示例#1
0
class TestZern(unittest.TestCase):
    def setUp(self):
        self.pupil = RZern(4)
        self.max_enorm = 1e-9
        self.max_ip_err = 5e-2

    def test_ntab(self):
        self.assertTrue(self.pupil.ntab.size == 15)
        expect = np.array([0, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4])
        self.assertTrue(norm(self.pupil.ntab - expect) < self.max_enorm)

    def test_mtab(self):
        self.assertTrue(self.pupil.mtab.size == 15)
        expect = np.array([0, 1, -1, 0, -2, 2, -1, 1, -3, 3, 0, 2, -2, 4, -4])
        self.assertTrue(norm(self.pupil.mtab - expect) < self.max_enorm)

    def test_rhotab(self):
        expect = [
            0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13.416407864999,
            12.649110640674, 12.649110640674, 3.1622776601684,
            3.1622776601684, 0, 0, 0, 0, 0, 0, 8.4852813742386,
            8.4852813742386, 2.8284271247462, 2.8284271247462,
            0, 0, 0, 0, 0, 0, 0, 0, 3.4641016151378,
            2.4494897427832, 2.4494897427832, 0, 0, 0, 0,
            -13.416407864999, -9.4868329805051, -9.4868329805051,
            0, 0, 0, 2, 2, 0, 0, 0, -5.6568542494924,
            -5.6568542494924, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
            -1.7320508075689, 0, 0, 0, 0, 0, 0, 2.2360679774998,
            0, 0, 0, 0
        ]
        for c, v in enumerate(expect):
            i, j = c % 15, c // 15
            err = abs(self.pupil.coefnorm[i]*self.pupil.rhotab[i, j] - v)
            self.assertTrue(err < self.max_enorm)

    def test_Rnm(self):
        inrho = [
            0.19343375193909, 0.75442458148825, 0.34626071666477,
            0.41862541430271, 0.15571983035489, 0.81900058392684,
            0.62492352784628, 0.73856042161065, 0.80511242070695,
            0.067222657563179, 0.95079031650557, 0.49757701102216,
            0.75514590470052, 0.74240507067694, 0.83112957571011,
            0.1565018467502, 0.45730872055141, 0.61810049609438,
            0.93218335504705, 0.83508823555935, 0.89542351634235,
            0.58251852466803, 0.58274680636179, 0.85492593896995,
            0.034865700047931, 0.8854200954848, 0.40773081135598,
            0.036382030447832, 0.74614794273772, 0.15482877075111
        ]
        out3 = [
            -1.6024358463019, 0.2395649672106, -1.3167172040235,
            -1.1249765690963, -1.6480509660176, 0.59153676922049,
            -0.37921722803669, 0.157517884017, 0.5134006785331,
            -1.716396928352, 1.3995047634699, -0.87439854650643,
            0.24333698669463, 0.177241760149, 0.66086873705921,
            -1.6472051624093, -1.0075988516153, -0.40859694027142,
            1.2781350494377, 0.68371791511127, 1.0454079255648,
            -0.55658471812649, -0.55566323680867, 0.79985538570113,
            -1.7278397866178, 0.98369658989472, -1.1561632626913,
            -1.7274655420545, 0.19654187580572, -1.6490095429101
        ]
        out4 = [
            0.091651618055082, 1.3941428842409, 0.29368520752156,
            0.42926631070763, 0.0593968575795, 1.6430245322286,
            0.95659779790408, 1.3361268353382, 1.5877739726481,
            0.011068964146113, 2.214344179944, 0.60645172969723,
            1.3968101047969, 1.3500737219024, 1.6920496368403,
            0.059994931046482, 0.51226489069861, 0.93582320415359,
            2.1285228321212, 1.7082064455855, 1.9639599046646,
            0.83118004289954, 0.83183162858811, 1.7903280385894,
            0.0029776414702216, 1.9203234007362, 0.4072139881838,
            0.0032422723387354, 1.3637209645609, 0.058719041358534
        ]
        out10 = [
            1.7528544047959, -1.0538684824995, 0.82035094947331,
            0.29691883664534, 1.9186268081509, -0.72681628778909,
            -0.95725432162119, -1.0902934593531, -0.82334230297547,
            2.1757147314369, 1.0717625678433, -0.2632155912034,
            -1.0518319661711, -1.082911351763, -0.62973545308711,
            1.915510691432, 0.017056106891689, -0.93137658244662,
            0.7084189870086, -0.59538643046011, 0.10384045987001,
            -0.7716820983231, -0.77282798892389, -0.40275090649042,
            2.2197785892442, -0.036158358505776, 0.37645712628727,
            2.2183328268091, -1.0748457792076, 1.9221603389389
        ]
        out13 = [
            0.0044271987866637, 1.0243852641201, 0.0454582689999,
            0.09711858840943, 0.0018594122493614, 1.4227770316249,
            0.48228916269284, 0.9409014176698, 1.3286974659506,
            6.4574746661877e-05, 2.5842766270514, 0.19383902995264,
            1.0283086425533, 0.96064675024684, 1.5089503417078,
            0.0018970460208737, 0.13830501642735, 0.4615687191036,
            2.3878408401262, 1.5379048343826, 2.0328904888789,
            0.36411532970706, 0.3646864342091, 1.6893279835042,
            4.6729760834851e-06, 1.9435579666012, 0.08739651710603,
            5.540484342947e-06, 0.98016633844227, 0.0018172164647309
        ]
        outi = [3, 4, 10, 13]
        outl = [out3, out4, out10, out13]
        for c, i in enumerate(outi):
            for j in range(len(inrho)):
                a = self.pupil.coefnorm[i]*self.pupil.Rnm(i, inrho[j])
                b = outl[c][j]
                err = abs(a - b)
                self.assertTrue(err < self.max_enorm)

