Python numpy.frexp() Examples

def clear_fuss(ar, fuss_binary_bits=7):
    """Clears trailing `fuss_binary_bits` of mantissa of a floating number"""
    x = np.asanyarray(ar)
    if np.iscomplexobj(x):
        return clear_fuss(x.real) + 1j * clear_fuss(x.imag)

    significant_binary_bits = np.finfo(x.dtype).nmant
    x_mant, x_exp = np.frexp(x)
    f = 2.0**(significant_binary_bits - fuss_binary_bits)
    x_mant *= f
    np.rint(x_mant, out=x_mant)
    x_mant /= f

    return np.ldexp(x_mant, x_exp)


# XXX: This function should be available through numpy.testing 

def test_failing_out_wrap(self):

        singleton = np.array([1.0])

        class Ok(np.ndarray):
            def __array_wrap__(self, obj):
                return singleton

        class Bad(np.ndarray):
            def __array_wrap__(self, obj):
                raise RuntimeError

        ok = np.empty(1).view(Ok)
        bad = np.empty(1).view(Bad)

        # double-free (segfault) of "ok" if "bad" raises an exception
        for i in range(10):
            assert_raises(RuntimeError, ncu.frexp, 1, ok, bad) 

def test_failing_out_wrap(self):

        singleton = np.array([1.0])

        class Ok(np.ndarray):
            def __array_wrap__(self, obj):
                return singleton

        class Bad(np.ndarray):
            def __array_wrap__(self, obj):
                raise RuntimeError

        ok = np.empty(1).view(Ok)
        bad = np.empty(1).view(Bad)

        # double-free (segfault) of "ok" if "bad" raises an exception
        for i in range(10):
            assert_raises(RuntimeError, ncu.frexp, 1, ok, bad) 

def test_failing_out_wrap(self):

        singleton = np.array([1.0])

        class Ok(np.ndarray):
            def __array_wrap__(self, obj):
                return singleton

        class Bad(np.ndarray):
            def __array_wrap__(self, obj):
                raise RuntimeError

        ok = np.empty(1).view(Ok)
        bad = np.empty(1).view(Bad)

        # double-free (segfault) of "ok" if "bad" raises an exception
        for i in range(10):
            assert_raises(RuntimeError, ncu.frexp, 1, ok, bad) 

def test_failing_out_wrap(self):

        singleton = np.array([1.0])

        class Ok(np.ndarray):
            def __array_wrap__(self, obj):
                return singleton

        class Bad(np.ndarray):
            def __array_wrap__(self, obj):
                raise RuntimeError

        ok = np.empty(1).view(Ok)
        bad = np.empty(1).view(Bad)

        # double-free (segfault) of "ok" if "bad" raises an exception
        for i in range(10):
            assert_raises(RuntimeError, ncu.frexp, 1, ok, bad) 

def test_failing_out_wrap(self):

        singleton = np.array([1.0])

        class Ok(np.ndarray):
            def __array_wrap__(self, obj):
                return singleton

        class Bad(np.ndarray):
            def __array_wrap__(self, obj):
                raise RuntimeError

        ok = np.empty(1).view(Ok)
        bad = np.empty(1).view(Bad)

        # double-free (segfault) of "ok" if "bad" raises an exception
        for i in range(10):
            assert_raises(RuntimeError, ncu.frexp, 1, ok, bad) 

def test_failing_out_wrap(self):

        singleton = np.array([1.0])

        class Ok(np.ndarray):
            def __array_wrap__(self, obj):
                return singleton

        class Bad(np.ndarray):
            def __array_wrap__(self, obj):
                raise RuntimeError

        ok = np.empty(1).view(Ok)
        bad = np.empty(1).view(Bad)

