Introduce SobolEngine (#10505)

Summary:
`SobolEngine` is a quasi-random sampler used to sample points evenly between [0,1]. Here we use direction numbers to generate these samples. The maximum supported dimension for the sampler is 1111.

Documentation has been added, tests have been added based on Balandat 's references. The implementation is an optimized / tensor-ized implementation of Balandat 's implementation in Cython as provided in #9332.

This closes #9332 .

cc: soumith Balandat
Pull Request resolved: https://github.com/pytorch/pytorch/pull/10505

Reviewed By: zou3519

Differential Revision: D9330179

Pulled By: ezyang

fbshipit-source-id: 01d5588e765b33b06febe99348f14d1e7fe8e55d

diff --git a/aten/src/ATen/native/SobolEngineOps.cpp b/aten/src/ATen/native/SobolEngineOps.cpp
new file mode 100644 (file)
index 0000000..1e0af21
--- /dev/null
+++ b/aten/src/ATen/native/SobolEngineOps.cpp
@@ -0,0 +1,159 @@
+#include <ATen/ATen.h>
+#include <ATen/Dispatch.h>
+#include <ATen/NativeFunctions.h>
+
+#include <ATen/native/SobolEngineOpsUtils.h>
+
+#include <vector>
+
+namespace at {
+namespace native {
+
+/// This is the core function to draw samples from a `SobolEngine` given
+/// its state variables (`sobolstate` and `quasi`). `dimension` can be
+/// inferred from `sobolstate`, but choosing to pass it explicitly to avoid
+/// an extra operation to obtain the size of the first dimension of
+/// `sobolstate`.
+std::tuple<Tensor, Tensor> _sobol_engine_draw(const Tensor& quasi, int64_t n, const Tensor& sobolstate,
+                                              int64_t dimension, int64_t num_generated, optional<ScalarType> dtype) {
+  AT_CHECK(sobolstate.dtype() == at::kLong,
+           "sobolstate needs to be of type ", at::kLong);
+  AT_CHECK(quasi.dtype() == at::kLong,
+           "quasi needs to be of type ", at::kLong);
+
+  Tensor wquasi = quasi.clone();
+  auto result_dtype = dtype.has_value() ? dtype.value() : at::kFloat;
+  Tensor result = at::empty({n, dimension}, sobolstate.options().dtype(result_dtype));
+
+  AT_DISPATCH_FLOATING_TYPES(result_dtype, "_sobol_engine_draw", [&]() -> void {
+    // We deal with `data` and `strides` due to performance issues.
+    int64_t l;
+    int64_t* wquasi_data = wquasi.data<int64_t>();
+    int64_t* sobolstate_data = sobolstate.data<int64_t>();
+    scalar_t* result_data = result.data<scalar_t>();
+
+    int64_t wquasi_stride = wquasi.stride(0);
+    int64_t sobolstate_row_stride = sobolstate.stride(0), sobolstate_col_stride = sobolstate.stride(1);
+    int64_t result_row_stride = result.stride(0), result_col_stride = result.stride(1);
+
+    for (int64_t i = 0; i < n; i++, num_generated++) {
+      l = rightmost_zero(num_generated);
+      for (int64_t j = 0; j < dimension; j++) {
+        wquasi_data[j * wquasi_stride] ^= sobolstate_data[j * sobolstate_row_stride + l * sobolstate_col_stride];
+        result_data[i * result_row_stride + j * result_col_stride] = wquasi_data[j * wquasi_stride];
+      }
+    }
+  });
+
+  result.mul_(RECIPD);
+  return std::tuple<Tensor, Tensor>(result, wquasi);
+}
+
+/// This is the core function to fast-forward a `SobolEngine` given
+/// its state variables (`sobolstate` and `quasi`). `dimension` can be
+/// inferred from `sobolstate`, but is passed as an argument for the same reasons
+/// specified above.
+Tensor& _sobol_engine_ff_(Tensor& quasi, int64_t n, const Tensor& sobolstate,
+                        int64_t dimension, int64_t num_generated) {
+  AT_CHECK(sobolstate.dtype() == at::kLong,
+           "sobolstate needs to be of type ", at::kLong);
+  AT_CHECK(quasi.dtype() == at::kLong,
+           "quasi needs to be of type ", at::kLong);
+
+  // We deal with `data` and `strides` due to performance issues.
