Python numpy.linalg.lstsq() Examples

def error(self, start, end):
        """Return the approximation cost on the segment [start:end].

        Args:
            start (int): start of the segment
            end (int): end of the segment

        Returns:
            float: segment cost

        Raises:
            NotEnoughPoints: when the segment is too short (less than ``'min_size'`` samples).
        """
        if end - start < self.min_size:
            raise NotEnoughPoints
        y, X = self.signal[start:end], self.covar[start:end]
        _, residual, _, _ = lstsq(X, y, rcond=None)
        return residual.sum() 

def do(self, a, b):
        arr = np.asarray(a)
        m, n = arr.shape
        u, s, vt = linalg.svd(a, 0)
        x, residuals, rank, sv = linalg.lstsq(a, b)
        if m <= n:
            assert_almost_equal(b, dot(a, x))
            assert_equal(rank, m)
        else:
            assert_equal(rank, n)
        assert_almost_equal(sv, sv.__array_wrap__(s))
        if rank == n and m > n:
            expect_resids = (np.asarray(abs(np.dot(a, x) - b))**2).sum(axis=0)
            expect_resids = np.asarray(expect_resids)
            if len(np.asarray(b).shape) == 1:
                expect_resids.shape = (1,)
                assert_equal(residuals.shape, expect_resids.shape)
        else:
            expect_resids = type(x)([])
        assert_almost_equal(residuals, expect_resids)
        assert_(np.issubdtype(residuals.dtype, np.floating))
        assert_(imply(isinstance(b, matrix), isinstance(x, matrix)))
        assert_(imply(isinstance(b, matrix), isinstance(residuals, matrix))) 

def do(self, a, b):
        arr = np.asarray(a)
        m, n = arr.shape
        u, s, vt = linalg.svd(a, 0)
        x, residuals, rank, sv = linalg.lstsq(a, b)
        if m <= n:
            assert_almost_equal(b, dot(a, x))
            assert_equal(rank, m)
        else:
            assert_equal(rank, n)
        assert_almost_equal(sv, sv.__array_wrap__(s))
        if rank == n and m > n:
            expect_resids = (
                np.asarray(abs(np.dot(a, x) - b)) ** 2).sum(axis=0)
            expect_resids = np.asarray(expect_resids)
            if len(np.asarray(b).shape) == 1:
                expect_resids.shape = (1,)
                assert_equal(residuals.shape, expect_resids.shape)
        else:
            expect_resids = np.array([]).view(type(x))
        assert_almost_equal(residuals, expect_resids)
        assert_(np.issubdtype(residuals.dtype, np.floating))
        assert_(imply(isinstance(b, matrix), isinstance(x, matrix)))
        assert_(imply(isinstance(b, matrix), isinstance(residuals, matrix))) 

def test_future_rcond(self):
        a = np.array([[0., 1.,  0.,  1.,  2.,  0.],
                      [0., 2.,  0.,  0.,  1.,  0.],
                      [1., 0.,  1.,  0.,  0.,  4.],
                      [0., 0.,  0.,  2.,  3.,  0.]]).T

        b = np.array([1, 0, 0, 0, 0, 0])
        with suppress_warnings() as sup:
            w = sup.record(FutureWarning, "`rcond` parameter will change")
            x, residuals, rank, s = linalg.lstsq(a, b)
            assert_(rank == 4)
            x, residuals, rank, s = linalg.lstsq(a, b, rcond=-1)
            assert_(rank == 4)
            x, residuals, rank, s = linalg.lstsq(a, b, rcond=None)
            assert_(rank == 3)
            # Warning should be raised exactly once (first command)
            assert_(len(w) == 1) 

