Python numpy.count_nonzero() Examples

def _accuracy(self, y_test, Y_vote):
        """Calculates accuracy

            This method calculates the accuracy based on a vector of
            ground-truth labels (y_test) and a 2D voting matrix (Y_vote) of
            size (len(y_test), num_classes).

            :param y_test: vector of ground-truth labels
            :param Y_vote: 2D voting matrix (rows=samples, cols=class votes)
            :returns: accuracy e[0,1]
        """
        # predicted classes
        y_hat = np.argmax(Y_vote, axis=1)

        # all cases where predicted class was correct
        mask = y_hat == y_test
        return np.float32(np.count_nonzero(mask)) / len(y_test) 

def _confusion(self, y_test, Y_vote):
        """Calculates confusion matrix

            This method calculates the confusion matrix based on a vector of
            ground-truth labels (y-test) and a 2D voting matrix (Y_vote) of
            size (len(y_test), num_classes).
            Matrix element conf[r,c] will contain the number of samples that
            were predicted to have label r but have ground-truth label c.

            :param y_test: vector of ground-truth labels
            :param Y_vote: 2D voting matrix (rows=samples, cols=class votes)
            :returns: confusion matrix
        """
        y_hat = np.argmax(Y_vote, axis=1)
        conf = np.zeros((self.num_classes, self.num_classes)).astype(np.int32)
        for c_true in xrange(self.num_classes):
            # looking at all samples of a given class, c_true
            # how many were classified as c_true? how many as others?
            for c_pred in xrange(self.num_classes):
                y_this = np.where((y_test == c_true) * (y_hat == c_pred))
                conf[c_pred, c_true] = np.count_nonzero(y_this)
        return conf 

def test_gen_mass(self):
        r"""Test gen_mass method.

        Approach: Ensures the output is set, of the correct type, length, and units.
        Check the range of the returned values.  Check that, for this power law, there
        are more small than large masses (for n large).
        """

        plan_pop = self.fixture
        n = 10000
        # call the routine
        masses = plan_pop.gen_mass(n)
        # check the type
        self.assertEqual(type(masses), type(1.0 * u.kg))
        # crude check on the shape (more small than large for this power law)
        midpoint = np.mean(plan_pop.Mprange)
        self.assertGreater(np.count_nonzero(masses < midpoint),
                           np.count_nonzero(masses > midpoint))
        # test some illegal "n" values
        n_list_bad = [-1, '100', 22.5]
        for n in n_list_bad:
            with self.assertRaises(AssertionError):
                masses = plan_pop.gen_mass(n) 

def test_gen_mass(self):
        r"""Test gen_mass method.

        Approach: Ensures the output is set, of the correct type, length, and units.
        Check that returned values are nonnegative.  Check that, for this power law, there
        are more small than large masses (for n large).
        """

        plan_pop = self.fixture
        n = 10000
        masses = plan_pop.gen_mass(n)

        self.assertEqual(len(masses), n)
        self.assertTrue(np.all(masses.value >= 0))
        self.assertTrue(np.all(np.isfinite(masses.value)))

        midpoint = np.mean(masses)
        self.assertGreater(np.count_nonzero(masses < midpoint),
                           np.count_nonzero(masses > midpoint))

        # test some illegal "n" values
        n_list_bad = [-1, '100', 22.5]
        for n in n_list_bad:
            with self.assertRaises(AssertionError):
                masses = plan_pop.gen_mass(n) 

def test_init_indexes(self):
        r"""Test of initialization and __init__ -- indexes.