    def test_Zj(self):
        rho = [
            0, 0.11111111111111, 0.22222222222222,
            0.33333333333333, 0.44444444444444,
            0.55555555555556, 0.66666666666667,
            0.77777777777778, 0.88888888888889, 1
        ]
        theta = [
            0, 0.69813170079773, 1.3962634015955,
            2.0943951023932, 2.7925268031909,
            3.4906585039887, 4.1887902047864,
            4.8869219055841, 5.5850536063819,
            6.2831853071796
        ]
        c = [
            0.54031374569774, 0.99075098653197, 0.98937811670199,
            -0.68884118291816, -0.85683760660055, 0.048390017659746,
            -0.66485340286758, 1.4527419609898, 1.3798457521444,
            0.095136418969694, -0.42712706398395, 0.51080780984162,
            -0.65627362438046, -0.12501677594865, -0.53046670030726
        ]
        z = [
            0.77833652275983, 0.085651919598506, -0.53679726827283,
            -0.98349975448282, -1.1477173085559, -0.92148475591224,
            -0.19560997786786, 1.1403260883655, 3.1979694496802,
            6.090193057073, 0.77833652275983, 0.74923429103286,
            0.92966992705808, 1.3229751043261, 1.8849792604988,
            2.524009597409, 3.1008910810612, 3.4289464416307,
            3.2739961734642, 2.3543585350795, 0.77833652275983,
            1.3880071769557, 2.1381716926469, 2.8957139599519,
            3.4767967033161, 3.6468614815119, 3.1206286876391,
            1.5620975491243, -1.4154538722785, -6.2494686804882,
            0.77833652275983, 1.6882064144334, 2.5555787288029,
            3.2751193339259, 3.7304210304525, 3.7940035516249,
            3.3273135632778, 2.1807246638382, 0.19353738432559,
            -2.8060208116485, 0.77833652275983, 1.5982868830036,
            2.2744826664559, 2.7560978140881, 3.0147604484415,
            3.0445528736273, 2.8620115753266, 2.5061272207906,
            2.0383446588402, 1.5425629198664, 0.77833652275983,
            1.2214350933728, 1.5980879771486, 1.7569084557018,
            1.5178403949563, 0.67215824514518, -1.0175329591891,
            -3.8172975991948, -8.0218694717109, -13.954651789267,
            0.77833652275983, 0.68350110425162, 0.77861386147368,
            0.97581235178894, 1.1341939908368, 1.0598160525329,
            0.50569566906943, -0.82819016908496, -3.2949046131853,
            -7.3005509562103, 0.77833652275983, 0.12208636455387,
            -0.30877246905582, -0.48094227889849, -0.39896357657152,
            -0.10521508444048, 0.32008626436092, 0.75888532593079,
            1.0552887455991, 1.0155649579277, 0.77833652275983,
            -0.16765298701795, -1.0634255875761, -1.8055846686938,
            -2.2742293038136, -2.3329542500415, -1.8288499481469,
            -0.59250252256298, 1.5620062186141, 4.8370987836243,
            0.77833652275983, 0.085651919598506, -0.53679726827283,
            -0.98349975448283, -1.1477173085559, -0.92148475591224,
            -0.19560997786786, 1.1403260883655, 3.1979694496802,
            6.090193057073
        ]
        count = 0
        for th in theta:
            for rh in rho:
                zv = 0.0
                for j, ci in enumerate(c):
                    zv += ci*self.pupil.Zk(j, rh, th)
                err = abs(zv - z[count])
                self.assertTrue(err <= self.max_enorm)
                count += 1

