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ds.functions

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metmajer edited this page Mar 16, 2013 · 5 revisions

The ds.functions module is a collection of functions y = f(x), which map an input value x to an output value y.

cos(x, [a=1], [f=1], [φ=0], [b=0])

Computes the output of the cosine function f(x, a, f, φ, b) = a · cos(2 · π · f · x + φ) + b for a particular x.

Examples:

ds.functions.cos(0);
// f(x) = cos(0)

ds.functions.cos(0.25);
// f(x) = cos(π/2)

ds.functions.cos(0.5, { a: 10, f: 2, φ: Math.PI / 2, b: 1 });
// f(x) = 10·cos(2.5·π) + 1

Params:

  • Number x The input value.

  • Number [a=1] The amplitude.

  • Number [f=1] The frequency (in Hz) (>= 0).

  • Number [φ=0] The phase shift.

  • Number [b=0]

Returns:

  • Number Returns the output value.

Throws:

  • Error Throws if x is not a number.

  • Error Throws if a is not a number.

  • Error Throws if f is not a number >= 0.

  • Error Throws if φ is not a number.

  • Error Throws if b is not a number.

cubic(x, [a=1], [b=0], [c=0], [d=0])

Computes the output of the cubic function f(x) = a · x3 + b · x2 + c · x + d for a particular x.

Examples:

ds.functions.cubic(2);
// f(x) = x³ for x = 2 => 8

ds.functions.cubic(2, { a: 4, b: 3, c: 2, d: 1 });
// f(x) = 4·x³ + 3·x² + 2·x + 1 for x = 2 => 49

Params:

  • Number x The input value.

  • Number [a=1]

  • Number [b=0]

  • Number [c=0]

  • Number [d=0]

Returns:

  • Number Returns the output value.

Throws:

  • Error Throws if x is not a number.

exp(x, [a=Math.E], [b=1], [c=1], [d=0])

Computes the output of the exponential function f(x, a, b, c, d) = c · ab · x + d for a particular x.

Examples:

ds.functions.exp(2);
// f(x) = e²

ds.functions.exp(2, { a: Math.E, b: 2, c: 10 });
// f(x) = 10·e⁴

ds.functions.exp(2, { a: 2, b: 3, c: 10, d: 4 });
// f(x) = 10·2⁶ + 4

Params:

  • Number x The input value.

  • Number [a=Math.E] The base.

  • Number [b=1]

  • Number [c=1]

  • Number [d=0]

Returns:

  • Number Returns the output value.

Throws:

  • Error Throws if x is not a number.

  • Error Throws if a is not a number.

  • Error Throws if b is not a number.

  • Error Throws if c is not a number.

  • Error Throws if d is not a number.

identity(x)

Computes the output of the identity function f(x) = x for a particular x.

Params:

  • * x The input value.

Returns:

  • * Returns the output value.

linear(x, [a=1], [b=0])

Computes the output of the linear function f(x) = a · x + b for a particular x.

Examples:

ds.functions.linear(2);
// f(x) = x for x = 2 => 2

ds.functions.linear(2, { a: 2, b: 1 });
// f(x) = 2·x + 1 for x = 2 => 5

Params:

  • Number x The input value.

  • Number [a=1]

  • Number [b=0]

Returns:

  • Number Returns the output value.

Throws:

  • Error Throws if x is not a number.

log(x, [a=Math.E], [b=1], [c=0])

Computes the output of the logarithmic function f(x, a, b, c) = b · loga(x) + c for a particular x.

Examples:

ds.functions.log(2);
// f(x) = logₑ(2)

ds.functions.log(4, { a: 2 });
// f(x) = log₂(4)

ds.functions.log(4, { a: 2, b: 10, c: 8 });
// f(x) = 10·log₂(4) + 8

Params:

  • Number x The input value.

  • Number [a=Math.E] The base (>= 0).

  • Number [b=1]

  • Number [c=0]

Returns:

  • Number Returns the output value.

Throws:

  • Error Throws if x is not a number.

  • Error Throws if a is not a number >= 0.

  • Error Throws if b is not a number.

  • Error Throws if c is not a number.

polynomial(x, [a=[]])

Computes the output of the polynomial function f(x) = a[n] · xn + a[n-1] · xn-1 + ... + a[1] · x + a[0] with coefficients a[n] for a particular x.

Examples:

ds.functions.polynomial(2, { a: [1, 2] });
// f(x) = 2·x + 1 for x = 2 => 5

ds.functions.polynomial(2, { a: [1, 2, 3] });
// f(x) = 3·x² + 2·x + 1 for x = 2 => 17

ds.functions.polynomial(2, { a: [1, 2, 3, 4] });
// f(x) = 4·x³ + 3·x² + 2·x + 1 for x = 2 => 49

Params:

  • Number x The input value.

  • Array [a=[]] The coefficients of the polynomial function. An array of length n will produce a polynomial of degree n-1, an empty array will result in an output value of 0.

Returns:

  • Number Returns the output value.

Throws:

  • Error Throws if x is not a number.

  • Error Throws if a is not a (possibly empty) array of numbers.

sin(x, [a=1], [f=1], [φ=0], [b=0])

Computes the output of the sine function f(x, a, f, φ, b) = a · sin(2 · π · f · x + φ) + b for a particular x.

Examples:

ds.functions.sin(0);
// f(x) = sin(0)

ds.functions.sin(0.25);
// f(x) = sin(π/2)

ds.functions.sin(0.5, { a: 10, f: 2, φ: Math.PI / 2, b: 1 });
// f(x) = 10·sin(2.5·π) + 1

Params:

  • Number x The input value.

  • Number [a=1] The amplitude.

  • Number [f=1] The frequency (in Hz) (>= 0).

  • Number [φ=0] The phase shift.

  • Number [b=0]

Returns:

  • Number Returns the output value.

Throws:

  • Error Throws if x is not a number.

  • Error Throws if a is not a number.

  • Error Throws if f is not a number >= 0.

  • Error Throws if φ is not a number.

  • Error Throws if b is not a number.

square(x, [a=1], [b=0], [c=0])

Computes the output of the square function f(x) = a · x2 + b · x + c for a particular x.

Examples:

ds.functions.square(2);
// f(x) = x² for x = 2 => 4

ds.functions.square(2, { a: 3, b: 2, c: 1 });
// f(x) = 3·x² + 2·x + 1 for x = 2 => 17

Params:

  • Number x The input value.

  • Number [a=1]

  • Number [b=0]

  • Number [c=0]

Returns:

  • Number Returns the output value.

Throws:

  • Error Throws if x is not a number.
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