On Tue, Jun 3, 2014 at 6:06 AM, Benoit Jacob <jacob.benoi...@gmail.com>
wrote:
>
>
>
> 2014-06-03 3:34 GMT-04:00 Dirk Schulze <dschu...@adobe.com>:
>
>
>> On Jun 2, 2014, at 12:11 AM, Benoit Jacob <jacob.benoi...@gmail.com>
>> wrote:
>>
>> > Objection #6:
>> >
>> > The determinant() method, being in this API the only easy way to get
>> > something that looks roughly like a measure of invertibility, will
>> probably
>> > be (mis-)used as a measure of invertibility. So I'm quite confident
>> that it
>> > has a strong mis-use case. Does it have a strong good use case? Does it
>> > outweigh that? Note that if the intent is precisely to offer some kind
>> of
>> > measure of invertibility, then that is yet another thing that would be
>> best
>> > done with a singular values decomposition (along with solving, and with
>> > computing a polar decomposition, useful for interpolating matrices), by
>> > returning the ratio between the lowest and the highest singular value.
>>
>> Looking at use cases, then determinant() is indeed often used for:
>>
>> * Checking if a matrix is invertible.
>> * Part of actually inverting the matrix.
>> * Part of some decomposing algorithms as the one in CSS Transforms.
>>
>> I should note that the determinant is the most common way to check for
>> invertibility of a matrix and part of actually inverting the matrix. Even
>> Cairo Graphics, Skia and Gecko’s representation of matrix3x3 do use the
>> determinant for these operations.
>>
>
> I didn't say that determinant had no good use case. I said that it had
> more bad use cases than it had good ones. If its only use case if checking
> whether the cofactors formula will succeed in computing the inverse, then
> make that part of the inversion API so you don't compute the determinant
> twice.
>
> Here is a good use case of determinant, except it's bad because it
> computes the determinant twice:
>
> if (matrix.determinant() != 0) { // once
> result = matrix.inverse(); // twice
> }
>
> If that's the only thing we use the determinant for, then we're better
> served by an API like this, allowing to query success status:
>
> var matrixInversionResult = matrix.inverse(); // once
> if (matrixInversionResult.invertible()) {
> result = matrixInversionResult.inverse();
> }
>
> Typical bad uses of the determinant as "measures of invertibility"
> typically occur in conjunction with people thinking they do the right thing
> with "fuzzy compares", like this typical bad pattern:
>
> if (matrix.determinant() < 1e-6) {
> return error;
> }
> result = matrix.inverse();
>
> Multiple things are wrong here:
>
> 1. First, as mentioned above, the determinant is being computed twice
> here.
>
> 2. Second, floating-point scale invariance is broken: floating point
> computations should generally work for all values across the whole exponent
> range, which for doubles goes from 1e-300 to 1e+300 roughly. Take the
> matrix that's 0.01*identity, and suppose we're dealing with 4x4 matrices.
> The determinant of that matrix is 1e-8, so that matrix is incorrectly
> treated as non-invertible here.
>
> 3. Third, if the primary use for the determinant is invertibility and
> inversion is implemented by cofactors (as it would be for 4x4 matrices)
> then in that case only an exact comparison of the determinant to 0 is
> relevant. That's a case where no fuzzy comparison is meaningful. If one
> wanted to guard against cancellation-induced imprecision, one would have to
> look at cofactors themselves, not just at the determinant.
>
> In full generality, the determinant is just the volume of the unit cube
> under the matrix transformation. It is exactly zero if and only if the
> matrix is singular. That doesn't by itself give any interpretation of other
> nonzero values of the determinant, not even "very small" ones.
>
> For special classes of matrices, things are different. Some classes of
> matrices have a specific determinant, for example rotations have
> determinant one, which can be used to do useful things. So in a
> sufficiently advanced or specialized matrix API, the determinant is useful
> to expose. DOMMatrix is special in that it is not advanced and not
> specialized.
>
I agree with your points. Let's drop determinant for now.
If authors start to demand it, we can add it back in later.
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