mirror of
https://github.com/BelfrySCAD/BOSL2.git
synced 2024-12-29 00:09:41 +00:00
Synopses, etc for math.scad
This commit is contained in:
Revar Desmera
parent
e80fe3ea85
commit
9aec87247a
1 changed files with 193 additions and 12 deletions
205
math.scad
205
math.scad
|
|
@ -14,18 +14,30 @@
|
|||
// Section: Math Constants
|
||||
|
||||
// Constant: PHI
|
||||
// Description: The golden ratio phi.
|
||||
// Synopsis: The golden ratio φ (phi). Approximately 1.6180339887
|
||||
// Topics: Constants, Math
|
||||
// See Also: EPSILON, INF, NAN
|
||||
// Description: The golden ratio φ (phi). Approximately 1.6180339887
|
||||
PHI = (1+sqrt(5))/2;
|
||||
|
||||
// Constant: EPSILON
|
||||
// Description: A really small value useful in comparing floating point numbers. ie: abs(a-b)<EPSILON
|
||||
// Synopsis: A tiny value to compare floating point values. `1e-9`
|
||||
// Topics: Constants, Math
|
||||
// See Also: PHI, EPSILON, INF, NAN
|
||||
// Description: A really small value useful in comparing floating point numbers. ie: abs(a-b)<EPSILON `1e-9`
|
||||
EPSILON = 1e-9;
|
||||
|
||||
// Constant: INF
|
||||
// Synopsis: The floating point value for Infinite.
|
||||
// Topics: Constants, Math
|
||||
// See Also: PHI, EPSILON, INF, NAN
|
||||
// Description: The value `inf`, useful for comparisons.
|
||||
INF = 1/0;
|
||||
|
||||
// Constant: NAN
|
||||
// Synopsis: The floating point value for Not a Number.
|
||||
// Topics: Constants, Math
|
||||
// See Also: PHI, EPSILON, INF, NAN
|
||||
// Description: The value `nan`, useful for comparisons.
|
||||
NAN = acos(2);
|
||||
|
||||
|
|
@ -35,6 +47,9 @@ NAN = acos(2);
|
|||
|
||||
|
||||
// Function: count()
|
||||
// Synopsis: Creates a list of incrementing numbers.
|
||||
// Topics: Math, Indexing
|
||||
// See Also: idx()
|
||||
// Usage:
|
||||
// list = count(n, [s], [step], [reverse]);
|
||||
// Description:
|
||||
|
|
@ -45,7 +60,6 @@ NAN = acos(2);
|
|||
// s = The starting value of the list of numbers.
|
||||
// step = The amount to increment successive numbers in the list.
|
||||
// reverse = Reverse the list. Default: false.
|
||||
// See Also: idx()
|
||||
// Example:
|
||||
// nl1 = count(5); // Returns: [0,1,2,3,4]
|
||||
// nl2 = count(5,3); // Returns: [3,4,5,6,7]
|
||||
|
|
@ -58,6 +72,9 @@ function count(n,s=0,step=1,reverse=false) = let(n=is_list(n) ? len(n) : n)
|
|||
|
||||
|
||||
// Function: lerp()
|
||||
// Synopsis: Linearly interpolates between two values.
|
||||
// Topics: Interpolation, Math
|
||||
// See Also: lookup_vector(), lerpn()
|
||||
// Usage:
|
||||
// x = lerp(a, b, u);
|
||||
// l = lerp(a, b, LIST);
|
||||
|
|
@ -95,6 +112,9 @@ function lerp(a,b,u) =
|
|||
|
||||
|
||||
// Function: lerpn()
|
||||
// Synopsis: Returns exactly `n` values, linearly interpolated between `a` and `b`.
|
||||
// Topics: Interpolation, Math
|
||||
// See Also: lookup_vector(), lerp()
|
||||
// Usage:
|
||||
// x = lerpn(a, b, n);
|
||||
// x = lerpn(a, b, n, [endpoint]);
|
||||
|
|
@ -124,6 +144,9 @@ function lerpn(a,b,n,endpoint=true) =
|
|||
// Section: Miscellaneous Functions
|
||||
|
||||
// Function: sqr()
|
||||
// Synopsis: Returns the square of the given value.