    def test_eval_a(self):
        rho = [
            0, 0.11111111111111, 0.22222222222222,
            0.33333333333333, 0.44444444444444,
            0.55555555555556, 0.66666666666667,
            0.77777777777778, 0.88888888888889, 1
        ]
        theta = [
            0, 0.69813170079773, 1.3962634015955,
            2.0943951023932, 2.7925268031909,
            3.4906585039887, 4.1887902047864,
            4.8869219055841, 5.5850536063819,
            6.2831853071796
        ]
        c = [
            0.54031374569774, 0.99075098653197, 0.98937811670199,
            -0.68884118291816, -0.85683760660055, 0.048390017659746,
            -0.66485340286758, 1.4527419609898, 1.3798457521444,
            0.095136418969694, -0.42712706398395, 0.51080780984162,
            -0.65627362438046, -0.12501677594865, -0.53046670030726
        ]
        phi = [
            0.77833652275983, 0.085651919598506, -0.53679726827283,
            -0.98349975448282, -1.1477173085559, -0.92148475591224,
            -0.19560997786786, 1.1403260883655, 3.1979694496802,
            6.090193057073, 0.77833652275983, 0.74923429103286,
            0.92966992705808, 1.3229751043261, 1.8849792604988,
            2.524009597409, 3.1008910810612, 3.4289464416307,
            3.2739961734642, 2.3543585350795, 0.77833652275983,
            1.3880071769557, 2.1381716926469, 2.8957139599519,
            3.4767967033161, 3.6468614815119, 3.1206286876391,
            1.5620975491243, -1.4154538722785, -6.2494686804882,
            0.77833652275983, 1.6882064144334, 2.5555787288029,
            3.2751193339259, 3.7304210304525, 3.7940035516249,
            3.3273135632778, 2.1807246638382, 0.19353738432559,
            -2.8060208116485, 0.77833652275983, 1.5982868830036,
            2.2744826664559, 2.7560978140881, 3.0147604484415,
            3.0445528736273, 2.8620115753266, 2.5061272207906,
            2.0383446588402, 1.5425629198664, 0.77833652275983,
            1.2214350933728, 1.5980879771486, 1.7569084557018,
            1.5178403949563, 0.67215824514518, -1.0175329591891,
            -3.8172975991948, -8.0218694717109, -13.954651789267,
            0.77833652275983, 0.68350110425162, 0.77861386147368,
            0.97581235178894, 1.1341939908368, 1.0598160525329,
            0.50569566906943, -0.82819016908496, -3.2949046131853,
            -7.3005509562103, 0.77833652275983, 0.12208636455387,
            -0.30877246905582, -0.48094227889849, -0.39896357657152,
            -0.10521508444048, 0.32008626436092, 0.75888532593079,
            1.0552887455991, 1.0155649579277, 0.77833652275983,
            -0.16765298701795, -1.0634255875761, -1.8055846686938,
            -2.2742293038136, -2.3329542500415, -1.8288499481469,
            -0.59250252256298, 1.5620062186141, 4.8370987836243,
            0.77833652275983, 0.085651919598506, -0.53679726827283,
            -0.98349975448283, -1.1477173085559, -0.92148475591224,
            -0.19560997786786, 1.1403260883655, 3.1979694496802,
            6.090193057073
        ]
        count = 0
        for th in theta:
            for rh in rho:
                phi2 = self.pupil.eval_a(c, rh, th)
                err = abs(phi2 - phi[count])
                self.assertTrue(err <= self.max_enorm)
                count += 1