        # double-free (segfault) of "ok" if "bad" raises an exception
        for i in range(10):
            assert_raises(RuntimeError, ncu.frexp, 1, ok, bad) 

def testFrexp(self):
        t1 = ones((3, 4, 5), chunk_size=2)
        t2 = empty((3, 4, 5), dtype=np.float_, chunk_size=2)
        op_type = type(t1.op)

        o1, o2 = frexp(t1)

        self.assertIs(o1.op, o2.op)
        self.assertNotEqual(o1.dtype, o2.dtype)

        o1, o2 = frexp(t1, t1)

        self.assertIs(o1, t1)
        self.assertIsNot(o1.inputs[0], t1)
        self.assertIsInstance(o1.inputs[0].op, op_type)
        self.assertIsNot(o2.inputs[0], t1)

        o1, o2 = frexp(t1, t2, where=t1 > 0)

        op_type = type(t2.op)
        self.assertIs(o1, t2)
        self.assertIsNot(o1.inputs[0], t1)
        self.assertIsInstance(o1.inputs[0].op, op_type)
        self.assertIsNot(o2.inputs[0], t1) 

def test_failing_out_wrap(self):

        singleton = np.array([1.0])

        class Ok(np.ndarray):
            def __array_wrap__(self, obj):
                return singleton

        class Bad(np.ndarray):
            def __array_wrap__(self, obj):
                raise RuntimeError

        ok = np.empty(1).view(Ok)
        bad = np.empty(1).view(Bad)

        # double-free (segfault) of "ok" if "bad" raises an exception
        for i in range(10):
            assert_raises(RuntimeError, ncu.frexp, 1, ok, bad) 

def test_failing_out_wrap(self):

        singleton = np.array([1.0])

        class Ok(np.ndarray):
            def __array_wrap__(self, obj):
                return singleton

        class Bad(np.ndarray):
            def __array_wrap__(self, obj):
                raise RuntimeError

        ok = np.empty(1).view(Ok)
        bad = np.empty(1).view(Bad)

        # double-free (segfault) of "ok" if "bad" raises an exception
        for i in range(10):
            assert_raises(RuntimeError, ncu.frexp, 1, ok, bad) 

def robust_outer_product(vec_1, vec_2):
    """
    Calculates a 'robust' outer product of two vectors that may or may not
    contain very small values.

    Parameters
    ----------
    vec_1 : 1D ndarray
    vec_2 : 1D ndarray

    Returns
    -------
    outer_prod : 2D ndarray. The outer product of vec_1 and vec_2
    """
    mantissa_1, exponents_1 = np.frexp(vec_1)
    mantissa_2, exponents_2 = np.frexp(vec_2)
    new_mantissas = mantissa_1[None, :] * mantissa_2[:, None]
    new_exponents = exponents_1[None, :] + exponents_2[:, None]
    return new_mantissas * np.exp2(new_exponents) 

def test_doc(self):
        # don't bother checking the long list of kwargs, which are likely to
        # change
        assert_(ncu.add.__doc__.startswith(
            "add(x1, x2, /, out=None, *, where=True"))
        assert_(ncu.frexp.__doc__.startswith(
            "frexp(x[, out1, out2], / [, out=(None, None)], *, where=True")) 

def test_ufunc_override_out(self):
        # 2016-01-29: NUMPY_UFUNC_DISABLED
        return

        class A(object):
            def __numpy_ufunc__(self, ufunc, method, pos, inputs, **kwargs):
                return kwargs

        class B(object):
            def __numpy_ufunc__(self, ufunc, method, pos, inputs, **kwargs):
                return kwargs

        a = A()
        b = B()
        res0 = np.multiply(a, b, 'out_arg')
        res1 = np.multiply(a, b, out='out_arg')
        res2 = np.multiply(2, b, 'out_arg')
        res3 = np.multiply(3, b, out='out_arg')
        res4 = np.multiply(a, 4, 'out_arg')
        res5 = np.multiply(a, 5, out='out_arg')

        assert_equal(res0['out'], 'out_arg')
        assert_equal(res1['out'], 'out_arg')
        assert_equal(res2['out'], 'out_arg')
        assert_equal(res3['out'], 'out_arg')
        assert_equal(res4['out'], 'out_arg')
        assert_equal(res5['out'], 'out_arg')

        # ufuncs with multiple output modf and frexp.
        res6 = np.modf(a, 'out0', 'out1')
        res7 = np.frexp(a, 'out0', 'out1')
        assert_equal(res6['out'][0], 'out0')
        assert_equal(res6['out'][1], 'out1')
        assert_equal(res7['out'][0], 'out0')
        assert_equal(res7['out'][1], 'out1') 

def test_ufunc_two_outputs(self):
        mantissa, exponent = np.frexp(2 ** -3)
        expected = (ArrayLike(mantissa), ArrayLike(exponent))
        _assert_equal_type_and_value(
            np.frexp(ArrayLike(2 ** -3)), expected)
        _assert_equal_type_and_value(
            np.frexp(ArrayLike(np.array(2 ** -3))), expected) 