|
||||
// Topics: Math
|
||||
// See Also: hypot(), log2()
|
||||
// Usage:
|
||||
// x2 = sqr(x);
|
||||
// Description:
|
||||
|
|
@ -141,6 +164,9 @@ function sqr(x) =
|
|||
|
||||
|
||||
// Function: log2()
|
||||
// Synopsis: Returns the log base 2 of the given value.
|
||||
// Topics: Math
|
||||
// See Also: hypot(), sqr()
|
||||
// Usage:
|
||||
// val = log2(x);
|
||||
// Description:
|
||||
|
|
@ -156,6 +182,9 @@ function log2(x) =
|
|||
// this may return NAN or INF; should it check x>0 ?
|
||||
|
||||
// Function: hypot()
|
||||
// Synopsis: Returns the hypotenuse length of a 2D or 3D triangle.
|
||||
// Topics: Math
|
||||
// See Also: hypot(), sqr(), log2()
|
||||
// Usage:
|
||||
// l = hypot(x, y, [z]);
|
||||
// Description:
|
||||
|
|
@ -173,6 +202,9 @@ function hypot(x,y,z=0) =
|
|||
|
||||
|
||||
// Function: factorial()
|
||||
// Synopsis: Returns the factorial of the given integer.
|
||||
// Topics: Math
|
||||
// See Also: hypot(), sqr(), log2()
|
||||
// Usage:
|
||||
// x = factorial(n, [d]);
|
||||
// Description:
|
||||
|
|
@ -191,6 +223,9 @@ function factorial(n,d=0) =
|
|||
|
||||
|
||||
// Function: binomial()
|
||||
// Synopsis: Returns the binomial coefficients of the integer `n`.
|
||||
// Topics: Math
|
||||
// See Also: hypot(), sqr(), log2(), factorial()
|
||||
// Usage:
|
||||
// x = binomial(n);
|
||||
// Description:
|
||||
|
|
@ -210,10 +245,13 @@ function binomial(n) =
|
|||
|
||||
|
||||
// Function: binomial_coefficient()
|
||||
// Synopsis: Returns the `k`-th binomial coefficient of the integer `n`.
|
||||
// Topics: Math
|
||||
// See Also: hypot(), sqr(), log2(), factorial()
|
||||
// Usage:
|
||||
// x = binomial_coefficient(n, k);
|
||||
// Description:
|
||||
// Returns the k-th binomial coefficient of the integer `n`.
|
||||
// Returns the `k`-th binomial coefficient of the integer `n`.
|
||||
// Arguments:
|
||||
// n = The integer to get the binomial coefficient of
|
||||
// k = The binomial coefficient index
|
||||
|
|
@ -233,6 +271,9 @@ function binomial_coefficient(n,k) =
|
|||
|
||||
|
||||
// Function: gcd()
|
||||
// Synopsis: Returns the Greatest Common Divisor/Factor of two integers.
|
||||
// Topics: Math
|
||||
// See Also: hypot(), sqr(), log2(), factorial(), binomial(), gcd(), lcm()
|
||||
// Usage:
|
||||
// x = gcd(a,b)
|
||||
// Description:
|
||||
|
|
@ -256,6 +297,9 @@ function _lcmlist(a) =
|
|||
|
||||
|
||||
// Function: lcm()
|
||||
// Synopsis: Returns the Least Common Multiple of two or more integers.
|
||||
// Topics: Math
|
||||
// See Also: hypot(), sqr(), log2(), factorial(), binomial(), gcd(), lcm()
|
||||
// Usage:
|
||||
// div = lcm(a, b);
|
||||
// divs = lcm(list);
|
||||
|
|
@ -276,6 +320,9 @@ function lcm(a,b=[]) =
|
|||
// Section: Hyperbolic Trigonometry
|
||||
|
||||
// Function: sinh()
|
||||
// Synopsis: Returns the hyperbolic sine of the given value.
|
||||
// Topics: Math, Trigonometry
|
||||
// See Also: sinh(), cosh(), tanh(), asinh(), acosh(), atanh()
|
||||
// Usage:
|
||||
// a = sinh(x);
|
||||
// Description: Takes a value `x`, and returns the hyperbolic sine of it.