+  int64_t l;
+  int64_t* quasi_data = quasi.data<int64_t>();
+  int64_t* sobolstate_data = sobolstate.data<int64_t>();
+
+  int64_t quasi_stride = quasi.stride(0);
+  int64_t sobolstate_row_stride = sobolstate.stride(0), sobolstate_col_stride = sobolstate.stride(1);
+
+  for (int64_t i = 0; i < n; i++, num_generated++) {
+    l = rightmost_zero(num_generated);
+    for (int64_t j = 0; j < dimension; j++) {
+      quasi_data[j * quasi_stride] ^= sobolstate_data[j * sobolstate_row_stride + l * sobolstate_col_stride];
+    }
+  }
+  return quasi;
+}
+
+/// This is an implicit function used for randomizing the state variables of the.
+/// `SobolEngine`. Arguments are a randomized `sobolstate` state variables
+/// and a list of random lower triangular matrices consisting of 0s and 1s. `dimension` is
+/// passed explicitly again.
+Tensor& _sobol_engine_scramble_(Tensor& sobolstate, const Tensor& ltm, int64_t dimension) {
+  AT_CHECK(sobolstate.dtype() == at::kLong,
+           "sobolstate needs to be of type ", at::kLong);
+
+  /// Require a tensor accessor for `sobolstate`
+  auto ss_a = sobolstate.accessor<int64_t, 2>();
+
+  /// For every tensor in the list of tensors, the diagonals are made 1
+  /// Require a dot product of every row with a specific vector of each of the matrices in `ltm`.
+  /// Instead, we perform an element-wise product of all the matrices and sum over the last dimension.
+  /// The required product of the m^{th} row in the d^{th} square matrix in `ltm` can be accessed
+  /// using ltm_d_a[d][m] m and d are zero-indexed
+  Tensor diag_true = ltm.clone();
+  diag_true.diagonal(0, -2, -1).fill_(1);
+  Tensor ltm_dots = cdot_pow2(diag_true);
+  auto ltm_d_a = ltm_dots.accessor<int64_t, 2>();
+
+  /// Main scrambling loop
+  for (int64_t d = 0; d < dimension; ++d) {
+    for (int64_t j = 0; j < MAXBIT; ++j) {
+      int64_t vdj = ss_a[d][j], l = 1, t2 = 0;
+      for (int64_t p = MAXBIT - 1; p >= 0; --p) {
+        int64_t lsmdp = ltm_d_a[d][p];
+        int64_t t1 = 0;
+        for (int64_t k = 0; k < MAXBIT; ++k) {
+          t1 += (bitsubseq(lsmdp, k, 1) * bitsubseq(vdj, k, 1));
+        }
+        t1 = t1 % 2;
+        t2 = t2 + t1 * l;
+        l = l << 1;
+      }
+      ss_a[d][j] = t2;
+    }
+  }
+  return sobolstate;
+}
+
+/// This is a core function to initialize the main state variable of a `SobolEngine`.
