test_response.py

#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""
Test suite for the response handling.

:copyright:
    Lion Krischer (krischer@geophysik.uni-muenchen.de), 2013
:license:
    GNU Lesser General Public License, Version 3
    (https://www.gnu.org/copyleft/lesser.html)
"""
import warnings
from copy import deepcopy
from math import pi

import numpy as np
import pytest
import scipy.interpolate

from obspy import UTCDateTime, read_inventory
from obspy.core.inventory.response import (
    _pitick2latex, PolesZerosResponseStage, PolynomialResponseStage, Response,
    ResponseListResponseStage, ResponseListElement, InstrumentSensitivity)
from obspy.core.util import CatchAndAssertWarnings
from obspy.core.util.misc import CatchOutput
from obspy.core.util.obspy_types import ComplexWithUncertainties
from obspy.core.util.testing import WarningsCapture
from obspy.signal.invsim import evalresp
from obspy.io.xseed import Parser


@pytest.mark.usefixtures('ignore_numpy_errors')
class TestResponse:
    """
    Tests the for :class:`~obspy.core.inventory.response.Response` class.
    """
    def test_evalresp_with_output_from_seed(self, datapath):
        """
        The StationXML file has been converted to SEED with the help of a tool
        provided by IRIS:

        https://seiscode.iris.washington.edu/projects/stationxml-converter
        """
        t_samp = 0.05
        nfft = 16384

        # Test for different output units.
        units = ["DISP", "VEL", "ACC"]
        filenames = ["IRIS_single_channel_with_response", "XM.05", "AU.MEEK"]

        for filename in filenames:
            path = datapath / filename
            xml_filename = str(path) + ".xml"
            seed_filename = str(path) + ".seed"

            p = Parser(seed_filename)

            # older systems don't like an end date in the year 2599
            t_ = UTCDateTime(2030, 1, 1)
            if p.blockettes[50][0].end_effective_date > t_:
                p.blockettes[50][0].end_effective_date = None
            if p.blockettes[52][0].end_date > t_:
                p.blockettes[52][0].end_date = None

            resp_filename = p.get_resp()[0][-1]

            inv = read_inventory(xml_filename)

            network = inv[0].code
            station = inv[0][0].code
            location = inv[0][0][0].location_code
            channel = inv[0][0][0].code
            date = inv[0][0][0].start_date

            for unit in units:
                resp_filename.seek(0, 0)

                seed_response, seed_freq = evalresp(
                    t_samp, nfft, resp_filename, date=date, station=station,
                    channel=channel, network=network, locid=location,
                    units=unit, freq=True)

                xml_response, xml_freq = \
                    inv[0][0][0].response.get_evalresp_response(t_samp, nfft,
                                                                output=unit)

                assert np.allclose(seed_freq, xml_freq, rtol=1E-5)
                assert np.allclose(seed_response, xml_response, rtol=1E-5)

                # also test getting response for a set of discrete frequencies
                indices = (-2, 0, -1, 1, 2, 20, -30, -100)
                freqs = [seed_freq[i_] for i_ in indices]
                response = inv[0][0][0].response
                got = response.get_evalresp_response_for_frequencies(
                    freqs, output=unit)
                expected = [seed_response[i_] for i_ in indices]
                np.testing.assert_allclose(got, expected, rtol=1E-5)

    def test_pitick2latex(self):
        assert _pitick2latex(3 * pi / 2) == r'$\frac{3\pi}{2}$'
        assert _pitick2latex(2 * pi / 2) == r'$\pi$'
        assert _pitick2latex(1 * pi / 2) == r'$\frac{\pi}{2}$'
        assert _pitick2latex(0 * pi / 2) == r'$0$'
        assert _pitick2latex(-1 * pi / 2) == r'$-\frac{\pi}{2}$'
        assert _pitick2latex(-2 * pi / 2) == r'$-\pi$'
        assert _pitick2latex(0.5) == r'0.500'
        assert _pitick2latex(3 * pi + 0.01) == r'9.43'
        assert _pitick2latex(30 * pi + 0.01) == r'94.3'
        assert _pitick2latex(300 * pi + 0.01) == r'942.'
        assert _pitick2latex(3000 * pi + 0.01) == r'9.42e+03'

    def test_response_plot(self, image_path):
        """
        Tests the response plot.
        """
        resp = read_inventory()[0][0][0].response
        with WarningsCapture():
            resp.plot(0.001, output="VEL", start_stage=1, end_stage=3,
                      outfile=image_path)

    def test_response_plot_degrees(self, image_path):
        """
        Tests the response plot in degrees.
        """
        resp = read_inventory()[0][0][0].response
        with WarningsCapture():
            resp.plot(0.001, output="VEL", start_stage=1, end_stage=3,
                      plot_degrees=True, outfile=image_path)

    def test_segfault_after_error_handling(self, testdata):
        """
        Many functions in evalresp call `error_return()` which uses longjmp()
        to jump to some previously set state.

