Gauss

Gauss (x,xc,wx[,y,yc,wy [,z,zc,wz [,t,tc,wt]]])

The Gauss function returns a normalized Gaussian for the specified dimension.

$$\displaystyle \operatorname{Gauss}(\mathbf{r}, \mathbf{c}, \mathbf{w})=\prod_{i=1}^{n} \frac{1}{w_{i} \sqrt{2 \pi}} \exp \left[-\frac{1}{2}\left(\frac{r_{i}-c_{i}}{w_{i}}\right)^{2}\right],$$

where n is the number of dimensions.

Parameters

xc, yc, zc, and tc are the centers of the Gaussian in the X, Y, Z, and T directions, respectively.

wx, wy, wz, and wt are the widths of the Gaussian in the X, Y, Z, and T directions, respectively.

Note that w_i here is the standard deviation of the Gaussian. This is different from the width parameter in the gauss curve fitting function, which is sqrt(2) times the standard deviation.

Note also that the Gauss function lacks the cross-correlation parameter that is included in the Gauss2D curve fitting function.

Examples

Make/N=100 eee=gauss(x,50,10)
Print area(eee,-inf,inf)
  0.999999
Make/N=(100,100) ddd=gauss(x,50,10,y,50,15)
Print area(ddd,-inf,inf)
  0.999137

See Also

Gauss1D (duplicates the Gauss built-in curve fitting function)

Gauss2D (duplicates the Gauss2D built-in curve fitting function)