Xi-Language Reference: Mathematical Functions

    • abs (Calculates the absolute value)
    • acos (Calculates the arccosine)
    • asin (Calculates the arcsine)
    • atan (Calculates the arctangent)
    • besseli0 (Calculates the modified Bessel funcion)
    • besseli1 (Calculates the modified Bessel funcion)
    • besselj0 (Calculates the Bessel function of the first kind)
    • besselj1 (Calculates the Bessel function of the first kind)
    • besselk0 (Calculates the modified Bessel function of the second kind)
    • besselk1 (Calculates the modified Bessel function of the second kind)
    • bessely0 (Calculates the Bessel function of the second kind)
    • bessely1 (Calculates the Bessel function of the second kind)
    • conj (computes the complex conjugate of the input value)
    • cos (Calculates the cosine)
    • cosh (Calculates the hyperbolic cosine)
    • erf (Calculates the error function)
    • erfc (Calculates the complementary error function)
    • exp (Raises e to the power of value)
    • gamma (Calculates the gamma function)
    • get_seed (Returns the random number generator status)
    • imag (Returns the imaginary part of complex numbers)
    • log (Calculates the natural logarithm)
    • log10 (Calculates the logarithm to the base 10)
    • norm (Calculates the norm of the complex numbers)
    • polar (complex number from its polar representation)
    • pow (Raises basis to the power of exponent)
    • randomn (Returns sequenze of normal distributed random numbers)
    • randomu (Returns sequenze of uniformal distributed random numbers)
    • real (Returns the real part of complex numbers)
    • recover_seed (Recover the random number generator status )
    • set_seed (Set the seed for the random number generator)
    • sin (Calculates the sine)
    • sinh (Calculates the hyperbolic sine)
    • sqrt (Calculates the square root)
    • tan (Calculates the tangent)
    • tanh (Calculates the hyperbolic tangent)

    abs (Calculates the absolute value)

    Parameters

              abs ( value )
    
              Types: value                  double/double[]/complex/complex[]
    

    Return

              double/double[]
    

    acos (Calculates the arccosine)

    Parameters

              acos ( value )
    
              Types: value                  double/double[]
    

    Return

              double/double[]
    

    asin (Calculates the arcsine)

    Parameters

              asin ( value )
    
              Types: value                  double/double[]
    

    Return

              double/double[]
    

    atan (Calculates the arctangent)

    Parameters

              atan ( value )
    
              Types: value                  double/double[]
    

    Return

              double/double[]
    

    besseli0 (Calculates the modified Bessel funcion)

    Parameters

              besseli0 ( value )
    
              Types: value                  double/double[]
    

    Return

              double/double[]
    

    Reference

    besseli1 This functions is based on the package SPECFUN available from ftp.netlib.org. /pre/ C C Authors: W. J. Cody and L. Stoltz C Applied Mathematics Division C Argonne National Laboratory C Argonne, IL 60439 /pre/

    besseli1 (Calculates the modified Bessel funcion)

    Parameters

              besseli1 ( value )
    
              Types: value                  double/double[]
    

    Return

              double/double[]
    

    See also

    besseli0

    Reference

    This functions is based on the package SPECFUN available from ftp.netlib.org. /pre/ C C Authors: W. J. Cody and L. Stoltz C Applied Mathematics Division C Argonne National Laboratory C Argonne, IL 60439 /pre/

    besselj0 (Calculates the Bessel function of the first kind)

    Parameters

              besselj0 ( value )
    
              Types: value                  double/double[]
    

    Return

              double/double[]
    

    See also

    besselj1

    Reference

    This functions is based on the package SPECFUN available from ftp.netlib.org. /pre/ C C Authors: W. J. Cody and L. Stoltz C Applied Mathematics Division C Argonne National Laboratory C Argonne, IL 60439 /pre/

    besselj1 (Calculates the Bessel function of the first kind)

    Parameters

              besselj1 ( value )
    
              Types: value                  double/double[]
    

    Return

              double/double[]
    

    See also

    besselj0

    Reference

    This functions is based on the package SPECFUN available from ftp.netlib.org. /pre/ C C Authors: W. J. Cody and L. Stoltz C Applied Mathematics Division C Argonne National Laboratory C Argonne, IL 60439 /pre/

    besselk0 (Calculates the modified Bessel function of the second kind)

    Parameters

              besselk0 ( value )
    
              Types: value                  double/double[]
    

    Return

              double/double[]
    

    See also

    besselk1

    Reference

    This functions is based on the package SPECFUN available from ftp.netlib.org. /pre/ C C Authors: W. J. Cody and L. Stoltz C Applied Mathematics Division C Argonne National Laboratory C Argonne, IL 60439 /pre/

    besselk1 (Calculates the modified Bessel function of the second kind)

