... | ... | @@ -24,141 +24,4 @@ Generic name of a function is `wderiv_operation_Nd_t`, where: |
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* `3` for [3D problems](Derivatives#3d-derivatives)
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* `t`:
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* `r` for real problems
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* `c` for complex problems
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# Function Documentation
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## 3D derivatives:
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### Basic 3D derivative function:
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```c
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int wderiv_derivative_3d_r(int direction, int n, double *f, double *deriv)
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```
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Function computes n-th derivative with respect to `direction` of 3D real function $`f(x,y,z)`$: $`\frac{\partial^n f}{\partial t^n}`$.
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* `direction` - predefined integer corresponding to direction of derivative: `WDERIV_DX` or `WDERIV_DY` or `WDERIV_DZ`
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* `f` - pointer to input function which is array of size [nx\*ny\*nz]
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* `deriv` - pointer to output derivative function which is array of size [nx\*ny\*nz]
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* `return` - error code
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`deriv` can be the same pointer as `f`, then result overwrites input.
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### First 3D derivative functions:
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```c
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int wderiv_dfdx_3d_r(double *f, double *dfdx)
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```
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Function computes first derivative with respect to $`x`$ of 3D real function $`f(x,y,z)`$: $`\frac{\partial f}{\partial x}`$.
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* `f` - pointer to input function which is array of size [nx\*ny\*nz]
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* `dfdx` - pointer to output derivative function which is array of size [nx\*ny\*nz]
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* `return` - error code
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`dfdx` can be the same pointer as `f`, then result overwrites input.
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```c
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int wderiv_dfdy_3d_r(double *f, double *dfdy)
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```
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Function computes first derivative with respect to $`y`$ of 3D real function $`f(x,y,z)`$: $`\frac{\partial f}{\partial y}`$.
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* `f` - pointer to input function which is array of size [nx*ny*nz]
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* `dfdy` - pointer to output derivative function which is array of size [nx*ny*nz]
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* `return` - error code
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`dfdy` can be the same pointer as `f`, then result overwrites input.
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```c
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int wderiv_dfdz_3d_r(double *f, double *dfdz)
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```
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Function computes first derivative with respect to $`z`$ of 3D real function $`f(x,y,z)`$: $`\frac{\partial f}{\partial x}`$.
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* `f` - pointer to input function which is array of size [nx*ny*nz]
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* `dfdz` - pointer to output derivative function which is array of size [nx*ny*nz]
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* `return` - error code
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`dfdz` can be the same pointer as `f`, then result overwrites input.
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### Second 3D derivative functions:
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```c
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int wderiv_d2fdx2_3d_r(double *f, double *d2fdx2)
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```
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Function computes second derivative with respect to $`x`$ of 3D real function $`f(x,y,z)`$: $`\frac{\partial^2 f}{\partial x^2}`$.
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* `f` - pointer to input function which is array of size [nx\*ny\*nz]
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* `d2fdx2` - pointer to output derivative function which is array of size [nx\*ny\*nz]
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* `return` - error code
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`d2fdx2` can be the same pointer as `f`, then result overwrites input.
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```c
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int wderiv_d2fdy2_3d_r(double *f, double *d2fdy2)
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```
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Function computes second derivative with respect to $`y`$ of 3D real function $`f(x,y,z)`$: $`\frac{\partial^2 f}{\partial y^2}`$.
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* `f` - pointer to input function which is array of size [nx\*ny\*nz]
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* `d2fdy2` - pointer to output derivative function which is array of size [nx\*ny\*nz]
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* `return` - error code
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`d2fdy2` can be the same pointer as `f`, then result overwrites input.
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```c
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int wderiv_d2fdz2_3d_r(double *f, double *d2fdz2)
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```
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Function computes second derivative with respect to $`z`$ of 3D real function $`f(x,y,z)`$: $`(\frac{d^2f}{dz^2})`$.
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* `f` - pointer to input function which is array of size [nx*ny*nz]
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* `d2fdz2` - pointer to output derivative function which is array of size [nx*ny*nz]
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* `return` - error code
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`d2fdz2` can be the same pointer as `f`, then result overwrites input.
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### n-th 3D derivative functions:
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```c
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int wderiv_dnfdxn_3d_r(int n, double *f, double *dnfdxn)
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```
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Function computes n-th derivative with respect to $`x`$ of 3D real function $`f(x,y,z)`$: $`(\frac{d^nf}{dx^n})`$.
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* `f` - pointer to input function which is array of size [nx*ny*nz]
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* `dnfdxn` - pointer to output derivative function which is array of size [nx*ny*nz]
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* `return` - error code
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`dnfdxn` can be the same pointer as `f`, then result overwrites input.
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```c
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int wderiv_dnfdyn_3d_r(int n, double *f, double *dnfdyn)
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```
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Function computes n-th derivative with respect to $`y`$ of 3D real function $`f(x,y,z)`$: $`(\frac{d^nf}{dy^n})`$.
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* `f` - pointer to input function which is array of size [nx*ny*nz]
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* `dnfdyn` - pointer to output derivative function which is array of size [nx*ny*nz]
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* `return` - error code
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`dnfdyn` can be the same pointer as `f`, then result overwrites input.
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```c
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int wderiv_dnfdzn_3d_r(int n, double *f, double *dnfdzn)
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```
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Function computes n-th derivative with respect to $`z`$ of 3D real function $`f(x,y,z)`$: $`(\frac{d^nf}{dz^n})`$.
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* `f` - pointer to input function which is array of size [nx*ny*nz]
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* `dnfdzn` - pointer to output derivative function which is array of size [nx*ny*nz]
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* `return` - error code
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`dnfdzn` can be the same pointer as `f`, then result overwrites input.
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/**
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* Function computes gradient
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* of 3D real function f(x,y,z)
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* @param f pointer to function, array of size [nx*ny*nz] (INPUT)
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* @param dfdx pointer to function, array of size [nx*ny*nz] (OUTPUT)
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* @param dfdy pointer to function, array of size [nx*ny*nz] (OUTPUT)
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* @param dfdz pointer to function, array of size [nx*ny*nz] (OUTPUT)
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* @return error code
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* */
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int wderiv_gradient_3d_r(double *f, double *dfdx, double *dfdy, double *dfdz);
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/**
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* Function computes second derivative with respect to z (d^2f/dz^2)
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* of 3D complex function f(x,y,z)
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* @param f pointer to function, array of size [nx*ny*nz] (INPUT)
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* @param d2fdz2 pointer to function, array of size [nx*ny*nz] (OUTPUT)
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* NOTE: d2fdz2 can be the same pointer as f, then result overwrites input
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* @return error code
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* */
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int wderiv_d2fdz2_3d_c(double complex *f, double complex *d2fdz2);
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/**
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* Function computes n-th derivative with respect to x (d^nf/dx^n)
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* of 1D complex function f(x)
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* @param n order of derivative
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* @param f pointer to function, array of size [nx] (INPUT)
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* @param dnfdxn pointer to function, array of size [nx] (OUTPUT)
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* NOTE: dnfdxn can be the same pointer as f, then result overwrites input
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* @return error code
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* */
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int wderiv_dnfdxn_1d_c(int n, double complex *f, double complex *dnfdxn);
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``` |
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* `c` for complex problems |
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\ No newline at end of file |