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Apologies in advance - I seem to be having a very fundamental misunderstanding that I can't clear up. I have a fourvector class with variables for ct and the position vector. I'm writing code to perform an x-direction lorentz boost. The problem I'm running in to is that I, as it's written below, ct returns with a proper float value, but x does not. Messing around, I find that tempx is a float, but assigning tempx to r[0] does not make that into a float, instead it rounds down to an int. I have previously posted a question on mutability vs immutability, and I suspect this is the issue. If so I clearly have a deeper misunderstanding than expected. Regardless, there are a couple of questions I have;
1a) If instantiate a with a = FourVector(ct=5,r=[55,2.,3]), then type(a._r[0]) returns numpy.float64 as opposed to numpy.int32. What is going on here? I expected just a._r[1] to be a float, and instead it changes the type of the whole list?
1b) How do I get the above behaviour (The whole list being floats), without having to instantiate the variables as floats? I read up on the documentation and have tried various methods, like using astype(float), but everything I do seems to keep it as an int. Again, thinking this is the mutable/immutable problem I'm having.
2) I had thought, in the tempx=... line, multiplying by 1.0 would convert it to a float, as it appears this is the reason ct converts to a float, but for some reason it doesn't. Perhaps the same reason as the others?
import numpy as np
class FourVector():
def __init__(self, ct=0, x=0, y=0, z=0, r=[]):
self._ct = ct
self._r = np.array(r)
if r == []:
self._r = np.array([x,y,z])
def boost(self, beta):
gamma=1/np.sqrt(1-(beta ** 2))
tempct=(self._ct*gamma-beta*gamma*self._r[0])
tempx=(-1.0*self._ct*beta*gamma+self._r[0]*gamma)
self._ct=tempct
print(type(self._r[0]))
self._r[0]=tempx.astype(float)
print(type(self._r[0]))
a = FourVector(ct=5,r=[55,2,3])
b = FourVector(ct=1,r=[4,5,6])
print(a._r)
a.boost(.5)
print(a._r)
All your problems are indeed related.
A numpy array is an array that holds objects efficiently. It does this by having these objects be of the same type, like strings (of equal length) or integers or floats. It can then easily calculate just how much space each element needs and how many bytes it must "jump" to access the next element (we call these the "strides").
When you create an array from a list, numpy will try to determine a suitable data type ("dtype") from that list, to ensure all elements can be represented well. Only when you specify the dtype explicitly, will it not make an educated guess.
Consider the following example:
>>> import numpy as np
>>> integer_array = np.array([1,2,3]) # pass in a list of integers
>>> integer_array
array([1, 2, 3])
>>> integer_array.dtype
dtype('int64')
As you can see, on my system it returns a data type of int64, which is a representation of integers using 8 bytes. It chooses this, because:
numpy recognizes all elements of the list are integers
my system is a 64-bit system
Now consider an attempt at changing that array:
>>> integer_array[0] = 2.4 # attempt to put a float in an array with dtype int
>>> integer_array # it is automatically converted to an int!
array([2, 2, 3])
As you can see, once a datatype for an array was set, automatic casting to that datatype is done.
Let's now consider what happens when you pass in a list that has at least one float:
>>> float_array = np.array([1., 2,3])
>>> float_array
array([ 1., 2., 3.])
>>> float_array.dtype
dtype('float64')
Once again, numpy determines a suitable datatype for this array.
Blindly attempting to change the datatype of an array is not wise:
>>> integer_array.dtype = np.float32
>>> integer_array
array([ 2.80259693e-45, 0.00000000e+00, 2.80259693e-45,
0.00000000e+00, 4.20389539e-45, 0.00000000e+00], dtype=float32)
Those numbers are gibberish you might say. That's because numpy tries to reinterpret the memory locations of that array as 4-byte floats (the skilled people will be able to convert the numbers to binary representation and from there reinterpret the original integer values).
If you want to cast, you'll have to do it explicitly and numpy will return a new array:
>>> integer_array.dtype = np.int64 # go back to the previous interpretation
>>> integer_array
array([2, 2, 3])
>>> integer_array.astype(np.float32)
array([ 2., 2., 3.], dtype=float32)
Now, to address your specific questions:
1a) If instantiate a with a = FourVector(ct=5,r=[55,2.,3]), then type(a._r[0]) returns numpy.float64 as opposed to numpy.int32. What is going on here? I expected just a._r[1] to be a float, and instead it changes the type of the whole list?