+/// `dimension` is passed explicitly as well (see why above)
+Tensor& _sobol_engine_initialize_state_(Tensor& sobolstate, int64_t dimension) {
+  AT_CHECK(sobolstate.dtype() == at::kLong,
+           "sobolstate needs to be of type ", at::kLong);
+
+  /// First row of `sobolstate` is 1
+  sobolstate.select(0, 0).fill_(1);
+
+  /// Use a tensor accessor for `sobolstate`
+  auto ss_a = sobolstate.accessor<int64_t, 2>();
+  for (int64_t d = 0; d < dimension; ++d) {
+    int64_t p = poly[d];
+    int64_t m = bit_length(p) - 1;
+
+    for (int64_t i = 0; i < m; ++i) {
+      ss_a[d][i] = initsobolstate[d][i];
+    }
+
+    for (int64_t j = m; j < MAXBIT; ++j) {
+      int64_t newv = ss_a[d][j - m];
+      int64_t pow2 = 1;
+      for (int64_t k = 0; k < m; ++k) {
+        pow2 <<= 1;
+        if ((p >> (m - 1 - k)) & 1) {
+          newv = newv ^ (pow2 * ss_a[d][j - k - 1]);
+        }
+      }
+      ss_a[d][j] = newv;
+    }
+  }
+
+  Tensor pow2s = at::pow(2, at::native::arange((MAXBIT - 1), -1, -1, sobolstate.options()));
+  sobolstate.mul_(pow2s);
+  return sobolstate;
+}
+
+} // namespace native
+} // namespace at

diff --git a/aten/src/ATen/native/SobolEngineOpsUtils.h b/aten/src/ATen/native/SobolEngineOpsUtils.h
new file mode 100644 (file)
index 0000000..511df7c
--- /dev/null
+++ b/aten/src/ATen/native/SobolEngineOpsUtils.h
@@ -0,0 +1,1265 @@
+/// This file contains some tensor-agnostic operations to be used in the
+/// core functions of the `SobolEngine`
+#include <ATen/ATen.h>
+
+/// Function to return the minimum of number of bits to represent the integer `n`
+static inline int64_t bit_length(const int64_t n) {
+  int64_t nbits, nloc;
+  for (nloc = n, nbits = 0; nloc > 0; nloc /= 2, nbits++);
+  return nbits;
+}
+
+/// Function to get the position of the rightmost zero in the bit representation of an integer
+/// This value is the zero-indexed position
+static inline int64_t rightmost_zero(const int64_t n) {
+  int64_t z, i;
+  for (z = n, i = 0; z % 2 == 1; z /= 2, i++);
+  return i;
+}
+
+/// Function to get a subsequence of bits in the representation of an integer starting from
+/// `pos` and of length `length`
+static inline int64_t bitsubseq(const int64_t n, const int64_t pos, const int64_t length) {
+  return (n >> pos) & ((1 << length) - 1);
+}
+
+/// Function to perform the inner product between a batched square matrix and a power of 2 vector
+static inline at::Tensor cdot_pow2(const at::Tensor& bmat) {
+  at::Tensor inter = at::arange(bmat.size(-1) - 1, -1, -1, bmat.options());
+  inter = at::pow(2, inter).expand_as(bmat);
+  return at::mul(inter, bmat).sum(-1);
+}
+
+/// All definitions below this point are data. These are constant, and should not be modified
+/// without notice
+
+static constexpr int64_t MAXBIT = 30;
+static constexpr int64_t LARGEST_NUMBER = 1 << 30;