def do(self, a, b):
        arr = np.asarray(a)
        m, n = arr.shape
        u, s, vt = linalg.svd(a, 0)
        x, residuals, rank, sv = linalg.lstsq(a, b)
        if m <= n:
            assert_almost_equal(b, dot(a, x))
            assert_equal(rank, m)
        else:
            assert_equal(rank, n)
        assert_almost_equal(sv, sv.__array_wrap__(s))
        if rank == n and m > n:
            expect_resids = (
                np.asarray(abs(np.dot(a, x) - b)) ** 2).sum(axis=0)
            expect_resids = np.asarray(expect_resids)
            if len(np.asarray(b).shape) == 1:
                expect_resids.shape = (1,)
                assert_equal(residuals.shape, expect_resids.shape)
        else:
            expect_resids = np.array([]).view(type(x))
        assert_almost_equal(residuals, expect_resids)
        assert_(np.issubdtype(residuals.dtype, np.floating))
        assert_(imply(isinstance(b, matrix), isinstance(x, matrix)))
        assert_(imply(isinstance(b, matrix), isinstance(residuals, matrix))) 

def test_future_rcond(self):
        a = np.array([[0., 1.,  0.,  1.,  2.,  0.],
                      [0., 2.,  0.,  0.,  1.,  0.],
                      [1., 0.,  1.,  0.,  0.,  4.],
                      [0., 0.,  0.,  2.,  3.,  0.]]).T

        b = np.array([1, 0, 0, 0, 0, 0])
        with suppress_warnings() as sup:
            w = sup.record(FutureWarning, "`rcond` parameter will change")
            x, residuals, rank, s = linalg.lstsq(a, b)
            assert_(rank == 4)
            x, residuals, rank, s = linalg.lstsq(a, b, rcond=-1)
            assert_(rank == 4)
            x, residuals, rank, s = linalg.lstsq(a, b, rcond=None)
            assert_(rank == 3)
            # Warning should be raised exactly once (first command)
            assert_(len(w) == 1) 

def test_future_rcond(self):
        a = np.array([[0., 1.,  0.,  1.,  2.,  0.],
                      [0., 2.,  0.,  0.,  1.,  0.],
                      [1., 0.,  1.,  0.,  0.,  4.],
                      [0., 0.,  0.,  2.,  3.,  0.]]).T

        b = np.array([1, 0, 0, 0, 0, 0])
        with suppress_warnings() as sup:
            w = sup.record(FutureWarning, "`rcond` parameter will change")
            x, residuals, rank, s = linalg.lstsq(a, b)
            assert_(rank == 4)
            x, residuals, rank, s = linalg.lstsq(a, b, rcond=-1)
            assert_(rank == 4)
            x, residuals, rank, s = linalg.lstsq(a, b, rcond=None)
            assert_(rank == 3)
            # Warning should be raised exactly once (first command)
            assert_(len(w) == 1) 

def test_future_rcond(self):
        a = np.array([[0., 1.,  0.,  1.,  2.,  0.],
                      [0., 2.,  0.,  0.,  1.,  0.],
                      [1., 0.,  1.,  0.,  0.,  4.],
                      [0., 0.,  0.,  2.,  3.,  0.]]).T

        b = np.array([1, 0, 0, 0, 0, 0])
        with suppress_warnings() as sup:
            w = sup.record(FutureWarning, "`rcond` parameter will change")
            x, residuals, rank, s = linalg.lstsq(a, b)
            assert_(rank == 4)
            x, residuals, rank, s = linalg.lstsq(a, b, rcond=-1)
            assert_(rank == 4)
            x, residuals, rank, s = linalg.lstsq(a, b, rcond=None)
            assert_(rank == 3)
            # Warning should be raised exactly once (first command)
            assert_(len(w) == 1) 

def solve_lms(all_tags, all_bits, segdata, bias=0.0):
    """
    Solves using direct least square solution (NumPy)

    Parameters
    ----------

    all_tags:
        List of considered tags.
    all_bits:
        List of considered bits.
    segdata:
        List of segdata used.
    bias:
        T.B.D.
    """