    def test_rhoitab(self):
        z = self.pupil
        for k in range(z.nk):
            for i in range(z.n + 1):
                a = (z.rhoitab[k, i])*(z.n + 2 - i)
                b = z.rhotab[k, i]
                self.assertTrue(abs(a - b) < self.max_enorm)

    def test_eval_grid(self):
        log = logging.getLogger('TestZern.test_eval_grid')
        z = self.pupil
        rho_j = np.array([
                0, 0.11111111111111, 0.22222222222222,
                0.33333333333333, 0.44444444444444,
                0.55555555555556, 0.66666666666667,
                0.77777777777778, 0.88888888888889, 1])
        theta_i = np.array([
                0, 0.69813170079773, 1.3962634015955,
                2.0943951023932, 2.7925268031909,
                3.4906585039887, 4.1887902047864,
                4.8869219055841, 5.5850536063819,
                6.2831853071796])
        a = normal(size=z.nk)

        t1 = time()
        Phi1 = [z.eval_a(a, rh, th) for rh in rho_j for th in theta_i]
        t2 = time()
        log.debug('list eval {:.6f}'.format(t2 - t1))

        z.make_pol_grid(rho_j, theta_i)
        t1 = time()
        Phi2 = z.eval_grid(np.array(a))
        t2 = time()
        log.debug('numpy eval {:.6f}'.format(t2 - t1))

        Phi1 = np.array(Phi1).ravel(order='F')
        Phi2 = np.array(Phi2).ravel(order='F')
        log.debug('norm(Phi1 - Phi2) {}'.format(norm(Phi1 - Phi2)))
        self.assertTrue(norm(Phi1 - Phi2) < self.max_enorm)

    def test_save_load(self):
        rho_j = np.array([
                0, 0.11111111111111, 0.22222222222222,
                0.33333333333333, 0.44444444444444,
                0.55555555555556, 0.66666666666667,
                0.77777777777778, 0.88888888888889, 1])
        theta_i = np.array([
                0, 0.69813170079773, 1.3962634015955,
                2.0943951023932, 2.7925268031909,
                3.4906585039887, 4.1887902047864,
                4.8869219055841, 5.5850536063819,
                6.2831853071796])

        def do_test(cls, complex_a):
            rz1 = cls(4)

            if complex_a:
                a = normal(size=rz1.nk) + 1j*normal(size=rz1.nk)
            else:
                a = normal(size=rz1.nk)

            rz1.make_pol_grid(rho_j, theta_i)
            PhiA = rz1.eval_grid(a)

            # create tmp path
            tmpfile = NamedTemporaryFile()
            tmppath = tmpfile.name
            tmpfile.close()

            rz1.save(tmppath)

            rz2 = cls.load(tmppath)
            PhiB = rz2.eval_grid(a)

            self.assertTrue(norm(PhiA - PhiB) < self.max_enorm)
            self.assertTrue(type(rz1) == type(rz2))
            self.assertTrue(norm(rz1.coefnorm - rz2.coefnorm) == 0)
            self.assertTrue(norm(rz1.ntab - rz2.ntab) == 0)
            self.assertTrue(norm(rz1.mtab - rz2.mtab) == 0)
            self.assertTrue(rz1.n == rz2.n)
            self.assertTrue(rz1.nk == rz2.nk)
            self.assertTrue(rz1.normalise == rz2.normalise)
            self.assertTrue(norm(rz1.rhoitab - rz2.rhoitab) == 0)
            self.assertTrue(norm(rz1.rhotab - rz2.rhotab) == 0)
            self.assertTrue(rz1.numpy_dtype == rz2.numpy_dtype)
            self.assertTrue(norm(rz1.ZZ - rz2.ZZ) == 0)

            os.unlink(tmppath)
            del rz1, rz2, a, PhiA, PhiB

        do_test(RZern, False)
        do_test(CZern, True)

    def test_normalisations_real(self):
        log = logging.getLogger('TestZern.test_normalisations_real')
        n_alpha = 6
        L, K = 400, 357