        Method: Insure the plan2star and sInds indexes are present. 
        Performs sanity check on the range of index values.
        TODO: More could be done to ensure the index values are correct.
        """
        universe = self.fixture
        self.basic_validation(universe)
        # indexes present
        self.assertIn('plan2star', universe.__dict__)
        self.assertIn('sInds', universe.__dict__)
        # range: 0 <= sInds < nStars
        self.assertEqual(0, np.count_nonzero(universe.sInds < 0))
        self.assertEqual(0, np.count_nonzero(universe.sInds >= universe.TargetList.nStars))
        # domain: plan2star covers 0...nPlans-1
        self.assertEqual(len(universe.plan2star), universe.nPlans)
        # range: 0 <= plan2star < nStars
        self.assertEqual(0, np.count_nonzero(universe.plan2star < 0))
        self.assertEqual(0, np.count_nonzero(universe.plan2star >= universe.TargetList.nStars)) 

def canonicalize(mf, mo_coeff_kpts, mo_occ_kpts, fock=None):
    if fock is None:
        dm = mf.make_rdm1(mo_coeff_kpts, mo_occ_kpts)
        fock = mf.get_fock(dm=dm)
    mo_coeff = []
    mo_energy = []
    for k, mo in enumerate(mo_coeff_kpts):
        mo1 = np.empty_like(mo)
        mo_e = np.empty_like(mo_occ_kpts[k])
        occidx = mo_occ_kpts[k] == 2
        viridx = ~occidx
        for idx in (occidx, viridx):
            if np.count_nonzero(idx) > 0:
                orb = mo[:,idx]
                f1 = reduce(np.dot, (orb.T.conj(), fock[k], orb))
                e, c = scipy.linalg.eigh(f1)
                mo1[:,idx] = np.dot(orb, c)
                mo_e[idx] = e
        mo_coeff.append(mo1)
        mo_energy.append(mo_e)
    return mo_energy, mo_coeff 

def _frozen_sanity_check(frozen, mo_occ, kpt_idx):
    '''Performs a few sanity checks on the frozen array and mo_occ.

    Specific tests include checking for duplicates within the frozen array.

    Args:
        frozen (array_like of int): The orbital indices that will be frozen.
        mo_occ (:obj:`ndarray` of int): The occupuation number for each orbital
            resulting from a mean-field-like calculation.
        kpt_idx (int): The k-point that `mo_occ` and `frozen` belong to.

    '''
    frozen = np.array(frozen)
    nocc = np.count_nonzero(mo_occ > 0)

    assert nocc, 'No occupied orbitals?\n\nnocc = %s\nmo_occ = %s' % (nocc, mo_occ)
    all_frozen_unique = (len(frozen) - len(np.unique(frozen))) == 0
    if not all_frozen_unique:
        raise RuntimeError('Frozen orbital list contains duplicates!\n\nkpt_idx %s\n'
                           'frozen %s' % (kpt_idx, frozen))
    if len(frozen) > 0 and np.max(frozen) > len(mo_occ) - 1:
        raise RuntimeError('Freezing orbital not in MO list!\n\nkpt_idx %s\n'
                           'frozen %s\nmax orbital idx %s' % (kpt_idx, frozen, len(mo_occ) - 1)) 

def _unpack(vo, mo_occ):
    za = []
    zb = []
    p1 = 0
    for k, occ in enumerate(mo_occ[0]):
        no = numpy.count_nonzero(occ > 0)
        nv = occ.size - no
        p0, p1 = p1, p1 + no * nv
        za.append(vo[p0:p1].reshape(no,nv))

    for k, occ in enumerate(mo_occ[1]):
        no = numpy.count_nonzero(occ > 0)
        nv = occ.size - no
        p0, p1 = p1, p1 + no * nv
        zb.append(vo[p0:p1].reshape(no,nv))
    return za, zb 

def canonicalize(mf, mo_coeff, mo_occ, fock=None):
    '''Canonicalization diagonalizes the Fock matrix within occupied, open,
    virtual subspaces separatedly (without change occupancy).
    '''
    if fock is None:
        dm = mf.make_rdm1(mo_coeff, mo_occ)
        fock = mf.get_fock(dm=dm)
    coreidx = mo_occ == 2
    viridx = mo_occ == 0
    openidx = ~(coreidx | viridx)
    mo = numpy.empty_like(mo_coeff)
    mo_e = numpy.empty(mo_occ.size)
    for idx in (coreidx, openidx, viridx):
        if numpy.count_nonzero(idx) > 0:
            orb = mo_coeff[:,idx]
            f1 = reduce(numpy.dot, (orb.conj().T, fock, orb))
            e, c = scipy.linalg.eigh(f1)
            mo[:,idx] = numpy.dot(orb, c)
            mo_e[idx] = e
    return mo_e, mo 