That's because numpy has to determine a datatype for the entire array (unless you use a structured array), ensuring all elements fit in that datatype. Only then can numpy iterate over the elements of that array efficiently.
1b) How do I get the above behaviour (The whole list being floats), without having to instantiate the variables as floats? I read up on the documentation and have tried various methods, like using astype(float), but everything I do seems to keep it as an int. Again, thinking this is the mutable/immutable problem I'm having.
Specify the dtype when you are creating the array. In your code, that would be:
self._r = np.array(r, dtype=np.float)
2) I had thought, in the tempx=... line, multiplying by 1.0 would convert it to a float, as it appears this is the reason ct converts to a float, but for some reason it doesn't. Perhaps the same reason as the others?
That is true. Try printing the datatype of tempx, it should be a float. However, later on, you are reinserting that value into the array self._r, which has the dtype of int. And as you saw previously, that will cast the float back to an integer type.
I'm encountering a problem with incorrect numpy calculations when the inputs to a calculation are a numpy array with a 32-bit integer data type, but the outputs include larger numbers that require 64-bit representation.
Here's a minimal working example:
arr = np.ones(5, dtype=int) * (2**24 + 300) # arr.dtype defaults to 'int32'
# Following comment from #hpaulj I changed the first line, which was originally:
# arr = np.zeros(5, dtype=int)
# arr[:] = 2**24 + 300
single_value_calc = 2**8 * (2**24 + 300)
numpy_calc = 2**8 * arr
print(single_value_calc)
print(numpy_calc[0])
# RESULTS
4295044096
76800
The desired output is that the numpy array contains the correct value of 4295044096, which requires 64 bits to represent it. i.e. I would have expected numpy arrays to automatically upcast from int32 to int64 when the output requires it, rather maintaining a 32-bit output and wrapping back to 0 after the value of 2^32 is exceeded.
Of course, I can fix the problem manually by forcing int64 representation:
numpy_calc2 = 2**8 * arr.astype('int64')
but this is undesirable for general code, since the output will only need 64-bit representation (i.e. to hold large numbers) in some cases and not all. In my use case, performance is critical so forcing upcasting every time would be costly.
Is this the intended behaviour of numpy arrays? And if so, is there a clean, performant solution please?
Type casting and promotion in numpy is fairly complicated and occasionally surprising. This recent unofficial write-up by Sebastian Berg explains some of the nuances of the subject (mostly concentrating on scalars and 0d arrays).
Quoting from this document:
Python Integers and Floats
Note that python integers are handled exactly like numpy ones. They are, however, special in that they do not have a dtype associated with them explicitly. Value based logic, as described here, seems useful for python integers and floats to allow:
arr = np.arange(10, dtype=np.int8)
arr += 1
# or:
res = arr + 1
res.dtype == np.int8
which ensures that no upcast (for example with higher memory usage) occurs.
(emphasis mine.)
See also Allan Haldane's gist suggesting C-style type coercion, linked from the previous document:
Currently, when two dtypes are involved in a binary operation numpy's principle is that "the output dtype's range covers the range of both input dtypes", and when a single dtype is involved there is never any cast.
(emphasis again mine.)
So my understanding is that the promotion rules for numpy scalars and arrays differ, primarily because it's not feasible to check every element inside an array to determine whether casting can be done safely. Again from the former document:
Scalar based rules
Unlike arrays, where inspection of all values is not feasable, for scalars (and 0-D arrays) the value is inspected.
This would mean that you can either use np.int64 from the start to be safe (and if you're on linux then dtype=int will actually do this on its own), or check the maximum value of your arrays before suspect operations and determine if you have to promote the dtype yourself, on a case-by-case basis. I understand that this might not be feasible if you are doing a lot of calculations, but I don't believe there is a way around this considering numpy's current type promotion rules.
