Title: Data in MathCAD
1Data in MathCAD
2Data in tables
- Tables are analogous to matrices
- The numbers of columns and rows can be
dynamically changed (in contrast to matrix) - To enter table
- Menu Insert/Data/Table (MC v. 15)
- In placeholder type variable name which will be
assigned to table - In cells type the values
- Each rows and columns must contains the same
number of data. If data are missing the value 0
will be assigned - Access to data in table is identical to matrix.
3Data in tables
4Data in tables
- Row/column appears in matrix when only 1 data is
inserted into the cell - Matrix size specified cell in the lowest row
and in last column - Unfilled cells contains 0
- Once specified cell can not be removed!
- To overcome problem create new matrix with
correct number of rows i and columns j using
5External data sources Data in files
- The most popular file formats accepted by
MathCAD - Text files
- Excel worksheets
- To insert text file containing data
- Menu Insert/Data/File Input
- Chose file format
- Browse to the file location
- In the appeared placeholder type variable name
that will be assigned to the contents of file
6Inserting the text file
7Inserting the text file
- Changes in the text file location
8Inserting the Excel worksheets
- A range of Excel cells can be inserted into the
MathCAD - There can be more then one range in single
insertion - One variable is being assigned to one range
- All variables forms a vector
- Cells can contain numbers as well as text (in
contrast to table and text files, ver. 2001) - Worksheets can be edited (double-click) using all
Excel functions (object embedded -Excel has to be
installed in system).
9Inserting the Excel sheets
- To insert worksheet
- Menu Insert/Component/Excel
- Browse file or create new
- Choose number of ranges for input and output
(relatively to Excel worksheet). If no data have
to be inserted into the Excel worksheet type
inputs number 0 - Type ranges corresponding to outputs e.g.
A1B10 (if worksheet name is different from
Sheet1 type sheet name e.g. Sheet4!A1B10) - In placeholder(s) type variable(s)
- Number of outputs/inputs and range of cells can
be edited in properties of insertion
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11MathCAD files as data source in MathCAD
- MathCAD can use data included in other MathCAD
files - Access to data is possible after embedding
MathCAD file - menu Insert/References,
- Brows file on disc or type file address
- Below the insertion all data, definitions,
assignment from inserted file are valid in the
present document - Problem matrix/vector elements numbers when
array origin is changed.
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13Data analysis and optimisation
14definition
- Approximation is a part of numerical analysis. It
is concerned with how functions f(x) can be best
approximated (fitted) with another functions F(x)
15application
- Simplifying calculations when original function
f(x) is defined by complicated expression - design of continuous dependency when function
f(x) is described on discrete set of arguments.
If the form of approximating function is given
only values of function parameters showing the
best approximation have to be determine.
16types of approximation
- Interpolating approximation
- Uniform approximation
- Square-mean approximation
17Interpolating approximation
- Needs to satisfy condition function given f(x)
and approximating function F(x) have the same
values on the set of nodes and (sometimes) the
same values of derivatives (if given) too.
18Uniform approximation
- Function F(x) approximating function f(x) in the
range a,b, satisfying condition maximal
residuum is set to minimum
19Square-mean approximation
- Approximating function is determined by the use
of condition - Geometrically condition means The area between
curves representing functions have to reach
minimum.
20Square-mean approximation
- Condition for discreet set of arguments
21Square-mean approximation in MathCAD
- Function
- minimize(function, p1, p2,...)
- can be used to determine parameters of
approximating function minimizing the sum of
square deviations between values given in the
table and calculated from the function. - function calculates the sum of square deviations
as a function of parameters. - p1, p2 parameters of approximating function
22Square-mean approximation in MathCAD
- Approximating algorithm
- Insert data to be approximate
- Build the approximating function
- Create a counting variable with values from 0 to
number of data minus 1 - Build function that calculates sum of square of
deviations with parameters of approximating
function as variables - Assign starting values of parameters
- Use the function minimize.
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24- Advantageous of minimize function
- simple
- explicit
- suitable for any approximating function
- can be used in optimisation problem solving
25Other MathCAD tools for approximation
26genfit
- Syntaxcgenfit(X, Y, c0, F)
- X vector of independent values from data set
- Y - vector of dependent values from data set
- c0 starting vector of searched parameters
- F vector function of independent variable and
vector c, consists of approximating function and
its derivatives on parameters - c - vector of searched parameters
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28regress
- Approximation by polynomial function
- Syntax Z regress(X, Y, s)
- X vector of independent values from data set
- Y - vector of dependent values from data set
- s polynomial degree
- Z result vector, s1 last elements are
parameters of polynomial (starting from x0
parameter)
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30Linear, cubic, polynomial - splineinterpolating
approximation
- Approximation by linear (cubic etc.) spline
function - Syntax Zlspline(X, Y) (cspline, pspline)
- X vector of independent values from data set
- Y - vector of dependent values from data set
- Data in set has to be sorted! Manually or by use
of function csort Wcsort(W,i), W matrix of
data, i nr of ordering column - Z result vector of parameters of cubic spline
function
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32Interpreting function
- Operates on vectors obtained from regress and
spline family functions - Building the continuous approximating function on
the base of determined parameters - Syntax F(x)interp(Z, X, Y, x)
- Z vector given by approximating function
- X vector of independent values from data set
- Y - vector of dependent values from data set
- x independent values
- Interpreting function is implicit but can be
derivated and integrated
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34MathCAD
35Animation
- Enhances understanding of numerical output
- Animations shows time dependences in real time,
fastened or slowed down. - Make impression on viewers
36Animation
- Base of animation is variable called
- FRAME
- Built in, integer type
- Definition only in dialog box of animation
- Parameters are
- starting value
- ending value
- frame rate (frames per seconds)
37Creating animation
- Solve a problem (e.g. create function)
- Assign counting variable to FRAME
- Define a variable representing each state of
solution assigned to counting variable - Create plot to animate
- Display animate dialog box and select plot
- Define FRAME variable parameters
- Choose format of compression for animation
recording. - Press Animate button.