Add simpson's rule API (not implemented)

Author: nshaffer

src/stdlib_experimental_quadrature.fypp

@@ -6,7 +6,13 @@ module stdlib_experimental_quadrature
     implicit none
 
     private
-    public :: trapz, trapz_weights
+
+    ! array integration
+    public :: trapz
+    public :: trapz_weights
+    public :: simps
+    public :: simps_weights
+
 
     interface trapz
         #:for KIND in REAL_KINDS
@@ -25,6 +31,7 @@ module stdlib_experimental_quadrature
         #:endfor
     end interface trapz
 
+
     interface trapz_weights
         #:for KIND in REAL_KINDS
         pure module function trapz_weights_${KIND}$(x) result(w)
@@ -34,4 +41,35 @@ module stdlib_experimental_quadrature
         #:endfor
     end interface trapz_weights
 
+
+    interface simps
+        #:for KIND in REAL_KINDS
+        pure module function simps_dx_${KIND}$(y, dx, even) result(integral)
+            real(${KIND}$), dimension(:), intent(in) :: y
+            real(${KIND}$), intent(in) :: dx
+            integer, intent(in), optional :: even
+            real(${KIND}$) :: integral
+        end function simps_dx_${KIND}$
+        #:endfor
+        #:for KIND in REAL_KINDS
+        pure module function simps_x_${KIND}$(y, x, even) result(integral)
+            real(${KIND}$), dimension(:), intent(in) :: y
+            real(${KIND}$), dimension(size(y)), intent(in) :: x
+            integer, intent(in), optional :: even
+            real(${KIND}$) :: integral
+        end function simps_x_${KIND}$
+        #:endfor
+    end interface simps
+
+
+    interface simps_weights
+        #:for KIND in REAL_KINDS
+        pure module function simps_weights_${KIND}$(x, even) result(w)
+            real(${KIND}$), dimension(:), intent(in) :: x
+            real(${KIND}$), dimension(size(x)) :: w
+            integer, intent(in), optional :: even
+        end function simps_weights_${KIND}$
+        #:endfor
+    end interface simps_weights
+
 end module stdlib_experimental_quadrature