Apologies in advance - I seem to be having a very fundamental misunderstanding that I can't clear up. I have a fourvector class with variables for ct and the position vector. I'm writing code to perform an x-direction lorentz boost. The problem I'm running in to is that I, as it's written below, ct returns with a proper float value, but x does not. Messing around, I find that tempx is a float, but assigning tempx to r[0] does not make that into a float, instead it rounds down to an int. I have previously posted a question on mutability vs immutability, and I suspect this is the issue. If so I clearly have a deeper misunderstanding than expected. Regardless, there are a couple of questions I have;
1a) If instantiate a with a = FourVector(ct=5,r=[55,2.,3]), then type(a._r[0]) returns numpy.float64 as opposed to numpy.int32. What is going on here? I expected just a._r[1] to be a float, and instead it changes the type of the whole list?
1b) How do I get the above behaviour (The whole list being floats), without having to instantiate the variables as floats? I read up on the documentation and have tried various methods, like using astype(float), but everything I do seems to keep it as an int. Again, thinking this is the mutable/immutable problem I'm having.
2) I had thought, in the tempx=... line, multiplying by 1.0 would convert it to a float, as it appears this is the reason ct converts to a float, but for some reason it doesn't. Perhaps the same reason as the others?
import numpy as np
class FourVector():
def __init__(self, ct=0, x=0, y=0, z=0, r=[]):
self._ct = ct
self._r = np.array(r)
if r == []:
self._r = np.array([x,y,z])
def boost(self, beta):
gamma=1/np.sqrt(1-(beta ** 2))
tempct=(self._ct*gamma-beta*gamma*self._r[0])
tempx=(-1.0*self._ct*beta*gamma+self._r[0]*gamma)
self._ct=tempct
print(type(self._r[0]))
self._r[0]=tempx.astype(float)
print(type(self._r[0]))
a = FourVector(ct=5,r=[55,2,3])
b = FourVector(ct=1,r=[4,5,6])
print(a._r)
a.boost(.5)
print(a._r)
All your problems are indeed related.
A numpy array is an array that holds objects efficiently. It does this by having these objects be of the same type, like strings (of equal length) or integers or floats. It can then easily calculate just how much space each element needs and how many bytes it must "jump" to access the next element (we call these the "strides").
When you create an array from a list, numpy will try to determine a suitable data type ("dtype") from that list, to ensure all elements can be represented well. Only when you specify the dtype explicitly, will it not make an educated guess.
Consider the following example:
>>> import numpy as np
>>> integer_array = np.array([1,2,3]) # pass in a list of integers
>>> integer_array
array([1, 2, 3])
>>> integer_array.dtype
dtype('int64')
As you can see, on my system it returns a data type of int64, which is a representation of integers using 8 bytes. It chooses this, because:
numpy recognizes all elements of the list are integers
my system is a 64-bit system
Now consider an attempt at changing that array:
>>> integer_array[0] = 2.4 # attempt to put a float in an array with dtype int
>>> integer_array # it is automatically converted to an int!
array([2, 2, 3])
As you can see, once a datatype for an array was set, automatic casting to that datatype is done.
Let's now consider what happens when you pass in a list that has at least one float:
>>> float_array = np.array([1., 2,3])
>>> float_array
array([ 1., 2., 3.])
>>> float_array.dtype
dtype('float64')
Once again, numpy determines a suitable datatype for this array.
Blindly attempting to change the datatype of an array is not wise:
>>> integer_array.dtype = np.float32
>>> integer_array
array([ 2.80259693e-45, 0.00000000e+00, 2.80259693e-45,
0.00000000e+00, 4.20389539e-45, 0.00000000e+00], dtype=float32)
Those numbers are gibberish you might say. That's because numpy tries to reinterpret the memory locations of that array as 4-byte floats (the skilled people will be able to convert the numbers to binary representation and from there reinterpret the original integer values).
If you want to cast, you'll have to do it explicitly and numpy will return a new array:
>>> integer_array.dtype = np.int64 # go back to the previous interpretation
>>> integer_array
array([2, 2, 3])
>>> integer_array.astype(np.float32)
array([ 2., 2., 3.], dtype=float32)
Now, to address your specific questions:
1a) If instantiate a with a = FourVector(ct=5,r=[55,2.,3]), then type(a._r[0]) returns numpy.float64 as opposed to numpy.int32. What is going on here? I expected just a._r[1] to be a float, and instead it changes the type of the whole list?
