Rescale

Linearly rescale a value or list from one range to another.

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Rescale(list)rescale every element of list so its own minimum maps to 0 and its maximum to 1.

Rescale(x, {min, max})(x - min) / (max - min) -- x rescaled from {min, max} to {0, 1}.

Rescale(x, {min, max}, {ymin, ymax})x rescaled from {min, max} to {ymin, ymax}.

Typed signatures

Type	Package	Applies
`(list<real> \| real, vector<real^2>?, vector<real^2>?) -> list<real> \| real`	`analytic`	always

Domain: Elementary functions

Details

A bare scalar with no range to rescale against -- Rescale(x) where x is not a list -- has no sensible reading and stays unevaluated.
Rescale(x, {min, max}) is Rescale(x, {min, max}, {0, 1}) with the target range left implicit.
Exact rational input and bounds give an exact rational result, which N(…, d) rounds once, so every digit asked for is right.

Examples

Basic #

List min -> 0, max -> 1

In

\mathrm{Rescale}(\bigl\lbrack1, 2, 3, 4\bigr\rbrack)

Out

\bigl\lbrack0, \frac{1}{3}, \frac{2}{3}, 1\bigr\rbrack

Scope #

In

\mathrm{Rescale}(5, \bigl\lbrack0, 10\bigr\rbrack)

Out

\frac{1}{2}

Rescaled into an explicit target range

In

\mathrm{Rescale}(5, \bigl\lbrack0, 10\bigr\rbrack, \bigl\lbrack100, 200\bigr\rbrack)

Out

150

Maps $-\frac32$ in $[-2,2]$ to the fraction $\frac18$ of the way across

In

\mathrm{Rescale}(-\frac{3}{2}, \bigl\lbrack-2, 2\bigr\rbrack)

Out

\frac{1}{8}

Maps 3 from $[-9,7]$ into $[11,28]$ linearly

In

\mathrm{Rescale}(3, \bigl\lbrack-9, 7\bigr\rbrack, \bigl\lbrack11, 28\bigr\rbrack)

Out

\frac{95}{4}

A list rescales to the unit interval

In

\mathrm{Rescale}(\bigl\lbrack-2, 0, 2\bigr\rbrack)

Out

\bigl\lbrack0, \frac{1}{2}, 1\bigr\rbrack

The derivative stays unevaluated when the limits are symbols

In

\mathrm{PiecewiseExpand}(\operatorname{D}(\mathrm{Rescale}(x, \bigl\lbrack a, b\bigr\rbrack), \bigl\lbrack x, k\bigr\rbrack))

Out

\operatorname{D}(\mathrm{Rescale}(x, \bigl\lbrack a, b\bigr\rbrack), \bigl\lbrack x, k\bigr\rbrack)

In

N(\mathrm{Rescale}(\frac{1}{11}, \bigl\lbrack\frac{1}{7}, 5\bigr\rbrack), 50)

Out

-0.010\,695\,187\,165\,775\,401\,069\,518\,716\,577\,540\,106\,951\,871\,657\,754\,011

About

Examples	8
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