    # Build matrices
    A, B = build_matrices(all_tags, all_bits, segdata, bias)

    # Solve
    X, res, r, s = linalg.lstsq(A, B, rcond=None)

    return X, compute_error(A, B, X) 

def test_future_rcond(self):
        a = np.array([[0., 1.,  0.,  1.,  2.,  0.],
                      [0., 2.,  0.,  0.,  1.,  0.],
                      [1., 0.,  1.,  0.,  0.,  4.],
                      [0., 0.,  0.,  2.,  3.,  0.]]).T

        b = np.array([1, 0, 0, 0, 0, 0])
        with suppress_warnings() as sup:
            w = sup.record(FutureWarning, "`rcond` parameter will change")
            x, residuals, rank, s = linalg.lstsq(a, b)
            assert_(rank == 4)
            x, residuals, rank, s = linalg.lstsq(a, b, rcond=-1)
            assert_(rank == 4)
            x, residuals, rank, s = linalg.lstsq(a, b, rcond=None)
            assert_(rank == 3)
            # Warning should be raised exactly once (first command)
            assert_(len(w) == 1) 

def test_future_rcond(self):
        a = np.array([[0., 1.,  0.,  1.,  2.,  0.],
                      [0., 2.,  0.,  0.,  1.,  0.],
                      [1., 0.,  1.,  0.,  0.,  4.],
                      [0., 0.,  0.,  2.,  3.,  0.]]).T

        b = np.array([1, 0, 0, 0, 0, 0])
        with suppress_warnings() as sup:
            w = sup.record(FutureWarning, "`rcond` parameter will change")
            x, residuals, rank, s = linalg.lstsq(a, b)
            assert_(rank == 4)
            x, residuals, rank, s = linalg.lstsq(a, b, rcond=-1)
            assert_(rank == 4)
            x, residuals, rank, s = linalg.lstsq(a, b, rcond=None)
            assert_(rank == 3)
            # Warning should be raised exactly once (first command)
            assert_(len(w) == 1) 

def _compute_affine_transform_cvpy(refpoints, points, w = None): # Copied from the book
    if w == None:
        w = [1] * (len(points) * 2)
    assert(len(w) == 2*len(points))
    y = []
    for n, p in enumerate(refpoints):
        y += [p[0]/w[n*2], p[1]/w[n*2+1]]
    A = []
    for n, p in enumerate(points):
        A.extend([ [p[0]/w[n*2], p[1]/w[n*2], 0, 0, 1/w[n*2], 0], [0, 0, p[0]/w[n*2+1], p[1]/w[n*2+1], 0, 1/w[n*2+1]] ])
    
    lstsq = linalg.lstsq(A,y)
    h11, h12, h21, h22, dx, dy = lstsq[0]
    err = lstsq[1]

    R = np.array([[h11, h12, dx], [h21, h22, dy]])
    return R, err 

def test_future_rcond(self):
        a = np.array([[0., 1.,  0.,  1.,  2.,  0.],
                      [0., 2.,  0.,  0.,  1.,  0.],
                      [1., 0.,  1.,  0.,  0.,  4.],
                      [0., 0.,  0.,  2.,  3.,  0.]]).T

        b = np.array([1, 0, 0, 0, 0, 0])
        with suppress_warnings() as sup:
            w = sup.record(FutureWarning, "`rcond` parameter will change")
            x, residuals, rank, s = linalg.lstsq(a, b)
            assert_(rank == 4)
            x, residuals, rank, s = linalg.lstsq(a, b, rcond=-1)
            assert_(rank == 4)
            x, residuals, rank, s = linalg.lstsq(a, b, rcond=None)
            assert_(rank == 3)
            # Warning should be raised exactly once (first command)
            assert_(len(w) == 1) 

def test_future_rcond(self):
        a = np.array([[0., 1.,  0.,  1.,  2.,  0.],
                      [0., 2.,  0.,  0.,  1.,  0.],
                      [1., 0.,  1.,  0.,  0.,  4.],
                      [0., 0.,  0.,  2.,  3.,  0.]]).T

