Exposing acb_theta_all

doc/source/acb_theta.rst

@@ -0,0 +1,5 @@
+**acb_theta** -- Riemann theta functions
+===============================================================================
+
+.. autofunction :: flint.types.acb_theta.acb_theta
+

doc/source/index.rst

@@ -61,6 +61,7 @@ Matrix types
    fmpz_mod_mat.rst
    arb_mat.rst
    acb_mat.rst
+   acb_theta.rst
 
 Polynomial types
 ................

meson.build

@@ -22,6 +22,9 @@ endif
 # flint.pc was missing -lflint until Flint 3.1.0
 if flint_dep.version().version_compare('<3.1')
   flint_dep = cc.find_library('flint')
+  have_acb_theta = false
+else
+  have_acb_theta = true
 endif
 
 pyflint_deps = [dep_py, gmp_dep, mpfr_dep, flint_dep]

src/flint/flintlib/acb_theta.pxd

@@ -0,0 +1,136 @@
+from flint.flintlib.acb cimport acb_t, acb_srcptr, acb_ptr
+from flint.flintlib.acb_poly cimport acb_poly_struct, acb_poly_t
+from flint.flintlib.arb cimport arb_t, arb_ptr, arb_srcptr
+from flint.flintlib.flint cimport ulong, slong, flint_rand_t
+from flint.flintlib.fmpz_mat cimport fmpz_mat_t, fmpz_mat_struct
+from flint.flintlib.acb_mat cimport acb_mat_t
+from flint.flintlib.arb_mat cimport arb_mat_t
+from flint.flintlib.arf cimport arf_t
+
+
+cdef extern from "flint/acb_theta.h":
+    ctypedef struct acb_theta_eld_struct:
+        slong dim
+        slong ambient_dim
+        slong * last_coords
+        slong min
+        slong mid
+        slong max
+        slong nr
+        slong nl
+        acb_theta_eld_struct * rchildren
+        acb_theta_eld_struct * lchildren
+        slong nb_pts, nb_border
+        slong * box
+    ctypedef acb_theta_eld_struct acb_theta_eld_t[1]
+    ctypedef void (*acb_theta_naive_worker_t)(acb_ptr, acb_srcptr, acb_srcptr, const slong *, slong, const acb_t, const slong *, slong, slong, slong, slong)
+    ctypedef int (*acb_theta_ql_worker_t)(acb_ptr, acb_srcptr, acb_srcptr, arb_srcptr, arb_srcptr, const acb_mat_t, slong, slong)
+
+    void acb_theta_all(acb_ptr th, acb_srcptr z, const acb_mat_t tau, int sqr, slong prec)
+    void acb_theta_naive_fixed_ab(acb_ptr th, ulong ab, acb_srcptr zs, slong nb, const acb_mat_t tau, slong prec)
+    void acb_theta_naive_all(acb_ptr th, acb_srcptr zs, slong nb, const acb_mat_t tau, slong prec)
+    void acb_theta_jet_all(acb_ptr dth, acb_srcptr z, const acb_mat_t tau, slong ord, slong prec)
+    void acb_theta_jet_naive_fixed_ab(acb_ptr dth, ulong ab, acb_srcptr z, const acb_mat_t tau, slong ord, slong prec)
+    void acb_theta_jet_naive_all(acb_ptr dth, acb_srcptr z, const acb_mat_t tau, slong ord, slong prec)
+    slong sp2gz_dim(const fmpz_mat_t mat)
+    void sp2gz_set_blocks(fmpz_mat_t mat, const fmpz_mat_t alpha, const fmpz_mat_t beta, const fmpz_mat_t gamma, const fmpz_mat_t delta)
+    void sp2gz_j(fmpz_mat_t mat)
+    void sp2gz_block_diag(fmpz_mat_t mat, const fmpz_mat_t U)
