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API, Reference Guides
Overview of external readers and the Altair Binary Format, the generic ASCII reader, running applications in batch mode, using Tcl/Tk commands, translators, and result math.
Templex and Math Reference Guide
Math Reference
Mathematical functions and operators, including syntax, operators and specific information about each function.
Functions and Operators
Overview of functions and operators.
Standard Functions
List of standard functions.
cdf
Returns the cumulative probability that a real-valued random variable x with a given continuous distribution will be found to have a value less than or equal to x.

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API, Reference Guides
Overview of external readers and the Altair Binary Format, the generic ASCII reader, running applications in batch mode, using Tcl/Tk commands, translators, and result math.
- Extensions
  Extensions are programs integrated with the application to enhance or extend the user experience.
- External Readers and Altair Binary Format
  Altair Binary Format (ABF) is the standard binary format read by the program. A library called abflib allows you to create files in ABF.
- Generic ASCII Reader
  A generic ASCII reader is now available which allows you to bring custom results directly into HyperView. The Altair ASCII format is useful for reading the results of any in-house or propriety codes which are saved in a generic format.
- Batch Mode
  Batch mode allows you perform a series of operations outside the program interface.
- External Resources
  External resources can be registered in preference files, session files, or Templex files. If an external resource is registered in a program session, it is automatically registered in the session file when the session is saved.
- Python API
  The Python API documentation for HyperMesh applications.
- Tcl/Tk Commands
  The application's scripting interface is a set of Tcl/Tk commands that follow a simple and consistent syntax.
- Translators
  Translators are utilities that are run from the command line of the operating system to convert various types of files into different formats.
- Result Math
  XML commands in the Result Math Module.
- HWC Console
  Record playback workflows in the application.
- HyperMesh Report
- Task Manager
  Use the Task Manager to load an XML file that defines tasks and their attributes.
- HyperMesh
- MotionView
- Templex and Math Reference Guide
  - Templex Reference
    Templex is a general purpose text and numeric processor which generates output text based on guidelines defined in a template.
  - Math Reference
    Mathematical functions and operators, including syntax, operators and specific information about each function.
    - Data Types
      The mathematical functions accept arguments of different data types.
    - Order of Precedence
      The standard mathematical order of operations is followed when an expression is evaluated.
    - Functions and Operators
      Overview of functions and operators.
      - Operators
        List of operators.
      - Standard Functions
        List of standard functions.
        abs
        Absolute value.
        absarea
        The total area between the curve and the independent axis regardless of sign.
        abstorelative
        Changes the reference to a file from absolute (root directory) to relative. The relative path will be the difference between path_1 and path_2.
        acos
        Trigonometric arccosine function.
        akima
        Akima spline interpolation function.
        akimaderivative
        Returns the akimaderivative values for a given new x vector.
        array
        Creates an empty vector or matrix.
        asc
        ASCII value.
        asdcal
        Amplitude Spectral Density function, which supports blocks, windows, overlap, and averages.
        asin
        Trigonometric arcsine function.
        atan
        Trigonometric arctangent function.
        atan2
        Trigonometric arctangent (quadrant dependent) function.
        atoi
        ASCII to integer converter.
        avgdev
        Average deviation from the mean.
        batch
        Batch digital filter.
        batchpolyfit
        Polyfit plus batch digital filter. batchpolyfit fits a polynomial to the data and subtracts that polynomial from the data, leaving only the residuals. It batch filters the residuals, then adds the polynomial back in.
        bins
        Creates bins for the probability density function, pdf.
        blackman
        Blackman windowing function.
        blockfftimag
        The imaginary component of a Fast Fourier Transform (FFT) calculated using blocking.
        blockfftmag
        The magnitude of a Fast Fourier Transform (FFT) calculated using blocking.
        blockfftphase
        The phase angle of a Fast Fourier Transform (FFT) calculated using blocking.
        blockfftreal
        The real component of a Fast Fourier Transform (FFT) calculated using blocking.
        blockfrfimag
        Imaginary component of a Frequency Response Function (FRF) calculated using blocking.
        blockfrfmag
        The magnitude of a Frequency Response Function (FRF) calculated using blocking.
        blockfrfphase
