# [Numpy-discussion] Vectorize or rewrite function to work with array inputs?

eat e.antero.tammi at gmail.com
Tue Feb 1 17:27:25 EST 2011

```Hi David,

(I think the discussion has divergegd, but newer mind ;-)

I didn't treat far as a vector (yet, but for sure it's doable). Anyway befor
going on more details I'll suggest you*ll study my new attachment. As far I
can see, you just have 'simple' polynomial evaluatons, which I have
refactored such a way that you just need to provide the coefficients arrays.
There is no need to write explicitly polynomial evaluation in the code. My
opinion is that the computational side (if your functions really are like
shown sofar) will be pretty straightforward. Then it boils down how to
handle the coefficient arrays reasonable (perhaps some kind of lightweigt
'database' for them ;-).

Regards,
eat

On Tue, Feb 1, 2011 at 10:20 PM, <DParker at chromalloy.com> wrote:

> I'm not sure I need to dive into cython or C for this - performance is not
> an issue for my problem - I just want a flexible function that will accept
> scalars or arrays.
>
> Both Sebastian's and eat's suggestions show using indexing to handle the
> conditional statements in the original function. The problem I'm having
> implementing this is in getting the input arguments and outputs to a common
> array size. Here's how I can do this but it seems ugly:
>
> # t and far are function arguments which may be scalars or arrays
> # ag is the output array
> # need to make everything array with common length
> t = np.array(t, ndmin=1)        # Convert t to an array
> far = np.array(far, ndmin=1)        # Convert far to an array
> ag = t*far*np.nan                        # Make an output array of the
> proper length using broadcasting rules
> t = np.zeros_like(ag)+t                # Expand t to the length of the
> output array
> far = np.zeros_like(ag)+far        # Expand far to the length of the output
> array
>
> Now with all arrays the same length I can use indexing with logical
> statements:
> ag[far<0.005] = -3.472487e-22 * t ** 6. + 6.218811e-18 * t ** 5. -
> 4.428098e-14 * t ** 4. + \
>                 1.569889e-10 * t ** 3. - 0.0000002753524 * t ** 2. +
> 0.0001684666 * t + 1.368652
>
> The resulting code looks like this:
> import numpy as np
>
> def air_gamma_dp(t, far=0.0):
>     """
>     Specific heat ratio (gamma) of Air/JP8
>     t - static temperature, Rankine
>     [far] - fuel air ratio [- defaults to 0.0 (dry air)]
>     air_gamma - specific heat ratio
>     """
>     t = np.array(t, ndmin=1)
>     far = np.array(far, ndmin=1)
>     ag = t*far*np.nan
>     t = np.zeros_like(ag)+t
>     far = np.zeros_like(ag)+far
>
>     far[(far<0.) | (far>0.069)] = np.nan
>     t[(t < 379.) | (t > 4731.)] = np.nan
>     ag[(far<0.005)] = -3.472487e-22 * t ** 6. + 6.218811e-18 * t ** 5. -
> 4.428098e-14 * t ** 4. +
>                        1.569889e-10 * t ** 3. - 0.0000002753524 * t ** 2. +
> 0.0001684666 * t + 1.368652
>     t[(t < 699.) | (t > 4731.)] = np.nan
>     a6 = 4.114808e-20 * far ** 3. - 1.644588e-20 * far ** 2. + 3.103507e-21
> * far - 3.391308e-22
>     a5 = -6.819015e-16 * far ** 3. + 2.773945e-16 * far ** 2. -
> 5.469399e-17 * far + 6.058125e-18
>     a4 = 4.684637e-12 * far ** 3. - 1.887227e-12 * far ** 2. + 3.865306e-13
> * far - 4.302534e-14
>     a3 = -0.00000001700602 * far ** 3. + 0.000000006593809 * far ** 2. -
> 0.000000001392629 * far + 1.520583e-10
>     a2 = 0.00003431136 * far ** 3. - 0.00001248285 * far ** 2. +
> 0.000002688007 * far - 0.0000002651616
>     a1 = -0.03792449 * far ** 3. + 0.01261025 * far ** 2. - 0.002676877 *
> far + 0.0001580424
>     a0 = 13.65379 * far ** 3. - 3.311225 * far ** 2. + 0.3573201 * far +
> 1.372714
>     ag[far>=0.005] = a6 * t ** 6. + a5 * t ** 5. + a4 * t ** 4. + a3 * t **
> 3. + a2 * t ** 2. + a1 * t + a0
>     return ag
>
> I was hoping there was a more elegant way to do this.
>
> David Parker
> Chromalloy - TDAG
>
>
>
> From:        John Salvatier <jsalvati at u.washington.edu>
> To:        Discussion of Numerical Python <numpy-discussion at scipy.org>
> Date:        02/01/2011 02:29 PM
>  Subject:        Re: [Numpy-discussion] Vectorize or rewrite function to
> work with array inputs?
> Sent by:        numpy-discussion-bounces at scipy.org
> ------------------------------
>
>
>
> Have you thought about using cython to work with the numpy C-API (*
> http://wiki.cython.org/tutorials/numpy#UsingtheNumpyCAPI*<http://wiki.cython.org/tutorials/numpy#UsingtheNumpyCAPI>)?
> This will be fast, simple (you can mix and match Python and Cython).