+static constexpr float RECIPD = 1.0 / LARGEST_NUMBER;
+
+static constexpr int64_t poly[1111] = {
+  1, 3, 7, 11, 13, 19, 25, 37, 59, 47, 61, 55, 41, 67, 97, 91, 109,
+  103, 115, 131, 193, 137, 145, 143, 241, 157, 185, 167, 229, 171,
+  213, 191, 253, 203, 211, 239, 247, 285, 369, 299, 301, 333, 351,
+  355, 357, 361, 391, 397, 425, 451, 463, 487, 501, 529, 539, 545,
+  557, 563, 601, 607, 617, 623, 631, 637, 647, 661, 675, 677, 687,
+  695, 701, 719, 721, 731, 757, 761, 787, 789, 799, 803, 817, 827,
+  847, 859, 865, 875, 877, 883, 895, 901, 911, 949, 953, 967, 971,
+  973, 981, 985, 995, 1001, 1019, 1033, 1051, 1063, 1069, 1125, 1135,
+  1153, 1163, 1221, 1239, 1255, 1267, 1279, 1293, 1305, 1315, 1329,
+  1341, 1347, 1367, 1387, 1413, 1423, 1431, 1441, 1479, 1509, 1527,
+  1531, 1555, 1557, 1573, 1591, 1603, 1615, 1627, 1657, 1663, 1673,
+  1717, 1729, 1747, 1759, 1789, 1815, 1821, 1825, 1849, 1863, 1869,
+  1877, 1881, 1891, 1917, 1933, 1939, 1969, 2011, 2035, 2041, 2053,
+  2071, 2091, 2093, 2119, 2147, 2149, 2161, 2171, 2189, 2197, 2207,
+  2217, 2225, 2255, 2257, 2273, 2279, 2283, 2293, 2317, 2323, 2341,
+  2345, 2363, 2365, 2373, 2377, 2385, 2395, 2419, 2421, 2431, 2435,
+  2447, 2475, 2477, 2489, 2503, 2521, 2533, 2551, 2561, 2567, 2579,
+  2581, 2601, 2633, 2657, 2669, 2681, 2687, 2693, 2705, 2717, 2727,
+  2731, 2739, 2741, 2773, 2783, 2793, 2799, 2801, 2811, 2819, 2825,
+  2833, 2867, 2879, 2881, 2891, 2905, 2911, 2917, 2927, 2941, 2951,
+  2955, 2963, 2965, 2991, 2999, 3005, 3017, 3035, 3037, 3047, 3053,
+  3083, 3085, 3097, 3103, 3159, 3169, 3179, 3187, 3205, 3209, 3223,
+  3227, 3229, 3251, 3263, 3271, 3277, 3283, 3285, 3299, 3305, 3319,
+  3331, 3343, 3357, 3367, 3373, 3393, 3399, 3413, 3417, 3427, 3439,
+  3441, 3475, 3487, 3497, 3515, 3517, 3529, 3543, 3547, 3553, 3559,
+  3573, 3589, 3613, 3617, 3623, 3627, 3635, 3641, 3655, 3659, 3669,
+  3679, 3697, 3707, 3709, 3713, 3731, 3743, 3747, 3771, 3791, 3805,
+  3827, 3833, 3851, 3865, 3889, 3895, 3933, 3947, 3949, 3957, 3971,
+  3985, 3991, 3995, 4007, 4013, 4021, 4045, 4051, 4069, 4073, 4179,
+  4201, 4219, 4221, 4249, 4305, 4331, 4359, 4383, 4387, 4411, 4431,
+  4439, 4449, 4459, 4485, 4531, 4569, 4575, 4621, 4663, 4669, 4711,
+  4723, 4735, 4793, 4801, 4811, 4879, 4893, 4897, 4921, 4927, 4941,
+  4977, 5017, 5027, 5033, 5127, 5169, 5175, 5199, 5213, 5223, 5237,
+  5287, 5293, 5331, 5391, 5405, 5453, 5523, 5573, 5591, 5597, 5611,
+  5641, 5703, 5717, 5721, 5797, 5821, 5909, 5913, 5955, 5957, 6005,
+  6025, 6061, 6067, 6079, 6081, 6231, 6237, 6289, 6295, 6329, 6383,
+  6427, 6453, 6465, 6501, 6523, 6539, 6577, 6589, 6601, 6607, 6631,
+  6683, 6699, 6707, 6761, 6795, 6865, 6881, 6901, 6923, 6931, 6943,
+  6999, 7057, 7079, 7103, 7105, 7123, 7173, 7185, 7191, 7207, 7245,
+  7303, 7327, 7333, 7355, 7365, 7369, 7375, 7411, 7431, 7459, 7491,
