Data in MathCAD

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Data in MathCAD
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Data 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.

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Data in tables
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Data 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

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External 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

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Inserting the text file
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Inserting the text file

• Changes in the text file location

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Inserting 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).

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Inserting 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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MathCAD 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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Data analysis and optimisation

• Approximation

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definition

• 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)

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application

• 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.

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types of approximation

• Interpolating approximation
• Uniform approximation
• Square-mean approximation

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Interpolating 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.

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Uniform approximation

• Function F(x) approximating function f(x) in the
  range a,b, satisfying condition maximal
  residuum is set to minimum

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Square-mean approximation

• Approximating function is determined by the use
  of condition
• Geometrically condition means The area between
  curves representing functions have to reach
  minimum.

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Square-mean approximation

• Condition for discreet set of arguments

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Square-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

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Square-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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• Advantageous of minimize function
• simple
• explicit
• suitable for any approximating function
• can be used in optimisation problem solving

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Other MathCAD tools for approximation
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genfit

• 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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regress

• 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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Linear, 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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Interpreting 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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MathCAD

• The animation

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Animation

• Enhances understanding of numerical output
• Animations shows time dependences in real time,
  fastened or slowed down.
• Make impression on viewers

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Animation

• 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)

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Creating 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.