+    void sp2gz_trig(fmpz_mat_t mat, const fmpz_mat_t S)
+    void sp2gz_embed(fmpz_mat_t res, const fmpz_mat_t mat)
+    void sp2gz_restrict(fmpz_mat_t res, const fmpz_mat_t mat)
+    slong sp2gz_nb_fundamental(slong g)
+    void sp2gz_fundamental(fmpz_mat_t mat, slong j)
+    int sp2gz_is_correct(const fmpz_mat_t mat)
+    int sp2gz_is_j(const fmpz_mat_t mat)
+    int sp2gz_is_block_diag(const fmpz_mat_t mat)
+    int sp2gz_is_trig(const fmpz_mat_t mat)
+    int sp2gz_is_embedded(fmpz_mat_t res, const fmpz_mat_t mat)
+    void sp2gz_inv(fmpz_mat_t inv, const fmpz_mat_t mat)
+    fmpz_mat_struct * sp2gz_decompose(slong * nb, const fmpz_mat_t mat)
+    void sp2gz_randtest(fmpz_mat_t mat, flint_rand_t state, slong bits)
+    void acb_siegel_cocycle(acb_mat_t c, const fmpz_mat_t mat, const acb_mat_t tau, slong prec)
+    void acb_siegel_transform_cocycle_inv(acb_mat_t w, acb_mat_t c, acb_mat_t cinv, const fmpz_mat_t mat, const acb_mat_t tau, slong prec)
+    void acb_siegel_transform(acb_mat_t w, const fmpz_mat_t mat, const acb_mat_t tau, slong prec)
+    void acb_siegel_transform_z(acb_ptr r, acb_mat_t w, const fmpz_mat_t mat, acb_srcptr z, const acb_mat_t tau, slong prec)
+    void acb_siegel_cho(arb_mat_t C, const acb_mat_t tau, slong prec)
+    void acb_siegel_yinv(arb_mat_t Yinv, const acb_mat_t tau, slong prec)
+    void acb_siegel_reduce(fmpz_mat_t mat, const acb_mat_t tau, slong prec)
+    int acb_siegel_is_reduced(const acb_mat_t tau, slong tol_exp, slong prec)
+    void acb_siegel_randtest(acb_mat_t tau, flint_rand_t state, slong prec, slong mag_bits)
+    void acb_siegel_randtest_reduced(acb_mat_t tau, flint_rand_t state, slong prec, slong mag_bits)
+    void acb_siegel_randtest_vec(acb_ptr z, flint_rand_t state, slong g, slong prec)
+    void acb_theta_char_get_slong(slong * n, ulong a, slong g)
+    ulong acb_theta_char_get_a(const slong * n, slong g)
+    void acb_theta_char_get_arb(arb_ptr v, ulong a, slong g)
+    void acb_theta_char_get_acb(acb_ptr v, ulong a, slong g)
+    slong acb_theta_char_dot(ulong a, ulong b, slong g)
+    slong acb_theta_char_dot_slong(ulong a, const slong * n, slong g)
+    void acb_theta_char_dot_acb(acb_t x, ulong a, acb_srcptr z, slong g, slong prec)
+    int acb_theta_char_is_even(ulong ab, slong g)
+    int acb_theta_char_is_goepel(ulong ch1, ulong ch2, ulong ch3, ulong ch4, slong g)
+    int acb_theta_char_is_syzygous(ulong ch1, ulong ch2, ulong ch3, slong g)
+    void acb_theta_eld_init(acb_theta_eld_t E, slong d, slong g)
+    void acb_theta_eld_clear(acb_theta_eld_t E)
+    int acb_theta_eld_set(acb_theta_eld_t E, const arb_mat_t C, const arf_t R2, arb_srcptr v)
+    void acb_theta_eld_points(slong * pts, const acb_theta_eld_t E)
+    void acb_theta_eld_border(slong * pts, const acb_theta_eld_t E)
+    int acb_theta_eld_contains(const acb_theta_eld_t E, slong * pt)
