This library provides a set of functions for computation derivatives using spectral methods. The lib depends on FFTW library. The library is compatible with W-SLDA Toolkit however, it can be used as standalone lib. It is written in C99 standard.

Name convention

Generic name of a function is wderiv_operation_Nd_t, where:

• wderiv: fixed, function belongs to wderiv lib,
• operation:
  • dfdx : \frac{\partial f}{\partial x}
  • dfdy : \frac{\partial f}{\partial y}
  • dfdz : \frac{\partial f}{\partial z}
  • d2fdx2 : \frac{\partial^2 f}{\partial x^2}
  • d2fdy2 : \frac{\partial^2 f}{\partial y^2}
  • d2fdz2 : \frac{\partial^2 f}{\partial z^2}
  • dnfdxn : \frac{\partial^n f}{\partial x^n}
  • dnfdyn : \frac{\partial^n f}{\partial y^n}
  • dnfdzn : \frac{\partial^n f}{\partial z^n}
  • gradient : (\frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}, \frac{\partial f}{\partial z})
  • gradient2 : |\nabla f|^2, see here for computation details
  • laplace : \frac{\partial^2 f}{\partial x^2} + \frac{\partial^2 f}{\partial y^2} + \frac{\partial^2 f}{\partial z^2}
  • divergence : \frac{\partial f}{\partial x} + \frac{\partial f}{\partial y} + \frac{\partial f}{\partial z}
  • curl : (\frac{\partial f_y}{\partial z} - \frac{\partial f_z}{\partial y},\frac{\partial f_z}{\partial x} - \frac{\partial f_x}{\partial z},\frac{\partial f_x}{\partial y} - \frac{\partial f_y}{\partial x})
• N:
  • 1 for 1D problems
  • 2 for 2D problems
  • 3 for 3D problems
• t:
  • r for real problems
  • c for complex problems

Sample declarations

/**
 * 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 dfdx 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);