Performs numerical integration using adaptive quadrature approach. You must manually select the polymorphic instance to use.


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Inputs/Outputs

  • cfxdt.png data —

    data is a variant that you can use to pass arbitrary values to the integrand VI.

  • csvrn.png integrand —

    integrand is a strictly typed reference to the VI that implements the expression to integrate. Create this VI by starting from the VI template located in labview\vi.lib\Analysis\8numeric.llb\3D Quadrature Integrand.vit.

    Note The elements in the X array, Y array and Z array of the integrand VI specify the values of the three integral variables at different time stamps. X array, Y array and Z array represent the first, second and third variable, respectively, so you cannot separate the elements in X array, Y array and Z array.
  • cnclst.png Upper Limits —

    Upper Limits specifies the upper limits of the integral.

  • cdbl.png x upper limit —

    x upper limit is the upper limit of the first integral variable x. The default is 1.

  • cdbl.png y upper limit —

    y upper limit is the upper limit of the second integral variable y. The default is 1.

  • cdbl.png z upper limit —

    z upper limit is the upper limit of the third integral variable z. The default is 1.

  • cnclst.png Lower Limits —

    Lower Limits specifies the lower limits of the integral.

  • cdbl.png x lower limit —

    x lower limit is the lower limit of the first integral variable x. The default is 0.

  • cdbl.png y lower limit —

    y lower limit is the lower limit of the second integral variable y. The default is 0.

  • cdbl.png z lower limit —

    z lower limit is the lower limit of the third integral variable z. The default is 0.

  • cdbl.png tolerance —

    tolerance controls the accuracy of the quadrature. A smaller tolerance leads to a more accurate result but more computation time. The default is 1E-5.

  • idbl.png result —

    result returns the integral result.

  • ii32.png error —

    error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

    • This VI compares the difference between the 4-points and 7-points Lobatto quadratures on the interval with tolerance to terminate the calculation iteration. If the difference is less than the tolerance, the algorithm stops the iteration and moves on to next interval.

    3D Quadrature

    This VI numerically evaluates the following integral using the adaptive Lobatto quadrature:

    where x1 is x upper limit, x0 is x lower limit, y1 is y upper limit, y0 is y lower limit, z1 is z upper limit, z0 is z lower limit.

    The 3D Quadrature instances divide an interval cube into many sub-cubes when the integrand f(x,y,z) varies sharply.

    Examples

    Refer to the following example files included with LabVIEW.

    • labview\examples\Mathematics\Integration and Differentiation\VI Reference Based Quadrature.vi