That's because numpy has to determine a datatype for the entire array (unless you use a structured array), ensuring all elements fit in that datatype. Only then can numpy iterate over the elements of that array efficiently.
1b) How do I get the above behaviour (The whole list being floats), without having to instantiate the variables as floats? I read up on the documentation and have tried various methods, like using astype(float), but everything I do seems to keep it as an int. Again, thinking this is the mutable/immutable problem I'm having.
Specify the dtype when you are creating the array. In your code, that would be:
self._r = np.array(r, dtype=np.float)
2) I had thought, in the tempx=... line, multiplying by 1.0 would convert it to a float, as it appears this is the reason ct converts to a float, but for some reason it doesn't. Perhaps the same reason as the others?
That is true. Try printing the datatype of tempx, it should be a float. However, later on, you are reinserting that value into the array self._r, which has the dtype of int. And as you saw previously, that will cast the float back to an integer type.
Suppose I enter:
a = uint8(200)
a*2
Then the result is 400, and it is recast to be of type uint16.
However:
a = array([200],dtype=uint8)
a*2
and the result is
array([144], dtype=uint8)
The multiplication has been performed modulo 256, to ensure that the result stays in one byte.
I'm confused about "types" and "dtypes" and where one is used in preference to another. And as you see, the type may make a significant difference in the output.
Can I, for example, create a single number of dtype uint8, so that operations on that number will be performed modulo 256? Alternatively, can I create an array of type (not dtype) uint8 so that operations on it will produce values outside the range 0-255?
The simple, high-level answer is that NumPy layers a second type system atop Python's type system.
When you ask for the type of an NumPy object, you get the type of the container--something like numpy.ndarray. But when you ask for the dtype, you get the (numpy-managed) type of the elements.
>>> from numpy import *
>>> arr = array([1.0, 4.0, 3.14])
>>> type(arr)
<type 'numpy.ndarray'>
>>> arr.dtype
dtype('float64')
Sometimes, as when using the default float type, the element data type (dtype) is equivalent to a Python type. But that's equivalent, not identical:
>>> arr.dtype == float
True
>>> arr.dtype is float
False
In other cases, there is no equivalent Python type. For example, when you specified uint8. Such data values/types can be managed by Python, but unlike in C, Rust, and other "systems languages," managing values that align directly to machine data types (like uint8 aligns closely with "unsigned bytes" computations) is not the common use-case for Python.
So the big story is that NumPy provides containers like arrays and matrices that operate under its own type system. And it provides a bunch of highly useful, well-optimized routines to operate on those containers (and their elements). You can mix-and-match NumPy and normal Python computations, if you use care.
There is no Python type uint8. There is a constructor function named uint8, which when called returns a NumPy type:
>>> u = uint8(44)
>>> u
44
>>> u.dtype
dtype('uint8')
>>> type(u)
<type 'numpy.uint8'>
So "can I create an array of type (not dtype) uint8...?" No. You can't. There is no such animal.
You can
do computations constrained to uint8 rules without using NumPy arrays (a.k.a. NumPy scalar values). E.g.:
>>> uint8(44 + 1000)
20
>>> uint8(44) + uint8(1000)
20
But if you want to compute values mod 256, it's probably easier to use Python's mod operator:
>> (44 + 1000) % 256
20
Driving data values larger than 255 into uint8 data types and then doing arithmetic is a rather backdoor way to get mod-256 arithmetic. If you're not careful, you'll either cause Python to "upgrade" your values to full integers (killing your mod-256 scheme), or trigger overflow exceptions (because tricks that work great in C and machine language are often flagged by higher level languages).
The type of a NumPy array is numpy.ndarray; this is just the type of Python object it is (similar to how type("hello") is str for example).
dtype just defines how bytes in memory will be interpreted by a scalar (i.e. a single number) or an array and the way in which the bytes will be treated (e.g. int/float). For that reason you don't change the type of an array or scalar, just its dtype.
As you observe, if you multiply two scalars, the resulting datatype is the smallest "safe" type to which both values can be cast. However, multiplying an array and a scalar will simply return an array of the same datatype. The documentation for the function np.inspect_types is clear about when a particular scalar or array object's dtype is changed:
Type promotion in NumPy works similarly to the rules in languages like C++, with some slight differences. When both scalars and arrays are used, the array's type takes precedence and the actual value of the scalar is taken into account.
