Module Scad_ml.Math

Various operations on floats (e.g. approximate equality, linear interpolation), and basic arbitrary size 2d matrix operations.

Float operations

val sign : float -> float

sign v

Return the sign of v as a float (-1., 0., or 1.).

val clamp : min:float -> max:float -> float -> float

clamp ~min ~max v

Clamp the float v between min and max.

val lerp : float -> float -> float -> float

lerp a b u

Linearly interpolate between floats a and b.

val lerpn : ?endpoint:bool -> float -> float -> int -> float list

lerpn ?endpoint a b n

Linearly interpolate n values between a and b. If endpoint is true, the last value will be equal to b, otherwise, it will be about a + (b - a) * (1 - 1 / n).

val quant : q:float -> float -> float

quant ~q v

Quantize v to a multiple of the quantum size q. For example:

quant ~q:0.2 1.5 = 1.6
val quant_down : q:float -> float -> float

quant_down ~q v

Quantize v to a multiple of the quantum size q, always rounding down. For example:

quant_down ~q:0.2 1.75 = 1.6
val quant_up : q:float -> float -> float

quant_up ~q v

Quantize v to a multiple of the quantum size q, always rounding up. For example:

quant_up ~q:0.2 1.51 = 1.6
val approx : ?eps:float -> float -> float -> bool

approx ?eps a b

Return true if a is within the tolerance eps of b.

val posmod : int -> int -> int

posmod a m

Compute the positive modulo m of a. The resulting value will be in the range of 0 to m - 1.

Angles and Trigonometry

val deg_of_rad : float -> float

deg_of_rad r

Convert r from radians to degrees.

val rad_of_deg : float -> float

rad_of_deg d

Convert d from degrees to radians.

val law_of_cosines : float -> float -> float -> float

law_of_cosines a b c

Apply the Law of Cosines for a triangle with side lengths a, b, and c. The angle in radians of the corner opposite of the third side c is returned.

2d matrix operations

val mat_dims : 'a array array -> int * int

mat_dims m

Return the dimensions ((n_rows, n_cols) of the 2d matrix m. An Invalid_argument exception is raised if the row lengths are inconsistent.

val matmul : float array array -> float array array -> float array array

matmul a b

Matrix multiplication of a and b. Invalid_argument is raised if the inner dimensions do not match, or if the rows of either matrix are ragged.

val transpose : 'a array array -> 'a array array

transpose m

Transpose rows and columns of the 2d matrix m.

Polynomials

val real_roots : ?eps:float -> ?tol:float -> float array -> float array

real_roots ?eps ?tol p

Compute the real roots of the real polynomial p. The polynomial is specified as [|a_n; ...; a_1; a_0|] where a_n is the x ** n coefficient.

  • eps is used to determine if the imaginary parts of the roots are zero
  • tol is the tolerance for the complex polynomial root finder

Adapted from the real_roots function found in the BOSL2 math module.

val bisection : ?max_iter:int -> ?tolerance:float -> lower:float -> upper:float -> ( float -> float ) -> float

bisection ?max_iter ?tolerance ~lower ~upper f

Perform a bisection search for the value that minimizes the function f between the bounds lower and upper. x is returned either when f x = 0., or the bound range falls below tolerance. Raises Failure if the iteration count reaches max_iter (default = 100).