        # polar grid
        pol = RZern(n_alpha)
        fitAlpha = FitZern(pol, L, K)
        t1 = time()
        pol.make_pol_grid(fitAlpha.rho_j, fitAlpha.theta_i)
        t2 = time()
        log.debug('make pol grid {:.6f}'.format(t2 - t1))

        # cartesian grid
        cart = RZern(n_alpha)
        dd = np.linspace(-1.0, 1.0, max(L, K))
        xx, yy = np.meshgrid(dd, dd)
        t1 = time()
        cart.make_cart_grid(xx, yy)
        t2 = time()
        log.debug('make cart grid {:.6f}'.format(t2 - t1))

        smap = np.isfinite(cart.eval_grid(np.zeros(cart.nk)))
        scale = (1.0/np.sum(smap))
        log.debug('')
        log.debug('{} modes, {} x {} grid'.format(n_alpha, L, K))
        for i in range(pol.nk):
            a = np.zeros(pol.nk)
            a[i] = 1.0
            Phi_a = cart.eval_grid(a)
            for j in range(pol.nk):
                b = np.zeros(pol.nk)
                b[j] = 1.0
                Phi_b = cart.eval_grid(b)
                ip = scale*np.sum(Phi_a[smap]*Phi_b[smap])
                if i == j:
                    eip = 1.0
                else:
                    eip = 0.0
                iperr = abs(ip - eip)
                log.debug('<{:02},{:02}> = {:+e} {:+e}'.format(
                    i + 1, j + 1, ip, iperr))
                self.assertTrue(iperr < self.max_ip_err)

    def test_normalisations_complex(self):
        log = logging.getLogger('TestZern.test_normalisations_complex')
        n_beta = 6
        L, K = 400, 393

        # polar grid
        pol = CZern(n_beta)
        fitBeta = FitZern(pol, L, K)
        t1 = time()
        pol.make_pol_grid(fitBeta.rho_j, fitBeta.theta_i)
        t2 = time()
        log.debug('make pol grid {:.6f}'.format(t2 - t1))

        # cartesian grid
        cart = CZern(n_beta)
        dd = np.linspace(-1.0, 1.0, max(L, K))
        xx, yy = np.meshgrid(dd, dd)
        t1 = time()
        cart.make_cart_grid(xx, yy)
        t2 = time()
        log.debug('make cart grid {:.6f}'.format(t2 - t1))

        smap = np.isfinite(cart.eval_grid(np.zeros(cart.nk)))
        scale = (1.0/np.sum(smap))
        log.debug('')
        log.debug('{} modes, {} x {} grid'.format(n_beta, L, K))
        for i in range(pol.nk):
            a = np.zeros(pol.nk)
            a[i] = 1.0
            Phi_a = cart.eval_grid(a)
            for j in range(pol.nk):
                b = np.zeros(pol.nk)
                b[j] = 1.0
                Phi_b = cart.eval_grid(b)
                ip = scale*np.sum(Phi_a[smap]*(Phi_b[smap].conj()))
                if i == j:
                    eip = 1.0
                else:
                    eip = 0.0
                iperr = abs(ip - eip)
                log.debug('<{:02},{:02}> = {:+e} {:+e}'.format(
                    i + 1, j + 1, ip, iperr))
                self.assertTrue(iperr < self.max_ip_err)
示例#2
0
def main_Calib(filename, output, mode, alg, basis, order, figure, verbose, offset, qt, pre, split):
    '''
    # main program
    # input: radius: %+.3f, 'str' (in makefile, str is default)
    #        path: file storage path, 'str'
    #        fout: file output name as .h5, 'str' (.h5 not included')
    #        cut_max: cut off of Legendre
    # output: the gathered result EventID, ChannelID, x, y, z
    '''
    if pre != 'r':
        print('begin reading file', flush=True)
        EventID, ChannelID, Q, PETime, photonTime, PulseTime, dETime, x, y, z = pub.ReadFile(filename)
        VertexTruth = (np.vstack((x, y, z))/1e3).T
        if(offset):
            off = pub.LoadBase(offset)
        else:
            off = np.zeros_like(PMTPos[:,0])
        print('total event: %d' % np.size(np.unique(EventID)), flush=True)
        print('begin processing legendre coeff', flush=True)
        # this part for the same vertex