def _dump_mo_energy(mol, mo_energy, mo_occ, ehomo, elumo, orbsym, title='',
                    verbose=logger.DEBUG):
    log = logger.new_logger(mol, verbose)
    for i, ir in enumerate(mol.irrep_id):
        irname = mol.irrep_name[i]
        ir_idx = (orbsym == ir)
        nso = numpy.count_nonzero(ir_idx)
        nocc = numpy.count_nonzero(mo_occ[ir_idx])
        e_ir = mo_energy[ir_idx]
        if nocc == 0:
            log.debug('%s%s nocc = 0', title, irname)
        elif nocc == nso:
            log.debug('%s%s nocc = %d  HOMO = %.15g',
                      title, irname, nocc, e_ir[nocc-1])
        else:
            log.debug('%s%s nocc = %d  HOMO = %.15g  LUMO = %.15g',
                      title, irname, nocc, e_ir[nocc-1], e_ir[nocc])
            if e_ir[nocc-1]+1e-3 > elumo:
                log.warn('%s%s HOMO %.15g > system LUMO %.15g',
                         title, irname, e_ir[nocc-1], elumo)
            if e_ir[nocc] < ehomo+1e-3:
                log.warn('%s%s LUMO %.15g < system HOMO %.15g',
                         title, irname, e_ir[nocc], ehomo)
        log.debug('   mo_energy = %s', e_ir) 

def float_occ_(mf):
    '''
    For UHF, allowing the Sz value being changed during SCF iteration.
    Determine occupation of alpha and beta electrons based on energy spectrum
    '''
    from pyscf.scf import uhf
    assert(isinstance(mf, uhf.UHF))
    def get_occ(mo_energy, mo_coeff=None):
        mol = mf.mol
        ee = numpy.sort(numpy.hstack(mo_energy))
        n_a = numpy.count_nonzero(mo_energy[0]<(ee[mol.nelectron-1]+1e-3))
        n_b = mol.nelectron - n_a
        if mf.nelec is None:
            nelec = mf.mol.nelec
        else:
            nelec = mf.nelec
        if n_a != nelec[0]:
            logger.info(mf, 'change num. alpha/beta electrons '
                        ' %d / %d -> %d / %d',
                        nelec[0], nelec[1], n_a, n_b)
            mf.nelec = (n_a, n_b)
        return uhf.UHF.get_occ(mf, mo_energy, mo_coeff)
    mf.get_occ = get_occ
    return mf 

def test_uniq_var(self):
        mo_occ = mf.mo_occ.copy()
        nmo = mo_occ.size
        nocc = numpy.count_nonzero(mo_occ > 0)
        nvir = nmo - nocc
        numpy.random.seed(1)
        f = numpy.random.random((nmo,nmo))
        f_uniq = scf.hf.pack_uniq_var(f, mo_occ)
        self.assertEqual(f_uniq.size, nocc*nvir)
        f1 = scf.hf.unpack_uniq_var(f_uniq, mo_occ)
        self.assertAlmostEqual(abs(f1 + f1.T).max(), 0, 12)

        mo_occ[4:7] = 1
        ndocc = 4
        nocc = 7
        f_uniq = scf.hf.pack_uniq_var(f, mo_occ)
        self.assertEqual(f_uniq.size, nocc*(nmo-ndocc)-(nocc-ndocc)**2)

        f1 = scf.hf.unpack_uniq_var(f_uniq, mo_occ)
        self.assertAlmostEqual(abs(f1 + f1.T).max(), 0, 12) 

def get_nocc(mp):
    if mp._nocc is not None:
        return mp._nocc
    elif mp.frozen is None:
        nocc = numpy.count_nonzero(mp.mo_occ > 0)
        assert(nocc > 0)
        return nocc
    elif isinstance(mp.frozen, (int, numpy.integer)):
        nocc = numpy.count_nonzero(mp.mo_occ > 0) - mp.frozen
        assert(nocc > 0)
        return nocc
    elif isinstance(mp.frozen[0], (int, numpy.integer)):
        occ_idx = mp.mo_occ > 0
        occ_idx[list(mp.frozen)] = False
        nocc = numpy.count_nonzero(occ_idx)
        assert(nocc > 0)
        return nocc
    else:
        raise NotImplementedError 

