Add include first spline basis option (#8)

Add include first spline basis option

src/xspline/core.py

@@ -272,7 +272,13 @@ def bspline_ifun(a, x, knots, degree, order, idx, l_extra=False, r_extra=False):
 class XSpline:
     """XSpline main class of the package.
     """
-    def __init__(self, knots, degree, l_linear=False, r_linear=False):
+
+    def __init__(self,
+                 knots,
+                 degree,
+                 l_linear=False,
+                 r_linear=False,
+                 include_first_basis: bool = False):
         r"""Constructor of the XSpline class.
 
         knots (numpy.ndarray):
@@ -295,6 +301,7 @@ def __init__(self, knots, degree, l_linear=False, r_linear=False):
         self.degree = degree
         self.l_linear = l_linear
         self.r_linear = r_linear
+        self.include_first_basis = include_first_basis
 
         # dimensions
         self.num_knots = knots.size
@@ -314,7 +321,7 @@ def __init__(self, knots, degree, l_linear=False, r_linear=False):
         self.inner_lb = self.inner_knots[0]
         self.inner_ub = self.inner_knots[-1]
 
-        self.num_spline_bases = self.inner_knots.size - 1 + self.degree
+        self.num_spline_bases = self.inner_knots.size - 1 + self.degree - self.include_first_basis
 
     def domain(self, idx, l_extra=False, r_extra=False):
         """Return the support of the XSpline.
@@ -644,7 +651,8 @@ def design_mat(self, x, l_extra=False, r_extra=False):
         """
         mat = np.vstack([
             self.fun(x, idx, l_extra=l_extra, r_extra=r_extra)
-            for idx in range(self.num_spline_bases)
+            for idx in range(self.include_first_basis,
+                             self.num_spline_bases)
         ]).T
         return mat
 
@@ -672,7 +680,8 @@ def design_dmat(self, x, order, l_extra=False, r_extra=False):
         """
         dmat = np.vstack([
             self.dfun(x, order, idx, l_extra=l_extra, r_extra=r_extra)
-            for idx in range(self.num_spline_bases)
+            for idx in range(self.include_first_basis,
+                             self.num_spline_bases)
         ]).T
         return dmat
 
@@ -705,7 +714,8 @@ def design_imat(self, a, x, order, l_extra=False, r_extra=False):
         """
         imat = np.vstack([
             self.ifun(a, x, order, idx, l_extra=l_extra, r_extra=r_extra)
-            for idx in range(self.num_spline_bases)
+            for idx in range(self.include_first_basis,
+                             self.num_spline_bases)
         ]).T
         return imat
 
@@ -733,9 +743,11 @@ def last_dmat(self):
 class NDXSpline:
     """Multi-dimensional xspline.
     """
+
     def __init__(self, ndim, knots_list, degree_list,
                  l_linear_list=None,
-                 r_linear_list=None):
+                 r_linear_list=None,
+                 include_first_basis_list=None):
         """Constructor of ndXSpline class
 
         Args:
@@ -757,11 +769,13 @@ def __init__(self, ndim, knots_list, degree_list,
         self.degree_list = degree_list
         self.l_linear_list = utils.option_to_list(l_linear_list, self.ndim)
         self.r_linear_list = utils.option_to_list(r_linear_list, self.ndim)
+        self.include_first_basis_list = utils.option_to_list(include_first_basis_list, self.ndim)
 
         self.spline_list = [
             XSpline(self.knots_list[i], self.degree_list[i],
                     l_linear=self.l_linear_list[i],
-                    r_linear=self.r_linear_list[i])
+                    r_linear=self.r_linear_list[i],
+                    include_first_basis=self.include_first_basis_list[i])
             for i in range(self.ndim)
         ]