        Phase angle of a Frequency Response Function (FRF) calculated using blocking.
        blockfrfreal
        Real component of a Frequency Response Function (FRF) calculated using blocking.
        cat
        Concatenation function.
        catoffset
        Attach vectors function.
        cdf
        Returns the cumulative probability that a real-valued random variable x with a given continuous distribution will be found to have a value less than or equal to x.
        cellmax
        Returns the maximum value of the referenced cells.
        cellmean
        Calculates the mean value of the referenced cells.
        cellmin
        Returns the minimum value of the referenced cells.
        cellrange
        Returns a vector of all referenced cell values of type scalar. This can be used to draw curves in HyperGraph based on cell values.
        cellrms
        Calculates the rms (the square root of the arithmetic mean of the squares) of the referenced cells.
        cellrss
        Calculates the rss (square root of the arithmetic sum of the squares) of the referenced cells.
        cellsum
        Calculates the sum of the referenced cells.
        centroid
        Center of the area under a curve.
        chr
        Returns the corresponding ASCII character for a given number.
        cint
        Closest integer function.
        coherence
        Coherence function.
        convert
        Converts string to integer value.
        correl
        Returns the correlation coefficient of the given curve vectors.
        cos
        Trigonometric cosine function.
        cosh
        Hyperbolic cosine function.
        cr
        Inserts a carriage return character.
        curveenv
        Curve Envelope Templex function, which allows you to create a minimum and maximum envelope across given set of curves.
        curvelabel
        Returns the label of a curve being exported.
        curvelength
        Length of a segmented path along a curve.
        curveproduct
        Multiplies multiple curves which have overlapping x vectors.
        curvesum
        Adds multiple curves which have overlapping x vectors.
        curvesync
        Creates a new x vector from the x vectors of multiple curves in the range between the maximum of all minima and the minimum of all maxima. All curves must have an overlapping x range. The returned vector contains only the points of the vector which has the most points in this range.
        curvex
        Returns the X vector of a curve being exported or a curve in the current plot.
        curvey
        Returns the Y vector of a curve being exported or a curve in the current plot.
        date
        System date function.
        dba
        Acoustic A-weighting function.
        dbb
        Acoustic B-weighting function.
        dbc
        Acoustic C-weighting function.
        dbu
        Acoustic U-weighting function.
        dcorr
        Cross correlation function using discrete Fourier Transforms (dFT).
        delta
        The difference between the first and last points of a vector.
        derivative
        Curve derivative function.
        determinant
        Matrix determinant function.
        deviation_metric
        Calculates the deviation metric for dynamic stiffness, loss angle curves.
        dfreq
        Frequency vector function.
        dftimag
        Imaginary component of a discrete Fourier Transform (dFT) function.
        dftmag
        Magnitude of a discrete Fourier Transform (dFT) function.
        dftphase
        Phase angle of a discrete Fourier Transform (dFT) function.
        dftreal
        Real component of a discrete Fourier Transform (dFT) function.
        dtor
        Convert degrees to radians.
        eigvalimag
        Imaginary eigenvalues of a matrix.
        eigvalreal
        Real eigenvalues of a matrix.
        eigvecimag
        Imaginary eigenvectors of a matrix.
        eigvecreal
        Real eigenvectors of a matrix.
        eval
        Evaluates the contents of a string as an expression.
        exp
        Exponential function.
        expfit
        Exponential least-squares curve fit function.
        extern
        fcorr
        Cross correlation function using Fast Fourier Transforms (FFT).
        fftimag
        Imaginary component of a Fast Fourier Transform (FFT) function.
        fftmag
        Magnitude of a Fast Fourier Transform (FFT) function. FFTMag performs a frequency analysis on a single curve's data and produces an output that indicates the magnitude of the frequency content of the input file.
        fftphase
        Phase angle of a Fast Fourier Transform (FFT) function.
        fftreal
        Real component of a Fast Fourier Transform (FFT) function.
        fileclose
        Closes an open file.
        fileexists
        Tests whether a file exists.
        filefindstring
        Locates a string in an open file.
        fileinfo
        Returns information about a file.
        fileopen
        Opens a file for reading or writing.
        fill
        Passes a source string through the Templex parser.
        fold
        Magnitude folding function.
        freeze
        Locks the value of the specified variable.
        freq
        Frequency vector function.
        frfimag
