[Numpy-discussion] Vector magnitude?
Hi, I have two questions: 1) Is there any way in numpy to represent vectors? Currently I'm using 'array' for vectors. 2) Is there a way to calculate the magnitude (length) of a vector in numpy? Thanks. ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://projects.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Vector magnitude?
On Wed, Sep 05, 2007 at 11:55:36AM -0500, Robert Dailey wrote: 1) Is there any way in numpy to represent vectors? Currently I'm using 'array' for vectors. What do you call a vector ? For me a vector is an element of an linear space. In numerical methods what is comonly called a vector is a 1D array of arbitrary length. I suspect you mean something different, given your question 2) Is there a way to calculate the magnitude (length) of a vector in numpy? I am being dumb. What do you mean by magnitude (or length) ? Maybe it is just because I am not a native English speaker. If you are talking about the euclidien norm, I don't know a built in way of doing it, but it is very easy to define a norm function: import numpy as N a = N.arange(3) norm = lambda x: N.sqrt(N.square(x).sum()) norm(a) - 2.2360679775 ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://projects.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Vector magnitude?
2007/9/5, Robert Dailey [EMAIL PROTECTED]: Hi, I have two questions: 1) Is there any way in numpy to represent vectors? Currently I'm using 'array' for vectors. A vector is an array with one dimension, it's OK. You could use a matrix of dimension 1xn or nx1 as well. 2) Is there a way to calculate the magnitude (length) of a vector in numpy? Yes, len(a) Matthieu ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://projects.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Vector magnitude?
Hello, 'len' is a (pretty basic) python builtin function for getting the length of anything with a list-like interface. (Or more generally, getting the size of anything that is sized, e.g. a set or dictionary.) Numpy arrays offer a list-like interface allowing you to iterate along their first dimension, etc. (*) Thus, len(numpy_array) is equivalent to numpy_array.shape[0], which is the number of elements along the first dimension of the array. Zach (*) For example, this is useful if you've got numerous data vectors packed into an array along the first dimension, and want to iterate across the different vectors. a = numpy.ones((number_of_data_elements, size_of_data_element)) for element in a: # element is a 1-D array with a length of 'size_of_data_element' Note further that this works even if your data elements are multi- dimensional; i.e. the above works the same if: element_shape = (x,y,z) a = numpy.ones((number_of_data_elements,)+element_shape) for element in a: # element is a 3-D array with a shape of (x,y,z) On Sep 5, 2007, at 2:40 PM, Robert Dailey wrote: Thanks for your response. I was not able to find len() in the numpy documentation at the following link: http://www.scipy.org/doc/numpy_api_docs/namespace_index.html Perhaps I'm looking in the wrong location? On 9/5/07, Matthieu Brucher [EMAIL PROTECTED] wrote: 2007/9/5, Robert Dailey [EMAIL PROTECTED]: Hi, I have two questions: 1) Is there any way in numpy to represent vectors? Currently I'm using 'array' for vectors. A vector is an array with one dimension, it's OK. You could use a matrix of dimension 1xn or nx1 as well. 2) Is there a way to calculate the magnitude (length) of a vector in numpy? Yes, len(a) Matthieu ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://projects.scipy.org/mailman/listinfo/numpy-discussion ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://projects.scipy.org/mailman/listinfo/numpy-discussion ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://projects.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Vector magnitude?
2007/9/5, Robert Dailey [EMAIL PROTECTED]: Thanks for your response. I was not able to find len() in the numpy documentation at the following link: http://www.scipy.org/doc/numpy_api_docs/namespace_index.html Perhaps I'm looking in the wrong location? Yes, it's a Python function ;) Matthieu ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://projects.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Vector magnitude?
Oh I think I get it. You mean the built-in len() function? This isn't what I am looking for. len() returns the number of components in the vector (e.g. whether it is a 2D, 3D, etc vector). I found that magnitude can be calculated using hypot() in the math module that comes with python. However, this method only appears to work with 2D vectors. And yes, by magnitude I mean euclidean norm: sqrt( x*x + y*y ) = magnitude (length) of a vector On 9/5/07, Robert Dailey [EMAIL PROTECTED] wrote: Thanks for your response. I was not able to find len() in the numpy documentation at the following link: http://www.scipy.org/doc/numpy_api_docs/namespace_index.html Perhaps I'm looking in the wrong location? On 9/5/07, Matthieu Brucher [EMAIL PROTECTED] wrote: 2007/9/5, Robert Dailey [EMAIL PROTECTED]: Hi, I have two questions: 1) Is there any way in numpy to represent vectors? Currently I'm using 'array' for vectors. A vector is an array with one dimension, it's OK. You could use a matrix of dimension 1xn or nx1 as well. 2) Is there a way to calculate the magnitude (length) of a vector in numpy? Yes, len(a) Matthieu ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://projects.scipy.org/mailman/listinfo/numpy-discussion ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://projects.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Vector magnitude?