|
||||
|
|
@ -285,6 +332,9 @@ function sinh(x) =
|
|||
|
||||
|
||||
// Function: cosh()
|
||||
// Synopsis: Returns the hyperbolic cosine of the given value.
|
||||
// Topics: Math, Trigonometry
|
||||
// See Also: sinh(), cosh(), tanh(), asinh(), acosh(), atanh()
|
||||
// Usage:
|
||||
// a = cosh(x);
|
||||
// Description: Takes a value `x`, and returns the hyperbolic cosine of it.
|
||||
|
|
@ -294,6 +344,9 @@ function cosh(x) =
|
|||
|
||||
|
||||
// Function: tanh()
|
||||
// Synopsis: Returns the hyperbolic tangent of the given value.
|
||||
// Topics: Math, Trigonometry
|
||||
// See Also: sinh(), cosh(), tanh(), asinh(), acosh(), atanh()
|
||||
// Usage:
|
||||
// a = tanh(x);
|
||||
// Description: Takes a value `x`, and returns the hyperbolic tangent of it.
|
||||
|
|
@ -303,6 +356,9 @@ function tanh(x) =
|
|||
|
||||
|
||||
// Function: asinh()
|
||||
// Synopsis: Returns the hyperbolic arc-sine of the given value.
|
||||
// Topics: Math, Trigonometry
|
||||
// See Also: sinh(), cosh(), tanh(), asinh(), acosh(), atanh()
|
||||
// Usage:
|
||||
// a = asinh(x);
|
||||
// Description: Takes a value `x`, and returns the inverse hyperbolic sine of it.
|
||||
|
|
@ -312,6 +368,9 @@ function asinh(x) =
|
|||
|
||||
|
||||
// Function: acosh()
|
||||
// Synopsis: Returns the hyperbolic arc-cosine of the given value.
|
||||
// Topics: Math, Trigonometry
|
||||
// See Also: sinh(), cosh(), tanh(), asinh(), acosh(), atanh()
|
||||
// Usage:
|
||||
// a = acosh(x);
|
||||
// Description: Takes a value `x`, and returns the inverse hyperbolic cosine of it.
|
||||
|
|
@ -321,6 +380,9 @@ function acosh(x) =
|
|||
|
||||
|
||||
// Function: atanh()
|
||||
// Synopsis: Returns the hyperbolic arc-tangent of the given value.
|
||||
// Topics: Math, Trigonometry
|
||||
// See Also: sinh(), cosh(), tanh(), asinh(), acosh(), atanh()
|
||||
// Usage:
|
||||
// a = atanh(x);
|
||||
// Description: Takes a value `x`, and returns the inverse hyperbolic tangent of it.
|
||||
|
|
@ -332,6 +394,9 @@ function atanh(x) =
|
|||
// Section: Quantization
|
||||
|
||||
// Function: quant()
|
||||
// Synopsis: Returns `x` quantized to the nearest integer multiple of `y`.
|
||||
// Topics: Math, Quantization
|
||||
// See Also: quant(), quantdn(), quantup()
|
||||
// Usage:
|
||||
// num = quant(x, y);
|
||||
// Description:
|
||||
|
|
@ -370,6 +435,9 @@ function _roundall(data) =
|
|||
|
||||
|
||||
// Function: quantdn()
|
||||
// Synopsis: Returns `x` quantized down to an integer multiple of `y`.
|
||||
// Topics: Math, Quantization
|
||||
// See Also: quant(), quantdn(), quantup()
|
||||
// Usage:
|
||||
// num = quantdn(x, y);
|
||||
// Description:
|
||||
|
|
@ -408,6 +476,9 @@ function _floorall(data) =
|
|||
|
||||
|
||||
// Function: quantup()
|
||||
// Synopsis: Returns `x` quantized uo to an integer multiple of `y`.
|
||||
// Topics: Math, Quantization
|
||||
// See Also: quant(), quantdn(), quantup()
|
||||
// Usage:
|
||||
// num = quantup(x, y);
|
||||
// Description:
|
||||
|
|
@ -448,6 +519,9 @@ function _ceilall(data) =
|
|||
// Section: Constraints and Modulos
|
||||
|
||||
// Function: constrain()
|
||||
// Synopsis: Returns a value constrained between `minval` and `maxval`, inclusive.