        b = np.array([1, 0, 0, 0, 0, 0])
        with suppress_warnings() as sup:
            w = sup.record(FutureWarning, "`rcond` parameter will change")
            x, residuals, rank, s = linalg.lstsq(a, b)
            assert_(rank == 4)
            x, residuals, rank, s = linalg.lstsq(a, b, rcond=-1)
            assert_(rank == 4)
            x, residuals, rank, s = linalg.lstsq(a, b, rcond=None)
            assert_(rank == 3)
            # Warning should be raised exactly once (first command)
            assert_(len(w) == 1) 

def do(self, a, b):
        arr = np.asarray(a)
        m, n = arr.shape
        u, s, vt = linalg.svd(a, 0)
        x, residuals, rank, sv = linalg.lstsq(a, b)
        if m <= n:
            assert_almost_equal(b, dot(a, x))
            assert_equal(rank, m)
        else:
            assert_equal(rank, n)
        assert_almost_equal(sv, sv.__array_wrap__(s))
        if rank == n and m > n:
            expect_resids = (
                np.asarray(abs(np.dot(a, x) - b)) ** 2).sum(axis=0)
            expect_resids = np.asarray(expect_resids)
            if len(np.asarray(b).shape) == 1:
                expect_resids.shape = (1,)
                assert_equal(residuals.shape, expect_resids.shape)
        else:
            expect_resids = np.array([]).view(type(x))
        assert_almost_equal(residuals, expect_resids)
        assert_(np.issubdtype(residuals.dtype, np.floating))
        assert_(imply(isinstance(b, matrix), isinstance(x, matrix)))
        assert_(imply(isinstance(b, matrix), isinstance(residuals, matrix))) 

def test_empty_a_b(self, m, n, n_rhs):
        a = np.arange(m * n).reshape(m, n)
        b = np.ones((m, n_rhs))
        x, residuals, rank, s = linalg.lstsq(a, b, rcond=None)
        if m == 0:
            assert_((x == 0).all())
        assert_equal(x.shape, (n, n_rhs))
        assert_equal(residuals.shape, ((n_rhs,) if m > n else (0,)))
        if m > n and n_rhs > 0:
            # residuals are exactly the squared norms of b's columns
            r = b - np.dot(a, x)
            assert_almost_equal(residuals, (r * r).sum(axis=-2))
        assert_equal(rank, min(m, n))
        assert_equal(s.shape, (min(m, n),)) 

def do(self, a, b, tags):
        if 'size-0' in tags:
            assert_raises(LinAlgError, linalg.lstsq, a, b)
            return

        arr = np.asarray(a)
        m, n = arr.shape
        u, s, vt = linalg.svd(a, 0)
        x, residuals, rank, sv = linalg.lstsq(a, b, rcond=-1)
        if m <= n:
            assert_almost_equal(b, dot(a, x))
            assert_equal(rank, m)
        else:
            assert_equal(rank, n)
        assert_almost_equal(sv, sv.__array_wrap__(s))
        if rank == n and m > n:
            expect_resids = (
                np.asarray(abs(np.dot(a, x) - b)) ** 2).sum(axis=0)
            expect_resids = np.asarray(expect_resids)
            if np.asarray(b).ndim == 1:
                expect_resids.shape = (1,)
                assert_equal(residuals.shape, expect_resids.shape)
        else:
            expect_resids = np.array([]).view(type(x))
        assert_almost_equal(residuals, expect_resids)
        assert_(np.issubdtype(residuals.dtype, np.floating))
        assert_(consistent_subclass(x, b))
        assert_(consistent_subclass(residuals, b)) 

def test_lstsq_complex_larger_rhs(self):
        # gh-9891
        size = 20
        n_rhs = 70
        G = np.random.randn(size, size) + 1j * np.random.randn(size, size)
        u = np.random.randn(size, n_rhs) + 1j * np.random.randn(size, n_rhs)
        b = G.dot(u)
        # This should work without segmentation fault.
        u_lstsq, res, rank, sv = linalg.lstsq(G, b, rcond=None)
        # check results just in case
        assert_array_almost_equal(u_lstsq, u) 

def do(self, a, b, tags):
        if 'size-0' in tags:
            assert_raises(LinAlgError, linalg.lstsq, a, b)
            return