>
> As for your specific issue: you can simply cast to all the inputs to numpy
> arrays (using asarray *
> http://docs.scipy.org/doc/numpy/reference/generated/numpy.asarray.html*<http://docs.scipy.org/doc/numpy/reference/generated/numpy.asarray.html>)
> to deal with scalars. This will make sure they get broadcast correctly.
>
> On Tue, Feb 1, 2011 at 11:22 AM, <*DParker at chromalloy.com*<DParker at chromalloy.com>>
> wrote:
>
> Using Sebastian's advice I was able to write a version that worked when the
> input arguments are both arrays with the same length. The code provided by
> eat works when t is an array, but not for an array of far.
>
> The numpy.vectorize version works with any combination of scalar or array
> input. I still haven't figured out how to rewrite my function to be as
> flexible as the numpy.vectorize version at accepting either scalars or array
> inputs and properly broadcasting the scalar arguments to the array
> arguments.
>
> David Parker
> Chromalloy - TDAG
>
>
>
> From:        eat <*e.antero.tammi at gmail.com* <e.antero.tammi at gmail.com>>
> To:        Discussion of Numerical Python <*numpy-discussion at scipy.org*<numpy-discussion at scipy.org>
> >
> Date:        01/31/2011 11:37 AM
> Subject:        Re: [Numpy-discussion] Vectorize or rewrite function to
> work with array inputs?
> Sent by:        *numpy-discussion-bounces at scipy.org*<numpy-discussion-bounces at scipy.org>
> ------------------------------
>
>
>
>
> Hi,
>
> On Mon, Jan 31, 2011 at 5:15 PM, <*DParker at chromalloy.com*<DParker at chromalloy.com>>
> wrote:
> I have several functions like the example below that I would like to make
> compatible with array inputs. The problem is the conditional statements give
> a *ValueError: The truth value of an array with more than one element is
> ambiguous. Use a.any() or a.all()*. I can use numpy.vectorize, but if
> possible I'd prefer to rewrite the function. Does anyone have any advice the
> best way to modify the code to accept array inputs? Thanks in advance for
> any assistance.
>
> If I understod your question correctly, then air_gamma could be coded as:
> def air_gamma_0(t, far=0.0):
>     """
>     Specific heat ratio (gamma) of Air/JP8
>     t - static temperature, Rankine
>     [far] - fuel air ratio [- defaults to 0.0 (dry air)]
>     air_gamma - specific heat ratio
>     """
>     if far< 0.:
>         return NAN
>     elif far < 0.005:
>         ag= air_gamma_1(t)
>         ag[np.logical_or(t< 379., t> 4731.)]= NAN
>         return ag
>     elif far< 0.069:
>         ag= air_gamma_2(t, far)
>         ag[np.logical_or(t< 699., t> 4731.)]= NAN
>         return ag
>     else:
>         return NAN
> Rest of the code is in the attachment.
>
>
> My two cents,
> eat
>
>
>
> NAN = float('nan')
>
> def air_gamma(t, far=0.0):
>     """
>     Specific heat ratio (gamma) of Air/JP8
>     t - static temperature, Rankine
>     [far] - fuel air ratio [- defaults to 0.0 (dry air)]
>     air_gamma - specific heat ratio
>     """
>     if far < 0.:
>         return NAN
>     elif far < 0.005:
>         if t < 379. or t > 4731.:
>             return NAN
>         else:
>             air_gamma = -3.472487e-22 * t ** 6. + 6.218811e-18 * t ** 5. -
> 4.428098e-14 * t ** 4. + 1.569889e-10 * t ** 3. - 0.0000002753524 * t ** 2.
> + 0.0001684666 * t + 1.368652
>     elif far < 0.069:
>         if t < 699. or t > 4731.:
>             return NAN
>         else:
>             a6 = 4.114808e-20 * far ** 3. - 1.644588e-20 * far ** 2. + *
> 3.103507* <tel:+13103507>e-21 * far - 3.391308e-22
>             a5 = -6.819015e-16 * far ** 3. + 2.773945e-16 * far ** 2. -
> 5.469399e-17 * far + 6.058125e-18
>             a4 = 4.684637e-12 * far ** 3. - 1.887227e-12 * far ** 2. +
> 3.865306e-13 * far - 4.302534e-14
>             a3 = -0.00000001700602 * far ** 3. + 0.000000006593809 * far **
> 2. - 0.000000001392629 * far + 1.520583e-10
>             a2 = 0.00003431136 * far ** 3. - 0.00001248285 * far ** 2. +
> 0.000002688007 * far - 0.0000002651616
>             a1 = -0.03792449 * far ** 3. + 0.01261025 * far ** 2. -
> 0.002676877 * far + 0.0001580424
>             a0 = 13.65379 * far ** 3. - 3.311225 * far ** 2. + 0.3573201 *
> far + 1.372714
>             air_gamma = a6 * t ** 6. + a5 * t ** 5. + a4 * t ** 4. + a3 * t
> ** 3. + a2 * t ** 2. + a1 * t + a0
>     elif far >= 0.069:
>         return NAN
>     else:
>         return NAN
>     return air_gamma
>
> David Parker
> Chromalloy - TDAG
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> [attachment "air_gamma.py" deleted by Dave Parker/Chromalloy]
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