        tmp = time.time()
        EventNo = np.size(np.unique(EventID))
        PMTNo = np.size(PMTPos[:,0])
        if mode == 'PE':
            PMTPosRep = np.tile(PMTPos, (EventNo,1))
            vertex = np.repeat(VertexTruth, PMTNo, axis=0)
        elif mode == 'time':
            counts = np.bincount(EventID)
            counts = counts[counts!=0]
            PMTPosRep = PMTPos[ChannelID]
            vertex = np.repeat(VertexTruth, counts, axis=0)
        elif mode == 'combined':
            PMTPosRep = np.tile(PMTPos, (EventNo,1))
            vertex = np.repeat(VertexTruth, PMTNo, axis=0)

        if basis == 'Legendre':
            X, cos_theta = pub.LegendreCoeff(PMTPosRep, vertex, order, Legendre=True)
        elif basis == 'Zernike':
            from zernike import RZern
            cos_theta = pub.LegendreCoeff(PMTPosRep, vertex, order, Legendre=False)
            cart = RZern(order)
            nk = cart.nk
            m = cart.mtab
            n = cart.ntab
            rho = np.linalg.norm(vertex, axis=1)/0.65
            theta = np.arccos(cos_theta)
            X = np.zeros((rho.shape[0], nk))

            for i in np.arange(nk):
                if not i % 5:
                    print(f'process {i}-th event')
                X[:,i] = cart.Zk(i, rho, theta)
            X = X[:,m>=0]
            print(f'rank: {np.linalg.matrix_rank(X)}')    
        print(f'use {time.time() - tmp} s')

        # which info should be used
        if mode == 'PE':
            y = Q
        elif mode == 'time':
            y = PulseTime 
        elif mode == 'combined':
            # PulseTime = PulseTime - np.min(PulseTime)
            # PulseTime = (PulseTime - np.max(PulseTime)/2)/np.max(PulseTime)*2
            # print(np.min(PulseTime), np.max(PulseTime))
            PulseTime = (PulseTime - np.max(PulseTime)/2)/np.max(PulseTime)*2
            bins = np.arange(-1, 0.05, 0.1)
            N = 10
            # Legendre coeff
            x = pub.legval(bins, np.eye(N).reshape(N, N, 1))
            # 1st basis
            Y = np.tile(x, len(np.unique(EventID))*len(np.unique(ChannelID))).T
            # 2nd basis
            X = np.repeat(X, bins.shape[0], axis=0)
            # output
            y = np.zeros((len(np.unique(EventID)), len(np.unique(ChannelID)), len(bins)))
            '''
            basis = np.zeros((X.shape[0], X.shape[1]*Y.shape[1]))
            for i_index, i in enumerate(np.arange(X.shape[1])):
                for j_index, j in enumerate(np.arange(Y.shape[1])):
                    total_index = i_index*Y.shape[1] + j_index
                    if not total_index % 10:
                        print(total_index)
                    basis[:, total_index] = X[:,i_index]*Y[:,j_index]
            X = basis
            '''
            split_index = np.unique(EventID).shape[0]
            for k_index, k in enumerate(np.unique(EventID)): # event begin with 1
                if k_index > split_index * split:
                    break
                if not k % 100:
                    print(k)
                index = EventID == k
                CID = ChannelID[index]
                Pulse_t = PulseTime[index]
                for i in np.unique(CID): # PMT begin with 0
                    y[k_index, i, 1:], _ = np.histogram(Pulse_t[CID==i], bins=bins)
            y = np.reshape(y,(-1))
        if verbose:
            print(f'the basis shape is {X.shape}, and the dependent variable shape is {y.shape}')
    if pre =='w':
        if split != 1:
            split_index = np.int(split*y.shape[0])
            X = X[:split_index]
            Y = Y[:split_index]
            y = y[:split_index]
        import pandas as pd
        import pyarrow as pa
        import pyarrow.parquet as pq
        y = np.atleast_2d(y).T
        #data = np.hstack((X, y, np.ones_like(y)))
        df_X = pd.DataFrame(X)
        X_names = []
        for i in df_X.columns:
            X_names.append('X' + str(i))
        df_X.columns = X_names    
        
        df_Y = pd.DataFrame(Y)
        Y_names = []
        for i in df_Y.columns:
            Y_names.append('Y' + str(i))
        df_Y.columns = Y_names
        
