Have you thought about using cython to work with the numpy C-API ( 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) to deal with scalars. This will make sure they get broadcast correctly. On Tue, Feb 1, 2011 at 11:22 AM, wrote:

Thanks for the advice.

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 To: Discussion of Numerical Python 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@scipy.org ------------------------------

Hi,

On Mon, Jan 31, 2011 at 5:15 PM, <*DParker@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:+13103507e-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 _______________________________________________ NumPy-Discussion mailing list* **NumPy-Discussion@scipy.org* * **http://mail.scipy.org/mailman/listinfo/numpy-discussion*http://mail.scipy.org/mailman/listinfo/numpy-discussion

[attachment "air_gamma.py" deleted by Dave Parker/Chromalloy] _______________________________________________

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

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

I am curious: why you recommend against this? Using the C-API through cython seems more attractive than using the Cython-specific numpy features since they need a specific number of dimensions (and I don't think they broadcast) and don't seem that much easier. Are there hidden disadvantages to using the C-API? Have I misunderstood something? John On Tue, Feb 1, 2011 at 11:41 AM, Sturla Molden wrote:

Den 01.02.2011 20:30, skrev John Salvatier:

...

Have you thought about using cython to work with the numpy C-API (http://wiki.cython.org/tutorials/numpy#UsingtheNumpyCAPI)? This will be fast, simple (you can mix and match Python and Cython).

Never do this. Cython has NumPy array support now:

http://docs.cython.org/src/tutorial/numpy.html

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

Den 01.02.2011 20:50, skrev John Salvatier:

I am curious: why you recommend against this? Using the C-API through cython seems more attractive than using the Cython-specific numpy features since they need a specific number of dimensions (and I don't think they broadcast) and don't seem that much easier. Are there hidden disadvantages to using the C-API? Have I misunderstood something?

There is one more thing which should be mentioned: If the algorithm needs to pass an ndarray to a function, this might cause excessive reference counting and boxing/unboxing with Cython. It gets even worse if we want to pass a subarray view of an ndarray, for which Cython will create a new array object. Cython will only play nicely with NumPy arrays if there are no function calls. If there are function calls, we must give up ndarrays and use C pointers directly. Users who don't know the internals of Cython might think that using an ndarray as a function argument is a good idea, or even use slicing to create a view of a subarray. Cython does not forbid this, but it hurts performance immensely. In the NumPy C API we can pass a pointer to a PyArrayObject, adding no overhead beyond the function call. But subarrays are as primitive as in Cython. This makes anything but trivial "computational kernels" painful in Cython or the NumPy C API. Personally I avoid both Cython and the NumPy C API for this reason. There is a very nive language called Fortran 95, for which the compiler knows how to work with arrays. For those that don't use Fortran 95, there are libraries for C++ such as Blitz++. Sturla

On Tue, Feb 1, 2011 at 1:30 PM, John Salvatier wrote:

Have you thought about using cython to work with the numpy C-API ( 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) to deal with scalars. This will make sure they get broadcast correctly.

Don't use "asarray" blindly! Using asarray causes masked_arrays to become regular arrays. If all of the operations in your function are vectorized already, then you are causing your function to unnecessarially break support for subclassed arrays like masked_arrays. Use asanyarray() by default unless it has to be asarray(). Sorry for my rant. I just love masked arrays too much... Ben Root

On Tue, Feb 1, 2011 at 3:20 PM, 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

Does this work? Shouldn't this raise an exception ?

...

...

x.shape (5, 4) y.shape (5, 4) x[y<10] = y Traceback (most recent call last): File "", line 1, in <module> x[y<10] = y ValueError: array is not broadcastable to correct shape

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.

I think delaying the broadcasting to before the assignment to ag might be better. Since your expressions are either in far or in t, delaying the broadcasting would avoid the calculations on the broadcasted array and only broad cast before the assignment maybe something like this with t that is not broadcasted cond = (far<0.005)*((t < 379.) | (t > 4731.)) ag[cond] = (np.zeros(ag.shape) + (-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))[cond]

Josef

David Parker Chromalloy - TDAG

From:        John Salvatier To:        Discussion of Numerical Python 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@scipy.org ________________________________

Have you thought about using cython to work with the numpy C-API (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) to deal with scalars. This will make sure they get broadcast correctly.

On Tue, Feb 1, 2011 at 11:22 AM, wrote: Thanks for the advice.

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 To:        Discussion of Numerical Python 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@scipy.org ________________________________

Hi,

On Mon, Jan 31, 2011 at 5:15 PM, 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. + 3.103507e-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             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 _______________________________________________ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion

[attachment "air_gamma.py" deleted by Dave Parker/Chromalloy] _______________________________________________

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

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

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

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

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 ;-). Please feel free to provide any more information. Regards, eat On Tue, Feb 1, 2011 at 10:20 PM, 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 To: Discussion of Numerical Python 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@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@chromalloy.com*> wrote: Thanks for the advice.

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@gmail.com* > To: Discussion of Numerical Python <*numpy-discussion@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@scipy.org* ------------------------------

Hi,

On Mon, Jan 31, 2011 at 5:15 PM, <*DParker@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:+13103507e-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 _______________________________________________ NumPy-Discussion mailing list* **NumPy-Discussion@scipy.org* * **http://mail.scipy.org/mailman/listinfo/numpy-discussion*http://mail.scipy.org/mailman/listinfo/numpy-discussion

[attachment "air_gamma.py" deleted by Dave Parker/Chromalloy] _______________________________________________

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

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

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

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