Difference between revisions of "StepInterp"

Revision as of 23:10, 22 January 2016

StepInterp(xi, yi, x, i)

Given arrays of numerical coordinates «xi» and «yi», indexed by «i», it returns the y value corresponding to the smallest value of xi>=x. Thus, it returns a step function, with risers at each value of «xi». If optional parameter «leftLookup» is True, it returns the y value corresponding to the largest value of xi<=x. «xi», «yi», and «x» must be numbers. The numbers in «xi» must be in increasing order. If «xi» is itself a simple index, «yi» must be indexed by «xi», and parameter «i» may be omitted. Otherwise, «i» must be a common index of «xi» and «yi». «x» may be a scalar or array. If «x» is less than the smallest (and first) value in «xi» (x < xi[@i = 1]), it returns that smallest value. Similarly, if «x» is larger than the last (largest) value in «xi» (x > xi[@i = Size(i)]), it returns that largest value.

If «x» is a single value, the result of StepInterp is an array indexed by all indexes of «yi» except «xi»’s index. If «x» is an array, the result of Stepinterp is also indexed by the indexes of «x».

StepInterp is similar to Subscript(u1, i, u2); however, Subscript selects based on the index value being equal to «x», while StepInterp selects based on the array value being greater than or equal to «x».

StepInterp can be used to perform table lookup.

Examples

The following examples use User Guide Examples.

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

StepInterp(Years, Car_prices, 2007.5, Years) →

Car_type ▶
VW	Honda	BMW
19	22	30

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

Optional Parameters

i

Specifies the common index of «xi» and «yi». You can omit this, if «xi» is itself an index of «yi».

extrapolationMethod

Specifies the value to return if «x» is outside the values of «xi»:

1: Use the «yi» for nearest «xi» (default method)
2: Return Null
3: Same as 1 (nearest point) for normal evaluation, but Null during optimization.

leftLookup

When the optional parameter, «leftLookup», is specified as True, StepInterp returns the element or slice of «yi» corresponding to the largest value in «xi» that is less than or equal to «x».

The two graphs interpolate from the same set of (xi, yi) points, with different settings for «leftLookup».


`leftLookup: False` (default)	`leftLookup: True`

@@ Line 2: / Line 2: @@
 [[Category:Doc Status D]] <!-- For Lumina use, do not change -->
 [[Category:Array Library]]
 == StepInterp(xi, yi, x, ''i'') ==
-Given  arrays of numerical coordinates «xi» and «yi», indexed by «i», it returns the y value corresponding to the smallest value of xi>=x.  Thus, it returns a step function, with risers at each value of «xi». If optional parameter «leftLookup» is <code>True</code>, it returns the y value corresponding to the largest value of xi<=x. «xi», «yi», and «x» must be numbers. The numbers in «xi» must be in increasing order. If «xi» is itself a simple index, «yi» must be indexed by «xi», and parameter «i» may be omitted.  Otherwise, «i» must be a common index of «xi» and «yi». «x» may be a scalar or array. If «x» is less than the smallest (and first) value in «xi» (x < xi[@i=1]), it returns that smallest value. Similarly, if «x» is larger than the last (largest) value in «xi» (x > xi[@i=Size(i)]), it returns that largest value.
+Given  arrays of numerical coordinates «xi» and «yi», indexed by «i», it returns the y value corresponding to the smallest value of xi>=x.  Thus, it returns a step function, with risers at each value of «xi». If optional parameter «leftLookup» is <code>True</code>, it returns the y value corresponding to the largest value of xi<=x. «xi», «yi», and «x» must be numbers. The numbers in «xi» must be in increasing order. If «xi» is itself a simple index, «yi» must be indexed by «xi», and parameter «i» may be omitted.  Otherwise, «i» must be a common index of «xi» and «yi». «x» may be a scalar or array. If «x» is less than the smallest (and first) value in «xi» (''x < xi[@i = 1]''), it returns that smallest value. Similarly, if «x» is larger than the last (largest) value in «xi» (''x > xi[@i = Size(i)]''), it returns that largest value.
 If «x» is a single value, the result of [[StepInterp]] is an array indexed by all indexes of «yi» except «xi»’s index. If «x» is an array, the result of [[Stepinterp]] is also indexed by the indexes of «x».
@@ Line 16: / Line 17: @@
 To see the values in <code>Car_prices</code> corresponding to <code>Years >= 2007.5</code>:
-<code>StepInterp(Years, Car_prices, 2007.5, Years) →</code>
+:<code>StepInterp(Years, Car_prices, 2007.5, Years) &rarr;</code>
-{| class="wikitable"
+:{| class="wikitable"
-!! colspan="3" style="text-align: left;" | Car_type &#9654;
+!! colspan="3" | Car_type &#9654;
 |-
 ! scope="col"| VW
@@ Line 31: / Line 32: @@
 Here '''v''' is a list of two values:
-<code>StepInterp(Years, Car_prices, [2007,2008], Years) →</code>
+:<code>StepInterp(Years, Car_prices, [2007, 2008], Years) &rarr;</code>
-{| class="wikitable"
+:{| class="wikitable"
 |-
 ! scope="col"|
@@ Line 56: / Line 57: @@
 === ''extrapolationMethod'' ===
 Specifies the value to return if «x» is outside the values of «xi»:
-*1: Use the «yi» for nearest «xi» (default method)
+*<code>1</code>: Use the «yi» for nearest «xi» (default method)
-*2: Return [[Null]]
+*<code>2</code>: Return [[Null]]
-*3: Same as 1 (nearest point) for normal evaluation, but [[Null]] during optimization.
+*<code>3</code>: Same as <code>1</code> (nearest point) for normal evaluation, but [[Null]] during optimization.
 === ''leftLookup'' ===
 When the optional parameter, «leftLookup», is specified as <code>True</code>, [[StepInterp]] returns the element or slice of «yi» corresponding to the largest value in «xi» that is less than or equal to «x».
-The two graphs interpolate from the same set of ''(xi,yi)'' points, with different settings for «leftLookup».
+The two graphs interpolate from the same set of ''(xi, yi)'' points, with different settings for «leftLookup».
 {|
 | [[Image:Stepinterp-graph.png|450px]]
 | [[Image:StepInterp2-graph.png|450px]]
 |-
-! leftLookup:False (default)
+| <center><code>leftLookup: False</code> (default) </center>
-! leftLookup:True
+| <center><code>leftLookup: True</code></center>
 |}