How to use the fluids.numerics.linspace function in fluids

def test_linspace():
    from fluids.numerics import linspace
    calc = linspace(-3,10, endpoint=True, num=8)
    expect = np.linspace(-3,10, endpoint=True, num=8)
    assert_allclose(calc, expect)
    
    calc = linspace(-3,10, endpoint=False, num=20)
    expect = np.linspace(-3,10, endpoint=False, num=20)
    assert_allclose(calc, expect)

    calc = linspace(0,1e-10, endpoint=False, num=3)
    expect = np.linspace(0,1e-10, endpoint=False, num=3)
    assert_allclose(calc, expect)
    
    calc = linspace(0,1e-10, endpoint=False, num=2)
    expect = np.linspace(0,1e-10, endpoint=False, num=2)
    assert_allclose(calc, expect)
    
    calc = linspace(0,1e-10, endpoint=False, num=1)
    expect = np.linspace(0,1e-10, endpoint=False, num=1)
    assert_allclose(calc, expect)
    
    calc, calc_step = linspace(0,1e-10, endpoint=False, num=2, retstep=True)

def test_Smith():
    assert_close(Smith(.4, 800, 2.5), 0.959981235534199)
    
    # Quick test function, to ensure results are the same regardless of 
    # the form of the expression
    def Smith2(x, rhol, rhog):
        K = 0.4
        first = 1 + rhog/rhol*K*(1/x-1)
        second = rhog/rhol*(1-K)*(1/x-1)
        third = ((rhol/rhog + K*(1/x-1))/(1 + K*(1/x -1)))**0.5
        return (first + second*third)**-1

    alpha_1 = [Smith(i, 800, 2.5) for i in linspace(1E-9,.99)]
    alpha_2 = [Smith2(i, 800, 2.5) for i in linspace(1E-9, .99)]
    assert_close1d(alpha_1, alpha_2)

def test_plate_enhancement_factor_fuzz():
    # Confirm it's correct to within 1E-7
    for x in linspace(1E-5, 100, 3):
        for y in linspace(1E-5, 100, 3):
            a = plate_enlargement_factor(x, y)
            b = plate_enlargement_factor_numerical(x, y)
            assert_close(a, b, rtol=1E-7)

def test_geometry_tank_fuzz_h_from_V():
    T = TANK(L=1.2, L_over_D=3.5, sideA='torispherical', sideB='torispherical', sideA_f=1., horizontal=True, sideA_k=0.06, sideB_f=1., sideB_k=0.06)
    T.set_chebyshev_approximators(deg_forward=100, deg_backwards=600)

    # test V_from_h - pretty easy to get right    
    for h in linspace(0, T.h_max, 30):
        # It's the top and the bottom of the tank that works poorly
        V1 = T.V_from_h(h, 'full')
        V2 = T.V_from_h(h, 'chebyshev')
        assert_close(V1, V2, rtol=1E-7, atol=1E-7)
        
    with pytest.raises(Exception):
        T.V_from_h(1E-5, 'NOTAMETHOD')

    # reverse - the spline is also pretty easy, with a limited number of points
    # when the required precision is low
    T.set_table(n=150)
    for V in linspace(0, T.V_total, 30):
        h1 = T.h_from_V(V, 'brenth')
        h2 = T.h_from_V(V, 'spline')
        assert_close(h1, h2, rtol=1E-5, atol=1E-6)

assert_allclose(calc, expect)
    
    calc = linspace(0,1e-10, endpoint=False, num=2)
    expect = np.linspace(0,1e-10, endpoint=False, num=2)
    assert_allclose(calc, expect)
    
    calc = linspace(0,1e-10, endpoint=False, num=1)
    expect = np.linspace(0,1e-10, endpoint=False, num=1)
    assert_allclose(calc, expect)
    
    calc, calc_step = linspace(0,1e-10, endpoint=False, num=2, retstep=True)
    expect, expect_step = np.linspace(0,1e-10, endpoint=False, num=2, retstep=True)
    assert_allclose(calc, expect)
    assert_allclose(calc_step, expect_step)

    calc, calc_step = linspace(0,1e-10, endpoint=False, num=1, retstep=True)
    expect, expect_step = np.linspace(0,1e-10, endpoint=False, num=1, retstep=True)
    assert_allclose(calc, expect)
    assert isnan(calc_step)
    # Cannot compare against numpy expect_step - it did not use to give nan in older versions

    calc, calc_step = linspace(100, 1000, endpoint=False, num=21, retstep=True)
    expect, expect_step = np.linspace(100, 1000, endpoint=False, num=21, retstep=True)
    assert_allclose(calc, expect)
    assert_allclose(calc_step, expect_step)

References
    ----------
    .. [1] ASTM E11 - 17 - Standard Specification for Woven Wire Test Sieve 
       Cloth and Test Sieves.
    .. [2] ISO 3310-1:2016 - Test Sieves -- Technical Requirements and Testing
       -- Part 1: Test Sieves of Metal Wire Cloth.
    '''
    if d_min is not None:
        d_min = float(d_min)
    if d_max is not None:
        d_max = float(d_max)
    if method == 'logarithmic':
        return logspace(log10(d_min), log10(d_max), pts)
    elif method == 'linear':
        return linspace(d_min, d_max, pts)
    elif method[0] in ('R', 'r'):
        ratio = 10**(1.0/float(method[1:]))
        if d_min is not None and d_max is not None:
            raise ValueError('For geometric (Renard) series, only '
                            'one of `d_min` and `d_max` should be provided')
        if d_min is not None:
            ds = [d_min]
            for i in range(pts-1):
                ds.append(ds[-1]*ratio)
            return ds
        elif d_max is not None:
            ds = [d_max]
            for i in range(pts-1):
                ds.append(ds[-1]/ratio)
            return list(reversed(ds))
    elif method in sieve_spacing_options:

volumes in the tank, for a fully defined tank. Normally run by the
        h_from_V method, this may be run prior to its use with a custom
        specification. Either the number of points on the table, or the
        vertical distance between steps may be specified.

        Parameters
        ----------
        n : float, optional
            Number of points in the interpolation table, [-]
        dx : float, optional
            Vertical distance between steps in the interpolation table, [m]
        '''
        if dx:
            self.heights = linspace(0.0, self.h_max, int(self.h_max/dx)+1)
        else:
            self.heights = linspace(0.0, self.h_max, n)
        self.volumes = [self.V_from_h(h) for h in self.heights]
        from scipy.interpolate import UnivariateSpline
        self.interp_h_from_V = UnivariateSpline(self.volumes, self.heights, ext=3, s=0.0)
        self.table = True