+    void acb_theta_eld_print(const acb_theta_eld_t E)
+    void acb_theta_naive_radius(arf_t R2, arf_t eps, const arb_mat_t C, slong ord, slong prec)
+    void acb_theta_naive_reduce(arb_ptr v, acb_ptr new_zs, arb_ptr as, acb_ptr cs, arb_ptr us, acb_srcptr zs, slong nb, const acb_mat_t tau, slong prec)
+    void acb_theta_naive_term(acb_t res, acb_srcptr z, const acb_mat_t tau, slong * tup, slong * n, slong prec)
+    void acb_theta_naive_worker(acb_ptr th, slong len, acb_srcptr zs, slong nb, const acb_mat_t tau, const acb_theta_eld_t E, slong ord, slong prec, acb_theta_naive_worker_t worker)
+    void acb_theta_naive_00(acb_ptr th, acb_srcptr zs, slong nb, const acb_mat_t tau, slong prec)
+    void acb_theta_naive_0b(acb_ptr th, acb_srcptr zs, slong nb, const acb_mat_t tau, slong prec)
+    void acb_theta_naive_fixed_a(acb_ptr th, ulong a, acb_srcptr zs, slong nb, const acb_mat_t tau, slong prec)
+    slong acb_theta_jet_nb(slong ord, slong g)
+    slong acb_theta_jet_total_order(const slong * tup, slong g)
+    void acb_theta_jet_tuples(slong * tups, slong ord, slong g)
+    slong acb_theta_jet_index(const slong * tup, slong g)
+    void acb_theta_jet_mul(acb_ptr res, acb_srcptr v1, acb_srcptr v2, slong ord, slong g, slong prec)
+    void acb_theta_jet_compose(acb_ptr res, acb_srcptr v, const acb_mat_t N, slong ord, slong prec)
+    void acb_theta_jet_exp_pi_i(acb_ptr res, arb_srcptr a, slong ord, slong g, slong prec)
+    void acb_theta_jet_naive_radius(arf_t R2, arf_t eps, arb_srcptr v, const arb_mat_t C, slong ord, slong prec)
+    void acb_theta_jet_naive_00(acb_ptr dth, acb_srcptr z, const acb_mat_t tau, slong ord, slong prec)
+    void acb_theta_jet_error_bounds(arb_ptr err, acb_srcptr z, const acb_mat_t tau, acb_srcptr dth, slong ord, slong prec)
+    void acb_theta_dist_pt(arb_t d, arb_srcptr v, const arb_mat_t C, slong * n, slong prec)
+    void acb_theta_dist_lat(arb_t d, arb_srcptr v, const arb_mat_t C, slong prec)
+    void acb_theta_dist_a0(arb_ptr d, acb_srcptr z, const acb_mat_t tau, slong prec)
+    slong acb_theta_dist_addprec(const arb_t d)
+    void acb_theta_agm_hadamard(acb_ptr res, acb_srcptr a, slong g, slong prec)
+    void acb_theta_agm_sqrt(acb_ptr res, acb_srcptr a, acb_srcptr rts, slong nb, slong prec)
+    void acb_theta_agm_mul(acb_ptr res, acb_srcptr a1, acb_srcptr a2, slong g, slong prec)
+    void acb_theta_agm_mul_tight(acb_ptr res, acb_srcptr a0, acb_srcptr a, arb_srcptr d0, arb_srcptr d, slong g, slong prec)
+    int acb_theta_ql_a0_naive(acb_ptr th, acb_srcptr t, acb_srcptr z, arb_srcptr d0, arb_srcptr d, const acb_mat_t tau, slong guard, slong prec)
+    int acb_theta_ql_a0_split(acb_ptr th, acb_srcptr t, acb_srcptr z, arb_srcptr d, const acb_mat_t tau, slong s, slong guard, slong prec, acb_theta_ql_worker_t worker)