        arr = np.asarray(a)
        m, n = arr.shape
        u, s, vt = linalg.svd(a, 0)
        x, residuals, rank, sv = linalg.lstsq(a, b)
        if m <= n:
            assert_almost_equal(b, dot(a, x))
            assert_equal(rank, m)
        else:
            assert_equal(rank, n)
        assert_almost_equal(sv, sv.__array_wrap__(s))
        if rank == n and m > n:
            expect_resids = (
                np.asarray(abs(np.dot(a, x) - b)) ** 2).sum(axis=0)
            expect_resids = np.asarray(expect_resids)
            if np.asarray(b).ndim == 1:
                expect_resids.shape = (1,)
                assert_equal(residuals.shape, expect_resids.shape)
        else:
            expect_resids = np.array([]).view(type(x))
        assert_almost_equal(residuals, expect_resids)
        assert_(np.issubdtype(residuals.dtype, np.floating))
        assert_(imply(isinstance(b, matrix), isinstance(x, matrix)))
        assert_(imply(isinstance(b, matrix), isinstance(residuals, matrix))) 

def findNonreflectiveSimilarity(self, uv, xy, options=None):
        options = {'K': 2}

        K = options['K']
        M = xy.shape[0]
        x = xy[:, 0].reshape((-1, 1))
        y = xy[:, 1].reshape((-1, 1))

        tmp1 = np.hstack((x, y, np.ones((M, 1)), np.zeros((M, 1))))
        tmp2 = np.hstack((y, -x, np.zeros((M, 1)), np.ones((M, 1))))
        X = np.vstack((tmp1, tmp2))

        u = uv[:, 0].reshape((-1, 1))
        v = uv[:, 1].reshape((-1, 1))
        U = np.vstack((u, v))

        if rank(X) >= 2 * K:
            r, _, _, _ = lstsq(X, U, rcond=-1)
            r = np.squeeze(r)
        else:
            raise Exception('cp2tform:twoUniquePointsReq')
        sc = r[0]
        ss = r[1]
        tx = r[2]
        ty = r[3]

        Tinv = np.array([
            [sc, -ss, 0],
            [ss, sc, 0],
            [tx, ty, 1]
        ])

        T = inv(Tinv)
        T[:, 2] = np.array([0, 0, 1])
        return T, Tinv 

def fit_directions(self, orders=None):
        """ Returns fit for computed directions.

            When dealing with degenerate states, it is better to look at each
            computed direction separately, since the order of bands might depend on
            the direction (in which case it is difficult to construct a tensor).
        """
        from numpy import dot, concatenate, pi
        from numpy.linalg import inv, lstsq
        from math import factorial
        from ..error import ValueError

        orders = self._orders(orders)
        if 2 not in orders:
            raise ValueError('Cannot compute effective masses without second order term.')

        results = []
        breakpoints = self.breakpoints
        recipcell = inv(self.structure.cell).T * 2e0 * pi / self.structure.scale
        for start, end, direction in zip(breakpoints[:-1],
                                         breakpoints[1:],
                                         self.directions):
            kpoints = self.kpoints[start:end]
            x = dot(direction, dot(recipcell, kpoints.T))
            measurements = self.eigenvalues[start:end].copy()
            parameters = concatenate([x[:, None]**i / factorial(i) for i in orders], axis=1)
            fit = lstsq(parameters, measurements)
            results.append(fit[0])

        return results 

def emass(self, orders=None):
        """ Computes effective mass for each direction. """
        from numpy import dot, concatenate, pi, array
        from numpy.linalg import inv, lstsq
        from math import factorial
        from quantities import angstrom, emass, h_bar
        from ..error import ValueError

        orders = self._orders(orders)
        if 2 not in orders:
            raise ValueError('Cannot compute effective masses without second order term.')

