Re: List of Interpolated functions inside plot

• To: mathgroup at smc.vnet.net
• Subject: [mg24844] Re: List of Interpolated functions inside plot
• From: "Allan Hayes" <hay at haystack.demon.co.uk>
• Date: Wed, 16 Aug 2000 03:24:09 -0400 (EDT)
• References: <8naq28\$esp@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Chris,

After
xyinterp[m_] := Interpolation[Table[{x, Sin[m x]}, {x, -5, 5, 0.25}]];

Plot[Table[xyinterp[m][x], {m, 1, 10, 3}], {x, -5, 5}]

does not work because it evaluates as follows:
the unevaluated
Table[xyinterp[m][x],{m,1,10,3}]
is examined; it is not a list; so  Mathematica expects that when x is set to
a real number then
Table[xyinterp[m][x],{m,1,10,3}]
will be a real number -- which it is not.

But

Plot[Evaluate[Table[xyinterp[m][x], {m, 1, 10, 3}]], {x, -5, 5}]

works because before any check is made,
Evaluate[Table[xyinterp[m][x],{m,1,10,3}]]
evaluates to
{xyinterp[1][x],  xyinterp[4][x],xyinterp[7][x], xyinterp[10][x] };
so the check finds a list and evaluates this successfully.

However please note that this way x might pick up an existing definition

x = 4;

Plot[Evaluate[Table[xyinterp[m][x], {m, 1, 10, 3}]], {x, -5, 5}]

To avoid this we can use Block

Block[{x}, Plot[Evaluate[Table[xyinterp[m][x], {m, 1, 10, 3}]], {x, -5,
5}]]

--
Allan
---------------------
Allan Hayes
Mathematica Training and Consulting
Leicester UK
www.haystack.demon.co.uk
hay at haystack.demon.co.uk
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565

"Krautschik, Chris G" <krautschikc at intel.co.jp> wrote in message
news:8naq28\$esp at smc.vnet.net...
> If have defined the following interpolation for arbitrary integer m:
>
> xyinterp[m_] := Interpolation[Table[{x, Sin[m x]}, {x, -5, 5, 0.25}]];
>
> I can plot a number of the interpolated functions on one plot as follows:
>
> Plot[ {xyinterp[1][x], xyinterp[2][x], xyinterp[3][x]}, {x,-5,5} ];
>
> Let's say I want to plot a large number of the functions of integer m but
I
> like to use the Table command since typing can become quite tedious:
>
> Then
>
> Plot[ Table[xyinterp[m][x], {m, 1, 10, 3}],{x,-5,5} ]
>
> doesn't work because the value of x needs to be defined pior to the
> execution of the Table command. I have tried various forms of Hold but
that
> doesn't seem to work.
>
> Any help or suggestions on how to make this work would be appreciated.
>
> thanks,
> Chris
>
>
>

```

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