        ObsPy calls some evalresp functions directly so evalresp cannot call
        setjmp(). In that case longjmp() jumps to an undefined location, most
        likely resulting in a segfault.

        This test tests a workaround for this issue.

        As long as it does not segfault the test is doing alright.
        """
        inv = read_inventory(testdata["TM.SKLT.__.BHZ_faulty_response.xml"])

        t_samp = 0.05
        nfft = 256

        resp = inv[0][0][0].response
        with CatchOutput():
            with pytest.raises(ValueError):
                resp.get_evalresp_response(t_samp, nfft, output="DISP")

    def test_custom_types_init(self):
        """
        Test initializations that involve custom decimal types like
        `ComplexWithUncertainties`.
        """
        # initializing poles / zeros from native types should work
        poles = [1 + 1j, 1, 1j]
        zeros = [2 + 3j, 2, 3j]
        stage = PolesZerosResponseStage(
            1, 1, 1, "", "", "LAPLACE (HERTZ)", 1, zeros, poles)
        assert isinstance(stage.zeros[0], ComplexWithUncertainties)
        assert isinstance(stage.poles[0], ComplexWithUncertainties)
        assert stage.poles == poles
        assert stage.zeros == zeros

    def test_response_list_stage(self, testdata):
        """
        This is quite rare but it happens.
        """
        inv = read_inventory(testdata["IM_IL31__BHZ.xml"])

        sampling_rate = 40.0
        t_samp = 1.0 / sampling_rate
        nfft = 100

        with WarningsCapture():
            cpx_response, freq = inv[0][0][0].response.get_evalresp_response(
                t_samp=t_samp, nfft=nfft, output="VEL", start_stage=None,
                end_stage=None)

        # Cut of the zero frequency.
        cpx_response = cpx_response[1:]

        amp = np.abs(cpx_response)
        phase = np.angle(cpx_response)
        freq = freq[1:]

        # The expected output goes from 1 to 20 Hz - its somehow really hard
        # to get evalresp to produce results for the desired frequencies so
        # I just gave up on it.
        exp_f, exp_amp, exp_ph = np.loadtxt(
            testdata["expected_response_IM_IL31__BHZ.txt"]).T
        # Interpolate.
        exp_amp = scipy.interpolate.InterpolatedUnivariateSpline(
            exp_f, exp_amp, k=3)(freq)
        exp_ph = scipy.interpolate.InterpolatedUnivariateSpline(
            exp_f, exp_ph, k=3)(freq)
        exp_ph = np.deg2rad(exp_ph)

        # The output is not exactle the same as ObsPy performs a different
        # but visually quite a bit better interpolation.
        np.testing.assert_allclose(amp, exp_amp, rtol=1E-3)
        np.testing.assert_allclose(phase, exp_ph, rtol=1E-3)

    def test_response_with_no_units_in_stage_1(self, testdata):
        """
        ObsPy has some heuristics to deal with this particular degenerate case.
        Test it here.
        """
        inv = read_inventory(testdata["stationxml_no_units_in_stage_1.xml"])
        r = inv[0][0][0].response

        # The units should already have been fixed from reading the StationXML
        # files...
        assert r.response_stages[0].input_units == "M/S"
        assert r.response_stages[0].input_units_description == \
            "Meters per second"
        assert r.response_stages[0].output_units == "V"
        assert r.response_stages[0].output_units_description == "VOLTS"

        # We have to set the units to None here as there is some other logic in
        # reading the StationXML files that sets them based on other units...
        r.response_stages[0].input_units = None
        r.response_stages[0].output_units = None

        with warnings.catch_warnings(record=True) as w:
            warnings.simplefilter("always")
            out = r.get_evalresp_response_for_frequencies(
                np.array([0.5, 1.0, 2.0]), output="DISP")

        assert len(w) == 2
        assert w[0].message.args[0] == \
            "Set the input units of stage 1 to the overall input units."
        assert w[1].message.args[0] == \
            "Set the output units of stage 1 to the input units of stage 2."

