diff options
Diffstat (limited to 'numpy')
| -rw-r--r-- | numpy/linalg/linalg.py | 56 | ||||
| -rw-r--r-- | numpy/linalg/tests/test_linalg.py | 29 |
2 files changed, 66 insertions, 19 deletions
diff --git a/numpy/linalg/linalg.py b/numpy/linalg/linalg.py index ae0da3685..b063a2ede 100644 --- a/numpy/linalg/linalg.py +++ b/numpy/linalg/linalg.py @@ -22,8 +22,9 @@ from numpy.core import array, asarray, zeros, empty, transpose, \ intc, single, double, csingle, cdouble, inexact, complexfloating, \ newaxis, ravel, all, Inf, dot, add, multiply, identity, sqrt, \ maximum, flatnonzero, diagonal, arange, fastCopyAndTranspose, sum, \ - isfinite, size, finfo, absolute, log, exp, errstate, geterrobj -from numpy.lib import triu + isfinite, size, finfo, absolute, log, exp, errstate, geterrobj, \ + float64, float128 +from numpy.lib import triu, asfarray from numpy.linalg import lapack_lite, _umath_linalg from numpy.matrixlib.defmatrix import matrix_power from numpy.compat import asbytes @@ -1865,7 +1866,8 @@ def lstsq(a, b, rcond=-1): st = s[:min(n, m)].copy().astype(result_real_t) return wrap(x), wrap(resids), results['rank'], st -def norm(x, ord=None): + +def norm(x, ord=None, axis=None): """ Matrix or vector norm. @@ -1880,11 +1882,14 @@ def norm(x, ord=None): ord : {non-zero int, inf, -inf, 'fro'}, optional Order of the norm (see table under ``Notes``). inf means numpy's `inf` object. + axis : int or None, optional + If `axis` is not None, it specifies the axis of `x` along which to + compute the vector norms. Returns ------- - n : float - Norm of the matrix or vector. + n : float or ndarray + Norm of the matrix or vector(s). Notes ----- @@ -1967,29 +1972,52 @@ def norm(x, ord=None): >>> LA.norm(a, -3) nan + Using the `axis` argument: + + >>> c = np.array([[ 1, 2, 3], + ... [-1, 1, 4]]) + >>> LA.norm(c, axis=0) + array([ 1.41421356, 2.23606798, 5. ]) + >>> LA.norm(c, axis=1) + array([ 3.74165739, 4.24264069]) + >>> LA.norm(c, ord=1, axis=1) + array([6, 6]) + """ x = asarray(x) - if ord is None: # check the default case first and handle it immediately + + # Check the default case first and handle it immediately. + if ord is None and axis is None: + s = (x.conj() * x).real return sqrt(add.reduce((x.conj() * x).ravel().real)) nd = x.ndim - if nd == 1: + if nd == 1 or axis is not None: if ord == Inf: - return abs(x).max() + return abs(x).max(axis=axis) elif ord == -Inf: - return abs(x).min() + return abs(x).min(axis=axis) elif ord == 0: - return (x != 0).sum() # Zero norm + # Zero norm + return (x != 0).sum(axis=axis) elif ord == 1: - return abs(x).sum() # special case for speedup - elif ord == 2: - return sqrt(((x.conj()*x).real).sum()) # special case for speedup + # special case for speedup + return add.reduce(abs(x), axis=axis) + elif ord is None or ord == 2: + # special case for speedup + s = (x.conj() * x).real + return sqrt(add.reduce(s, axis=axis)) else: try: ord + 1 except TypeError: raise ValueError("Invalid norm order for vectors.") - return ((abs(x)**ord).sum())**(1.0/ord) + if x.dtype != float128: + # Convert to a float type, so integer arrays give + # float results. Don't apply asfarray to float128 arrays, + # because it will downcast to float64. + absx = asfarray(abs(x)) + return add.reduce(absx**ord, axis=axis)**(1.0/ord) elif nd == 2: if ord == 2: return svd(x, compute_uv=0).max() diff --git a/numpy/linalg/tests/test_linalg.py b/numpy/linalg/tests/test_linalg.py index 2dc55ab5e..fdb243271 100644 --- a/numpy/linalg/tests/test_linalg.py +++ b/numpy/linalg/tests/test_linalg.py @@ -523,9 +523,9 @@ class _TestNorm(TestCase): assert_equal(norm(atleast_2d(array([], dtype=self.dt))), 0.0) def test_vector(self): - a = [1.0,2.0,3.0,4.0] - b = [-1.0,-2.0,-3.0,-4.0] - c = [-1.0, 2.0,-3.0, 4.0] + a = [1, 2, 3, 4] + b = [-1, -2, -3, -4] + c = [-1, 2, -3, 4] def _test(v): np.testing.assert_almost_equal(norm(v), 30**0.5, decimal=self.dec) @@ -548,8 +548,7 @@ class _TestNorm(TestCase): _test(v) def test_matrix(self): - A = matrix([[1.,3.],[5.,7.]], dtype=self.dt) - A = matrix([[1.,3.],[5.,7.]], dtype=self.dt) + A = matrix([[1, 3], [5, 7]], dtype=self.dt) assert_almost_equal(norm(A), 84**0.5) assert_almost_equal(norm(A,'fro'), 84**0.5) assert_almost_equal(norm(A,inf), 12.0) @@ -563,6 +562,21 @@ class _TestNorm(TestCase): self.assertRaises(ValueError, norm, A, -3) self.assertRaises(ValueError, norm, A, 0) + def test_axis(self): + # Compare the use of `axis` with computing the norm of each row + # or column separately. + A = array([[1, 2, 3], [4, 5, 6]], dtype=self.dt) + for order in [None, -1, 0, 1, 2, 3, np.Inf, -np.Inf]: + expected0 = [norm(A[:,k], ord=order) for k in range(A.shape[1])] + assert_almost_equal(norm(A, ord=order, axis=0), expected0) + expected1 = [norm(A[k,:], ord=order) for k in range(A.shape[0])] + assert_almost_equal(norm(A, ord=order, axis=1), expected1) + + # Check bad case. Using `axis` implies vector norms are being + # computed, so also using `ord='fro'` raises a ValueError + # (just like `norm([1,2,3], ord='fro')` does). + self.assertRaises(ValueError, norm, A, 'fro', 0) + class TestNormDouble(_TestNorm): dt = np.double @@ -574,6 +588,11 @@ class TestNormSingle(_TestNorm): dec = 6 +class TestNormInt64(_TestNorm): + dt = np.int64 + dec = 12 + + class TestMatrixRank(object): def test_matrix_rank(self): # Full rank matrix |