+    int acb_theta_ql_a0_steps(acb_ptr th, acb_srcptr t, acb_srcptr z, arb_srcptr d0, arb_srcptr d, const acb_mat_t tau, slong nb_steps, slong s, slong guard, slong prec, acb_theta_ql_worker_t worker)
+    slong acb_theta_ql_a0_nb_steps(const arb_mat_t C, slong s, slong prec)
+    int acb_theta_ql_a0(acb_ptr th, acb_srcptr t, acb_srcptr z, arb_srcptr d0, arb_srcptr d, const acb_mat_t tau, slong guard, slong prec)
+    slong acb_theta_ql_reduce(acb_ptr new_z, acb_t c, arb_t u, slong * n1, acb_srcptr z, const acb_mat_t tau, slong prec)
+    void acb_theta_ql_all(acb_ptr th, acb_srcptr z, const acb_mat_t tau, int sqr, slong prec)
+    void acb_theta_jet_ql_bounds(arb_t c, arb_t rho, acb_srcptr z, const acb_mat_t tau, slong ord)
+    void acb_theta_jet_ql_radius(arf_t eps, arf_t err, const arb_t c, const arb_t rho, slong ord, slong g, slong prec)
+    void acb_theta_jet_ql_finite_diff(acb_ptr dth, const arf_t eps, const arf_t err, acb_srcptr val, slong ord, slong g, slong prec)
+    void acb_theta_jet_ql_all(acb_ptr dth, acb_srcptr z, const acb_mat_t tau, slong ord, slong prec)
+    ulong acb_theta_transform_char(slong * e, const fmpz_mat_t mat, ulong ab)
+    void acb_theta_transform_sqrtdet(acb_t res, const acb_mat_t tau, slong prec)
+    slong acb_theta_transform_kappa(acb_t sqrtdet, const fmpz_mat_t mat, const acb_mat_t tau, slong prec)
+    slong acb_theta_transform_kappa2(const fmpz_mat_t mat)
+    void acb_theta_transform_proj(acb_ptr res, const fmpz_mat_t mat, acb_srcptr th, int sqr, slong prec)
+    void acb_theta_g2_jet_naive_1(acb_ptr dth, const acb_mat_t tau, slong prec)
+    void acb_theta_g2_detk_symj(acb_poly_t res, const acb_mat_t m, const acb_poly_t f, slong k, slong j, slong prec)
+    void acb_theta_g2_transvectant(acb_poly_t res, const acb_poly_t g, const acb_poly_t h, slong m, slong n, slong k, slong prec)
+    void acb_theta_g2_transvectant_lead(acb_t res, const acb_poly_t g, const acb_poly_t h, slong m, slong n, slong k, slong prec)
+    slong acb_theta_g2_character(const fmpz_mat_t mat)
+    void acb_theta_g2_psi4(acb_t res, acb_srcptr th2, slong prec)
+    void acb_theta_g2_psi6(acb_t res, acb_srcptr th2, slong prec)
+    void acb_theta_g2_chi10(acb_t res, acb_srcptr th2, slong prec)
+    void acb_theta_g2_chi12(acb_t res, acb_srcptr th2, slong prec)
+    void acb_theta_g2_chi5(acb_t res, acb_srcptr th, slong prec)
+    void acb_theta_g2_chi35(acb_t res, acb_srcptr th, slong prec)
+    void acb_theta_g2_chi3_6(acb_poly_t res, acb_srcptr dth, slong prec)
+    void acb_theta_g2_sextic(acb_poly_t res, const acb_mat_t tau, slong prec)
+    void acb_theta_g2_sextic_chi5(acb_poly_t res, acb_t chi5, const acb_mat_t tau, slong prec)
+    void acb_theta_g2_covariants(acb_poly_struct * res, const acb_poly_t f, slong prec)
+    void acb_theta_g2_covariants_lead(acb_ptr res, const acb_poly_t f, slong prec)