Robert Dailey wrote: Thanks for your response. I was not able to find len() in the numpy documentation at the following link: http://www.scipy.org/doc/numpy_api_docs/namespace_index.html http://www.scipy.org/doc/numpy_api_docs/namespace_index.html Perhaps I'm looking in the wrong location? It's a Python builtin function, but it doesn't do what you want. It returns the number of elements in a sequence (any sequence, not just arrays) not the magnitude of the vector. Besides constructing the Euclidean norm itself (as shown by others here), you can also use numpy.linalg.norm() to calculate any of several different norms of a vector or a matrix: In [7]: numpy.linalg.norm? Type: function Base Class: type 'function' Namespace:Interactive File: /Library/Frameworks/Python.framework/Versions/2.5/lib/python2.5/site-packages/numpy-1.0.4.dev4025-py2.5-macosx-10.3-fat.egg/numpy/linalg/linalg.py Definition: numpy.linalg.norm(x, ord=None) Docstring: norm(x, ord=None) - n Matrix or vector norm. Inputs: x -- a rank-1 (vector) or rank-2 (matrix) array ord -- the order of the norm. Comments: For arrays of any rank, if ord is None: calculate the square norm (Euclidean norm for vectors, Frobenius norm for matrices) For vectors ord can be any real number including Inf or -Inf. ord = Inf, computes the maximum of the magnitudes ord = -Inf, computes minimum of the magnitudes ord is finite, computes sum(abs(x)**ord,axis=0)**(1.0/ord) For matrices ord can only be one of the following values: ord = 2 computes the largest singular value ord = -2 computes the smallest singular value ord = 1 computes the largest column sum of absolute values ord = -1 computes the smallest column sum of absolute values ord = Inf computes the largest row sum of absolute values ord = -Inf computes the smallest row sum of absolute values ord = 'fro' computes the frobenius norm sqrt(sum(diag(X.H * X),axis=0)) For values ord 0, the result is, strictly speaking, not a mathematical 'norm', but it may still be useful for numerical purposes. -- 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 ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://projects.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Vector magnitude?
maybe numpy.vdot is good for you. In [3]: x = numpy.random.rand(4) In [4]: x Out[4]: array([ 0.45426898, 0.22369238, 0.98731244, 0.7758774 ]) In [5]: numpy.sqrt(numpy.vdot(x,x)) Out[5]: 1.35394615117 hth, lorenzo On 9/5/07, Robert Dailey [EMAIL PROTECTED] wrote: Oh I think I get it. You mean the built-in len() function? This isn't what I am looking for. len() returns the number of components in the vector (e.g. whether it is a 2D, 3D, etc vector). I found that magnitude can be calculated using hypot() in the math module that comes with python. However, this method only appears to work with 2D vectors. And yes, by magnitude I mean euclidean norm: sqrt( x*x + y*y ) = magnitude (length) of a vector On 9/5/07, Robert Dailey [EMAIL PROTECTED] wrote: Thanks for your response. I was not able to find len() in the numpy documentation at the following link: http://www.scipy.org/doc/numpy_api_docs/namespace_index.html Perhaps I'm looking in the wrong location? On 9/5/07, Matthieu Brucher [EMAIL PROTECTED] wrote: 2007/9/5, Robert Dailey [EMAIL PROTECTED]: Hi, I have two questions: 1) Is there any way in numpy to represent vectors? Currently I'm using 'array' for vectors. A vector is an array with one dimension, it's OK. You could use a matrix of dimension 1xn or nx1 as well. 2) Is there a way to calculate the magnitude (length) of a vector in numpy? Yes, len(a) Matthieu ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://projects.scipy.org/mailman/listinfo/numpy-discussion ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://projects.scipy.org/mailman/listinfo/numpy-discussion ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://projects.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Vector magnitude?
--- Robert Kern [EMAIL PROTECTED] wrote: Besides constructing the Euclidean norm itself (as shown by others here), you can also use numpy.linalg.norm() to calculate any of several different norms of a vector or a matrix: Right. linalg.norm also gives the proper magnitude of complex vectors -- Lou Pecora, my views are my own. --- Great spirits have always encountered violent opposition from mediocre minds. -Albert Einstein Moody friends. Drama queens. Your life? Nope! - their life, your story. Play Sims Stories at Yahoo! Games. http://sims.yahoo.com/ ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://projects.scipy.org/mailman/listinfo/numpy-discussion
