Difference between revisions of "Interpolation functions"

Revision as of 00:11, 13 December 2015

Analytica User GuideMore Array FunctionsInterpolation functions

These three functions interpolate across arrays. Given arrays y and x with a common index i, these functions interpolate a value for y corresponding to value v along the x axis.

LinearInterp() and CubicInterp() use these variables:

Index_a:

a	b	c

Index_b:

1	2	3

Array_a:

	Index_b ▶
Index_a: ▼	1	2	3
a	7	-3	1
b	-4	-1	6
c	5	0	-2

Stepinterp(x, y, v, i)

Returns the element or slice of array y for which v has the smallest value less than or equal to x. x and y must both be indexed by i, and x must be increasing along index i. If v is greater than all values of x, it returns the element of y for which x has the largest value.

When an optional parameter, LeftLookup, is specified as True, it returns the element or slice of y corresponding to the largest value in x that is less than or equal to v.

If v is an atom (scalar value), the result is an array indexed by all indexes of a except x’s index. If v is an array, the result is also indexed by the indexes of v.

If the first parameter x is an index of y, the fourth parameter is optional. Stepinterp(x, y, v) is similar to y[x = v] except that y[x = v] selects based on v being equal to x, while Stepinterp(x, y, v) selects based on v being greater than or equal to x.

Stepinterp() can be used to perform table lookup.

Library: Array

Examples: To see the values in Car_prices corresponding to Years >= 2007.5:

Stepinterp(Years, Car_prices, 2007.5, Years) →

VW	Honda	BMW
19K	22K	30K

Here v is a list of two values:

Stepinterp(Years, Car_prices, [2007, 2008], Years) →

VW	Honda	BMW
2007	18K	20K	28K
2008	19K	22K	30K

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 |}
-Array_a:
+<code>Array_a:</code>
 {| class="wikitable"
 !
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 !a
 |7
-|-3
+| -3
 |1
 |-
 !b
-|-4
+| -4
-|-1
+| -1
 |6
 |-
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 |5
 |0
-|-2
+| -2
 |}
+==Stepinterp(x, y, v, i)==
+Returns the element or slice of array '''y''' for which '''v''' has the smallest value less than or equal to '''x'''. '''x''' and '''y''' must both be indexed by i, and x must be increasing along index '''i'''. If '''v''' is greater than all values of '''x''', it returns the element of '''y''' for which '''x''' has the largest value.
+When an optional parameter, '''LeftLookup''', is specified as True, it returns the element or slice of '''y''' corresponding to the largest value in '''x''' that is less than or equal to '''v'''.
+If '''v''' is an atom (scalar value), the result is an array indexed by all indexes of '''a''' except '''x'''’s index. If '''v''' is an array, the result is also indexed by the indexes of '''v'''.
+If the first parameter '''x''' is an index of '''y''', the fourth parameter is optional. '''Stepinterp(x, y, v)''' is similar to '''y[x = v]''' except that '''y[x = v]''' selects based on '''v''' being ''equal'' to '''x''', while '''Stepinterp(x, y, v)''' selects based on '''v''' being ''greater than or equal'' to '''x'''.
+'''Stepinterp()''' can be used to perform table lookup.
+'''Library:''' Array
+'''Examples:''' To see the values in <code>Car_prices</code> corresponding to <code>Years >= 2007.5</code>:
+<code>Stepinterp(Years, Car_prices, 2007.5, Years) &rarr;</code>
+{| class="wikitable""
+! VW
+! Honda
+! BMW
+|-
+| 19K
+| 22K
+| 30K
+|}
+Here '''v''' is a list of two values:
+<code>Stepinterp(Years, Car_prices, [2007, 2008], Years) &rarr;</code>
+{| class="wikitable""
+! VW
+! Honda
+! BMW
+|-
+! 2007
+| 18K
+| 20K
+| 28K
+|-
+! 2008
+| 19K
+| 22K
+| 30K
+|}
 ==See Also==
 <footer>Relational tables and multiD arrays / {{PAGENAME}} / Fourier Transform</footer>