src/flint/test/__main__.py

@@ -80,9 +80,14 @@ def run_doctests(verbose=None):
                flint.types.acb_series,
                flint.types.dirichlet,
                flint.functions.showgood]
+    try:
+        from flint.types import acb_theta
+        modules.append(acb_theta)
+    except ImportError:
+        pass
     results = [doctest.testmod(x) for x in modules]
 #    ffmpz, tfmpz = doctest.testmod(flint._fmpz, verbose=verbose)
- #   failed, total = doctest.testmod(flint.pyflint, verbose=verbose)
+#    failed, total = doctest.testmod(flint.pyflint, verbose=verbose)
     return tuple(sum(res) for res in zip(*results))
 
 

src/flint/types/acb_mat.pyx

@@ -814,3 +814,22 @@ cdef class acb_mat(flint_mat):
         if left:
             return Elist, L
         return Elist, R
+
+    def theta(tau, z, square=False):
+        r"""
+        Computes the vector valued Riemann theta function
+        `(\theta_{a,b}(z, \tau) : a, b \in \{0,1\}^{g})` or its squares,
+        where `\tau` is given by ``self``.
+
+        This is a wrapper for :func:`.acb_theta.acb_theta`; see the
+        documentation for that method for details and examples.
+        This follows the same conventions of the C-function
+        `acb_theta_all <https://flintlib.org/doc/acb_theta.html#c.acb_theta_all>`_
+        for the ordering of the theta characteristics.
+
+        """
+        try:
+            from .acb_theta import acb_theta
+        except ImportError:
+            raise NotImplementedError("acb_mat.theta needs Flint >= 3.1.0")
+        return acb_theta(z, tau, square=square)