def pow_next_log_of_2_no_round(value, bound_shift, shift_max_shift=4):
    mul, shift = np.frexp(np.abs(value))    # value = mul(0~1)*(1 << shift)
    ret = bound_shift - 1 - shift           # shift to full bound_shift
    mul = np.sign(value) * mul * np.power(2, bound_shift - 1)   # scale mul
    # value = mul>>ret
    return ret, mul 

def test_ufunc_two_outputs(self):
        mantissa, exponent = np.frexp(2 ** -3)
        expected = (ArrayLike(mantissa), ArrayLike(exponent))
        _assert_equal_type_and_value(
            np.frexp(ArrayLike(2 ** -3)), expected)
        _assert_equal_type_and_value(
            np.frexp(ArrayLike(np.array(2 ** -3))), expected) 

def test_ufunc_two_outputs(self):
        mantissa, exponent = np.frexp(2 ** -3)
        expected = (ArrayLike(mantissa), ArrayLike(exponent))
        _assert_equal_type_and_value(
            np.frexp(ArrayLike(2 ** -3)), expected)
        _assert_equal_type_and_value(
            np.frexp(ArrayLike(np.array(2 ** -3))), expected) 

def test_ufunc_two_outputs(self):
        mantissa, exponent = np.frexp(2 ** -3)
        expected = (ArrayLike(mantissa), ArrayLike(exponent))
        _assert_equal_type_and_value(
            np.frexp(ArrayLike(2 ** -3)), expected)
        _assert_equal_type_and_value(
            np.frexp(ArrayLike(np.array(2 ** -3))), expected) 

def test_doc(self):
        # don't bother checking the long list of kwargs, which are likely to
        # change
        assert_(ncu.add.__doc__.startswith(
            "add(x1, x2, /, out=None, *, where=True"))
        assert_(ncu.frexp.__doc__.startswith(
            "frexp(x[, out1, out2], / [, out=(None, None)], *, where=True")) 

def test_doc(self):
        # don't bother checking the long list of kwargs, which are likely to
        # change
        assert_(ncu.add.__doc__.startswith(
            "add(x1, x2, /, out=None, *, where=True"))
        assert_(ncu.frexp.__doc__.startswith(
            "frexp(x[, out1, out2], / [, out=(None, None)], *, where=True")) 

def _roots(p):
    """Modified version of NumPy's roots function.

    NumPy's roots uses the companion matrix method, which divides by
    p[0]. This can causes overflows/underflows. Instead form a
    modified companion matrix that is scaled by 2^c * p[0], where the
    exponent c is chosen to balance the magnitudes of the
    coefficients. Since scaling the matrix just scales the
    eigenvalues, we can remove the scaling at the end.

    Scaling by a power of 2 is chosen to avoid rounding errors.

    """
    _, e = np.frexp(p)
    # Balance the most extreme exponents e_max and e_min by solving
    # the equation
    #
    # |c + e_max| = |c + e_min|.
    #
    # Round the exponent to an integer to avoid rounding errors.
    c = int(-0.5 * (np.max(e) + np.min(e)))
    p = np.ldexp(p, c)

    A = np.diag(np.full(p.size - 2, p[0]), k=-1)
    A[0,:] = -p[1:]
    eigenvalues = np.linalg.eigvals(A)
    return eigenvalues / p[0] 

def radiance_writer(out_path, image):
    with open(out_path, "wb") as f:
        f.write(b"#?RADIANCE\n# Made with Python & Numpy\nFORMAT=32-bit_rle_rgbe\n\n")
        f.write(b"-Y %d +X %d\n" %(image.shape[0], image.shape[1]))

        brightest = np.maximum(np.maximum(image[...,0], image[...,1]), image[...,2])
        mantissa = np.zeros_like(brightest)
        exponent = np.zeros_like(brightest)
        np.frexp(brightest, mantissa, exponent)
        scaled_mantissa = mantissa * 255.0 / brightest
        rgbe = np.zeros((image.shape[0], image.shape[1], 4), dtype=np.uint8)
        rgbe[...,0:3] = np.around(image[...,0:3] * scaled_mantissa[...,None])
        rgbe[...,3] = np.around(exponent + 128)

        rgbe.flatten().tofile(f) 

