Legacy ImageMagick Discussions Archive

IM 6.6.5.0 Q16 HDRI Mac OSX Tiger

Create gradient:

convert -size 1x256 gradient: -rotate 90 grad1.png

This does not work to make an gaussian:

convert grad1.png -fx "exp(-(u)^2)" grad1_gauss_a.png
identify -verbose grad1_gauss_a.png
Format: PNG (Portable Network Graphics)
Class: PseudoClass
Geometry: 256x1+0+0
Resolution: 72x72
Print size: 3.55556x0.0138889
Units: Undefined
Type: Bilevel
Base type: Bilevel
Endianess: Undefined
Colorspace: Gray
Depth: 16-bit
Channel depth:
gray: 1-bit
Channel statistics:
Gray:
min: 65535 (1)
max: 65535 (1)
mean: 65535 (1)



But this works fine:

convert grad1.png -fx "exp(-pow(u,2))" grad1_gauss_b.png
identify -verbose grad1_gauss_b.png
Format: PNG (Portable Network Graphics)
Class: PseudoClass
Geometry: 256x1+0+0
Resolution: 72x72
Print size: 3.55556x0.0138889
Units: Undefined
Type: Grayscale
Base type: Grayscale
Endianess: Undefined
Colorspace: Gray
Depth: 16-bit
Channel depth:
gray: 16-bit
Channel statistics:
Gray:
min: 24109 (0.36788)
max: 65535 (1)
mean: 48927 (0.746578)

Try this:

• convert grad1.png -fx "exp(-(u^2))" grad1_gauss_a.png

In the mean-time we'll investigate why -(u)^2 does not return a correct result.

Now this seems to work.


sig=0.5
convert grad1.png -fx "exp(-((u/$sig)^2))" grad1_gauss_a.png
identify -verbose grad1_gauss_a.png
...

Channel statistics:
Gray:
min: 1200 (0.0183108)
max: 65535 (1)
mean: 28921 (0.441307)


So perhaps I was looking at the wrong result?


But now this is not working (with a radial gradient):

convert -size 256x256 radial-gradient: -negate radgrad256.png

sig=0.5
convert radgrad256.png -fx "exp(-(u/$sig)^2)" radgrad256_gauss_b.png
identify -verbose radgrad256_gauss_b.png
...
Channel statistics:
Gray:
min: 65535 (1)
max: 65535 (1)
mean: 65535 (1)



But this still works:

sig=0.5
convert radgrad256.png -fx "exp(-pow((u/$sig),2))" radgrad256_gauss_a.png
identify -verbose radgrad256_gauss_a.png
...
Channel statistics:
Gray:
min: 1200 (0.0183108)
max: 65527 (0.999878)
mean: 12798.4 (0.195292)




So I am not sure if I am doing something wrong or there is some intermittent issue or what?

Looks like a parenthesis handling issue in FX. It really needs a proper parser (lex? yacc? bison?), even if a FX compiler is not yet on the cards.

Perhaps its not a bug afterall. Take a look at http://www.calculateforfree.com/sci.html. It returns the same results as -fx as follows:

• -(0.5)^2 = 0.25
  -(0.5^2) = -0.25

Which suggests the results of exp(-(u)^2) is expected to be different from exp(-(u^2)). Instead exp(-(u^2)) is equivalent to exp(-pow(u,2)).

magick wrote:Perhaps its not a bug afterall. Take a look at http://www.calculateforfree.com/sci.html. It returns the same results as -fx as follows:

• -(0.5)^2 = 0.25
  -(0.5^2) = -0.25

Which suggests the results of exp(-(u)^2) is expected to be different from exp(-(u^2)). Instead exp(-(u^2)) is equivalent to exp(-pow(u,2)).

Thanks. Strange that the parens don't seem to take precedence in -(0.5)^2 = 0.25 and behaves like (-0.5)^2 = 0.25

Not sure I am using your link correctly, but I get from it:

-(0.5)^2 = NaN

It isn't the parenthesis precedence, but the precendence between unary minus '-' and '^' The uneray minus should be lower precedence (performed AFTER ^) just as normal + and - operators.

The problem is few languages defined this precedence in relation to other operators.
See http://en.wikipedia.org/wiki/Order_of_o ... _languages
for example which does not list 'power-of' though talks about it in the sections above.


Note the parenthesis in -(0.5)^2 should be equivalent to -0.5^2 if precedence rules are being obeyed correctly.
however whether that results in (-0.5)^2 or -(0.5^2) is a matter for the order of the precedence.

magick wrote:Under normal left-to-right associativity, -(0.5)^2 is 0.25, however, in Fortran its interpretted as -0.25. We'll investigate supporting the later interpretation in the next few days.

It is not urgent or really needed as long it is explained somewhere.

We can reproduce the problem you posted and have a patch in ImageMagick 6.6.5-4 Beta available by sometime tomorrow. Thanks.

It has been updated, however i would like to point out that "Debug()" seems to give a indication of how the unary minus is being handled.

convert null: -channel R -fx 'debug(-(0.5)^2)' null:
[0,0].red: -1.0*(0.5)^2=-0.25
convert null: -channel R -fx 'debug(-0.5^2)' null:
[0,0].red: -1.0*0.5^2=-0.25

As such the parenthesis around the single element no-longer matters, which is as it should be.
Note how the unary minus now expands to be "-1.0" multiplier. And that by precedence ^ is now higher than multiply.

Continuing this, using parenthesis to modify the precedence...

convert null: -channel R -fx 'debug(-(0.5^2))' null:
[0,0].red: -1.0*(0.5^2)=-0.25
convert null: -channel R -fx 'debug((-0.5)^2)' null:
[0,0].red: (-1.0*0.5)^2=0.25

Which shows parenthesis is doing as it should.

If you are not certain of the order - apply parenthesis, including the operation you want to take precedence.

However the FX page does not list "-(unary)" in its precedence list. (same level as multiply).