diff options
Diffstat (limited to 'numpy/linalg/linalg.py')
| -rw-r--r-- | numpy/linalg/linalg.py | 35 |
1 files changed, 24 insertions, 11 deletions
diff --git a/numpy/linalg/linalg.py b/numpy/linalg/linalg.py index eb8c8379a..c044176cf 100644 --- a/numpy/linalg/linalg.py +++ b/numpy/linalg/linalg.py @@ -1680,12 +1680,13 @@ def lstsq(a, b, rcond=-1): """ Return the least-squares solution to a linear matrix equation. - Solves the equation `a x = b` by computing a vector `x` that minimizes - the norm `|| b - a x ||`. The equation may be under-, well-, or over- - determined (i.e., the number of linearly independent rows of `a` can be - less than, equal to, or greater than its number of linearly independent - columns). If `a` is square and of full rank, then `x` (but for round-off - error) is the "exact" solution of the equation. + Solves the equation `a x = b` by computing a vector `x` that + minimizes the Euclidean 2-norm `|| b - a x ||^2`. The equation may + be under-, well-, or over- determined (i.e., the number of + linearly independent rows of `a` can be less than, equal to, or + greater than its number of linearly independent columns). If `a` + is square and of full rank, then `x` (but for round-off error) is + the "exact" solution of the equation. Parameters ---------- @@ -1706,7 +1707,7 @@ def lstsq(a, b, rcond=-1): Least-squares solution. The shape of `x` depends on the shape of `b`. residues : ndarray, shape (), (1,), or (K,) - Sums of residues; squared Euclidean norm for each column in + Sums of residues; squared Euclidean 2-norm for each column in ``b - a*x``. If the rank of `a` is < N or > M, this is an empty array. If `b` is 1-dimensional, this is a (1,) shape array. @@ -1772,6 +1773,7 @@ def lstsq(a, b, rcond=-1): if m != b.shape[0]: raise LinAlgError, 'Incompatible dimensions' t, result_t = _commonType(a, b) + result_real_t = _realType(result_t) real_t = _linalgRealType(t) bstar = zeros((ldb, n_rhs), t) bstar[:b.shape[0],:n_rhs] = b.copy() @@ -1811,16 +1813,27 @@ def lstsq(a, b, rcond=-1): 0, work, lwork, iwork, 0) if results['info'] > 0: raise LinAlgError, 'SVD did not converge in Linear Least Squares' - resids = array([], t) + resids = array([], result_real_t) if is_1d: x = array(ravel(bstar)[:n], dtype=result_t, copy=True) if results['rank'] == n and m > n: - resids = array([sum((ravel(bstar)[n:])**2)], dtype=result_t) + if isComplexType(t): + resids = array([sum(abs(ravel(bstar)[n:])**2)], + dtype=result_real_t) + else: + resids = array([sum((ravel(bstar)[n:])**2)], + dtype=result_real_t) else: x = array(transpose(bstar)[:n,:], dtype=result_t, copy=True) if results['rank'] == n and m > n: - resids = sum((transpose(bstar)[n:,:])**2, axis=0).astype(result_t) - st = s[:min(n, m)].copy().astype(_realType(result_t)) + if isComplexType(t): + resids = sum(abs(transpose(bstar)[n:,:])**2, axis=0).astype( + result_real_t) + else: + resids = sum((transpose(bstar)[n:,:])**2, axis=0).astype( + result_real_t) + + st = s[:min(n, m)].copy().astype(result_real_t) return wrap(x), wrap(resids), results['rank'], st def norm(x, ord=None): |