        results = []
        breakpoints = self.breakpoints
        recipcell = inv(self.structure.cell).T * 2e0 * pi / self.structure.scale
        for start, end, direction in zip(breakpoints[:-1],
                                         breakpoints[1:],
                                         self.directions):
            kpoints = self.kpoints[start:end]
            x = dot(direction, dot(recipcell, kpoints.T))
            measurements = self.eigenvalues[start:end].copy()
            parameters = concatenate([x[:, None]**i / factorial(i) for i in orders], axis=1)
            fit = lstsq(parameters, measurements)
            results.append(fit[0][orders.index(2)])

        result = (array(results) * self.eigenvalues.units * angstrom**2 / h_bar**2)
        return 1. / result.rescale(1 / emass) 

def test_lstsq_complex_larger_rhs(self):
        # gh-9891
        size = 20
        n_rhs = 70
        G = np.random.randn(size, size) + 1j * np.random.randn(size, size)
        u = np.random.randn(size, n_rhs) + 1j * np.random.randn(size, n_rhs)
        b = G.dot(u)
        # This should work without segmentation fault.
        u_lstsq, res, rank, sv = linalg.lstsq(G, b, rcond=None)
        # check results just in case
        assert_array_almost_equal(u_lstsq, u) 

def initialize(self):
        S = sum([np.dot(unit.X.T, unit.X) for unit in self.units])
        Y = sum([np.dot(unit.X.T, unit.Y) for unit in self.units])
        self.a = L.lstsq(S, Y)[0]

        D = 0
        t = 0
        sigmasq = 0
        for unit in self.units:
            unit.r = unit.Y - np.dot(unit.X, self.a)
            if self.q > 1:
                unit.b = L.lstsq(unit.Z, unit.r)[0]
            else:
                Z = unit.Z.reshape((unit.Z.shape[0], 1))
                unit.b = L.lstsq(Z, unit.r)[0]

            sigmasq += (np.power(unit.Y, 2).sum() -
                        (self.a * np.dot(unit.X.T, unit.Y)).sum() -
                        (unit.b * np.dot(unit.Z.T, unit.r)).sum())
            D += np.multiply.outer(unit.b, unit.b)
            t += L.pinv(np.dot(unit.Z.T, unit.Z))

        #TODO: JP added df_resid check
        self.df_resid = (self.N - (self.m - 1) * self.q - self.p)
        sigmasq /= (self.N - (self.m - 1) * self.q - self.p)
        self.sigma = np.sqrt(sigmasq)
        self.D = (D - sigmasq * t) / self.m 

def compute_average_regress(x, idx_chan):
    """Take the mean across channels and regress out the mean from each channel

    Parameters
    ----------
    x : ndarray
        2d array with channels on one dimension
    idx_chan:
        which axis contains channels

    Returns
    -------
    ndarray
        same as x, but with the mean being regressed out
    """
    if x.ndim != 2:
        raise ValueError(f'The number of dimensions must be 2, not {x.ndim}')

    x = moveaxis(x, idx_chan, 0)  # move axis to the front
    avg = mean(x, axis=0)

    x_o = []
    for i in range(x.shape[0]):
        r = lstsq(avg[:, None], x[i, :][:, None], rcond=0)[0]
        x_o.append(
            x[i, :] - r[0, 0] * avg
            )
    return moveaxis(asarray(x_o), 0, idx_chan) 

def do(self, a, b):
        arr = np.asarray(a)
        m, n = arr.shape
        u, s, vt = linalg.svd(a, 0)
        x, residuals, rank, sv = linalg.lstsq(a, b)
        if m <= n:
            assert_almost_equal(b, dot(a, x))
            assert_equal(rank, m)
        else:
            assert_equal(rank, n)
        assert_almost_equal(sv, sv.__array_wrap__(s))
        if rank == n and m > n:
            expect_resids = (np.asarray(abs(np.dot(a, x) - b))**2).sum(axis=0)
            expect_resids = np.asarray(expect_resids)
            if len(np.asarray(b).shape) == 1:
                expect_resids.shape = (1,)
                assert_equal(residuals.shape, expect_resids.shape)
        else:
            expect_resids = np.array([]).view(type(x))
        assert_almost_equal(residuals, expect_resids)
        assert_(np.issubdtype(residuals.dtype, np.floating))
        assert_(imply(isinstance(b, matrix), isinstance(x, matrix)))
        assert_(imply(isinstance(b, matrix), isinstance(residuals, matrix))) 

