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author | Pauli Virtanen <pav@iki.fi> | 2009-03-24 22:25:21 +0000 |
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committer | Pauli Virtanen <pav@iki.fi> | 2009-03-24 22:25:21 +0000 |
commit | 7b751f66c7feb71646f0c2540aca2e5e67cd5db5 (patch) | |
tree | 3c33eab7a5933af7300ee4949c541511ebb7f915 /numpy/linalg | |
parent | 940a7d3b4e6398a742873347a2f3c605ceffe481 (diff) | |
download | numpy-7b751f66c7feb71646f0c2540aca2e5e67cd5db5.tar.gz |
Merge from the doc wiki
Diffstat (limited to 'numpy/linalg')
-rw-r--r-- | numpy/linalg/linalg.py | 31 |
1 files changed, 22 insertions, 9 deletions
diff --git a/numpy/linalg/linalg.py b/numpy/linalg/linalg.py index 1570407ff..dcf7fde26 100644 --- a/numpy/linalg/linalg.py +++ b/numpy/linalg/linalg.py @@ -202,6 +202,18 @@ def solve(a, b): LinAlgError If `a` is singular or not square. + Notes + ----- + + ``linalg.solve`` is a wrapper to the LAPACK http://www.netlib.org/lapack + routines `dgesv`_ and `zgesv`_. The solution to the system of linear + equations is computed using an LU decomposition with partial pivoting and + row interchanges. + + .. _dgesv: http://www.netlib.org/lapack/double/dgesv.f + + .. _zgesv: http://www.netlib.org/lapack/complex16/zgesv.f + Examples -------- Solve the system of equations ``3 * x0 + x1 = 9`` and ``x0 + 2 * x1 = 8``: @@ -756,16 +768,17 @@ def eig(a): complex arrays respectively. The number `w` is an eigenvalue of a if there exists a vector `v` - satisfying the equation ``dot(a,v) = w*v``. Alternately, if `w` is a root of - the characteristic equation ``det(a - w[i]*I) = 0``, where `det` is the - determinant and `I` is the identity matrix. The arrays `a`, `w`, and `v` - satisfy the equation ``dot(a,v[i]) = w[i]*v[:,i]``. + satisfying the equation ``dot(a,v) = w*v``. Alternately, if `w` is + a root of the characteristic equation ``det(a - w[i]*I) = 0``, where + `det` is the determinant and `I` is the identity matrix. The arrays + `a`, `w`, and `v` satisfy the equation ``dot(a,v[i]) = w[i]*v[:,i]``. The array `v` of eigenvectors may not be of maximum rank, that is, some - of the columns may be dependent, although roundoff error may obscure - that fact. If the eigenvalues are all different, then theoretically the - eigenvectors are independent. Likewise, the matrix of eigenvectors is - unitary if the matrix `a` is normal, i.e., if ``dot(a, a.H) = dot(a.H, a)``. + of the columns may be dependent, although roundoff error may + obscure that fact. If the eigenvalues are all different, then theoretically + the eigenvectors are independent. Likewise, the matrix of eigenvectors + is unitary if the matrix `a` is normal, i.e., if + ``dot(a, a.H) = dot(a.H, a)``. The left and right eigenvectors are not necessarily the (Hermitian) transposes of each other. @@ -1332,7 +1345,7 @@ def norm(x, ord=None): ---------- x : array_like, shape (M,) or (M, N) Input array. - ord : {int, 1, -1, 2, -2, inf, -inf, 'fro'} + ord : {2, int, inf, -inf, 'fro'} Order of the norm (see table under ``Notes``). Returns |