def test_out_subok(self):
        for b in (True, False):
            aout = np.array(0.5)

            r = np.add(aout, 2, out=aout)
            assert_(r is aout)
            assert_array_equal(r, aout)

            r = np.add(aout, 2, out=aout, subok=b)
            assert_(r is aout)
            assert_array_equal(r, aout)

            r = np.add(aout, 2, aout, subok=False)
            assert_(r is aout)
            assert_array_equal(r, aout)

            d = np.ones(5)
            o1 = np.zeros(5)
            o2 = np.zeros(5, dtype=np.int32)
            r1, r2 = np.frexp(d, o1, o2, subok=b)
            assert_(r1 is o1)
            assert_array_equal(r1, o1)
            assert_(r2 is o2)
            assert_array_equal(r2, o2)

            r1, r2 = np.frexp(d, out=o1, subok=b)
            assert_(r1 is o1)
            assert_array_equal(r1, o1) 

def test_doc(self):
        # don't bother checking the long list of kwargs, which are likely to
        # change
        assert_(ncu.add.__doc__.startswith(
            "add(x1, x2, /, out=None, *, where=True"))
        assert_(ncu.frexp.__doc__.startswith(
            "frexp(x[, out1, out2], / [, out=(None, None)], *, where=True")) 

def test_frexp_scalar(self):
        q = np.frexp(3. * u.m / (6. * u.m))
        assert q == (np.array(0.5), np.array(0.0)) 

def test_ufunc_override_out(self):
        class A(object):
            def __numpy_ufunc__(self, ufunc, method, pos, inputs, **kwargs):
                return kwargs


        class B(object):
            def __numpy_ufunc__(self, ufunc, method, pos, inputs, **kwargs):
                return kwargs

        a = A()
        b = B()
        res0 = np.multiply(a, b, 'out_arg')
        res1 = np.multiply(a, b, out='out_arg')
        res2 = np.multiply(2, b, 'out_arg')
        res3 = np.multiply(3, b, out='out_arg')
        res4 = np.multiply(a, 4, 'out_arg')
        res5 = np.multiply(a, 5, out='out_arg')

        assert_equal(res0['out'], 'out_arg')
        assert_equal(res1['out'], 'out_arg')
        assert_equal(res2['out'], 'out_arg')
        assert_equal(res3['out'], 'out_arg')
        assert_equal(res4['out'], 'out_arg')
        assert_equal(res5['out'], 'out_arg')

        # ufuncs with multiple output modf and frexp.
        res6 = np.modf(a, 'out0', 'out1')
        res7 = np.frexp(a, 'out0', 'out1')
        assert_equal(res6['out'][0], 'out0')
        assert_equal(res6['out'][1], 'out1')
        assert_equal(res7['out'][0], 'out0')
        assert_equal(res7['out'][1], 'out1') 

def test_frexp_array(self):
        q = np.frexp(np.array([2., 3., 6.]) * u.m / (6. * u.m))
        assert all((_q0, _q1) == np.frexp(_d) for _q0, _q1, _d
                   in zip(q[0], q[1], [1. / 3., 1. / 2., 1.])) 

def test_ufunc_two_outputs(self):
        mantissa, exponent = np.frexp(2 ** -3)
        expected = (ArrayLike(mantissa), ArrayLike(exponent))
        _assert_equal_type_and_value(
            np.frexp(ArrayLike(2 ** -3)), expected)
        _assert_equal_type_and_value(
            np.frexp(ArrayLike(np.array(2 ** -3))), expected) 

def test_ufunc_two_outputs(self):
        mantissa, exponent = np.frexp(2 ** -3)
        expected = (ArrayLike(mantissa), ArrayLike(exponent))
        _assert_equal_type_and_value(
            np.frexp(ArrayLike(2 ** -3)), expected)
        _assert_equal_type_and_value(
            np.frexp(ArrayLike(np.array(2 ** -3))), expected) 

def test_frexp(self, dtype):
        numpy_a = numpy.array([-300, -20, -10, -1, 0, 1, 10, 20, 300],
                              dtype=dtype)
        numpy_b, numpy_c = numpy.frexp(numpy_a)

        cupy_a = cupy.array(numpy_a)
        cupy_b, cupy_c = cupy.frexp(cupy_a)

        testing.assert_array_equal(cupy_b, numpy_b)
        testing.assert_array_equal(cupy_c, numpy_c)