|
||||
// Topics: Math
|
||||
// See Also: posmod(), modang()
|
||||
// Usage:
|
||||
// val = constrain(v, minval, maxval);
|
||||
// Description:
|
||||
|
|
@ -468,6 +542,9 @@ function constrain(v, minval, maxval) =
|
|||
|
||||
|
||||
// Function: posmod()
|
||||
// Synopsis: Returns the positive modulo of a value.
|
||||
// Topics: Math
|
||||
// See Also: constrain(), posmod(), modang()
|
||||
// Usage:
|
||||
// mod = posmod(x, m)
|
||||
// Description:
|
||||
|
|
@ -489,6 +566,9 @@ function posmod(x,m) =
|
|||
|
||||
|
||||
// Function: modang()
|
||||
// Synopsis: Returns an angle normalized to between -180º and 180º.
|
||||
// Topics: Math
|
||||
// See Also: constrain(), posmod(), modang()
|
||||
// Usage:
|
||||
// ang = modang(x);
|
||||
// Description:
|
||||
|
|
@ -509,6 +589,9 @@ function modang(x) =
|
|||
// Section: Operations on Lists (Sums, Mean, Products)
|
||||
|
||||
// Function: sum()
|
||||
// Synopsis: Returns the sum of a list of values.
|
||||
// Topics: Math
|
||||
// See Also: mean(), median(), product(), cumsum()
|
||||
// Usage:
|
||||
// x = sum(v, [dflt]);
|
||||
// Description:
|
||||
|
|
@ -534,6 +617,9 @@ function _sum(v,_total,_i=0) = _i>=len(v) ? _total : _sum(v,_total+v[_i], _i+1);
|
|||
|
||||
|
||||
// Function: mean()
|
||||
// Synopsis: Returns the mean value of a list of values.
|
||||
// Topics: Math, Statistics
|
||||
// See Also: sum(), mean(), median(), product()
|
||||
// Usage:
|
||||
// x = mean(v);
|
||||
// Description:
|
||||
|
|
@ -551,6 +637,9 @@ function mean(v) =
|
|||
|
||||
|
||||
// Function: median()
|
||||
// Synopsis: Returns the median value of a list of values.
|
||||
// Topics: Math, Statistics
|
||||
// See Also: sum(), mean(), median(), product()
|
||||
// Usage:
|
||||
// middle = median(v)
|
||||
// Description:
|
||||
|
|
@ -567,6 +656,9 @@ function median(v) =
|
|||
|
||||
|
||||
// Function: deltas()
|
||||
// Synopsis: Returns the deltas between a list of values.
|
||||
// Topics: Math, Statistics
|
||||
// See Also: sum(), mean(), median(), product()
|
||||
// Usage:
|
||||
// delts = deltas(v,[wrap]);
|
||||
// Description:
|
||||
|
|
@ -585,6 +677,9 @@ function deltas(v, wrap=false) =
|
|||
|
||||
|
||||
// Function: cumsum()
|
||||
// Synopsis: Returns the running cumulative sum of a list of values.
|
||||
// Topics: Math, Statistics
|
||||
// See Also: sum(), mean(), median(), product()
|
||||
// Usage:
|
||||
// sums = cumsum(v);
|
||||
// Description:
|
||||
|
|
@ -609,6 +704,9 @@ function _cumsum(v,_i=0,_acc=[]) =
|
|||
|
||||
|
||||
// Function: product()
|
||||
// Synopsis: Returns the multiplicative product of a list of values.
|
||||
// Topics: Math, Statistics
|
||||
// See Also: sum(), mean(), median(), product(), cumsum()
|
||||
// Usage:
|
||||
// x = product(v);
|
||||
// Description:
|
||||
|
|
@ -634,6 +732,9 @@ function _product(v, i=0, _tot) =
|
|||
|
||||
|
||||
// Function: cumprod()
|
||||
// Synopsis: Returns the running cumulative product of a list of values.