def pick_real_eigs(w, v, nroots, envs):
    '''This function searchs the real eigenvalues or eigenvalues with small
    imaginary component.
    '''
    threshold = 1e-3
    abs_imag = abs(w.imag)
    # Grab `nroots` number of e with small(est) imaginary components
    max_imag_tol = max(threshold, numpy.sort(abs_imag)[min(w.size,nroots)-1])
    real_idx = numpy.where((abs_imag <= max_imag_tol))[0]
    nbelow_thresh = numpy.count_nonzero(abs_imag[real_idx] < threshold)
    if nbelow_thresh < nroots and w.size >= nroots:
        warnings.warn('Only %d eigenvalues (out of %3d requested roots) with imaginary part < %4.3g.\n'
                      % (nbelow_thresh, min(w.size,nroots), threshold))

    # Guess whether the matrix to diagonalize is real or complex
    if envs.get('dtype') == numpy.double:
        w, v, idx = _eigs_cmplx2real(w, v, real_idx, real_eigenvectors=True)
    else:
        w, v, idx = _eigs_cmplx2real(w, v, real_idx, real_eigenvectors=False)
    return w, v, idx 

def _sort_by_similarity(w, v, nroots, conv, vlast, emin=None, heff=None):
    if not any(conv) or vlast is None:
        return w[:nroots], v[:,:nroots]

    head, nroots = vlast.shape
    conv = numpy.asarray(conv[:nroots])
    ovlp = vlast[:,conv].T.conj().dot(v[:head])
    ovlp = numpy.einsum('ij,ij->j', ovlp, ovlp)
    nconv = numpy.count_nonzero(conv)
    nleft = nroots - nconv
    idx = ovlp.argsort()
    sorted_idx = numpy.zeros(nroots, dtype=int)
    sorted_idx[conv] = numpy.sort(idx[-nconv:])
    sorted_idx[~conv] = numpy.sort(idx[:-nconv])[:nleft]

    e = w[sorted_idx]
    c = v[:,sorted_idx]
    return e, c 

def from_ucisdvec(civec, nocc, orbspin):
    '''Convert the (spin-separated) CISD coefficient vector to GCISD
    coefficient vector'''
    nmoa = numpy.count_nonzero(orbspin == 0)
    nmob = numpy.count_nonzero(orbspin == 1)
    if isinstance(nocc, int):
        nocca = numpy.count_nonzero(orbspin[:nocc] == 0)
        noccb = numpy.count_nonzero(orbspin[:nocc] == 1)
    else:
        nocca, noccb = nocc
    nvira = nmoa - nocca

    if civec.size == nocca*nvira + (nocca*nvira)**2 + 1:  # RCISD
        c0, c1, c2 = cisd.cisdvec_to_amplitudes(civec, nmoa, nocca)
    else:  # UCISD
        c0, c1, c2 = ucisd.cisdvec_to_amplitudes(civec, (nmoa,nmob), (nocca,noccb))
    c1 = spatial2spin(c1, orbspin)
    c2 = spatial2spin(c2, orbspin)
    return amplitudes_to_cisdvec(c0, c1, c2) 

def to_fcivec(cisdvec, nelec, orbspin, frozen=None):
    assert(numpy.count_nonzero(orbspin == 0) ==
           numpy.count_nonzero(orbspin == 1))
    norb = len(orbspin)
    frozen_mask = numpy.zeros(norb, dtype=bool)
    if frozen is None:
        pass
    elif isinstance(frozen, (int, numpy.integer)):
        frozen_mask[:frozen] = True
    else:
        frozen_mask[frozen] = True
    frozen = (numpy.where(frozen_mask[orbspin == 0])[0],
              numpy.where(frozen_mask[orbspin == 1])[0])
    nelec = (numpy.count_nonzero(orbspin[:nelec] == 0),
             numpy.count_nonzero(orbspin[:nelec] == 1))
    orbspin = orbspin[~frozen_mask]
    nmo = len(orbspin)
    nocc = numpy.count_nonzero(~frozen_mask[:sum(nelec)])
    ucisdvec = to_ucisdvec(cisdvec, nmo, nocc, orbspin)
    return ucisd.to_fcivec(ucisdvec, norb//2, nelec, frozen) 

