BUILT-IN MATHEMATICA SYMBOL

ShenCastanMatrix

ShenCastanMatrix[r]
gives a matrix that corresponds to an exponential kernel of radius r.

ShenCastanMatrix[{r, }]
gives a matrix corresponding to an exponential kernel with radius r and region of support specified by .

ShenCastanMatrix[r, {n₁, n₂}]
gives a matrix formed from the derivative of the exponential with respect to rows and the derivative with respect to columns.

ShenCastanMatrix[r, {{n₁₁, n₁₂}, {n₂₁, n₂₂}, ...}]
gives a matrix formed from the sums of the and derivatives.

ShenCastanMatrix[{{r₁, r₂, ...}, }, ...]
gives an array corresponding to an exponential kernel with radius in the i index direction.

Details and Options Details and Options

ShenCastanMatrix[{r, }] gives values proportional to at x index positions from the center, where b is proportional to , so that a value of gives approximately 95% of the total area under the exponential.
ShenCastanMatrix[r] uses .
By default, the elements of ShenCastanMatrix[r] sum to 1.
ShenCastanMatrix[..., {n₁, n₂}] constructs derivatives as finite differences.
ShenCastanMatrix[{Automatic, , f}, ...] constructs a matrix just large enough to include at least a fraction f of the discrete integral of an exponential in each direction.
ShenCastanMatrix allows any of r, , and f to be lists, specifying different values for different directions.
For integer r, ShenCastanMatrix[r, ...] yields a × matrix.
For noninteger r, the value of r is effectively rounded to an integer.
Options for ShenCastanMatrix include:

	WorkingPrecision	Automatic	the precision with which to compute matrix elements
	"Standardization"	True	whether to rescale and shift the matrix to account for truncation

With "Standardization"->True, the elements of ShenCastanMatrix[r] will sum to 1. However, the elements of ShenCastanMatrix[r, {n₁, n₂, ...}] with at least one nonzero will sum to 0, and the sum of the elements, weighted in each direction by times the distance from the origin to the power of , will be 1.