Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
sage: A.norm(p=’bogus’)
Traceback (most recent call last):
...
ValueError: matrix norm ’p’ must be +/- infinity, ’frob’ or an integer, not bogus
sage: A.norm(p=632)
Traceback (most recent call last):
...
ValueError: matrix norm integer values of ’p’ must be -2, -1, 1 or 2, not 632
numpy(dtype=None)
This method returns a copy of the matrix as a numpy array. It uses the numpy C/api so is very fast.
INPUT:
•dtype - The desired data-type for the array. If not given, then the type will be determined as the
minimum type required to hold the objects in the sequence.
EXAMPLES:
sage: m = matrix(RDF,[[1,2],[3,4]])
sage: n = m.numpy()
sage: import numpy
sage: numpy.linalg.eig(n)
(array([-0.37228132, 5.37228132]), array([[-0.82456484, -0.41597356],
[ 0.56576746, -0.90937671]]))
sage: m = matrix(RDF, 2, range(6)); m
[0.0 1.0 2.0]
[3.0 4.0 5.0]
sage: m.numpy()
array([[ 0., 1., 2.],
[ 3., 4., 5.]])
Alternatively, numpy automatically calls this function (via the magic __array__() method) to convert
Sage matrices to numpy arrays:
sage: import numpy
sage: m = matrix(RDF, 2, range(6)); m
[0.0 1.0 2.0]
[3.0 4.0 5.0]
sage: numpy.array(m)
array([[ 0., 1., 2.],
[ 3., 4., 5.]])
sage: numpy.array(m).dtype
dtype(’float64’)
sage: m = matrix(CDF, 2, range(6)); m
[0.0 1.0 2.0]
[3.0 4.0 5.0]
sage: numpy.array(m)
array([[ 0.+0.j, 1.+0.j, 2.+0.j],
[ 3.+0.j, 4.+0.j, 5.+0.j]])
sage: numpy.array(m).dtype
dtype(’complex128’)
TESTS:
sage: m = matrix(RDF,0,5,[]); m
[]
sage: m.numpy()
array([], shape=(0, 5), dtype=float64)
sage: m = matrix(RDF,5,0,[]); m
380 Chapter 19. Dense matrices using a NumPy backend.