def from_fcivec(ci0, nelec, orbspin, frozen=None):
    if not (frozen is None or frozen == 0):
        raise NotImplementedError

    assert(numpy.count_nonzero(orbspin == 0) ==
           numpy.count_nonzero(orbspin == 1))
    norb = len(orbspin)
    frozen_mask = numpy.zeros(norb, dtype=bool)
    if frozen is None:
        pass
    elif isinstance(frozen, (int, numpy.integer)):
        frozen_mask[:frozen] = True
    else:
        frozen_mask[frozen] = True
    #frozen = (numpy.where(frozen_mask[orbspin == 0])[0],
    #          numpy.where(frozen_mask[orbspin == 1])[0])
    nelec = (numpy.count_nonzero(orbspin[:nelec] == 0),
             numpy.count_nonzero(orbspin[:nelec] == 1))
    ucisdvec = ucisd.from_fcivec(ci0, norb//2, nelec, frozen)
    nocc = numpy.count_nonzero(~frozen_mask[:sum(nelec)])
    return from_ucisdvec(ucisdvec, nocc, orbspin[~frozen_mask]) 

def test_ab_hf(self):
        mf = scf.RHF(mol).run()
        a, b = rhf.get_ab(mf)
        fock = mf.get_hcore() + mf.get_veff()
        ftda = rhf.gen_tda_operation(mf, fock, singlet=True)[0]
        ftdhf = rhf.gen_tdhf_operation(mf, singlet=True)[0]
        nocc = numpy.count_nonzero(mf.mo_occ == 2)
        nvir = numpy.count_nonzero(mf.mo_occ == 0)
        numpy.random.seed(2)
        x, y = xy = numpy.random.random((2,nocc,nvir))
        ax = numpy.einsum('iajb,jb->ia', a, x)
        self.assertAlmostEqual(abs(ax - ftda([x]).reshape(nocc,nvir)).max(), 0, 6)

        ab1 = ax + numpy.einsum('iajb,jb->ia', b, y)
        ab2 =-numpy.einsum('iajb,jb->ia', b, x)
        ab2-= numpy.einsum('iajb,jb->ia', a, y)
        abxy_ref = ftdhf([xy]).reshape(2,nocc,nvir)
        self.assertAlmostEqual(abs(ab1 - abxy_ref[0]).max(), 0, 9)
        self.assertAlmostEqual(abs(ab2 - abxy_ref[1]).max(), 0, 9) 

def test_ab_lda(self):
        mf = mf_lda
        a, b = rhf.get_ab(mf)
        ftda = rhf.gen_tda_operation(mf, singlet=True)[0]
        ftdhf = rhf.gen_tdhf_operation(mf, singlet=True)[0]
        nocc = numpy.count_nonzero(mf.mo_occ == 2)
        nvir = numpy.count_nonzero(mf.mo_occ == 0)
        numpy.random.seed(2)
        x, y = xy = numpy.random.random((2,nocc,nvir))
        ax = numpy.einsum('iajb,jb->ia', a, x)
        self.assertAlmostEqual(abs(ax - ftda([x]).reshape(nocc,nvir)).max(), 0, 9)

        ab1 = ax + numpy.einsum('iajb,jb->ia', b, y)
        ab2 =-numpy.einsum('iajb,jb->ia', b, x)
        ab2-= numpy.einsum('iajb,jb->ia', a, y)
        abxy_ref = ftdhf([xy]).reshape(2,nocc,nvir)
        self.assertAlmostEqual(abs(ab1 - abxy_ref[0]).max(), 0, 9)
        self.assertAlmostEqual(abs(ab2 - abxy_ref[1]).max(), 0, 9) 

