an introduction to mathcad animation, interpolation and other pretty pictures

An Introduction to MathCAD

Animation, Interpolation and other pretty pictures

2MathCAD #7 dpl 2001

AnimationExample

Example from our LCR circuit


Animation #2Basics

Use FRAME variable FRAME automatically set by

mathCAD for each frame of animation

Select View|Animation… to bring up animation dialog

Give start & end values for FRAME

Select area to animate Select Animate to produce Save As… to create .avi file


Animation #3Hints

“Error initialising Video Stream” => Nothing Selected

May want to scale FRAME Animations can:

– Take a long time to create– Produce big files

Windows video player allows thumb bar to step forward & back


Animation #4More Hints

Fix scale on graphs Don’t need to include

calculations in animation Echo FRAME= in shot If scaling, echo scaled variable For frequency plots, scale

FRAME thus:PtsPerDecade 5

10

FRAME

PtsPerDecade


Vector Field Plots #1

Plot matrix of complex numbers Each point shown as vector Plot scaled so that largest vector

is gap between points Useful for:

– Electric fields– Magnetic fields– Dynamic Flows– Plotting Gradient of functions


Vector Field Plots #2x 0 19 y 0 19

Mx y y ei x 0.3

M


Data Analysis #1Get data from file

Read data in from datafile Use either:

– Insert|Component|File Read or Write & follow the wizard

– READPRN(“filename”) Reads data from file into vector

or matrix File Read component offers

many more file types


Data Analysis #2Select the data we want

Use matrix functions to select data we are interested in

Rows(M) & Cols(M) to get size of data array

Submatrix(M,rs,rf,cs,cf) to select rectangular chunk

M<x> to select column Csort to sort array Augment & stack to build

arrays


Data Analysis #3Smoothing Data

medsmooth(vy,n) returns vy smoothed with running medians

smootheds

s 50 medsmooth data s( )

600 610 620 630 640 6500

200

400

600

800

smootheds

i

i


Data Analysis #4Linear regression

Slope & intercept functions take vectors of X & Y values

0 20 40 60 80 1000

200

400

600

800

Y

X

intercept X Y( ) 4.914

slope X Y( ) 6.955


Data Analysis #5Interpolation

2 stage process– Fit polynomial through points

cspline – cubic spline Bspline – B-spline

– Interpolate using polynomial obtained in stage 1

interp


Cubic Spline fit & Interpolated Fit

X-Y data Cubic spline interpolation

90.693003

0.462302

Y

fit z( )

max X( ) 1min X( ) 1 X z


Function Fitting

Cspline & Bspline fit smooth curve through data points

In physical modelling, we know the shape of the function to fit, just need parameters

Example:– Response of photon counting

detector


Function FittingExample #1

Determine parameters &

1 107

1 106

1 105

1 104

1 103

0.01 0.1 10.1

1

10

100

1 103

1 104

1 105

Data1

Data0

Fit to function f x( ) x e x



Rewrite f(x) and derivatives Replace a,b by u0, u1… Find partial derivatives of f(x) Create vector of function & pds

f x( ) x e x

x e xd

dx exp x( )

F x u( )

u0

x eu1

x

x exp u1

x

u0

x2 exp u1

x

x e xd

d x2 exp x( )


Function fittingExample #3

Create vector of guess values

guess5 105

7

Call genfit to solve Define function using params

params genfit Data 0 Data 1 guess F

f x( ) F x params( )0



Plot f(x) against data

1 107

1 106

1 105

1 104

1 103

0.01 0.1 10.01

0.1

1

10

100

1 103

1 104

1 105

2.451 104

0.066

Data1

f Data0

0.351.542 10

7 Data0

an introduction to mathcad animation, interpolation and other pretty pictures

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