home.md

@@ -22,4 +22,47 @@ Generic name of a function is `wderiv_operation_Nd_t`, where:
 * `t`:
   * `r` for real problems
   * `c` for complex problems
-# Examples
+# Sample declarations
+```c
+/**
+ * Function computes first derivative with respect to x (df/dx)
+ * of 3D real function f(x,y,z)   
+ * @param f pointer to function, array of size [nx*ny*nz] (INPUT)
+ * @param df_dx pointer to function, array of size [nx*ny*nz] (OUTPUT)
+ *                NOTE: dfdx can be the same pointer as f, then result overwrites input 
+ * @return error code
+ * */
+int wderiv_dfdx_3d_r(double *f, double *dfdx);
+
+/**
+ * Function computes gradient
+ * of 3D real function f(x,y,z)   
+ * @param f pointer to function, array of size [nx*ny*nz] (INPUT)
+ * @param dfdx pointer to function, array of size [nx*ny*nz] (OUTPUT)
+ * @param dfdy pointer to function, array of size [nx*ny*nz] (OUTPUT)
+ * @param dfdz pointer to function, array of size [nx*ny*nz] (OUTPUT)
+ * @return error code
+ * */
+int wderiv_gradient_3d_r(double *f, double *dfdx, double *dfdy, double *dfdz);
+
+/**
+ * Function computes second derivative with respect to z (d^2f/dz^2)
+ * of 3D complex function f(x,y,z)   
+ * @param f pointer to function, array of size [nx*ny*nz] (INPUT)
+ * @param d2fdz2 pointer to function, array of size [nx*ny*nz] (OUTPUT)
+ *                NOTE: d2fdz2 can be the same pointer as f, then result overwrites input 
+ * @return error code
+ * */
+int wderiv_d2fdz2_3d_c(double complex *f, double complex *d2fdz2);
+
+/**
+ * Function computes n-th derivative with respect to x (d^nf/dx^n)
+ * of 1D complex function f(x)   
+ * @param n order of derivative
+ * @param f pointer to function, array of size [nx] (INPUT)
+ * @param dnfdxn pointer to function, array of size [nx] (OUTPUT)
+ *                NOTE: dnfdxn can be the same pointer as f, then result overwrites input 
+ * @return error code
+ * */
+int wderiv_dnfdxn_1d_c(int n, double complex *f, double complex *dnfdxn);
+```