def __init__(self, cc, mo_coeff):
        nocc = numpy.count_nonzero(cc.mo_occ > 0)
        eri0 = ao2mo.full(cc._scf._eri, mo_coeff)
        eri0 = ao2mo.restore(1, eri0, mo_coeff.shape[1])
        eri0 = eri0.reshape((mo_coeff.shape[1],)*4)
        self.oooo = eri0[:nocc,:nocc,:nocc,:nocc].copy()
        self.ooov = eri0[:nocc,:nocc,:nocc,nocc:].copy()
        self.ovoo = eri0[:nocc,nocc:,:nocc,:nocc].copy()
        self.oovo = eri0[:nocc,:nocc,nocc:,:nocc].copy()
        self.oovv = eri0[:nocc,:nocc,nocc:,nocc:].copy()
        self.ovov = eri0[:nocc,nocc:,:nocc,nocc:].copy()
        self.ovvo = eri0[:nocc,nocc:,nocc:,:nocc].copy()
        self.ovvv = eri0[:nocc,nocc:,nocc:,nocc:].copy()
        self.vvvv = eri0[nocc:,nocc:,nocc:,nocc:].copy()
        self.vvvo = eri0[nocc:,nocc:,nocc:,:nocc].copy()
        self.vovv = eri0[nocc:,:nocc,nocc:,nocc:].copy()
        self.vvov = eri0[nocc:,nocc:,:nocc,nocc:].copy()
        self.vvoo = eri0[nocc:,nocc:,:nocc,:nocc].copy()
        self.voov = eri0[nocc:,:nocc,:nocc,nocc:].copy()
        self.vooo = eri0[nocc:,:nocc,:nocc,:nocc].copy()
        self.mo_coeff = mo_coeff
        self.fock = numpy.diag(cc._scf.mo_energy) 

def _gamma1_intermediates(cc, t1, t2, l1, l2):
    d1 = ccsd_rdm._gamma1_intermediates(cc, t1, t2, l1, l2)
    if cc.frozen is None:
        return d1
    nocc = numpy.count_nonzero(cc.mo_occ>0)
    nvir = cc.mo_occ.size - nocc
    OA, VA, OF, VF = index_frozen_active(cc)
    doo = numpy.zeros((nocc,nocc))
    dov = numpy.zeros((nocc,nvir))
    dvo = numpy.zeros((nvir,nocc))
    dvv = numpy.zeros((nvir,nvir))
    doo[OA[:,None],OA] = d1[0]
    dov[OA[:,None],VA] = d1[1]
    dvo[VA[:,None],OA] = d1[2]
    dvv[VA[:,None],VA] = d1[3]
    return doo, dov, dvo, dvv 

def make_pso(sscobj, mol, mo1, mo_coeff, mo_occ, nuc_pair=None):
    if nuc_pair is None: nuc_pair = sscobj.nuc_pair
    para = []
    nocc = numpy.count_nonzero(mo_occ> 0)
    nvir = numpy.count_nonzero(mo_occ==0)
    atm1lst = sorted(set([i for i,j in nuc_pair]))
    atm2lst = sorted(set([j for i,j in nuc_pair]))
    atm1dic = dict([(ia,k) for k,ia in enumerate(atm1lst)])
    atm2dic = dict([(ia,k) for k,ia in enumerate(atm2lst)])
    mo1 = mo1.reshape(len(atm1lst),3,nvir,nocc)
    h1 = make_h1_pso(mol, mo_coeff, mo_occ, atm1lst)
    h1 = numpy.asarray(h1).reshape(len(atm1lst),3,nvir,nocc)
    for i,j in nuc_pair:
        # PSO = -Tr(Im[h1_ov], Im[mo1_vo]) + cc = 2 * Tr(Im[h1_vo], Im[mo1_vo])
        e = numpy.einsum('xij,yij->xy', h1[atm1dic[i]], mo1[atm2dic[j]])
        para.append(e*4)  # *4 for +c.c. and double occupnacy
    return numpy.asarray(para) * nist.ALPHA**4 