|
||||
// Topics: Math, Statistics
|
||||
// See Also: sum(), mean(), median(), product(), cumsum()
|
||||
// Description:
|
||||
// Returns a list where each item is the cumulative product of all items up to and including the corresponding entry in the input list.
|
||||
// If passed an array of vectors, returns a list of elementwise vector products. If passed a list of square matrices returns matrix
|
||||
|
|
@ -673,6 +774,9 @@ function _cumprod_vec(v,_i=0,_acc=[]) =
|
|||
|
||||
|
||||
// Function: convolve()
|
||||
// Synopsis: Returns the convolution of `p` and `q`.
|
||||
// Topics: Math, Statistics
|
||||
// See Also: sum(), mean(), median(), product(), cumsum()
|
||||
// Usage:
|
||||
// x = convolve(p,q);
|
||||
// Description:
|
||||
|
|
@ -706,13 +810,20 @@ function convolve(p,q) =
|
|||
|
||||
|
||||
// Function: sum_of_sines()
|
||||
// Synopsis: Returns the sum of one or more sine waves at a given angle.
|
||||
// Topics: Math, Statistics
|
||||
// See Also: sum(), mean(), median(), product(), cumsum()
|
||||
// Usage:
|
||||
// sum_of_sines(a,sines)
|
||||
// Description:
|
||||
// Gives the sum of a series of sines, at a given angle.
|
||||
// Given a list of sine waves, returns the sum of the sines at the given angle.
|
||||
// Each sine wave is given as an `[AMPLITUDE, FREQUENCY, PHASE_ANGLE]` triplet.
|
||||
// - `AMPLITUDE` is the height of the sine wave above (and below) `0`.
|
||||
// - `FREQUENCY` is the number of times the sine wave repeats in 360º.
|
||||
// - `PHASE_ANGLE` is the offset in degrees of the sine wave.
|
||||
// Arguments:
|
||||
// a = Angle to get the value for.
|
||||
// sines = List of [amplitude, frequency, offset] items, where the frequency is the number of times the cycle repeats around the circle.
|
||||
// sines = List of [amplitude, frequency, phase_angle] items, where the frequency is the number of times the cycle repeats around the circle.
|
||||
// Example:
|
||||
// v = sum_of_sines(30, [[10,3,0], [5,5.5,60]]);
|
||||
function sum_of_sines(a, sines) =
|
||||
|
|
@ -729,6 +840,9 @@ function sum_of_sines(a, sines) =
|
|||
// Section: Random Number Generation
|
||||
|
||||
// Function: rand_int()
|
||||
// Synopsis: Returns a random integer.
|
||||
// Topics: Random
|
||||
// See Also: rand_int(), random_points(), gaussian_rands(), random_polygon(), spherical_random_points(), exponential_rands()
|
||||
// Usage:
|
||||
// rand_int(minval, maxval, n, [seed]);
|
||||
// Description:
|
||||
|
|
@ -749,10 +863,11 @@ function rand_int(minval, maxval, n, seed=undef) =
|
|||
|
||||
|
||||
// Function: random_points()
|
||||
// Synopsis: Returns a list of random points.
|
||||
// Topics: Random, Points
|
||||
// See Also: rand_int(), random_points(), random_polygon(), spherical_random_points()
|
||||
// Usage:
|
||||
// points = random_points(n, dim, [scale], [seed]);
|
||||
// See Also: random_polygon(), spherical_random_points()
|
||||
// Topics: Random, Points
|
||||
// Description:
|
||||
// Generate `n` uniform random points of dimension `dim` with data ranging from -scale to +scale.
|
||||
// The `scale` may be a number, in which case the random data lies in a cube,
|
||||
|
|
@ -776,6 +891,9 @@ function random_points(n, dim, scale=1, seed) =
|
|||
|
||||
|
||||
// Function: gaussian_rands()
|
||||
// Synopsis: Returns a list of random numbers with a gaussian distribution.
