Mathematics

gistfile1.hs

data Vector3 a = Vector3 
    (
        a, 
        a, 
        a
    ) deriving (Show, Eq)
data Matrix3 a = Matrix3 
    (
        (a, a, a), 
        (a, a, a),
        (a, a, a)
    ) deriving (Show, Eq)

vplus :: (Num a) => Vector3 a -> Vector3 a -> Vector3 a
vplus (Vector3 (i, j, k)) (Vector3 (l, m, n)) = 
    Vector3 (
        (i+l), 
        (j+m), 
        (k+n)
    )

vdotProd :: (Num a) => Vector3 a -> Vector3 a -> a
vdotProd (Vector3 (i, j, k)) (Vector3 (l, m, n)) = i*l + j*m + k*n

vsmult :: (Num a) => a -> Vector3 a -> Vector3 a
vsmult m (Vector3 (i, j, k)) = 
    Vector3 (
        (m*i), 
        (m*j), 
        (m*k)
    )

vmmult :: (Num a) => Matrix3 a -> Vector3 a -> Vector3 a
vmmult
    (Matrix3 (
        (a00, a01, a02),
        (a10, a11, a12),
        (a20, a21, a22)
    ))
    (Vector3 (
        b0,
        b1,
        b2
    ))
    =
    Vector3(
        a00*b0+a01*b1+a02*b2,
        a10*b0+a11*b1+a12*b2,
        a20*b0+a21*b1+a22*b2
    )

vcrsProd :: (Num a) => Vector3 a -> Vector3 a -> Vector3 a
vcrsProd (Vector3 (i, j, k)) (Vector3 (l, m, n)) = 
    Vector3 (
        (j*n - k*m), 
        (i*n - k*l), 
        (i*m - j*l)
    )

mplus :: (Num a) => Matrix3 a -> Matrix3 a -> Matrix3 a
mplus 
    (Matrix3 (
        (a00, a01, a02),
        (a10, a11, a12),
        (a20, a21, a22)
    ))
    (Matrix3 (
        (b00, b01, b02),
        (b10, b11, b12),
        (b20, b21, b22)
    ))
    =
    (Matrix3 (
        (a00+b00, a01+b01, a02+b02),
        (a10+b10, a11+b11, a12+b12),
        (a20+b20, a21+b21, a22+b22)
    ))

msmult :: (Num a) => a -> Matrix3 a -> Matrix3 a
msmult 
    m 
    (Matrix3 (
        (a00, a01, a02),
        (a10, a11, a12),
        (a20, a21, a22)
    ))
    =
    (Matrix3 (
        (m*a00, m*a01, m*a02),
        (m*a10, m*a11, m*a12),
        (m*a20, m*a21, m*a22)
    ))

mmult :: (Num a) => Matrix3 a -> Matrix3 a -> Matrix3 a
mmult 
    (Matrix3 (
        (a00, a01, a02),
        (a10, a11, a12),
        (a20, a21, a22)
    ))
    (Matrix3 (
        (b00, b01, b02),
        (b10, b11, b12),
        (b20, b21, b22)
    ))
    =
    (Matrix3 (
        (a00*b00+a01*b10+a02*b20, a00*b01+a01*b11+a02*b21, a00*b02+a01*b12+a02*b22),
        (a10*b00+a11*b10+a12*b20, a10*b01+a11*b11+a12*b21, a10*b02+a11*b12+a12*b22),
        (a20*b00+a21*b10+a22*b20, a20*b01+a21*b11+a22*b21, a20*b02+a21*b12+a22*b22)
    ))

mtrans :: (Num a) => Matrix3 a -> Matrix3 a
mtrans 
    (Matrix3 (
        (a00, a01, a02),
        (a10, a11, a12),
        (a20, a21, a22)
    ))
    =
    (Matrix3 (
        (a00, a10, a20),
        (a01, a11, a21),
        (a02, a12, a22)
    ))