        # Values compared to evalresp output from RESP file - might not be
        # right but it does guarantee that ObsPy behaves like evalresp - be
        # that a good thing or a bad thing.
        np.testing.assert_allclose(
            out, [0 + 9869.2911771081963j, 0 + 19738.582354216393j,
                  0 + 39477.164708432785j])

    def test_resp_from_paz_setting_zeros_poles_and_sensitivity(self):
        poles = [1 + 2j, 1 - 2j, 2 + 1j, 2 - 1j]
        zeros = [0, 0, 5]
        sensitivity = 1201. * (2 ** 26 / 40.)
        # a0 normalization factor at 1Hz for these values
        normalization = np.prod(2 * pi * 1j - np.array(zeros))
        normalization /= np.prod(2 * pi * 1j - np.array(poles))
        normalization = np.abs(normalization)
        resp = Response.from_paz(zeros, poles, sensitivity)
        r_zeros = resp.response_stages[0].zeros
        r_poles = resp.response_stages[0].poles
        r_stage_gain = resp.response_stages[0].stage_gain
        r_sens = resp.instrument_sensitivity.value
        np.testing.assert_array_equal(r_zeros, zeros)
        np.testing.assert_array_equal(r_poles, poles)
        np.testing.assert_equal(r_stage_gain, sensitivity)
        np.testing.assert_allclose(r_sens / normalization, sensitivity, atol=0,
                                   rtol=1e-8)

    def test_resp_from_paz_loading_vs_evalresp(self, testdata):
        zeros = [0., 0.]
        poles = [-8.443 + 1.443j, -8.443 - 1.443j]
        filename = testdata['RESP.XX.NS306..SHZ.GS13.1.2180']
        resp_er = read_inventory(filename)[0][0][0].response
        loaded_resp = resp_er.get_evalresp_response(.1, 2**6, output='VEL')
        # The optional kwargs are the same as those being set in the RESP file.
        resp = Response.from_paz(zeros=zeros, poles=poles, stage_gain=22.0,
                                 stage_gain_frequency=5.0,
                                 normalization_frequency=5.0,
                                 normalization_factor=1.070401)
        paz_resp = resp.get_evalresp_response(.1, 2**6, output='VEL')
        np.testing.assert_allclose(paz_resp, loaded_resp)

    def test_str_method_of_the_polynomial_response_stage(self):
        # First with gain and gain frequency.
        assert str(PolynomialResponseStage(
            stage_sequence_number=2,
            stage_gain=12345.0,
            stage_gain_frequency=1.0,
            input_units="PA",
            input_units_description="Pascal",
            output_units="COUNTS",
            output_units_description="digital_counts",
            frequency_lower_bound=1.0,
            frequency_upper_bound=2.0,
            approximation_lower_bound=3.0,
            approximation_upper_bound=4.0,
            maximum_error=1.5,
            coefficients=[1.0, 2.0, 3.0],
            approximation_type="MACLAURIN",
            decimation_input_sample_rate=1.0,
            decimation_factor=2,
            decimation_offset=3.0,
            decimation_delay=4.0,
            decimation_correction=True)) == \
            "Response type: PolynomialResponseStage, " \
            "Stage Sequence Number: 2\n" \
            "\tFrom PA (Pascal) to COUNTS (digital_counts)\n" \
            "\tStage gain: 12345.0, defined at 1.00 Hz\n" \
            "\tDecimation:\n" \
            "\t\tInput Sample Rate: 1.00 Hz\n" \
            "\t\tDecimation Factor: 2\n" \
            "\t\tDecimation Offset: 3\n" \
            "\t\tDecimation Delay: 4.00\n" \
            "\t\tDecimation Correction: 1.00\n" \
            "\tPolynomial approximation type: MACLAURIN\n" \
            "\tFrequency lower bound: 1.0\n" \
            "\tFrequency upper bound: 2.0\n" \
            "\tApproximation lower bound: 3.0\n" \
            "\tApproximation upper bound: 4.0\n" \
            "\tMaximum error: 1.5\n" \
            "\tNumber of coefficients: 3"