|
||||
// Topics: Random, Statistics
|
||||
// See Also: rand_int(), random_points(), gaussian_rands(), random_polygon(), spherical_random_points(), exponential_rands()
|
||||
// Usage:
|
||||
// arr = gaussian_rands([n],[mean], [cov], [seed]);
|
||||
// Description:
|
||||
|
|
@ -806,6 +924,9 @@ function gaussian_rands(n=1, mean=0, cov=1, seed=undef) =
|
|||
|
||||
|
||||
// Function: exponential_rands()
|
||||
// Synopsis: Returns a list of random numbers with an exponential distribution.
|
||||
// Topics: Random, Statistics
|
||||
// See Also: rand_int(), random_points(), gaussian_rands(), random_polygon(), spherical_random_points()
|
||||
// Usage:
|
||||
// arr = exponential_rands([n], [lambda], [seed])
|
||||
// Description:
|
||||
|
|
@ -821,11 +942,13 @@ function exponential_rands(n=1, lambda=1, seed) =
|
|||
)
|
||||
-(1/lambda) * [for(x=unif) x==1 ? 708.3964185322641 : ln(1-x)]; // Use ln(min_float) when x is 1
|
||||
|
||||
|
||||
// Function: spherical_random_points()
|
||||
// Synopsis: Returns a list of random points on the surface of a sphere.
|
||||
// Topics: Random, Points
|
||||
// See Also: rand_int(), random_points(), gaussian_rands(), random_polygon(), spherical_random_points()
|
||||
// Usage:
|
||||
// points = spherical_random_points([n], [radius], [seed]);
|
||||
// See Also: random_polygon(), random_points()
|
||||
// Topics: Random, Points
|
||||
// Description:
|
||||
// Generate `n` 3D uniformly distributed random points lying on a sphere centered at the origin with radius equal to `radius`.
|
||||
// Arguments:
|
||||
|
|
@ -849,10 +972,11 @@ function spherical_random_points(n=1, radius=1, seed) =
|
|||
|
||||
|
||||
// Function: random_polygon()
|
||||
// Synopsis: Returns the CCW path of a simple random polygon.
|
||||
// Topics: Random, Polygon
|
||||
// See Also: random_points(), spherical_random_points()
|
||||
// Usage:
|
||||
// points = random_polygon([n], [size], [seed]);
|
||||
// See Also: random_points(), spherical_random_points()
|
||||
// Topics: Random, Polygon
|
||||
// Description:
|
||||
// Generate the `n` vertices of a random counter-clockwise simple 2d polygon
|
||||
// inside a circle centered at the origin with radius `size`.
|
||||
|
|
@ -876,6 +1000,9 @@ function random_polygon(n=3,size=1, seed) =
|
|||
// Section: Calculus
|
||||
|
||||
// Function: deriv()
|
||||
// Synopsis: Returns the first derivative estimate of a list of data.
|
||||
// Topics: Math, Calculus
|
||||
// See Also: deriv(), deriv2(), deriv3()
|
||||
// Usage:
|
||||
// x = deriv(data, [h], [closed])
|
||||
// Description:
|
||||
|
|
@ -941,6 +1068,9 @@ function _deriv_nonuniform(data, h, closed) =
|
|||
|
||||
|
||||
// Function: deriv2()
|
||||
// Synopsis: Returns the second derivative estimate of a list of data.
|
||||
// Topics: Math, Calculus
|
||||
// See Also: deriv(), deriv2(), deriv3()
|
||||
// Usage:
|
||||
// x = deriv2(data, [h], [closed])
|
||||
// Description:
|
||||
|
|
@ -985,6 +1115,9 @@ function deriv2(data, h=1, closed=false) =
|
|||
|
||||
|
||||
// Function: deriv3()
|
||||
// Synopsis: Returns the third derivative estimate of a list of data.
|
||||
// Topics: Math, Calculus
|
||||
// See Also: deriv(), deriv2(), deriv3()
|
||||
// Usage:
|
||||
// x = deriv3(data, [h], [closed])
|
||||
// Description:
|
||||
|
|
@ -1030,6 +1163,9 @@ function deriv3(data, h=1, closed=false) =
|
|||
|
||||
|
||||
// Function: complex()
|
||||
// Synopsis: Replaces scalars in a list or matrix with complex number 2-vectors.
