Add my linear algebra library

2 files changed, 145 insertions, 0 deletions

diff --git a/lalge/tests/nim.cfg b/lalge/tests/nim.cfg
new file mode 100644
index 0000000..85bf6c4
--- /dev/null
+++ b/lalge/tests/nim.cfg
@@ -0,0 +1 @@
+--path:"../src/"
diff --git a/lalge/tests/tests.nim b/lalge/tests/tests.nim
new file mode 100644
index 0000000..e798c39
--- /dev/null
+++ b/lalge/tests/tests.nim
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+import std/math
+import types, vectors, matrices
+
+let A: Matrix = @[
+  @[10.0, 2.0, 3.0, 5.0, 6.0],
+  @[8.0, 7.0, 6.0, 4.0, 3.0],
+  @[4.0, 6.0, 0.0, 9.0, 0.0],
+  @[6.0, 7.0, 9.0, 3.0, 9.0],
+  @[3.0, 0.0, 7.0, 9.0, 9.0],
+]
+let B: Matrix = @[
+  @[1.0, 2.0, 3.0, 4.0, 5.0],
+  @[5.0, 3.0, 1.0, 22.0, 3.0],
+  @[5.0, 21.0, 4.0, 6.0, 3.0],
+  @[12.0, 1.0, 5.0, 0.0, 9.0],
+  @[6.0, 7.0, 1.0, 3.0, 5.0],
+]
+
+let L: Matrix = @[
+  @[1.0, 0.0, 0.0, 0.0, 0.0, 0.0],
+  @[-1.0, 1.0, 0.0, 0.0, 0.0, 0.0],
+  @[0.0, -1.0, 1.0, 0.0, 0.0, 0.0],
+  @[0.0, 0.0, -1.0, 1.0, 0.0, 0.0],
+  @[0.0, 0.0, 0.0, -1.0, 1.0, 0.0],
+  @[0.0, 0.0, 0.0, 0.0, -1.0, 1.0],
+]
+let U: Matrix = @[
+  @[1.0, -1.0, 0.0, 0.0, 0.0, 0.0],
+  @[0.0, 1.0, -1.0, 0.0, 0.0, 0.0],
+  @[0.0, 0.0, 1.0, -1.0, 0.0, 0.0],
+  @[0.0, 0.0, 0.0, 1.0, -1.0, 0.0],
+  @[0.0, 0.0, 0.0, 0.0, 1.0, -1.0],
+  @[0.0, 0.0, 0.0, 0.0, 0.0, 1.0],
+]
+
+let
+  P13: Matrix = @[
+    @[0.0, 0.0, 1.0],
+    @[0.0, 1.0, 0.0],
+    @[1.0, 0.0, 0.0],
+  ]
+  P23: Matrix = @[
+    @[1.0, 0.0, 0.0],
+    @[0.0, 0.0, 1.0],
+    @[0.0, 1.0, 0.0],
+  ]
+
+let foo = @[
+  @[1.0, 1.0, 1.0],
+  @[3.0, 4.0, 5.0],
+  @[40.0, 51.0, 12.0]
+]
+
+let eliminationMatrix: Matrix = @[
+  @[1.0, 0.0, 0.0],
+  @[-2.0, 1.0, 0.0],
+  @[0.0, 0.0, 1.0]
+]
+
+let
+  ones: Matrix = @[
+    @[1.0, 2.0, 3.0],
+    @[4.0, 5.0, 6.0]
+  ]
+  twos: Matrix = @[
+    @[7.0, 8.0],
+    @[9.0, 10.0],
+    @[11.0, 12.0]
+  ]
+
+# Addition and subtraction
+assert I2 + I2 == 2 * I2
+assert I3-I3 == gen(3, 3, 0.0)
+
+# Num. of rows / columns
+assert rows(I2) == 2
+assert I2.rows() == 2
+assert I2.rows == 2
+assert cols(I3) == 3
+assert I3.cols() == 3
+assert I3.cols == 3
+
+# Identity Matrices
+assert I1 == @[
+  @[1.0],
+]
+assert I2 == @[
+  @[1.0, 0.0],
+  @[0.0, 1.0],
+]
+assert I3 == @[
+  @[1.0, 0.0, 0.0],
+  @[0.0, 1.0, 0.0],
+  @[0.0, 0.0, 1.0],
+]
+assert I4 == @[
+  @[1.0, 0.0, 0.0, 0.0],
+  @[0.0, 1.0, 0.0, 0.0],
+  @[0.0, 0.0, 1.0, 0.0],
+  @[0.0, 0.0, 0.0, 1.0],
+]
+assert I5 == @[
+  @[1.0, 0.0, 0.0, 0.0, 0.0],
+  @[0.0, 1.0, 0.0, 0.0, 0.0],
+  @[0.0, 0.0, 1.0, 0.0, 0.0],
+  @[0.0, 0.0, 0.0, 1.0, 0.0],
+  @[0.0, 0.0, 0.0, 0.0, 1.0],
+]
+
+assert det(@[
+  @[2.0, -1.0, 0.0, -1.0],
+  @[-1.0, 2.0, -1.0, 0.0],
+  @[0.0, -1.0, 2.0, -1.0],
+  @[-1.0, 0.0, -1.0, 2.0],
+]) == 0
+
+assert det(A * B) == (det(A) * det(B))
+assert det(I3) == 1
+assert det(2*I4) == 16
+
+# Vectors
+
+let
+  alice: Vector = @[1.0, 1.0, 1.0]
+  bob = @[3.0, 4.0, 5.0]
+  carol = @[40.0, 51.0, 12.0]
+  dan: Vector = @[10.0, 20.0, 30.0, 40.0]
+  eve = @[2.0, 3.0, 4.0]
+
+assert alice + bob == bob + alice
+assert alice + carol == carol + alice
+assert carol - eve != eve - carol
+assert alice.length() == sqrt(3.0)
+
+# echo transpose(ones)
+# echo P13 * 8
+# echo P13 + P23
+# echo ones * twos
+# assert col(eliminationMatrix, 0) == col(eliminationMatrix, 0)
+# echo identity(0)
+# echo identity(2)
+# echo (1/0)
+# echo L*U
+# echo U*L