        Imaginary component of a Frequency Response Function (FRF) function.
        frfmag
        Magnitude of a Frequency Response Function (FRF) function.
        frfphase
        Phase angle of a Frequency Response Function (FRF) function.
        frfreal
        Real component of a Frequency Response Function (FRF) function.
        getenv
        Returns the value of an environment variable.
        getval2
        Returns the value of a vector at the same index of a specified value in a corresponding vector.
        getvalue
        Gets a value corresponding to a name for a particular data channel.
        hamming
        Hamming windowing function.
        hanning
        Hanning windowing function.
        hilbert
        Hilbert transform function.
        idft
        Real component of an inverse Discrete Fourier Transform (IDFT) function.
        ifft
        Real component of an inverse Fast Fourier Transform (iFFT) function.
        iffunc
        Chooses between two values based on a third value.
        indexofmax
        Index of vector maximum value function.
        indexofmin
        Index of vector minimum value function.
        int
        Integer function.
        integral
        The integral function.
        intercepts
        intersect
        invcdf
        Returns the standard normal value for a given cumulative (Gaussian) probability.
        inverse
        Matrix inversion function.
        irfilter
        Impulse response filter function.
        itoa
        Integer to ASCII converter.
        kaiser
        Kaiser-Bessel windowing function.
        lininterp
        Linear interpolation function.
        log, ln
        Natural logarithm (base e).
        log10
        Common logarithm (base 10).
        logint
        Logarithmic interpolation function.
        mag
        Magnitude function.
        max
        Maximum value function.
        maxindex
        Maximum index of the vector.
        mean
        Statistical mean function.
        median
        Statistical median of a data set.
        mid
        Returns a subrange out of a string.
        min
        Minimum value function.
        mstep
        For a given set of x values, returns a vector of values that smoothly transitions from (or steps from) one level of y value to another. This function can create a vector that has many steps and can use different forms of interpolating step functions.
        nr
        The Newton-Raphson method uses an iterative process to approach one root of a function.
        nonlinfit
        Returns a vector of fitted points according to the equation specified.
        numcurves
        numpts
        The element counting function.
        OLC
        The OLC function is able to calculate both the Occupant Load Criteria (OLC) and OLC++. OLC++ combines OLC with the time of maximum deformation (Tv=0) and the sliding mean integral over a window of 25 ms (SM25), as shown in the formulas below.
        parzen
        Parzen windowing function.
        pdf
        Probability density function.
        peaks
        Determines all of the local extreme values of a vector.
        polyfit
        Polynomial least squares curve fit function.
        polyrootsimag
        Imaginary roots of a polynomial.
        polyrootsreal
        Real roots of a polynomial.
        polyval
        Evaluates a given polynomial using specified coefficients and datapoints.
        projectcurvetosurface
        Projects a curve onto a surface or waterfall plot and returns the specified channel’s values of the projection in the specified direction.
        psd
        Power spectral density function.
        psd5
        Modified power spectral density function.
        rand
        Random number generator.
        read
        Returns a vector from the specified data file.
        readsim
        Returns a vector or matrix of values based on the channel name (string), not on the index. Indices will only be used for specifying the range of the returned vector.
        readsubcase
        Returns a vector from the specified data file.
        relativetoabs
        Changes the reference to a file from relative to absolute.
        reldisp
        The relative displacement (reldisp) math function allows you to transform vector results from time history or animation result files according to a coordinate system defined by three nodes from the same result file.
        remove_succ_dup_indx
        Takes a vector and returns a vector containing the indices of the points from the input vector, which are non-duplicate points (for successive points).
        replace
        Replaces one substring with another.
        resampresp
        Creates a vector of resampled response values.
        resamprevs
        Creates a vector of resampled revolution values.
        resamptime
        Creates a vector of resampled time values.
        resvector
        Returns a vector or matrix of values at a given timestep.
        rms
        Root mean square of a vector.
        rrs
        The rrs (Random Response Spectrum) is a standard mathematical function that is commonly used in random load analyses for space systems. The rrs is defined as the rms response of a 1-DOF system as a function of its natural frequency for a given damping ratio.