        df_y = pd.DataFrame(y)
        df_y.columns = ['output']
        df = pd.concat([df_X, df_Y, df_y], axis=1)
        table = pa.Table.from_pandas(df)
        
        pq.write_table(table, 'test1.parquet')
        return

    if not pre:
        # Regression methods:
        if alg == 'sms':
            import statsmodels.api as sm
            if mode == 'PE':
                model = sm.GLM(y, X, family=sm.families.Poisson(), fit_intercept=False)
                result = model.fit()
                if verbose:
                    print(result.summary())
                AIC = result.aic
                coef_ = result.params
                std = result.bse
                
            elif mode == 'time':
                import pandas as pd
                data = pd.DataFrame(data = np.hstack((X, np.atleast_2d(y).T)))                
                strs = 'y ~ '
                start = data.keys().start
                stop = data.keys().stop
                step = data.keys().step

                cname = []
                cname.append('X0')
                for i in np.arange(start+1, stop, step):
                    if i == start + 1:
                        strs += 'X%d ' % i
                    elif i == stop - step:
                        pass
                    else:
                        strs += ' + X%d ' % i                      

                    if i == stop - step:
                        cname.append('y')
                    else:
                        cname.append('X%d' % i)
                data.columns = cname

                mod = sm.formula.quantreg(strs, data[cname])

                result = mod.fit(q=qt,)
                coef_ = result.params
                AIC = np.zeros_like(coef_)
                std = np.zeros_like(coef_)           
                print('Waring! No AIC and std value')
            elif mode == 'combined':
                # data = pd.DataFrame(data = np.hstack((basis, np.atleast_2d(y).T)))  
                with h5py.File(output,'w') as out:        
                    out.create_dataset('X', data = X)
                    out.create_dataset('Y', data = y)
                print('begin...')
                model = sm.GLM(y, X, family=sm.families.Poisson())
                result = model.fit()
                if verbose:
                    print(result.summary())
                coef_ = result.params
                std = result.bse
                AIC = result.aic
            if verbose:
                print(result.summary())

        elif (alg == 'custom'):
            from scipy.optimize import minimize
            x0 = np.zeros_like(X[0]) # initial value (be careful of Zernike order)
            
            if mode == 'PE':
                x0[0] = 0.8 + np.log(2) # intercept is much more important
                result = minimize(pub.CalibPE, x0=x0, method='SLSQP', args = (y, PMTPos, X))
            elif mode == 'time':
                x0[0] = np.mean(y)
                qt = 0.1
                ts = 2.6
                result = minimize(pub.CalibTime, x0=x0, method='SLSQP', args = (np.hstack((EventID, EventID)), y, X, qt, ts))
            elif mode == 'combined':
                x0 = np.zeros_like(X[0])
                x0[0] = 0.8 + np.log(2) # intercept is much more important
                result = minimize(pub.CalibPE, x0=x0, method='SLSQP', args = (y, PMTPos, X))

            coef_ = np.array(result.x, dtype=float)
            if verbose:
                print(result.message)
            AIC = np.zeros_like(coef_)
            std = np.zeros_like(coef_)

            H = pub.MyHessian(result.x, pub.CalibPE, *(y, PMTPos, X))
            # H = pub.MyHessian(result.x, *(Q, PMTPos, X, pub.CalibTime))
            # std = 1/np.sqrt(-np.diag(np.linalg.pinv(H1)))
            print(coef_)
            # print(std)
            print('Waring! No AIC and std value, std is testing')

        elif alg == 'sk':
            from sklearn.linear_model import TweedieRegressor
            alpha = 0.001
            reg = TweedieRegressor(power=1, alpha=alpha, link='log', max_iter=1000, tol=1e-6, fit_intercept=False)
            reg.fit(X, y)