|
||||
// Topics: Math, Complex Numbers
|
||||
// See Also: c_mul(), c_div(), c_conj(), c_real(), c_imag(), c_ident(), c_norm()
|
||||
// Usage:
|
||||
// z = complex(list)
|
||||
// Description:
|
||||
|
|
@ -1041,6 +1177,9 @@ function complex(list) =
|
|||
|
||||
|
||||
// Function: c_mul()
|
||||
// Synopsis: Multiplies two complex numbers.
|
||||
// Topics: Math, Complex Numbers
|
||||
// See Also: complex(), c_mul(), c_div(), c_conj(), c_real(), c_imag(), c_ident(), c_norm()
|
||||
// Usage:
|
||||
// c = c_mul(z1,z2)
|
||||
// Description:
|
||||
|
|
@ -1077,6 +1216,9 @@ function _c_mul(z1,z2) =
|
|||
|
||||
|
||||
// Function: c_div()
|
||||
// Synopsis: Divides two complex numbers.
|
||||
// Topics: Math, Complex Numbers
|
||||
// See Also: complex(), c_mul(), c_div(), c_conj(), c_real(), c_imag(), c_ident(), c_norm()
|
||||
// Usage:
|
||||
// x = c_div(z1,z2)
|
||||
// Description:
|
||||
|
|
@ -1093,6 +1235,9 @@ function c_div(z1,z2) =
|
|||
|
||||
|
||||
// Function: c_conj()
|
||||
// Synopsis: Returns the complex conjugate of the input.
|
||||
// Topics: Math, Complex Numbers
|
||||
// See Also: complex(), c_mul(), c_div(), c_conj(), c_real(), c_imag(), c_ident(), c_norm()
|
||||
// Usage:
|
||||
// w = c_conj(z)
|
||||
// Description:
|
||||
|
|
@ -1104,6 +1249,9 @@ function c_conj(z) =
|
|||
|
||||
|
||||
// Function: c_real()
|
||||
// Synopsis: Returns the real part of a complex number, vector or matrix..
|
||||
// Topics: Math, Complex Numbers
|
||||
// See Also: complex(), c_mul(), c_div(), c_conj(), c_real(), c_imag(), c_ident(), c_norm()
|
||||
// Usage:
|
||||
// x = c_real(z)
|
||||
// Description:
|
||||
|
|
@ -1115,6 +1263,9 @@ function c_real(z) =
|
|||
|
||||
|
||||
// Function: c_imag()
|
||||
// Synopsis: Returns the imaginary part of a complex number, vector or matrix..
|
||||
// Topics: Math, Complex Numbers
|
||||
// See Also: complex(), c_mul(), c_div(), c_conj(), c_real(), c_imag(), c_ident(), c_norm()
|
||||
// Usage:
|
||||
// x = c_imag(z)
|
||||
// Description:
|
||||
|
|
@ -1126,6 +1277,9 @@ function c_imag(z) =
|
|||
|
||||
|
||||
// Function: c_ident()
|
||||
// Synopsis: Returns an n by n complex identity matrix.
|
||||
// Topics: Math, Complex Numbers
|
||||
// See Also: complex(), c_mul(), c_div(), c_conj(), c_real(), c_imag(), c_ident(), c_norm()
|
||||
// Usage:
|
||||
// I = c_ident(n)
|
||||
// Description:
|
||||
|
|
@ -1134,6 +1288,9 @@ function c_ident(n) = [for (i = [0:1:n-1]) [for (j = [0:1:n-1]) (i==j)?[1,0]:[0,
|
|||
|
||||
|
||||
// Function: c_norm()
|
||||
// Synopsis: Returns the norm of a complex number or vector.
|
||||
// Topics: Math, Complex Numbers
|
||||
// See Also: complex(), c_mul(), c_div(), c_conj(), c_real(), c_imag(), c_ident(), c_norm()
|
||||
// Usage:
|
||||
// n = c_norm(z)
|
||||
// Description:
|
||||
|
|
@ -1144,6 +1301,9 @@ function c_norm(z) = norm_fro(z);
|
|||
// Section: Polynomials
|
||||
|
||||
// Function: quadratic_roots()
|
||||
// Synopsis: Computes roots for the quadratic equation.