    Parameters

              besselk1 ( value )
    
              Types: value                  double/double[]
    

    Return

              double/double[]
    

    See also

    besselk0

    Reference

    This functions is based on the package SPECFUN available from ftp.netlib.org. /pre/ C C Authors: W. J. Cody and L. Stoltz C Applied Mathematics Division C Argonne National Laboratory C Argonne, IL 60439 /pre/

    bessely0 (Calculates the Bessel function of the second kind)

    Parameters

              bessely0 ( value )
    
              Types: value                  double/double[]
    

    Return

              double/double[]
    

    See also

    bessely1

    Reference

    This functions is based on the package SPECFUN available from ftp.netlib.org. /pre/ C C Authors: W. J. Cody and L. Stoltz C Applied Mathematics Division C Argonne National Laboratory C Argonne, IL 60439 /pre/

    bessely1 (Calculates the Bessel function of the second kind)

    Parameters

              bessely1 ( value )
    
              Types: value                  double/double[]
    

    Return

              double/double[]
    

    See also

    bessely0

    Reference

    This functions is based on the package SPECFUN available from ftp.netlib.org. /pre/ C C Authors: W. J. Cody and L. Stoltz C Applied Mathematics Division C Argonne National Laboratory C Argonne, IL 60439 /pre/

    conj (computes the complex conjugate of the input value)

    Parameters

              conj ( value )
    
              Types: value                  complex/complex[]
    

    Return

              complex/complex[]  (complex conjugate)
    

    Description

    The function conj returns the complex conjugate of the input value.

    Example

    >print(conj( (1,2 )));
    <complex> (1, -2)
    

    See also

    imag, real

    cos (Calculates the cosine)

    Parameters

              cos ( value )
    
              Types: value                  double/double[]/complex/complex[]
    

    Return

              double/double[]/complex/complex[]
    

    cosh (Calculates the hyperbolic cosine)

    Parameters

              cosh ( value )
    
              Types: value                  double/double[]/complex/complex[]
    

    Return

              double/double[]/complex/complex[]
    

    erf (Calculates the error function)

    Parameters

              erf ( value )
    
              Types: value                  double/double[]
    

    Return

              double/double[]
    

    See also

    erfc

    Reference

    This functions is based on the package SPECFUN available from ftp.netlib.org. /pre/ C C Authors: W. J. Cody and L. Stoltz C Applied Mathematics Division C Argonne National Laboratory C Argonne, IL 60439 /pre/

    erfc (Calculates the complementary error function)

    Parameters

              erfc ( value )
    
              Types: value                  double/double[]
    

    Return

              double/double[]
    

    See also

    (unknown)

    Reference

    This functions is based on the package SPECFUN available from ftp.netlib.org. /pre/ C C Authors: W. J. Cody and L. Stoltz C Applied Mathematics Division C Argonne National Laboratory C Argonne, IL 60439 /pre/

    exp (Raises e to the power of value)

    Parameters

              exp ( value )
    
              Types: value                  double/double[]/complex/complex[]
    

    Return

              double/double[]/complex/complex[]
    

    gamma (Calculates the gamma function)

    Parameters

              gamma ( value )
    
              Types: value                  double/double[]
    

    Return

              double/double[]
    

    Reference

    This functions is based on the package SPECFUN available from ftp.netlib.org. /pre/ C C Authors: W. J. Cody and L. Stoltz C Applied Mathematics Division C Argonne National Laboratory C Argonne, IL 60439 /pre/

    get_seed (Returns the random number generator status)

    Parameters

              get_seed ( )
    

    Return

              double[]  (1634 entries)
    

    See also

    set_seed, recover_seed

    Reference

    This functions are based on the file zufall.f available from ftp.netlib.org. /pre/ * * External documentation, "Lagged Fibonacci Random Number Generators * for the NEC SX-3," is to be published in the International * Journal of High Speed Computing (1994). Otherwise, ask the * author: * * W. P. Petersen * IPS, RZ F-5 * ETHZ * CH 8092, Zurich * Switzerland * * e-mail: wpp@ips.ethz.ch. * /pre/

    imag (Returns the imaginary part of complex numbers)

    Parameters

              imag ( value )
    
              Types: value                  double/double[]/complex/complex[]
    

    Return

              double/double[]
    

    Description

    The function imag returns the imaginary part of a complex number.