+  7505, 7515, 7541, 7557, 7561, 7701, 7705, 7727, 7749, 7761, 7783,
+  7795, 7823, 7907, 7953, 7963, 7975, 8049, 8089, 8123, 8125, 8137,
+  8219, 8231, 8245, 8275, 8293, 8303, 8331, 8333, 8351, 8357, 8367,
+  8379, 8381, 8387, 8393, 8417, 8435, 8461, 8469, 8489, 8495, 8507,
+  8515, 8551, 8555, 8569, 8585, 8599, 8605, 8639, 8641, 8647, 8653,
+  8671, 8675, 8689, 8699, 8729, 8741, 8759, 8765, 8771, 8795, 8797,
+  8825, 8831, 8841, 8855, 8859, 8883, 8895, 8909, 8943, 8951, 8955,
+  8965, 8999, 9003, 9031, 9045, 9049, 9071, 9073, 9085, 9095, 9101,
+  9109, 9123, 9129, 9137, 9143, 9147, 9185, 9197, 9209, 9227, 9235,
+  9247, 9253, 9257, 9277, 9297, 9303, 9313, 9325, 9343, 9347, 9371,
+  9373, 9397, 9407, 9409, 9415, 9419, 9443, 9481, 9495, 9501, 9505,
+  9517, 9529, 9555, 9557, 9571, 9585, 9591, 9607, 9611, 9621, 9625,
+  9631, 9647, 9661, 9669, 9679, 9687, 9707, 9731, 9733, 9745, 9773,
+  9791, 9803, 9811, 9817, 9833, 9847, 9851, 9863, 9875, 9881, 9905,
+  9911, 9917, 9923, 9963, 9973, 10003, 10025, 10043, 10063, 10071,
+  10077, 10091, 10099, 10105, 10115, 10129, 10145, 10169, 10183,
+  10187, 10207, 10223, 10225, 10247, 10265, 10271, 10275, 10289,
+  10299, 10301, 10309, 10343, 10357, 10373, 10411, 10413, 10431,
+  10445, 10453, 10463, 10467, 10473, 10491, 10505, 10511, 10513,
+  10523, 10539, 10549, 10559, 10561, 10571, 10581, 10615, 10621,
+  10625, 10643, 10655, 10671, 10679, 10685, 10691, 10711, 10739,
+  10741, 10755, 10767, 10781, 10785, 10803, 10805, 10829, 10857,
+  10863, 10865, 10875, 10877, 10917, 10921, 10929, 10949, 10967,
+  10971, 10987, 10995, 11009, 11029, 11043, 11045, 11055, 11063,
+  11075, 11081, 11117, 11135, 11141, 11159, 11163, 11181, 11187,
+  11225, 11237, 11261, 11279, 11297, 11307, 11309, 11327, 11329,
+  11341, 11377, 11403, 11405, 11413, 11427, 11439, 11453, 11461,
+  11473, 11479, 11489, 11495, 11499, 11533, 11545, 11561, 11567,
+  11575, 11579, 11589, 11611, 11623, 11637, 11657, 11663, 11687,
+  11691, 11701, 11747, 11761, 11773, 11783, 11795, 11797, 11817,
+  11849, 11855, 11867, 11869, 11873, 11883, 11919, 11921, 11927,
+  11933, 11947, 11955, 11961, 11999, 12027, 12029, 12037, 12041,
+  12049, 12055, 12095, 12097, 12107, 12109, 12121, 12127, 12133,
+  12137, 12181, 12197, 12207, 12209, 12239, 12253, 12263, 12269,
+  12277, 12287, 12295, 12309, 12313, 12335, 12361, 12367, 12391,
+  12409, 12415, 12433, 12449, 12469, 12479, 12481, 12499, 12505,
+  12517, 12527, 12549, 12559, 12597, 12615, 12621, 12639, 12643,
+  12657, 12667, 12707, 12713, 12727, 12741, 12745, 12763, 12769,
+  12779, 12781, 12787, 12799, 12809, 12815, 12829, 12839, 12857,
+  12875, 12883, 12889, 12901, 12929, 12947, 12953, 12959, 12969,
+  12983, 12987, 12995, 13015, 13019, 13031, 13063, 13077, 13103,
+  13137, 13149, 13173, 13207, 13211, 13227, 13241, 13249, 13255,
+  13269, 13283, 13285, 13303, 13307, 13321, 13339, 13351, 13377,