        # Now only the very minimum.
        assert str(PolynomialResponseStage(
            stage_sequence_number=4,
            stage_gain=None,
            stage_gain_frequency=None,
            input_units=None,
            input_units_description=None,
            output_units=None,
            output_units_description=None,
            frequency_lower_bound=None,
            frequency_upper_bound=None,
            approximation_lower_bound=None,
            approximation_upper_bound=None,
            maximum_error=None,
            coefficients=[],
            approximation_type="MACLAURIN")) == \
            "Response type: PolynomialResponseStage, " \
            "Stage Sequence Number: 4\n" \
            "\tFrom UNKNOWN to UNKNOWN\n" \
            "\tStage gain: UNKNOWN, defined at UNKNOWN Hz\n" \
            "\tPolynomial approximation type: MACLAURIN\n" \
            "\tFrequency lower bound: None\n" \
            "\tFrequency upper bound: None\n" \
            "\tApproximation lower bound: None\n" \
            "\tApproximation upper bound: None\n" \
            "\tMaximum error: None\n" \
            "\tNumber of coefficients: 0"

    def test_get_sampling_rates(self, testdata):
        """
        Tests for the get_sampling_rates() method.
        """
        # Test for the default inventory.
        resp = read_inventory()[0][0][0].response
        assert resp.get_sampling_rates() == \
            {1: {'decimation_factor': 1,
                 'input_sampling_rate': 200.0,
                 'output_sampling_rate': 200.0},
             2: {'decimation_factor': 1,
                 'input_sampling_rate': 200.0,
                 'output_sampling_rate': 200.0}}

        # Another, well behaved file.
        inv = read_inventory(testdata['AU.MEEK.xml'])
        assert inv[0][0][0].response.get_sampling_rates() == \
            {1: {'decimation_factor': 1,
                 'input_sampling_rate': 600.0,
                 'output_sampling_rate': 600.0},
             2: {'decimation_factor': 1,
                 'input_sampling_rate': 600.0,
                 'output_sampling_rate': 600.0},
             3: {'decimation_factor': 1,
                 'input_sampling_rate': 600.0,
                 'output_sampling_rate': 600.0},
             4: {'decimation_factor': 3,
                 'input_sampling_rate': 600.0,
                 'output_sampling_rate': 200.0},
             5: {'decimation_factor': 10,
                 'input_sampling_rate': 200.0,
                 'output_sampling_rate': 20.0}}

        # This file lacks decimation attributes for the first two stages as
        # well as one of the later ones. These thus have to be inferred.
        inv = read_inventory(testdata['DK.BSD..BHZ.xml'])
        assert inv[0][0][0].response.get_sampling_rates() == \
            {1: {'decimation_factor': 1,
                 'input_sampling_rate': 30000.0,
                 'output_sampling_rate': 30000.0},
             2: {'decimation_factor': 1,
                 'input_sampling_rate': 30000.0,
                 'output_sampling_rate': 30000.0},
             3: {'decimation_factor': 1,
                 'input_sampling_rate': 30000.0,
                 'output_sampling_rate': 30000.0},
             4: {'decimation_factor': 5,
                 'input_sampling_rate': 30000.0,
                 'output_sampling_rate': 6000.0},
             5: {'decimation_factor': 3,
                 'input_sampling_rate': 6000.0,
                 'output_sampling_rate': 2000.0},
             6: {'decimation_factor': 2,
                 'input_sampling_rate': 2000.0,
                 'output_sampling_rate': 1000.0},
             7: {'decimation_factor': 5,
                 'input_sampling_rate': 1000.0,
                 'output_sampling_rate': 200.0},
             8: {'decimation_factor': 2,
                 'input_sampling_rate': 200.0,
                 'output_sampling_rate': 100.0},
             9: {'decimation_factor': 1,
                 'input_sampling_rate': 100.0,
                 'output_sampling_rate': 100.0},
             10: {'decimation_factor': 5,
                  'input_sampling_rate': 100.0,
                  'output_sampling_rate': 20.0}}

    def test_response_calculation_paz_without_decimation(self, testdata):
        """
        This test files has two PAZ stages with no decimation attributes.

        Evalresp does not like this so we have to add dummy decimation
        attributes before calling it.
        """
        inv = read_inventory(testdata['DK.BSD..BHZ.xml'])
        np.testing.assert_allclose(
            inv[0][0][0].response.get_evalresp_response_for_frequencies(
                [0.1, 1.0, 10.0], hide_sensitivity_mismatch_warning=True),
            [6.27191825e+08 + 1.38925202e+08j,
             6.51826202e+08 + 1.28404787e+07j,
             2.00067263e+04 - 2.63711751e+03j])

    def test_regression_evalresp(self, testdata):
        """
        Regression test for an evalresp issue with a micropressure instrument.

