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Question about numpy.arange()

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Gökhan Sever

1 May 2010 1 May '10

8:36 p.m.

Hello,

Is "b" an expected value? I am suspecting another floating point arithmetic issue.

I[1]: a = np.arange(1.6, 1.8, 0.1, dtype='float32')

I[2]: a O[2]: array([ 1.60000002, 1.70000005], dtype=float32)

I[3]: b = np.arange(1.7, 1.8, 0.1, dtype='float32')

I[4]: b O[4]: array([ 1.70000005, 1.79999995], dtype=float32)

A bit conflicting with the np.arange docstring:

"* Values are generated within the half-open interval ``[start, stop)`` (in other words, the interval including `start` but excluding `stop`). * "

Thanks.

-- Gökhan

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Anne Archibald

2 May 2 May

12:57 a.m.

On 1 May 2010 16:36, Gökhan Sever gokhansever@gmail.com wrote:

...

Hello,

Is "b" an expected value? I am suspecting another floating point arithmetic issue.

I[1]: a = np.arange(1.6, 1.8, 0.1, dtype='float32')

I[2]: a O[2]: array([ 1.60000002, 1.70000005], dtype=float32)

I[3]: b = np.arange(1.7, 1.8, 0.1, dtype='float32')

I[4]: b O[4]: array([ 1.70000005, 1.79999995], dtype=float32)

A bit conflicting with the np.arange docstring:

" Values are generated within the half-open interval ``[start, stop)`` (in other words, the interval including `start` but excluding `stop`). "

This is a floating-point issue; since 1.79999995 does not actually equal 1.8, it is included. This arises because 0.1, 1.7, and 1.8 cannot be exactly represented in floating-point.

A good rule to avoid being annoyed by this is: only use arange for integers. Use linspace if you want floating-point.

Anne

...

Thanks.

-- Gökhan

NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion

Keith Goodman

12:59 a.m.

On Sat, May 1, 2010 at 1:36 PM, Gökhan Sever gokhansever@gmail.com wrote:

...

Hello,

Is "b" an expected value? I am suspecting another floating point arithmetic issue.

I[1]: a = np.arange(1.6, 1.8, 0.1, dtype='float32')

I[2]: a O[2]: array([ 1.60000002, 1.70000005], dtype=float32)

I[3]: b = np.arange(1.7, 1.8, 0.1, dtype='float32')

I[4]: b O[4]: array([ 1.70000005, 1.79999995], dtype=float32)

A bit conflicting with the np.arange docstring:

" Values are generated within the half-open interval ``[start, stop)`` (in other words, the interval including `start` but excluding `stop`). "

Try np.linspace(). It works better with floats:

...

...
np.linspace(1.7, 1.8, 2)

array([ 1.7, 1.8])

Warren Weckesser

2:43 a.m.

Gökhan Sever wrote:

...

Hello,

Is "b" an expected value? I am suspecting another floating point arithmetic issue.

Exactly. You'll see the same type of problem with float64, too:

In [17]: z = np.arange(1.7, 1.8, 0.1)

In [18]: z Out[18]: array([ 1.7, 1.8])

In [19]: z[1] == 1.8 Out[19]: True

In [20]: z[1] - 1 Out[20]: 0.80000000000000004

Fun stuff, eh?

To avoid problems like this, I generally use linspace instead of arange.

Warren

...

I[1]: a = np.arange(1.6, 1.8, 0.1, dtype='float32')

I[2]: a O[2]: array([ 1.60000002, 1.70000005], dtype=float32)

I[3]: b = np.arange(1.7, 1.8, 0.1, dtype='float32')

I[4]: b O[4]: array([ 1.70000005, 1.79999995], dtype=float32)

A bit conflicting with the np.arange docstring:

"/ Values are generated within the half-open interval ``[start, stop)`` (in other words, the interval including `start` but excluding `stop`). /"

Thanks.

-- Gökhan

NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion

Robert Kern

3:03 a.m.

On Sat, May 1, 2010 at 15:36, Gökhan Sever gokhansever@gmail.com wrote:

...

Hello,

Is "b" an expected value? I am suspecting another floating point arithmetic issue.

I[1]: a = np.arange(1.6, 1.8, 0.1, dtype='float32')

I[2]: a O[2]: array([ 1.60000002, 1.70000005], dtype=float32)

I[3]: b = np.arange(1.7, 1.8, 0.1, dtype='float32')

I[4]: b O[4]: array([ 1.70000005, 1.79999995], dtype=float32)

A bit conflicting with the np.arange docstring:

" Values are generated within the half-open interval ``[start, stop)`` (in other words, the interval including `start` but excluding `stop`). "

Not at all. 1.79999995 < 1.8 . However, also note this warning in the arange() docs:

""" For floating point arguments, the length of the result is ``ceil((stop - start)/step)``. Because of floating point overflow, this rule may result in the last element of `out` being greater than `stop`. """

You probably want linspace() instead.

-- Robert Kern "I have come to believe that the whole world is an enigma, a harmless enigma that is made terrible by our own mad attempt to interpret it as though it had an underlying truth." -- Umberto Eco

Gökhan Sever

5:51 p.m.

On Sat, May 1, 2010 at 3:36 PM, Gökhan Sever gokhansever@gmail.com wrote:

...

Hello,

Is "b" an expected value? I am suspecting another floating point arithmetic issue.

I[1]: a = np.arange(1.6, 1.8, 0.1, dtype='float32')

I[2]: a O[2]: array([ 1.60000002, 1.70000005], dtype=float32)

I[3]: b = np.arange(1.7, 1.8, 0.1, dtype='float32')

I[4]: b O[4]: array([ 1.70000005, 1.79999995], dtype=float32)

A bit conflicting with the np.arange docstring:

"* Values are generated within the half-open interval ``[start, stop)`` (in other words, the interval including `start` but excluding `stop`). *"

Thanks.

-- Gökhan

Fair enough explanations to use np.linspace instead. What was confusing me above while a[1] and b[0] shows 1.70000005 only "b" steps up to 1.79999995 which "a" can't.

The following is another surprise output:

I[5]: c = np.arange(0.4, 0.5, 0.1, dtype='float32')

I[6]: c O[6]: array([ 0.40000001], dtype=float32)

Anyways, a Slashdotter might have seen me asking these questions. I will go read What Every Programmer Should Know About Floating-Point Arithmetichttp://developers.slashdot.org/story/10/05/02/1427214/What-Every-Programmer-Should-Know-About-Floating-Point-Arithmeticarticle.

-- Gökhan