+  13389, 13407, 13417, 13431, 13435, 13447, 13459, 13465, 13477,
+  13501, 13513, 13531, 13543, 13561, 13581, 13599, 13605, 13617,
+  13623, 13637, 13647, 13661, 13677, 13683, 13695, 13725, 13729,
+  13753, 13773, 13781, 13785, 13795, 13801, 13807, 13825, 13835,
+  13855, 13861, 13871, 13883, 13897, 13905, 13915, 13939, 13941,
+  13969, 13979, 13981, 13997, 14027, 14035, 14037, 14051, 14063,
+  14085, 14095, 14107, 14113, 14125, 14137, 14145, 14151, 14163,
+  14193, 14199, 14219, 14229, 14233, 14243, 14277, 14287, 14289,
+  14295, 14301, 14305, 14323, 14339, 14341, 14359, 14365, 14375,
+  14387, 14411, 14425, 14441, 14449, 14499, 14513, 14523, 14537,
+  14543, 14561, 14579, 14585, 14593, 14599, 14603, 14611, 14641,
+  14671, 14695, 14701, 14723, 14725, 14743, 14753, 14759, 14765,
+  14795, 14797, 14803, 14831, 14839, 14845, 14855, 14889, 14895,
+  14909, 14929, 14941, 14945, 14951, 14963, 14965, 14985, 15033,
+  15039, 15053, 15059, 15061, 15071, 15077, 15081, 15099, 15121,
+  15147, 15149, 15157, 15167, 15187, 15193, 15203, 15205, 15215,
+  15217, 15223, 15243, 15257, 15269, 15273, 15287, 15291, 15313,
+  15335, 15347, 15359, 15373, 15379, 15381, 15391, 15395, 15397,
+  15419, 15439, 15453, 15469, 15491, 15503, 15517, 15527, 15531,
+  15545, 15559, 15593, 15611, 15613, 15619, 15639, 15643, 15649,
+  15661, 15667, 15669, 15681, 15693, 15717, 15721, 15741, 15745,
+  15765, 15793, 15799, 15811, 15825, 15835, 15847, 15851, 15865,
+  15877, 15881, 15887, 15899, 15915, 15935, 15937, 15955, 15973,
+  15977, 16011, 16035, 16061, 16069, 16087, 16093, 16097, 16121,
+  16141, 16153, 16159, 16165, 16183, 16189, 16195, 16197, 16201,
+  16209, 16215, 16225, 16259, 16265, 16273, 16299, 16309, 16355,
+  16375, 16381
+};
+
+static constexpr int64_t initsobolstate[1111][13] = {
+  {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
+  {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
+  {1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
+  {1, 3, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
+  {1, 1, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
+  {1, 3, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0},
+  {1, 1, 3, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0},
+  {1, 3, 3, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0},
+  {1, 3, 7, 13, 3, 0, 0, 0, 0, 0, 0, 0, 0},
+  {1, 1, 5, 11, 27, 0, 0, 0, 0, 0, 0, 0, 0},
+  {1, 3, 5, 1, 15, 0, 0, 0, 0, 0, 0, 0, 0},
+  {1, 1, 7, 3, 29, 0, 0, 0, 0, 0, 0, 0, 0},
+  {1, 3, 7, 7, 21, 0, 0, 0, 0, 0, 0, 0, 0},
+  {1, 1, 1, 9, 23, 37, 0, 0, 0, 0, 0, 0, 0},
+  {1, 3, 3, 5, 19, 33, 0, 0, 0, 0, 0, 0, 0},
+  {1, 1, 3, 13, 11, 7, 0, 0, 0, 0, 0, 0, 0},
+  {1, 1, 7, 13, 25, 5, 0, 0, 0, 0, 0, 0, 0},
+  {1, 3, 5, 11, 7, 11, 0, 0, 0, 0, 0, 0, 0},
+  {1, 1, 1, 3, 13, 39, 0, 0, 0, 0, 0, 0, 0},
+  {1, 3, 1, 15, 17, 63, 13, 0, 0, 0, 0, 0, 0},
