Powers and Exponents Filter

The powers and exponents filter applies a unary operation (such as performing exponentiation) to all individual coefficients of a data set.

Category	Math
Node
Parameters	Operation Type: which operation to perform (see below) X: a number that is used as a parameter for some operations
Inputs	Input: the input of the operation
Outputs	Output: the result of the operation

Effect of the Filter

The filter performs one of the following operations on each individual scalar value of the input:

Negate: inverts the sign of the value ( $f(v) = -v$ ), e.g. $3$ becomes $-3$ and $-0.5$ becomes $0.5$ .

Invert: calculates the inverse value ( $f(v) = \frac{1}{v}$ ), e.g. $3$ becomes $1/3$ and $-0.5$ becomes $-2$ .

Natural Log: calculates the natural logartihm (basis $e$ ; $f(v) = \mathrm{ln}(v)$ ), e.g. $1$ becomes $0$ , and $10$ becomes approximately $2.303$ .

Natural Exp: calculates the exponential function ( $f(v) = \mathrm{e}^v$ ), i.e. $1$ becomes approximately $2.718$ and $10$ becomes approximately 22026.

Decimal Log: calculates the logartihm of basis 10 ( $f(v) = \mathrm{log}_{10}(v)$ ), e.g. $10$ becomes $1$ , and $1$ becomes $0$ .

Decimal Exp: calculates 10 to the power of the input ( $f(v) = 10^v$ ), e.g. $1$ becomes $10$ and $-3$ becomes $0.001$ .

Negative Decimal Log: calculates the negation of the logartihm of basis 10 ( $-\mathrm{log}_{10}(v)$ ), e.g. $10$ becomes $-1$ , and $0.01$ becomes $2$ . (This can be used to convert reflectances into abundances.)

Decimal Exp of Negative: calculates 10 to the power of the input negated ( $f(v) = 10^{-v}$ ), e.g. $1$ becomes $0.1$ and $-3$ becomes $1000$ . (This can be used to convert abundances into reflectances.)

Binary Log: calculates the logartihm of basis 2 ( $f(v) = \mathrm{log}_{2}(v)$ ), e.g. $2$ becomes $1$ , and $1$ becomes $0$ .

Binary Exp: calculates 2 to the power of the input ( $f(v) = 2^v$ ), e.g. $1$ becomes $2$ and $-3$ becomes $0.125$ .

Square: calculates the square of the input ( $f(v) = v^2$ ), e.g. $3$ becomes $9$ and $5$ becomes $25$ .

Square Root: calculates the square root of the input ( $f(v) = \sqrt{v}$ ), e.g. $16$ becomes $4$ , and $100$ becomes $10$ .

Generic Log: calculates a generic logartihm to the basis of the supplied parameter X of the input (X must be positive and not equal to 1, $f(v) = \mathrm{log}_X(v)$ ), e.g. $9$ becomes $2$ if X is $3$ .

Generic Exp: calculates the supplied parameter X raised to the power of the input (X must be non-negative, $f(v) = X^v$ ), e.g. $2$ becomes $0.25$ if X is $0.5$ .

Generic Power: calculates the input raised to the power of the supplied parameter X ( $f(v) = v^X$ ), e.g. $2.5$ becomes $15.625$ if X is $3$ .

Note

The result of this operation may be NaN (not a number) or infinity if the input data has certain values. Notably, a fractional power of a negative input will give NaN (this includes the square root operation); the inverse of 0 will give infinity.