtx - (l * u)
-        check(err.norm2() < 1e-5)
+        check(err.squared_norm2() == Rational[int64].zero)
 
     test "Linear system solve":
         var rng = initRand(101325)