math module reference

math module reference

Mathematical functions.

This module is exactly like math-simple, except that the operators also work componentwise with vectors (num[X]) and matrices (num[X][Y]). All operators are PureOps.

(+ 1 2 3) #(<num= 6>)
(+ [1 2] [3 4]) #(<num[2]= [4 6]>)

The arguments for an operator generally have to be of the same type. However it is also okay to pass in scalar numbers together with a different type. The scalars will be repeated as necessary to fit the shape of other arguments:

(* [[1 2] [3 4]]
   2)
#(<num[2][2]= [[2 4] [6 8]]>)

The mul (*) operator is the only exception to this, as it handles matrix-matrix and matrix-vector multiplication according to linear algebra.

index

• % (opdef):  – alias of mod
• * (opdef):  – alias of mul
• + (opdef):  – alias of add
• - (opdef):  – alias of sub
• / (opdef):  – alias of div
• // (opdef):  – alias of idiv
• ^ (opdef):  – alias of pow
• abs (opdef):  – Get the absolute value.
• acos (opdef):  – Inverse cosine function (radians).
• add (opdef):  – Add values.
• asin (opdef):  – Inverse sine function (radians).
• atan (opdef):  – Inverse tangent function (radians).
• atan2 (opdef):  – Inverse tangent function (two argument version).
• ceil (opdef):  – Round towards positive infinity.
• clamp (opdef):  – Clamp a value to a range.
• cos (opdef):  – Cosine function (radians).
• cosh (opdef):  – Hyperbolic cosine function (radians).
• dec (opdef):  – Decrement by 1.
• div (opdef):  – Divide values.
• exp (opdef):  – *e* number raised to a power.
• floor (opdef):  – Round towards negative infinity.
• huge (num):  – Positive infinity constant.
• idiv (opdef):  – Divide values and floor.
• inc (opdef):  – Increment by 1.
• log (opdef):  – Logarithm with optional base.
• log10 (opdef):  – Logarithm with base 10.
• max (opdef):  – Find the maximum.
• min (opdef):  – Find the minimum.
• mix (opdef):  – Linearly interpolate.
• mod (opdef):  – Modulo operator.
• mul (opdef):  – Multiply scalars, vectors and matrices.
• pi (num):  – The pi constant.
• pow (opdef):  – Raise to a power.
• sin (opdef):  – Sine function (radians).
• sinh (opdef):  – Hyperbolic sine function (radians).
• sqrt (opdef):  – Square root function.
• sub (opdef):  – Subtract values.
• tan (opdef):  – Tangent function (radians).
• tanh (opdef):  – Hyperbolic tangent function (radians).
• tau (num):  – The tau constant.

details

• abs (opdef):  – Get the absolute value.

  (abs val)

• acos (opdef):  – Inverse cosine function (radians).

  (acos cos)

• add (opdef):  – Add values.

  (+ a b [c…]) (add a b [c…])

  Sum all arguments.

• asin (opdef):  – Inverse sine function (radians).

  (asin sin)

• atan (opdef):  – Inverse tangent function (radians).

  (atan tan)

• atan2 (opdef):  – Inverse tangent function (two argument version).

  (atan2 y x)

• ceil (opdef):  – Round towards positive infinity.

  (ceil val)

• clamp (opdef):  – Clamp a value to a range.

  (clamp min max val)

  Returns min if val < min; max if val > max; and val otherwise.

• cos (opdef):  – Cosine function (radians).

  (cos alpha)

• cosh (opdef):  – Hyperbolic cosine function (radians).

  (cosh alpha)

• dec (opdef):  – Decrement by 1.

  (dec i)

• div (opdef):  – Divide values.

  (/ a b [c…]) (div a b [c…])

  Divide a by all other arguments.

• exp (opdef):  – *e* number raised to a power.

  (exp exp)

• floor (opdef):  – Round towards negative infinity.

  (floor val)

• huge (num):  – Positive infinity constant.
• idiv (opdef):  – Divide values and floor.

  (// a b [c…]) (idiv a b [c…])

  Divide a by all other arguments, flooring each time.

• inc (opdef):  – Increment by 1.

  (inc i)

• log (opdef):  – Logarithm with optional base.

  (log val [base])

• log10 (opdef):  – Logarithm with base 10.

  (log10 val)

• max (opdef):  – Find the maximum.

  (max a b [c…])

  Return the highest of arguments.

• min (opdef):  – Find the minimum.

  (min a b [c…])

  Return the lowest of arguments.

• mix (opdef):  – Linearly interpolate.

  (mix a b i)

  Interpolate between a and b using i in range 0-1.

• mod (opdef):  – Modulo operator.

  (% num div) (mod num div)

  Calculate remainder of division by div.

• mul (opdef):  – Multiply scalars, vectors and matrices.

  (* a b [c…]) (mul a b [c…])

  Multiplies all arguments.

  For every pair of arguments, from left to right:

  • If either argument is a scalar, or both are vectors, multiply componentwise.
  • If either argument is a matrix and the other is a vector, apply the matrix transformation.
    • (* num[L][M] num[M]) → num[L] (forward transform)
    • (* num[M] num[M][N]) → num[N] (reverse transform)
  • If both arguments are matrices, multiply them using matrix multiplication.
    • (* num[L][M] num[M][N]) → num[M][N]
• pi (num):  – The pi constant.
• pow (opdef):  – Raise to a power.

  (^ base exp) (pow base exp

  Raise base to the power exp.

• sin (opdef):  – Sine function (radians).

  (sin alpha)

• sinh (opdef):  – Hyperbolic sine function (radians).

  (sinh alpha)

• sqrt (opdef):  – Square root function.

  (sqrt val)

• sub (opdef):  – Subtract values.

  (- a b [c…]) (sub a b [c…])

  Subtract all other arguments from a.

• tan (opdef):  – Tangent function (radians).

  (tan alpha)

• tanh (opdef):  – Hyperbolic tangent function (radians).

  (tanh alpha)

• tau (num):  – The tau constant.