src/flint/types/acb_theta.pyx

@@ -0,0 +1,93 @@
+from flint.flint_base.flint_context cimport getprec
+from flint.types.acb cimport acb
+from flint.types.acb_mat cimport acb_mat
+from flint.flintlib.acb cimport *
+from flint.flintlib.acb_mat cimport *
+from flint.flintlib.acb_theta cimport *
+
+def acb_theta(acb_mat z, acb_mat tau, ulong square=False):
+    r"""
+    Computes the vector valued Riemann theta function
+    `(\theta_{a,b}(z, \tau) : a, b \in \{0,1\}^{g})` or its squares.
+
+    This is a wrapper for the C-function
+    `acb_theta_all <https://flintlib.org/doc/acb_theta.html#c.acb_theta_all>`_
+    and it follows the same conventions for the ordering of the theta characteristics.
+
+    This should be used via the method :meth:`.acb_mat.theta`, explicitly ``tau.theta(z)``.
+
+        >>> from flint import acb, acb_mat, showgood, ctx
+        >>> z = acb(1+1j); tau = acb(1.25+3j)
+        >>> t0, t1, t2, t3 = acb_mat([[tau]]).theta(acb_mat([[z]])).entries()
+        >>> sum([abs(x) for x in acb_mat([z.modular_theta(tau)]) - acb_mat([[-t3,t2,t0,t1]])])
+        [+/- 3.82e-14]
+        >>> showgood(lambda: acb_mat([[tau]]).theta(acb_mat([[z]])).transpose(), dps=25)
+        [0.9694430387796704100046143 - 0.03055696120816803328582847j]
+        [ 1.030556961196006476576271 + 0.03055696120816803328582847j]
+        [  -1.220790267576967690128359 - 1.827055516791154669091679j]
+        [  -1.820235910124989594900076 + 1.216251950154477951760042j]
+        >>> acb_mat([[1j,0],[0,2*1j]]).theta(acb_mat([[0],[0]])).transpose()
+        [ [1.09049252082308 +/- 3.59e-15] + [+/- 2.43e-16]j]
+        [ [1.08237710165638 +/- 4.15e-15] + [+/- 2.43e-16]j]
+        [[0.916991251621117 +/- 6.30e-16] + [+/- 2.43e-16]j]
+        [[0.910167024735558 +/- 7.93e-16] + [+/- 2.43e-16]j]
+        [[0.451696791791346 +/- 5.46e-16] + [+/- 2.43e-16]j]
+        [                  [+/- 2.43e-16] + [+/- 2.43e-16]j]
+        [[0.379830212998946 +/- 4.47e-16] + [+/- 2.43e-16]j]
+        [                  [+/- 2.43e-16] + [+/- 2.43e-16]j]
+        [[0.916991251621117 +/- 6.30e-16] + [+/- 2.43e-16]j]
+        [[0.910167024735558 +/- 7.93e-16] + [+/- 2.43e-16]j]
+        [                  [+/- 2.43e-16] + [+/- 2.43e-16]j]
+        [                  [+/- 2.43e-16] + [+/- 2.43e-16]j]
+        [[0.379830212998946 +/- 4.47e-16] + [+/- 2.43e-16]j]
+        [                  [+/- 2.43e-16] + [+/- 2.43e-16]j]
+        [                  [+/- 2.43e-16] + [+/- 2.43e-16]j]
+        [                  [+/- 2.43e-16] + [+/- 2.43e-16]j]
+        >>> ctx.prec = 10000
+        >>> print(acb_mat([[1j, 0],[0,1j]]).theta(acb_mat([[0],[0]])).transpose().str(25))
+        [ [1.180340599016096226045338 +/- 5.95e-26] + [+/- 1.23e-3010]j]
+        [[0.9925441784910574194770081 +/- 3.15e-26] + [+/- 1.23e-3010]j]
+        [[0.9925441784910574194770081 +/- 3.15e-26] + [+/- 1.23e-3010]j]
+        [[0.8346268416740731862814297 +/- 3.29e-26] + [+/- 1.23e-3010]j]
+        [[0.9925441784910574194770081 +/- 3.15e-26] + [+/- 1.23e-3010]j]
+        [                          [+/- 1.23e-3010] + [+/- 1.23e-3010]j]
+        [[0.8346268416740731862814297 +/- 3.29e-26] + [+/- 1.23e-3010]j]
+        [                          [+/- 1.23e-3010] + [+/- 1.23e-3010]j]
+        [[0.9925441784910574194770081 +/- 3.15e-26] + [+/- 1.23e-3010]j]
+        [[0.8346268416740731862814297 +/- 3.29e-26] + [+/- 1.23e-3010]j]
+        [                          [+/- 1.23e-3010] + [+/- 1.23e-3010]j]
+        [                          [+/- 1.23e-3010] + [+/- 1.23e-3010]j]
+        [[0.8346268416740731862814297 +/- 3.29e-26] + [+/- 1.23e-3010]j]
+        [                          [+/- 1.23e-3010] + [+/- 1.23e-3010]j]
+        [                          [+/- 1.23e-3010] + [+/- 1.23e-3010]j]
+        [                          [+/- 1.23e-3010] + [+/- 1.23e-3010]j]
+        >>> ctx.default()
+
+    """
+    g = tau.nrows()
+    assert tau.ncols() == g
+    assert z.nrows() == g
+    assert z.ncols() == 1
+
+    # convert input
+    cdef acb_ptr zvec
+    zvec = _acb_vec_init(g)
+    cdef long i
+    for i in range(g):
+        acb_set(zvec + i, acb_mat_entry(z.val, i, 0))
+
+    # initialize the output
+    cdef slong nb = 1 << (2 * g)
+    cdef acb_ptr theta = _acb_vec_init(nb)
+
+    acb_theta_all(theta, zvec, tau.val, square, getprec())
+    _acb_vec_clear(zvec, g)
+    # copy the output
+    res = []
+    cdef acb r
+    for i in range(nb):
+        r = acb.__new__(acb)
+        acb_set(r.val, theta + i)
+        res.append(r)
+    _acb_vec_clear(theta, nb)
+    return acb_mat([res])

src/flint/types/meson.build

@@ -41,6 +41,10 @@ exts = [
   'fmpz_mpoly',
 ]
 
+if have_acb_theta
+  exts += ['acb_theta']
+endif
+
 py.install_sources(
   pyfiles,
   pure: false,