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