modify a colorSpec responder to emulate (approximate) another responder
The two possible modifications are:
pre-multiplication by a transmitting filter
post-multiplication by a matrix
Both of these are optional.
If neither of these modifications is enabled, the original x is returned.
## S3 method for class 'colorSpec' emulate( x, y, filter=FALSE, matrix=TRUE )
x |
a colorSpec responder with M spectra, to be modified.
The |
y |
a colorSpec responder with N spectra, to be emulated by a modified |
filter |
enable filter pre-multiplication. |
matrix |
enable matrix post-multiplication.
If |
If filter=FALSE and matrix=TRUE then
the returned value is multiply(x,A),
where the matrix A is computed to minimize the difference with
y, in the least squares sense (Frobenius matrix norm).
The function MASS::ginv() is used here.
If filter=TRUE and matrix=FALSE then
the returned value is product(filter,x),
where the object filter is computed to minimize the difference with
y, in the least squares sense (Frobenius matrix norm).
This calculation is fairly straightforward,
but requires that the responsivity of x does not vanish at any wavelength.
It also requires that M=N.
The computed filter may be unrealistic, i.e. the transmittance may be > 1.
If this happens a WARN message is issued.
If filter=TRUE and matrix=TRUE then
the returned value is product(filter,multiply(x,A)),
where (filter,A) are chosen with the above minimization criterion.
If N=1 then we must have M=1 as well;
the calculation is trivial and the emulation is exact.
If N ≥ 2,
the calculation is iterative - solving alternatively for
filter and A until convergence.
The function MASS::ginv() is used on each iteration.
This is a bilinear optimization.
If convergence fails, it is an error and the function returns NULL.
If convergence succeeds, there is 1 degree of freedom in the (filter,A) pair.
If one is scaled by a positive constant, the other can be scaled by the inverse,
and the returned object is the same.
The filter is scaled so the maximum transmittance is 1.
If filter=FALSE and matrix=FALSE then
the original x is returned, with a WARN message.
a colorSpec object close to y, as in Details.
The quantity is the same as y.
The specnames() are the same as those of y,
except that ".em" is appended to each one.
The function attaches attribute "emulate",
whose value is a list containing filter and/or A as appropriate.
see the vignette Emulation of one Camera by another Camera
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