The documentation continues:
If there are only scalars or the maximum category of the scalars is higher than the maximum category of the arrays, the data types are combined with promote_types to produce the return value.
So for np.uint8(200) * 2, two scalars, the resulting datatype will be the type returned by np.promote_types:
>>> np.promote_types(np.uint8, int)
dtype('int32')
For np.array([200], dtype=np.uint8) * 2 the array's datatype takes precedence over the scalar int and a np.uint8 datatype is returned.
To address your final question about retaining the dtype of a scalar during operations, you'll have to restrict the datatypes of any other scalars you use to avoid NumPy's automatic dtype promotion:
>>> np.array([200], dtype=np.uint8) * np.uint8(2)
144
The alternative, of course, is to simply wrap the single value in a NumPy array (and then NumPy won't cast it in operations with scalars of different dtype).
To promote the type of an array during an operation, you could wrap any scalars in an array first:
>>> np.array([200], dtype=np.uint8) * np.array([2])
array([400])
A numpy array contains elements of the same type, so np.array([200],dtype=uint8) is an array with one value of type uint8. When you do np.uint8(200), you don't have an array, only a single value. This make a huge difference.
When performing some operation on the array, the type stays the same, irrespective of a single value overflows or not. Automatic upcasting in arrays is forbidden, as the size of the whole array has to change. This is only done if the user explicitly wants that. When performing an operation on a single value, it can easily upcast, not influencing other values.
I am trying to port a portion of a code written in a different language (an obscure one called Igor Pro by Wavemetrics for those of you have heard of it) to Python.
In this code, there is a conversion of a data type from a 16-bit integer (read in from a 16-bit, big endian binary file) to single-precision (32-bit) floating-point. In this program, the conversion is as follows:
Signed 16-bit integer:
print tmp
tmp[0]={-24160,18597,-24160,18597,-24160}
converted to 32-bit floating-point:
Redimension/S/E=1 tmp
print tmp
tmp[0]={339213,339213,5.79801e-41,0,0}
The /S flag/option indicates that the data type of tmp should be float32 instead of int16. However, I believe the important flag/option is /E=1, which is said to "Force reshape without converting or moving data."
In Python, the conversion is as follows:
>>> tmp[:5]
array([-24160, 18597, -24160, 18597, -24160], dtype=int16)
>>> tmp.astype('float32')
array([-24160., 18597., -24160., ..., 18597., -24160., 18597.], dtype=float32)
Which is what I expect, but I need to find a function/operation that emulates the /E=1 option in the original code above. Is there an obvious way in which -24160 and 18597 would both be converted to 339213? Does this have anything to do with byteswap or newbyteorder or something else?
import numpy
tmp=numpy.array([-24160,18597,-24160,18597,-24160, 0], numpy.int16)
tmp.dtype = numpy.float32
print tmp
Result:
[ 3.39213000e+05 3.39213000e+05 5.79801253e-41]
I had to add a zero to the list of value because there are an odd number of values. It cannot interpret those as 32 bit floats since there 5 16 bit values.
Use view instead of astype:
In [9]: tmp=np.array([-24160, 18597, -24160, 18597, -24160, 18597], dtype=int16)
In [10]: tmp.view('float32')
Out[10]: array([ 339213., 339213., 339213.], dtype=float32)
.astype creates a copy of the array cast to the new dtype
.view returns a view of the array (with the same underlying data),
with the data interpreted according to the new dtype.
Is there an obvious way in which -24160 and 18597 would both be converted to 339213?
No, but neither is there any obvious way in which -24160 would convert to 339213 and 5.79801e-41 and 0.
It looks more like the conversion takes two input numbers to create one output (probably by concatenating the raw 2×16 bits to 32 bits and calling the result a float). In that case the pair -24160,18597 consistently becomes 339213, and 5.79801e-41 probably results from -24160,0 where the 0 is invented because we run out of inputs. Since 5.79801e-41 looks like it might be a single-precision denormal, this implies that the two 16-bit blocks are probably concatenated in little-endian order.
It remains to see whether you need to byte-swap each of the 16-bit inputs, but you can check that for yourself.