        See #2171.
        """
        inv = read_inventory(testdata["IM_I53H1_BDF.xml"])
        cha_response = inv[0][0][0].response
        freq_resp = cha_response.get_evalresp_response_for_frequencies([0.0])
        assert freq_resp == 0.0 + 0.0j
        np.testing.assert_allclose(
            inv[0][0][0].response.get_evalresp_response_for_frequencies(
                [0.1, 1.0, 10.0]),
            [2.411908e+05 + 2.283852e+04j,
             2.445572e+05 - 2.480459e+03j,
             -2.455459e-01 + 4.888214e-02j], rtol=1e-6)

    def test_recalculate_overall_sensitivity(self):
        """
        Tests the recalculate_overall_sensitivity_method().

        This is not yet an exhaustive test as responses are complicated...
        """
        resp = read_inventory()[0][0][0].response
        np.testing.assert_allclose(
            resp.instrument_sensitivity.value,
            943680000.0)
        np.testing.assert_allclose(
            resp.instrument_sensitivity.frequency,
            0.02)
        # Recompute - it is not much different but a bit.
        resp.recalculate_overall_sensitivity(0.02)
        np.testing.assert_allclose(
            resp.instrument_sensitivity.value,
            943681500.0)
        np.testing.assert_allclose(
            resp.instrument_sensitivity.frequency,
            0.02)

        # There is some logic to automatically determine a suitable frequency.
        # Make sure this does something here.
        resp = read_inventory()[0][0][0].response
        resp.recalculate_overall_sensitivity()
        np.testing.assert_allclose(
            resp.instrument_sensitivity.value,
            957562105.3939067)
        np.testing.assert_allclose(
            resp.instrument_sensitivity.frequency,
            1.0)

        # Passing an integer also works. See #2338.
        resp = read_inventory()[0][0][0].response
        resp.recalculate_overall_sensitivity(1)
        np.testing.assert_allclose(
            resp.instrument_sensitivity.value,
            957562105.3939067)
        np.testing.assert_allclose(
            resp.instrument_sensitivity.frequency,
            1.0)

    def test_warning_response_list_extrapolation(self):
        """
        Tests that a warning message is shown when a response calculation
        involving a response list stage includes (spline) extrapolation into
        frequency ranges outside of the band defined by the response list stage
        elements (frequency-amplitude-phase pairs).
        """
        # create some bogus response list stage for the test
        elems = [
            ResponseListElement(x, 1, 0) for x in (1, 2, 5, 10, 20, 40, 50)]
        stage = ResponseListResponseStage(
            1, 1, 10, "M/S", "M/S", response_list_elements=elems)
        sens = InstrumentSensitivity(1, 10, "M/S", "M/S")
        resp = Response(response_stages=[stage], instrument_sensitivity=sens)
        msg = ("The response contains a response list stage with frequencies "
               "only from 1.0000 - 50.0000 Hz. You are requesting a response "
               "from 25.0000 - 100.0000 Hz. The calculated response will "
               "contain extrapolation beyond the frequency band constrained "
               "by the response list stage. Please consider adjusting "
               "'pre_filt' and/or 'water_level' during response removal "
               "accordingly.")
        with CatchAndAssertWarnings(expected=[(UserWarning, msg)]):
            resp.get_evalresp_response(0.005, 2**3)

    def test_unknown_units_no_integration(self, testdata):
        """
        Makes sure that when a unit in the list of response stages is not known
        to evalresp, no tampering (integration/differentiation) is done and
        response is just calculated as is specified.
        It used to be that unkown units where reported to evalresp as
        displacement ("DIS") which led to a differentiation being added
        internally with the default "output='VEL'".
        Example is a rotational sensor with input units RAD/S and a flat
        response and since evalresp does not know RAD or RAD/S the only thing
        that makes sense is have evalresp not do anything else than use the
        response as is and ignore "output" option.
        """
        inv = read_inventory(testdata['response_radian_per_second.xml'],
                             format="STATIONXML")
        resp = inv[0][0][0].response
        freqs = [0.01, 0.1, 1, 10, 100]
        overall_sensitivity = 1.00000000e+09
        msg = (r"The unit 'RAD/S' is not known to ObsPy. It will be passed in "
               r"to evalresp as 'undefined'. This should result in evalresp "
               r"using the response as is, without adding any integration or "
               r"differentiation and the 'output' parameter \(here: 'VEL'\) "
               r"not having any effect. Please double check output data.")
        with pytest.warns(UserWarning, match=msg):
            data = resp.get_evalresp_response_for_frequencies(freqs)
        assert resp.instrument_sensitivity.value == overall_sensitivity
        assert np.abs(data).tolist() == [overall_sensitivity] * len(freqs)

    def test_non_SI_unit_input_first_stage(self, testdata):
        """
        Regression test for #3369

        Test that non-SI units input (e.g. nanometer/second) is properly taken
        into account when removing the instrument response, i.e. the additional
        scaling factor (e.g. 1e09 for nm/s) is applied to the output.