        rtod
        Convert radians to degrees.
        saefilter
        SAE class filter.
        sgcm
        Returns a vector with four values: combined metric, SG combined metric, magnitude, and phase difference.
        signedarea
        Calculates the area between the curve and the independent axis according to sign.
        sin
        Trigonometric sine function.
        sinh
        Hyperbolic sine function.
        size
        Computes the dimensions of an expression.
        skewness
        Skewness of a distribution.
        smean (sliding mean integral)
        Sliding mean integral filter. Smooths the curve by moving a sliding window over the curve and calculating the mean value. This is done by calculating the area of the sliding window regardless of whether or not there are points at the window boundary, and divides this area by the window size.
        sort
        Sorts arrays based on a key.
        spline
        Cubic spline interpolation function.
        srs
        Shock response system standard mathematical function that is commonly used in space systems, with acceleration time history as the base input.
        sqrt
        Algebraic square root function.
        stfreq
        Creates a vector of frequency values for use in a short time waterfall plot.
        stft
        Creates a vector of short time Fourier transform outputs.
        storder
        Creates a vector of order values for use in a short time waterfall plot.
        strchr
        Searches forward for a character within a string starting at the beginning of an array.
        stringarray
        Generates a structure for a string array of a specified size.
        strlen
        Returns the length of the string.
        strrchr
        Searches backward for a character within a string starting at the end of the string
        strsegrevs
        Creates a vector of unevenly spaced times that segment an input time vector for use in a short time resampled waterfall plot.
        strsegrps
        Creates a vector of unevenly spaced times that segment an input time vector for use in a short time resampled waterfall plot.
        strstr
        Searches for a substring within a string starting at the beginning of the array.
        stsegrps
        Creates a vector of unevenly spaced times that segment an input time vector for use in a short time waterfall plot.
        stsegtime
        Creates a vector of evenly spaced times that segment an input time vector for use in a short time waterfall plot.
        subrange
        Vector subrange extractor.
        sum
        The algebraic sum function.
        suppress
        Removes spikes from a curve.
        sysid
        Returns an ID string identifying the system on which Templex is being run.
        system
        Passes a Unix command to a shell for execution and returns the result.
        tan
        Trigonometric tangent function.
        tanh
        Hyperbolic tangent function.
        tcleval
        Executes a Tcl statement or an array of statements.
        tclevalfile
        Executes a Tcl script file (or list of script files).
        tclgetvar
        Retrieve the value of a Tcl variable as a string.
        thaw
        Unlocks the values of the specified variable.
        time
        System time function.
        timer
        Returns the elapsed time.
        tolower
        Converts a string to lowercase.
        toupper
        Converts a string to uppercase.
        typeof
        Returns the type of variable and identifies it as scalar, vector, or a string.
        variance
        Describes the spread of distribution.
        vtdft
        Creates a vector of variable time Discrete Fourier transform outputs.
        vtfreq
        Creates a vector of frequency values for use in a variable time waterfall plot.
        vtorder
        Creates a vector of frequency values for use in a variable time waterfall plot.
        vtsegrps
        Creates a vector of unevenly spaced times that segment an input time vector for use in a variable time waterfall plot.
        vtsegtime
        Creates a vector of evenly spaced times that segment an input time vector for use in a variable time waterfall plot.
        welch
        Welch windowing function.
        wifac
        Weighted Integrated Factor returns a vector with four values: peak, peak time, wifac, and total.
        zerocrossings
        The number of sign reversals in a vector.
      - External Functions
        List of external functions.
    - Signal Processing
      Overview of Fast Fourier Transform, phenomena, windowing, Filtering Frequency Response, functions, blocking, and Hilbert Transform.
- Script and Model Library
  The Script and Model Library is a database of freely accessible scripts and models posted by users and Altair engineers.

cdf

Returns the cumulative probability that a real-valued random variable x with a given continuous distribution will be found to have a value less than or equal to x.

Syntax

cdf(x

Argument

x: Real-valued random variable.

Example


Templex Expression	Result
`cdf(0) =`	`0.5`
The cumulative probability for an event with a standard normal value of 0 is 50%.

Comments

The cumulative distribution function: