Complex derivatives

3D derivatives

Basic 3D derivative function:

int wderiv_derivative_3d_c(int direction, int n, double complex *f, double complex *deriv)

Function computes n-th derivative with respect to direction of 3D complex function f(x,y,z): \frac{\partial^n f}{\partial t^n}.

• direction - predefined integer corresponding to direction of derivative: WDERIV_DX or WDERIV_DY or WDERIV_DZ
• f - pointer to input function which is array of size [nx*ny*nz]
• deriv - pointer to output derivative function which is array of size [nx*ny*nz]
• return - error code

deriv can be the same pointer as f, then result overwrites input.

First 3D derivative functions:

int wderiv_dfdx_3d_c(double complex *f, double complex *dfdx)

Function computes first derivative with respect to x of 3D complex function f(x,y,z): \frac{\partial f}{\partial x}.

• f - pointer to input function which is array of size [nx*ny*nz]
• dfdx - pointer to output derivative function which is array of size [nx*ny*nz]
• return - error code

dfdx can be the same pointer as f, then result overwrites input.

int wderiv_dfdy_3d_c(double complex *f, double complex *dfdy)

Function computes first derivative with respect to y of 3D complex function f(x,y,z): \frac{\partial f}{\partial y}.

• f - pointer to input function which is array of size [nxnynz]
• dfdy - pointer to output derivative function which is array of size [nxnynz]
• return - error code

dfdy can be the same pointer as f, then result overwrites input.

int wderiv_dfdz_3d_c(double complex *f, double complex *dfdz)

Function computes first derivative with respect to z of 3D complex function f(x,y,z): \frac{\partial f}{\partial x}.

• f - pointer to input function which is array of size [nxnynz]
• dfdz - pointer to output derivative function which is array of size [nxnynz]
• return - error code

dfdz can be the same pointer as f, then result overwrites input.

Second 3D derivative functions:

int wderiv_d2fdx2_3d_c(double complex *f, double complex *d2fdx2)

Function computes second derivative with respect to x of 3D complex function f(x,y,z): \frac{\partial^2 f}{\partial x^2}.

• f - pointer to input function which is array of size [nx*ny*nz]
• d2fdx2 - pointer to output derivative function which is array of size [nx*ny*nz]
• return - error code

d2fdx2 can be the same pointer as f, then result overwrites input.

int wderiv_d2fdy2_3d_c(double complex *f, double complex *d2fdy2)

Function computes second derivative with respect to y of 3D complex function f(x,y,z): \frac{\partial^2 f}{\partial y^2}.

• f - pointer to input function which is array of size [nx*ny*nz]
• d2fdy2 - pointer to output derivative function which is array of size [nx*ny*nz]
• return - error code

d2fdy2 can be the same pointer as f, then result overwrites input.

int wderiv_d2fdz2_3d_c(double complex *f, double complex *d2fdz2)

Function computes second derivative with respect to z of 3D complex function f(x,y,z): (\frac{d^2f}{dz^2}).

• f - pointer to input function which is array of size [nxnynz]
• d2fdz2 - pointer to output derivative function which is array of size [nxnynz]
• return - error code

d2fdz2 can be the same pointer as f, then result overwrites input.

n-th 3D derivative functions:

int wderiv_dnfdxn_3d_c(int n, double complex *f, double complex *dnfdxn)

Function computes n-th derivative with respect to x of 3D complex function f(x,y,z): (\frac{d^nf}{dx^n}).

• f - pointer to input function which is array of size [nxnynz]
• dnfdxn - pointer to output derivative function which is array of size [nxnynz]
• return - error code

dnfdxn can be the same pointer as f, then result overwrites input.

int wderiv_dnfdyn_3d_c(int n, double complex *f, double complex *dnfdyn)

Function computes n-th derivative with respect to y of 3D complex function f(x,y,z): (\frac{d^nf}{dy^n}).

• f - pointer to input function which is array of size [nxnynz]
• dnfdyn - pointer to output derivative function which is array of size [nxnynz]
• return - error code

dnfdyn can be the same pointer as f, then result overwrites input.

int wderiv_dnfdzn_3d_c(int n, double complex *f, double complex *dnfdzn)

Function computes n-th derivative with respect to z of 3D complex function f(x,y,z): (\frac{d^nf}{dz^n}).

• f - pointer to input function which is array of size [nxnynz]
• dnfdzn - pointer to output derivative function which is array of size [nxnynz]
• return - error code

dnfdzn can be the same pointer as f, then result overwrites input.

3D gradient:

int wderiv_gradient_3d_c(double complex *f, double complex *dfdx, double complex *dfdy, double complex *dfdz);

Function computes gradient of 3D complex function f(x,y,z): \nabla f = (\frac{df}{dx},\frac{df}{dy},\frac{df}{dz}).

• f - pointer to input function which is array of size [nxnynz]
• dfdx - pointer to output derivative function which is array of size [nxnynz]
• dfdy - pointer to output derivative function which is array of size [nxnynz]
• dfdz - pointer to output derivative function which is array of size [nxnynz]
• return - error code

3D gradient squared:

int wderiv_gradient2_3d_c(double complex *f, double complex *gradient_square)

Function computes squared gradient of 3D complex function f(x,y,z): |\nabla f|^2 = |\frac{df}{dx}|^2 +|\frac{df}{dy}|^2 +|\frac{df}{dz}|^2 .

• f - pointer to input function which is array of size [nx*ny*nz]
• gradient_square - pointer to output gradient squared function which is array of size [nx*ny*nz]
• return - error code

gradient_square can be the same pointer as f, then result overwrites input.

3D laplacian:

int wderiv_laplace_3d_c(double complex *f, double complex *laplace)

Function computes laplacian of 3D complex function f(x,y,z): |\Delta f|^2 = \frac{d^2f}{dx^2} +\frac{d^2f}{dy^2} +\frac{d^2f}{dz^2} .

• f - pointer to input function which is array of size [nx*ny*nz]
• laplace - pointer to output laplacian function which is array of size [nx*ny*nz]
• return - error code

laplace can be the same pointer as f, then result overwrites input.

3D divergence:

int wderiv_divergence_3d_c(double complex *f, double complex *divergence)

Function divergence of 3D complex function f(x,y,z): \nabla \cdot f = \frac{df}{dx} +\frac{df}{dy} +\frac{df}{dz} .

• f - pointer to input function which is array of size [nx*ny*nz]
• divergence - pointer to output divergence function which is array of size [nx*ny*nz]
• return - error code

divergence can be the same pointer as f, then result overwrites input.

3D curl:

int wderiv_curl_3d_c(double complex *fx, double complex *fy, double complex *fz, double complex *curl_x, double complex *curl_y, double complex *curl_z);

Function computes curl of 3D complex vector (f_x, f_y, f_z): \nabla \times \vec{f} = (\frac{df_y}{dz} - \frac{df_z}{dy}, \frac{df_z}{dx} - \frac{df_x}{dz}, \frac{df_x}{dy} - \frac{df_y}{dx}).

• fx - pointer to input function which is array of size [nx*ny*nz]
• fy - pointer to input function which is array of size [nx*ny*nz]
• fz - pointer to input function which is array of size [nx*ny*nz]
• curl_x - pointer to output x-component function which is array of size [nx*ny*nz]
• curl_y - pointer to output y-component function which is array of size [nx*ny*nz]
• curl_z - pointer to output z-component function which is array of size [nx*ny*nz]
• return - error code

2D derivatives:

Basic 2D derivative function:

int wderiv_derivative_2d_c(int direction, int n, double complex *f, double complex *deriv)

Function computes n-th derivative with respect to direction of 2D complex function f(x,y): \frac{\partial^n f}{\partial t^n}.

• direction - predefined integer corresponding to direction of derivative: WDERIV_DX or WDERIV_DY
• f - pointer to input function which is array of size [nx*ny]
• deriv - pointer to output derivative function which is array of size [nx*ny]
• return - error code

deriv can be the same pointer as f, then result overwrites input.

First 2D derivative functions:

int wderiv_dfdx_2d_c(double complex *f, double complex *dfdx)

Function computes first derivative with respect to x of 2D complex function f(x,y): \frac{\partial f}{\partial x}.

• f - pointer to input function which is array of size [nx*ny]
• dfdx - pointer to output derivative function which is array of size [nx*ny]
• return - error code

dfdx can be the same pointer as f, then result overwrites input.

int wderiv_dfdy_2d_c(double complex *f, double complex *dfdy)

Function computes first derivative with respect to y of 2D complex function f(x,y): \frac{\partial f}{\partial y}.

• f - pointer to input function which is array of size [nx*ny]
• dfdy - pointer to output derivative function which is array of size [nx*ny]
• return - error code

dfdy can be the same pointer as f, then result overwrites input.

Second 2D derivative functions:

int wderiv_d2fdx2_2d_c(double complex *f, double complex *d2fdx2)

Function computes second derivative with respect to x of 2D complex function f(x,y): \frac{\partial^2 f}{\partial x^2}.

• f - pointer to input function which is array of size [nx*ny]
• d2fdx2 - pointer to output derivative function which is array of size [nx*ny]
• return - error code

d2fdx2 can be the same pointer as f, then result overwrites input.

int wderiv_d2fdy2_2d_c(double complex *f, double complex *d2fdy2)

Function computes second derivative with respect to y of 2D complex function f(x,y): \frac{\partial^2 f}{\partial y^2}.

• f - pointer to input function which is array of size [nx*ny]
• d2fdy2 - pointer to output derivative function which is array of size [nx*ny]
• return - error code

d2fdy2 can be the same pointer as f, then result overwrites input.

n-th 2D derivative functions:

int wderiv_dnfdxn_2d_c(int n, double complex *f, double complex *dnfdxn)

Function computes n-th derivative with respect to x of 2D complex function f(x,y): (\frac{d^nf}{dx^n}).

• f - pointer to input function which is array of size [nx*ny]
• dnfdxn - pointer to output derivative function which is array of size [nx*ny]
• return - error code

dnfdxn can be the same pointer as f, then result overwrites input.

int wderiv_dnfdyn_2d_c(int n, double complex *f, double complex *dnfdyn)

Function computes n-th derivative with respect to y of 2D complex function f(x,y): (\frac{d^nf}{dy^n}).

• f - pointer to input function which is array of size [nx*ny]
• dnfdyn - pointer to output derivative function which is array of size [nx*ny]
• return - error code

dnfdyn can be the same pointer as f, then result overwrites input.

2D gradient:

int wderiv_gradient_2d_c(double complex *f, double complex *dfdx, double complex *dfdy);

Function computes gradient of 2D complex function f(x,y): \nabla f = (\frac{df}{dx},\frac{df}{dy}).

• f - pointer to input function which is array of size [nx*ny]
• dfdx - pointer to output derivative function which is array of size [nx*ny]
• dfdy - pointer to output derivative function which is array of size [nx*ny]
• return - error code

2D gradient squared:

int wderiv_gradient2_2d_c(double complex *f, double complex *gradient_square)

Function computes squared gradient of 2D complex function f(x,y): |\nabla f|^2 = |\frac{df}{dx}|^2 +|\frac{df}{dy}|^2.

• f - pointer to input function which is array of size [nx*ny]
• gradient_square - pointer to output gradient squared function which is array of size [nx*ny]
• return - error code

gradient_square can be the same pointer as f, then result overwrites input.

2D laplacian:

int wderiv_laplace_2d_c(double complex *f, double complex *laplace)

Function computes laplacian of 2D complex function f(x,y): |\Delta f|^2 = \frac{d^2f}{dx^2} +\frac{d^2f}{dy^2}.

• f - pointer to input function which is array of size [nx*ny]
• laplace - pointer to output laplacian function which is array of size [nx*ny]
• return - error code

laplace can be the same pointer as f, then result overwrites input.

2D divergence:

int wderiv_divergence_2d_c(double complex *f, double complex *divergence)

Function divergence of 2D complex function f(x,y): \nabla \cdot f = \frac{df}{dx} +\frac{df}{dy}.

• f - pointer to input function which is array of size [nx*ny]
• divergence - pointer to output divergence function which is array of size [nx*ny]
• return - error code

divergence can be the same pointer as f, then result overwrites input.

1D derivatives:

Basic 1D derivative function:

int wderiv_derivative_1d_c(int direction, int n, double complex *f, double complex *deriv)

Function computes n-th derivative with respect to direction of 1D complex function f(x): \frac{\partial^n f}{\partial t^n}.

• direction - predefined integer corresponding to direction of derivative: WDERIV_DX
• f - pointer to input function which is array of size [nx]
• deriv - pointer to output derivative function which is array of size [nx]
• return - error code

deriv can be the same pointer as f, then result overwrites input.

First 1D derivative functions:

int wderiv_dfdx_1d_c(double complex *f, double complex *dfdx)

Function computes first derivative with respect to x of 1D complex function f(x): \frac{\partial f}{\partial x}.

• f - pointer to input function which is array of size [nx]
• dfdx - pointer to output derivative function which is array of size [nx]
• return - error code

dfdx can be the same pointer as f, then result overwrites input.

Second 1D derivative functions:

int wderiv_d2fdx2_1d_c(double complex *f, double complex *d2fdx2)

Function computes second derivative with respect to x of 1D complex function f(x): \frac{\partial^2 f}{\partial x^2}.

• f - pointer to input function which is array of size [nx]
• d2fdx2 - pointer to output derivative function which is array of size [nx]
• return - error code

d2fdx2 can be the same pointer as f, then result overwrites input.

n-th 1D derivative functions:

int wderiv_dnfdxn_1d_c(int n, double complex *f, double complex *dnfdxn)

Function computes n-th derivative with respect to x of 1D complex function f(x): (\frac{d^nf}{dx^n}).

• f - pointer to input function which is array of size [nx]
• dnfdxn - pointer to output derivative function which is array of size [nx]
• return - error code

dnfdxn can be the same pointer as f, then result overwrites input.

1D gradient:

int wderiv_gradient_1d_c(double complex *f, double complex *dfdx);

Function computes gradient of 1D complex function f(x): \nabla f = (\frac{df}{dx}).

• f - pointer to input function which is array of size [nx]
• dfdx - pointer to output derivative function which is array of size [nx]
• return - error code

1D gradient squared:

int wderiv_gradient2_1d_c(double complex *f, double complex *gradient_square)

Function computes squared gradient of 1D complex function f(x): |\nabla f|^2 = |\frac{df}{dx}|^2.

• f - pointer to input function which is array of size [nx]
• gradient_square - pointer to output gradient squared function which is array of size [nx]
• return - error code

gradient_square can be the same pointer as f, then result overwrites input.

1D laplacian:

int wderiv_laplace_1d_c(double complex *f, double complex *laplace)

Function computes laplacian of 1D complex function f(x): |\Delta f|^2 = \frac{d^2f}{dx^2}.

• f - pointer to input function which is array of size [nx]
• laplace - pointer to output laplacian function which is array of size [nx]
• return - error code

laplace can be the same pointer as f, then result overwrites input.

1D divergence:

int wderiv_divergence_1d_c(double complex *f, double complex *divergence)

Function divergence of 1D complex function f(x): \nabla \cdot f = \frac{df}{dx}.

• f - pointer to input function which is array of size [nx]
• divergence - pointer to output divergence function which is array of size [nx]
• return - error code

divergence can be the same pointer as f, then result overwrites input.