            # just for point data
            # pred = reg.predict(X[0:30,0:cut+1])

            print('coeff:\n', reg.coef_,'\n')

            coef_ = reg.coef_ 

            AIC = np.zeros_like(coef_)
            std = np.zeros_like(coef_)
            print('Waring! No AIC and std value')

        elif alg == 'h2o':
            import h2o
            from h2o.estimators.gbm import H2OGradientBoostingEstimator
            from h2o.estimators.glm import H2OGeneralizedLinearEstimator           
            if mode != 'combined':
                y = np.atleast_2d(y).T
                data = np.hstack((X, y, np.ones_like(y)))

                h2o.init()
                hf = h2o.H2OFrame(data)
                predictors = hf.columns[0:-2]
                response_col = hf.columns[-2]

                if mode == 'PE':
                    #offset_col = hf.columns[-1]
                    glm_model = H2OGeneralizedLinearEstimator(family= "poisson",
                        #offset_column = offset_col, 
                        lambda_ = 0,
                        compute_p_values = True)

                    glm_model.train(predictors, response_col, training_frame=hf)

                    coef_table = glm_model._model_json['output']['coefficients_table']
                    coef_ = glm_model.coef()

                elif mode == 'time':
                    gbm = H2OGradientBoostingEstimator(distribution="quantile", seed = 1234,
                                                      stopping_metric = "mse", stopping_tolerance = 1e-4)
                    gbm.train(x = predictors, y = response_col, training_frame = hf)
                    breakpoint()
                    print(gbm)
                    exit()
            elif mode == 'combined':
                y = np.atleast_2d(y).T
                data = np.hstack((X, Y, y, np.ones_like(y)))

                h2o.init() 
                hf = h2o.H2OFrame(data)
                predictors = hf.columns[0:-2]
                response_col = hf.columns[-2]           

            if verbose:
                print(coef_)
                if basis == 'Zernike':
                    print(f'Regession coef shape is f{np.array(coef_).shape}, Zernike shape is {nk}')
            coef_ = coef_table['coefficients']
            std = coef_table['std_error']
            AIC = glm_model.aic()

            h2o.cluster().shutdown()

    elif pre == 'r':
        import h2o
        from h2o.estimators.gbm import H2OGradientBoostingEstimator
        from h2o.estimators.glm import H2OGeneralizedLinearEstimator           
        h2o.init()
        hf = h2o.import_file("electron-1.parquet")
        pairs = []
        for i in hf.columns:
            for j in hf.columns:
                if (i.startswith('Z') and j.startswith('L')):
                    if ((i!='X0') and (j != 'Y0')):
                        pairs.append((i,j))
        predictors = hf.columns[2:]
        response_col = hf.columns[0]
        
        print(predictors)
        print(response_col)
        print(pairs)
        if mode == 'PE':
            #offset_col = hf.columns[-1]
            glm_model = H2OGeneralizedLinearEstimator(family= "poisson",
                #offset_column = offset_col, 
                lambda_ = 0,
                compute_p_values = True)

            glm_model.train(predictors, response_col, training_frame=hf)
        
        elif mode == 'combined':
            #offset_col = hf.columns[-1]
            glm_model = H2OGeneralizedLinearEstimator(family= "poisson",
                #offset_column = offset_col, 
                interaction_pairs=pairs,
                lambda_ = 0,
                #remove_collinear_columns = True, 
                compute_p_values = True)

            glm_model.train(predictors, response_col, training_frame=hf)
        breakpoint()
        coef_table = glm_model._model_json['output']['coefficients_table']
        coef_ = coef_table['coefficients']
        std = coef_table['std_error']
        AIC = glm_model.aic()
        print(f'Regession coef is f{np.array(coef_)}')             
        if (figure=='ON'):
            import matplotlib.pyplot as plt
            L, K = 500, 500
            ddx = np.linspace(-1.0, 1.0, K)
            ddy = np.linspace(-1.0, 1.0, L)
            xv, yv = np.meshgrid(ddx, ddy)
            cart.make_cart_grid(xv, yv)
            # normal scale
            # im = plt.imshow(np.exp(cart.eval_grid(np.array(coef_), matrix=True)), origin='lower', extent=(-1, 1, -1, 1))
            # log scale
            im = plt.imshow(cart.eval_grid(np.array(coef_), matrix=True), origin='lower', extent=(-1, 1, -1, 1))
            plt.colorbar()
            plt.savefig('test.png')
    else:
        print('error regression algorithm')
            
    with h5py.File(output,'w') as out:        
        out.create_dataset('coeff' + str(order), data = coef_)
        out.create_dataset('std' + str(order), data = std)
        out.create_dataset('AIC' + str(order), data = AIC)