def make_para(sscobj, mol, mo1, mo_coeff, mo_occ, nuc_pair=None):
    if nuc_pair is None: nuc_pair = sscobj.nuc_pair
    if sscobj.mb.upper().startswith('ST'):
        nmo = mo_occ.size
        mo_coeff = mo_coeff[:,nmo//2:]
        mo_occ   = mo_occ[nmo//2:]

    nocc = numpy.count_nonzero(mo_occ> 0)
    nvir = numpy.count_nonzero(mo_occ==0)
    atm1lst = sorted(set([i for i,j in nuc_pair]))
    atm2lst = sorted(set([j for i,j in nuc_pair]))
    atm1dic = dict([(ia,k) for k,ia in enumerate(atm1lst)])
    atm2dic = dict([(ia,k) for k,ia in enumerate(atm2lst)])
    mo1 = mo1.reshape(len(atm1lst),3,nvir,nocc)
    h1 = make_h1(mol, mo_coeff, mo_occ, atm1lst)
    h1 = numpy.asarray(h1).reshape(len(atm1lst),3,nvir,nocc)

    para = []
    for i,j in nuc_pair:
        e = numpy.einsum('xij,yij->xy', h1[atm1dic[i]], mo1[atm2dic[j]].conj()) * 2
        para.append(e.real)
    return numpy.asarray(para) * nist.ALPHA**4 

def get_marge(self):

        nonzero = np.count_nonzero(self.W[1:])

        if nonzero == 0:
            return 0
        else:
            return 1 / np.linalg.norm(self.W[1:]) 

def update(self, labels, preds):
        mx.metric.check_label_shapes(labels, preds)
        label_weight = labels[0].asnumpy()
        preds = preds[0].asnumpy()
        tmp = []
        for i in range(preds.shape[0]):
            tmp.append((label_weight[i], preds[i]))
        tmp = sorted(tmp, key=itemgetter(1), reverse=True)
        label_sum = label_weight.sum()
        if label_sum == 0 or label_sum == label_weight.size:
            raise Exception("AUC with one class is undefined")

        label_one_num = np.count_nonzero(label_weight)
        label_zero_num = len(label_weight) - label_one_num
        total_area = label_zero_num * label_one_num
        height = 0
        width = 0
        area = 0
        for a, _ in tmp:
            if a == 1.0:
                height += 1.0
            else:
                width += 1.0
                area += height

        self.sum_metric += area / total_area
        self.num_inst += 1 

def calc_state(self):
		j = np.array([j.current_relative_position() for j in self.ordered_joints], dtype=np.float32).flatten()
		# even elements [0::2] position, scaled to -1..+1 between limits
		# odd elements  [1::2] angular speed, scaled to show -1..+1
		self.joint_speeds = j[1::2]
		self.joints_at_limit = np.count_nonzero(np.abs(j[0::2]) > 0.99)

		body_pose = self.robot_body.pose()
		parts_xyz = np.array([p.pose().xyz() for p in self.parts.values()]).flatten()
		self.body_xyz = (
		parts_xyz[0::3].mean(), parts_xyz[1::3].mean(), body_pose.xyz()[2])  # torso z is more informative than mean z
		self.body_rpy = body_pose.rpy()
		z = self.body_xyz[2]
		if self.initial_z == None:
			self.initial_z = z
		r, p, yaw = self.body_rpy
		self.walk_target_theta = np.arctan2(self.walk_target_y - self.body_xyz[1],
											self.walk_target_x - self.body_xyz[0])
		self.walk_target_dist = np.linalg.norm(
			[self.walk_target_y - self.body_xyz[1], self.walk_target_x - self.body_xyz[0]])
		angle_to_target = self.walk_target_theta - yaw

		rot_speed = np.array(
			[[np.cos(-yaw), -np.sin(-yaw), 0],
			 [np.sin(-yaw), np.cos(-yaw), 0],
			 [		0,			 0, 1]]
		)
		vx, vy, vz = np.dot(rot_speed, self.robot_body.speed())  # rotate speed back to body point of view

		more = np.array([ z-self.initial_z,
			np.sin(angle_to_target), np.cos(angle_to_target),
			0.3* vx , 0.3* vy , 0.3* vz ,  # 0.3 is just scaling typical speed into -1..+1, no physical sense here
			r, p], dtype=np.float32)
		return np.clip( np.concatenate([more] + [j] + [self.feet_contact]), -5, +5) 

def add_noise_python(words, dropout=0.1, k=3):
  """Applies the noise model in input words.

