class_docstr: Base class for bivariate splines.
  
  This describes a spline ``s(x, y)`` of degrees ``kx`` and ``ky`` on
  the rectangle ``[xb, xe] * [yb, ye]`` calculated from a given set
  of data points ``(x, y, z)``.
  
  This class is meant to be subclassed, not instantiated directly.
  To construct these splines, call either `SmoothBivariateSpline` or
  `LSQBivariateSpline` or `RectBivariateSpline`.
  
  See Also
  --------
  UnivariateSpline :
      a smooth univariate spline to fit a given set of data points.
  SmoothBivariateSpline :
      a smoothing bivariate spline through the given points
  LSQBivariateSpline :
      a bivariate spline using weighted least-squares fitting
  RectSphereBivariateSpline :
      a bivariate spline over a rectangular mesh on a sphere
  SmoothSphereBivariateSpline :
      a smoothing bivariate spline in spherical coordinates
  LSQSphereBivariateSpline :
      a bivariate spline in spherical coordinates using weighted
      least-squares fitting
  RectBivariateSpline :
      a bivariate spline over a rectangular mesh.
  bisplrep :
      a function to find a bivariate B-spline representation of a surface
  bisplev :
      a function to evaluate a bivariate B-spline and its derivatives
class_docstr_tok: ["Base","class","for","bivariate","splines",".","This","describes","a","spline","``","s","(","x",",","y",")","``","of","degrees","``","kx","``","and","``","ky","``","on","the","rectangle","``","[","xb",",","xe","]","*","[","yb",",","ye","]","``","calculated","from","a","given","set","of","data","points","``","(","x",",","y",",","z",")","``",".","This","class","is","meant","to","be","subclassed",",","not","instantiated","directly",".","To","construct","these","splines",",","call","either","`","SmoothBivariateSpline","`","or","`","LSQBivariateSpline","`","or","`","RectBivariateSpline","`",".","See","Also","--","--","--","--","UnivariateSpline",":","a","smooth","univariate","spline","to","fit","a","given","set","of","data","points",".","SmoothBivariateSpline",":","a","smoothing","bivariate","spline","through","the","given","points","LSQBivariateSpline",":","a","bivariate","spline","using","weighted","least-squares","fitting","RectSphereBivariateSpline",":","a","bivariate","spline","over","a","rectangular","mesh","on","a","sphere","SmoothSphereBivariateSpline",":","a","smoothing","bivariate","spline","in","spherical","coordinates","LSQSphereBivariateSpline",":","a","bivariate","spline","in","spherical","coordinates","using","weighted","least-squares","fitting","RectBivariateSpline",":","a","bivariate","spline","over","a","rectangular","mesh",".","bisplrep",":","a","function","to","find","a","bivariate","B-spline","representation","of","a","surface","bisplev",":","a","function","to","evaluate","a","bivariate","B-spline","and","its","derivatives"]
docstr: Evaluate the integral of the spline over area [xa,xb] x [ya,yb].
  
  Parameters
  ----------
  xa, xb : float
      The end-points of the x integration interval.
  ya, yb : float
      The end-points of the y integration interval.
  
  Returns
  -------
  integ : float
      The value of the resulting integral.
docstr_tok: ["Evaluate","the","integral","of","the","spline","over","area","[","xa",",","xb","]","x","[","ya",",","yb","]",".","Parameters","--","--","--","--","--","xa",",","xb",":","float","The","end-points","of","the","x","integration","interval",".","ya",",","yb",":","float","The","end-points","of","the","y","integration","interval",".","Returns","--","--","--","-","integ",":","float","The","value","of","the","resulting","integral","."]
code: def integral(self, xa, xb, ya, yb):
      """
      Evaluate the integral of the spline over area [xa,xb] x [ya,yb].
  
      Parameters
      ----------
      xa, xb : float
          The end-points of the x integration interval.
      ya, yb : float
          The end-points of the y integration interval.
  
      Returns
      -------
      integ : float
          The value of the resulting integral.
  
      """
      tx, ty, c = self.tck[:3]
      kx, ky = self.degrees
      return dfitpack.dblint(tx, ty, c, kx, ky, xa, xb, ya, yb)
  
imports: import warnings
  from numpy import zeros, concatenate, ravel, diff, array, ones
  import numpy
  from .None import fitpack
  from .None import dfitpack
label_desc: Use image node_id 3 for calling the BivariateSpline obj's underlying member method code with example usage: obj.integral(xa, xb, ya, yb) and returns: dfitpack