|
||||
// Topics: Math, Geometry, Complex Numbers
|
||||
// See Also: quadratic_roots(), polynomial(), poly_mult(), poly_div(), poly_add()
|
||||
// Usage:
|
||||
// roots = quadratic_roots(a, b, c, [real])
|
||||
// Description:
|
||||
|
|
@ -1177,6 +1337,9 @@ function quadratic_roots(a,b,c,real=false) =
|
|||
|
||||
|
||||
// Function: polynomial()
|
||||
// Synopsis: Calculates a polynomial equation at a given value.
|
||||
// Topics: Math, Complex Numbers
|
||||
// See Also: quadratic_roots(), polynomial(), poly_mult(), poly_div(), poly_add(), poly_roots()
|
||||
// Usage:
|
||||
// x = polynomial(p, z)
|
||||
// Description:
|
||||
|
|
@ -1194,6 +1357,9 @@ function polynomial(p,z,k,total) =
|
|||
|
||||
|
||||
// Function: poly_mult()
|
||||
// Synopsis: Returns the polynomial result of multiplying two polynomial equations.
|
||||
// Topics: Math
|
||||
// See Also: quadratic_roots(), polynomial(), poly_mult(), poly_div(), poly_add(), poly_roots()
|
||||
// Usage:
|
||||
// x = polymult(p,q)
|
||||
// x = polymult([p1,p2,p3,...])
|
||||
|
|
@ -1213,6 +1379,9 @@ function poly_mult(p,q) =
|
|||
|
||||
|
||||
// Function: poly_div()
|
||||
// Synopsis: Returns the polynomial quotient and remainder results of dividing two polynomial equations.
|
||||
// Topics: Math
|
||||
// See Also: quadratic_roots(), polynomial(), poly_mult(), poly_div(), poly_add(), poly_roots()
|
||||
// Usage:
|
||||
// [quotient,remainder] = poly_div(n,d)
|
||||
// Description:
|
||||
|
|
@ -1251,6 +1420,9 @@ function _poly_trim(p,eps=0) =
|
|||
|
||||
|
||||
// Function: poly_add()
|
||||
// Synopsis: Returns the polynomial sum of adding two polynomial equations.
|
||||
// Topics: Math
|
||||
// See Also: quadratic_roots(), polynomial(), poly_mult(), poly_div(), poly_add(), poly_roots()
|
||||
// Usage:
|
||||
// sum = poly_add(p,q)
|
||||
// Description:
|
||||
|
|
@ -1266,6 +1438,9 @@ function poly_add(p,q) =
|
|||
|
||||
|
||||
// Function: poly_roots()
|
||||
// Synopsis: Returns all complex number roots of the given real polynomial.
|
||||
// Topics: Math, Complex Numbers
|
||||
// See Also: quadratic_roots(), polynomial(), poly_mult(), poly_div(), poly_add(), poly_roots()
|
||||
// Usage:
|
||||
// roots = poly_roots(p, [tol]);
|
||||
// Description:
|
||||
|
|
@ -1336,6 +1511,9 @@ function _poly_roots(p, pderiv, s, z, tol, i=0) =
|
|||
|
||||
|
||||
// Function: real_roots()
|
||||
// Synopsis: Returns all real roots of the given real polynomial.
|
||||
// Topics: Math, Complex Numbers
|
||||
// See Also: quadratic_roots(), polynomial(), poly_mult(), poly_div(), poly_add(), poly_roots()
|
||||
// Usage:
|
||||
// roots = real_roots(p, [eps], [tol])
|
||||
// Description:
|
||||
|
|
@ -1378,6 +1556,9 @@ function real_roots(p,eps=undef,tol=1e-14) =
|
|||
// Section: Operations on Functions
|
||||
|
||||
// Function: root_find()
|
||||
// Synopsis: Finds a root of the given continuous function.
|
||||
// Topics: Math
|
||||
// See Also: quadratic_roots(), polynomial(), poly_mult(), poly_div(), poly_add(), poly_roots()
|
||||
// Usage:
|
||||
// x = root_find(f, x0, x1, [tol])
|
||||
// Description:
|
||||
|
|
|
|||
Loading…
Reference in a new issue