  Args:
    words: A numpy vector of word ids.
    dropout: The probability to drop words.
    k: Maximum distance of the permutation.

  Returns:
    A noisy numpy vector of word ids.
  """

  def _drop_words(words, probability):
    """Drops words with the given probability."""
    length = len(words)
    keep_prob = np.random.uniform(size=length)
    keep = np.random.uniform(size=length) > probability
    if np.count_nonzero(keep) == 0:
      ind = np.random.randint(0, length)
      keep[ind] = True
    words = np.take(words, keep.nonzero())[0]
    return words

  def _rand_perm_with_constraint(words, k):
    """Randomly permutes words ensuring that words are no more than k positions
    away from their original position."""
    length = len(words)
    offset = np.random.uniform(size=length) * (k + 1)
    new_pos = np.arange(length) + offset
    return np.take(words, np.argsort(new_pos))

  words = _drop_words(words, dropout)
  words = _rand_perm_with_constraint(words, k)
  return words 

def _precision(self, y_test, Y_vote):
        """Calculates precision

            This method calculates precision extended to multi-class
            classification by help of a confusion matrix.

            :param y_test: vector of ground-truth labels
            :param Y_vote: 2D voting matrix (rows=samples, cols=class votes)
            :returns: precision e[0,1]
        """
        # predicted classes
        y_hat = np.argmax(Y_vote, axis=1)

        if self.mode == "one-vs-one":
            # need confusion matrix
            conf = self._confusion(y_test, Y_vote)

            # consider each class separately
            prec = np.zeros(self.num_classes)
            for c in xrange(self.num_classes):
                # true positives: label is c, classifier predicted c
                tp = conf[c, c]

                # false positives: label is c, classifier predicted not c
                fp = np.sum(conf[:, c]) - conf[c, c]

                if tp + fp != 0:
                    prec[c] = tp * 1. / (tp + fp)
        elif self.mode == "one-vs-all":
            # consider each class separately
            prec = np.zeros(self.num_classes)
            for c in xrange(self.num_classes):
                # true positives: label is c, classifier predicted c
                tp = np.count_nonzero((y_test == c) * (y_hat == c))

                # false positives: label is c, classifier predicted not c
                fp = np.count_nonzero((y_test == c) * (y_hat != c))

                if tp + fp != 0:
                    prec[c] = tp * 1. / (tp + fp)
        return prec 

def _recall(self, y_test, Y_vote):
        """Calculates recall
            This method calculates recall extended to multi-class
            classification by help of a confusion matrix.

            :param y_test: vector of ground-truth labels
            :param Y_vote: 2D voting matrix (rows=samples, cols=class votes)
            :returns: recall e[0,1]
        """
        # predicted classes
        y_hat = np.argmax(Y_vote, axis=1)

        if self.mode == "one-vs-one":
            # need confusion matrix
            conf = self._confusion(y_test, Y_vote)

            # consider each class separately
            recall = np.zeros(self.num_classes)
            for c in xrange(self.num_classes):
                # true positives: label is c, classifier predicted c
                tp = conf[c, c]

                # false negatives: label is not c, classifier predicted c
                fn = np.sum(conf[c, :]) - conf[c, c]
                if tp + fn != 0:
                    recall[c] = tp * 1. / (tp + fn)
        elif self.mode == "one-vs-all":
            # consider each class separately
            recall = np.zeros(self.num_classes)
            for c in xrange(self.num_classes):
                # true positives: label is c, classifier predicted c
                tp = np.count_nonzero((y_test == c) * (y_hat == c))

                # false negatives: label is not c, classifier predicted c
                fn = np.count_nonzero((y_test != c) * (y_hat == c))

                if tp + fn != 0:
                    recall[c] = tp * 1. / (tp + fn)
        return recall