    Example

     >print(imag( (1,2) ));
     <double> 2
    

    log (Calculates the natural logarithm)

    Parameters

              log ( value )
    
              Types: value                  double/double[]/complex/complex[]
    

    Return

              double/double[]/complex/complex[]
    

    log10 (Calculates the logarithm to the base 10)

    Parameters

              log10 ( value )
    
              Types: value                  double/double[]/complex/complex[]
    

    Return

              double/double[]/complex/complex[]
    

    norm (Calculates the norm of the complex numbers)

    Parameters

              norm ( value )
    
              Types: value                  double/double[]/complex/complex[]
    

    Return

              double/double[]
    

    polar (complex number from its polar representation)

    Parameters

              polar ( r, phi )
    
              Types: r                      double/double[]
                     phi                    double/double[]
    

    Return

              complex/complex[]
    

    Example

     >print(polar(1, ~pi));
     <complex> (-1, 1.22461e-16);
    

    pow (Raises basis to the power of exponent)

    Parameters

              pow ( basis, exponent )
    
              Types: basis                  double/double[]/complex/complex[]
                     exponent               double/complex
    

    Return

              double/double[]/complex/complex[]
    

    randomn (Returns sequenze of normal distributed random numbers)

    Parameters

              randomn ( number )
    
              Types: number                 int
    

    Return

              double[]
              -1
    

    See also

    randomu

    Reference

    This functions are based on the file zufall.f available from ftp.netlib.org. /pre/ * * External documentation, "Lagged Fibonacci Random Number Generators * for the NEC SX-3," is to be published in the International * Journal of High Speed Computing (1994). Otherwise, ask the * author: * * W. P. Petersen * IPS, RZ F-5 * ETHZ * CH 8092, Zurich * Switzerland * * e-mail: wpp@ips.ethz.ch. * /pre/

    randomu (Returns sequenze of uniformal distributed random numbers)

    Parameters

              randomu ( number )
    
              Types: number                 int
    

    Return

              double[]
              -1
    

    See also

    randomn

    Reference

    This functions are based on the file zufall.f available from ftp.netlib.org. /pre/ * * External documentation, "Lagged Fibonacci Random Number Generators * for the NEC SX-3," is to be published in the International * Journal of High Speed Computing (1994). Otherwise, ask the * author: * * W. P. Petersen * IPS, RZ F-5 * ETHZ * CH 8092, Zurich * Switzerland * * e-mail: wpp@ips.ethz.ch. * /pre/

    real (Returns the real part of complex numbers)

    Parameters

              real ( value )
    
              Types: value                  double/double[]/complex/complex[]
    

    Return

              double/double[]
    

    recover_seed (Recover the random number generator status )

    Parameters

              recover_seed ( value )
    
              Types: value                  double[]
    

    Return

              -1
    

    See also

    get_seed, set_seed

    Reference

    This functions are based on the file zufall.f available from ftp.netlib.org. /pre/ * * External documentation, "Lagged Fibonacci Random Number Generators * for the NEC SX-3," is to be published in the International * Journal of High Speed Computing (1994). Otherwise, ask the * author: * * W. P. Petersen * IPS, RZ F-5 * ETHZ * CH 8092, Zurich * Switzerland * * e-mail: wpp@ips.ethz.ch. * /pre/

    set_seed (Set the seed for the random number generator)

    Parameters

              set_seed ( number )
    
              Types: number                 int
    

    Return

              int  (seed set)
    

    See also

    get_seed

    Reference

    This functions is based on the package SPECFUN available from ftp.netlib.org. /pre/ C C Authors: W. J. Cody and L. Stoltz C Applied Mathematics Division C Argonne National Laboratory C Argonne, IL 60439 /pre/

    sin (Calculates the sine)

    Parameters

              sin ( value )
    
              Types: value                  double/double[]/complex/complex[]
    

    Return

              double/double[]/complex/complex[]
    

    sinh (Calculates the hyperbolic sine)

    Parameters

              sinh ( value )
    
              Types: value                  double/double[]/complex/complex[]
    

    Return

              double/double[]/complex/complex[]
    

    sqrt (Calculates the square root)

    Parameters

              sqrt ( value )
    
              Types: value                  double/double[]/complex/complex[]
    

    Return

              double/double[]/complex/complex[]
    

    tan (Calculates the tangent)

    Parameters

              tan ( value )
    
              Types: value                  double/double[]/complex/complex[]
    

    Return

              double/double[]/complex/complex[]
    

    tanh (Calculates the hyperbolic tangent)

    Parameters

              tanh ( value )
    
              Types: value                  double/double[]/complex/complex[]
    

    Return

              double/double[]/complex/complex[]
    

    © 1995 by Bodo Junglas, Klaus Spanderen and Fabian Weis
    - Last revised: Wed Jun 19 16:58:32 1996