        The change in that issue affects
        Response._call_eval_resp_for_frequencies() which in turn gets called
        by..
         - Response._get_overall_sensitivity_and_gain()
         - Response.get_evalresp_response_for_frequencies()

        Test all of those three for good measure.
        """
        inv = read_inventory(testdata['SL_BOJS_LHZ.xml'], "STATIONXML")

        # original data has nm/s as a non-SI input unit. setup clones with some
        # different input units
        inv_nms = inv
        inv_ms = inv_nms.copy()
        inv_ms[0][0][0].response.instrument_sensitivity.input_units = 'm/s'
        inv_ms[0][0][0].response.instrument_sensitivity.value *= 1e9
        inv_ms[0][0][0].response.response_stages[0].input_units = 'm/s'
        inv_ms[0][0][0].response.response_stages[0].stage_gain *= 1e9
        inv_mms = inv_nms.copy()
        inv_mms[0][0][0].response.instrument_sensitivity.input_units = 'mm/s'
        inv_mms[0][0][0].response.instrument_sensitivity.value *= 1e6
        inv_mms[0][0][0].response.response_stages[0].input_units = 'mm/s'
        inv_mms[0][0][0].response.response_stages[0].stage_gain *= 1e6
        inv_cms = inv_nms.copy()
        inv_cms[0][0][0].response.instrument_sensitivity.input_units = 'cm/s'
        inv_cms[0][0][0].response.instrument_sensitivity.value *= 1e7
        inv_cms[0][0][0].response.response_stages[0].input_units = 'cm/s'
        inv_cms[0][0][0].response.response_stages[0].stage_gain *= 1e7

        # test at two frequencies in the flat response part
        freqs = [0.01, 0.1]
        expected = [1.84e+09, 1.85e+09]

        for inv in (inv_nms, inv_ms, inv_mms, inv_cms):
            resp = inv[0][0][0].response

            # test _call_eval_resp_for_frequencies()
            got, _ = resp._call_eval_resp_for_frequencies(
                freqs, output='VEL', start_stage=None, end_stage=None)
            got = np.abs(got)
            np.testing.assert_allclose(got, expected, rtol=1e-2)

            # test get_evalresp_response_for_frequencies()
            got = resp.get_evalresp_response_for_frequencies(
                freqs, output='VEL', start_stage=None, end_stage=None)
            got = np.abs(got)
            np.testing.assert_allclose(got, expected, rtol=1e-2)

            # test _get_overall_sensitivity_and_gain()
            got = [resp._get_overall_sensitivity_and_gain(f, output='VEL')[1]
                   for f in freqs]
            np.testing.assert_allclose(got, expected, rtol=1e-2)

    def test_pazresponsestage_hertz_to_radians(self, testdata):
        """
        Tests converting a PAZResponseStage from Hertz to Radians/s
        """
        inv = read_inventory(testdata['G_CAN__LHZ.xml'], 'STATIONXML')
        paz_before = inv[0][0][0].response.response_stages[0]
        paz_after = deepcopy(paz_before)
        paz_after.to_radians_per_second()

        expected_zeros = [0j, 0j]
        expected_poles = [-1.233948e-02+1.234319e-02j,
                          -1.233948e-02-1.234319e-02j,
                          -3.917566e+01+4.912339e+01j,
                          -3.917566e+01-4.912339e+01j]

        assert paz_before.pz_transfer_function_type == 'LAPLACE (HERTZ)'
        assert paz_after.pz_transfer_function_type == \
            'LAPLACE (RADIANS/SECOND)'
        assert round(paz_after.normalization_factor, 3) == 3.959488e+03
        np.testing.assert_allclose(
            paz_after.zeros, expected_zeros, rtol=1e-6)
        np.testing.assert_allclose(
            paz_after.poles, expected_poles, rtol=1e-6)