def hfd(X, Kmax):
	""" Compute Hjorth Fractal Dimension of a time series X, kmax
	 is an HFD parameter
	"""
	L = [];
	x = []
	N = len(X)
	for k in xrange(1,Kmax):
		Lk = []
		for m in xrange(0,k):
			Lmk = 0
			for i in xrange(1,int(floor((N-m)/k))):
				Lmk += abs(X[m+i*k] - X[m+i*k-k])
			Lmk = Lmk*(N - 1)/floor((N - m) / float(k)) / k
			Lk.append(Lmk)
		L.append(log(mean(Lk)))
		x.append([log(float(1) / k), 1])
	
	(p, r1, r2, s)=lstsq(x, L)
	return p[0] 

def sigmoid_adjust(xs, ys):
        ys_max = np.max(ys) + 0.1
        ys_min = np.min(ys) - 0.1

        # normalize to [0, 1]
        ys = list((np.array(ys) - ys_min) / (ys_max - ys_min))

        zs = -np.log(1.0 / np.array(ys).T - 1.0)
        Y_mtx = np.matrix((np.ones(len(ys)), zs)).T
        x_vec = np.matrix(xs).T
        a_b = lstsq(Y_mtx, x_vec, rcond=1)[0]
        a = a_b.item(0)
        b = a_b.item(1)

        xs = 1.0 / (1.0 + np.exp(- (np.array(xs) - a) / b))

        # denormalize
        xs = xs * (ys_max - ys_min) + ys_min

        return xs 

def do(self, a, b, tags):
        if 'size-0' in tags:
            assert_raises(LinAlgError, linalg.lstsq, a, b)
            return

        arr = np.asarray(a)
        m, n = arr.shape
        u, s, vt = linalg.svd(a, 0)
        x, residuals, rank, sv = linalg.lstsq(a, b)
        if m <= n:
            assert_almost_equal(b, dot(a, x))
            assert_equal(rank, m)
        else:
            assert_equal(rank, n)
        assert_almost_equal(sv, sv.__array_wrap__(s))
        if rank == n and m > n:
            expect_resids = (
                np.asarray(abs(np.dot(a, x) - b)) ** 2).sum(axis=0)
            expect_resids = np.asarray(expect_resids)
            if np.asarray(b).ndim == 1:
                expect_resids.shape = (1,)
                assert_equal(residuals.shape, expect_resids.shape)
        else:
            expect_resids = np.array([]).view(type(x))
        assert_almost_equal(residuals, expect_resids)
        assert_(np.issubdtype(residuals.dtype, np.floating))
        assert_(imply(isinstance(b, matrix), isinstance(x, matrix)))
        assert_(imply(isinstance(b, matrix), isinstance(residuals, matrix))) 

def do(self, a, b, tags):
        arr = np.asarray(a)
        m, n = arr.shape
        u, s, vt = linalg.svd(a, 0)
        x, residuals, rank, sv = linalg.lstsq(a, b, rcond=-1)
        if m == 0:
            assert_((x == 0).all())
        if m <= n:
            assert_almost_equal(b, dot(a, x))
            assert_equal(rank, m)
        else:
            assert_equal(rank, n)
        assert_almost_equal(sv, sv.__array_wrap__(s))
        if rank == n and m > n:
            expect_resids = (
                np.asarray(abs(np.dot(a, x) - b)) ** 2).sum(axis=0)
            expect_resids = np.asarray(expect_resids)
            if np.asarray(b).ndim == 1:
                expect_resids.shape = (1,)
                assert_equal(residuals.shape, expect_resids.shape)
        else:
            expect_resids = np.array([]).view(type(x))
        assert_almost_equal(residuals, expect_resids)
        assert_(np.issubdtype(residuals.dtype, np.floating))
        assert_(consistent_subclass(x, b))
        assert_(consistent_subclass(residuals, b))