+  {1, 1, 5, 5, 1, 59, 33, 0, 0, 0, 0, 0, 0},
+  {1, 3, 3, 3, 25, 17, 115, 0, 0, 0, 0, 0, 0},
+  {1, 1, 7, 15, 29, 15, 41, 0, 0, 0, 0, 0, 0},
+  {1, 3, 1, 7, 3, 23, 79, 0, 0, 0, 0, 0, 0},
+  {1, 3, 7, 9, 31, 29, 17, 0, 0, 0, 0, 0, 0},
+  {1, 1, 5, 13, 11, 3, 29, 0, 0, 0, 0, 0, 0},
+  {1, 1, 1, 9, 5, 21, 119, 0, 0, 0, 0, 0, 0},
+  {1, 1, 3, 1, 23, 13, 75, 0, 0, 0, 0, 0, 0},
+  {1, 3, 7, 11, 27, 31, 73, 0, 0, 0, 0, 0, 0},
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+  {1, 1, 1, 13, 25, 59, 125, 91, 53, 273, 313, 553, 6939},
+  {1, 1, 5, 13, 29, 41, 41, 253, 25, 89, 1, 1499, 3515},
+  {1, 3, 1, 15, 15, 33, 117, 239, 333, 589, 1963, 3529, 2985},
+  {1, 3, 1, 9, 21, 35, 43, 91, 17, 487, 963, 1081, 2787},
+  {1, 1, 5, 13, 11, 27, 77, 145, 201, 859, 1905, 2877, 2123},
+  {1, 3, 5, 7, 19, 19, 97, 19, 475, 343, 821, 3077, 1969},
+  {1, 1, 3, 15, 15, 13, 15, 179, 257, 91, 1677, 845, 3307},
+  {1, 1, 3, 3, 3, 25, 29, 231, 417, 847, 185, 1793, 353},
+  {1, 3, 7, 9, 7, 27, 5, 121, 345, 341, 709, 2409, 4359},
+  {1, 3, 5, 3, 13, 43, 59, 7, 381, 173, 545, 3995, 7059},
+  {1, 3, 5, 1, 11, 33, 25, 225, 377, 287, 1723, 2559, 5273},
+  {1, 3, 1, 13, 25, 35, 63, 237, 55, 1003, 215, 4081, 5873},
+  {1, 3, 1, 7, 17, 17, 87, 125, 403, 289, 1885, 1195, 6657},
+  {1, 1, 1, 5, 1, 17, 39, 191, 77, 639, 1249, 2955, 6765},
+  {1, 3, 3, 9, 5, 23, 39, 119, 389, 983, 583, 1117, 6229},
+  {1, 1, 1, 3, 31, 7, 77, 59, 347, 685, 1803, 1409, 3179},
+  {1, 1, 5, 1, 13, 35, 85, 175, 363, 697, 839, 785, 1583},
+  {1, 1, 7, 7, 29, 15, 37, 237, 211, 35, 885, 287, 6237},
+  {1, 3, 7, 1, 23, 61, 81, 131, 413, 701, 485, 1521, 2155},
+  {1, 1, 1, 1, 9, 61, 73, 79, 419, 645, 413, 1607, 371},
+  {1, 1, 7, 13, 5, 53, 89, 43, 5, 911, 1767, 85, 273},
+  {1, 1, 5, 3, 29, 5, 29, 45, 167, 501, 425, 3055, 7491},
+  {1, 3, 7, 3, 7, 15, 125, 205, 219, 705, 129, 3123, 3309},
+  {1, 1, 3, 11, 17, 23, 109, 199, 201, 873, 1035, 2533, 6805},
+  {1, 1, 7, 1, 27, 11, 21, 251, 285, 763, 329, 2329, 3015},
+  {1, 3, 3, 7, 7, 13, 23, 153, 425, 745, 1263, 3477, 6831},
+  {1, 1, 1, 13, 17, 43, 119, 207, 11, 657, 1881, 799, 7819},
+  {1, 3, 3, 15, 31, 55, 105, 37, 77, 559, 1779, 3683, 713},
+  {1, 3, 7, 15, 9, 47, 43, 179, 269, 699, 1565, 3715, 4747},
+  {1, 3, 3, 5, 31, 25, 93, 113, 489, 315, 359, 337, 3935},
+  {1, 3, 1, 7, 9, 43, 97, 255, 281, 347, 367, 3139, 4109},
+  {1, 3, 5, 13, 9, 15, 15, 107, 403, 429, 453, 3311, 1311},
+  {1, 1, 5, 13, 7, 57, 125, 217, 79, 197, 707, 431, 709},
+  {1, 1, 3, 15, 21, 45, 29, 61, 425, 165, 1419, 3511, 3089},
+  {1, 1, 5, 11, 3, 1, 51, 7, 125, 955, 831, 2299, 7059},
+  {1, 3, 1, 13, 3, 49, 69, 181, 81, 859, 1889, 365, 4247},
+  {1, 3, 3, 1, 3, 63, 37, 247, 331, 167, 887, 2941, 2989},
+  {1, 3, 5, 13, 9, 57, 45, 31, 437, 303, 1871, 3067, 1509},
+  {1, 3, 5, 13, 11, 15, 31, 13, 271, 833, 1869, 1331, 4919},
+  {1, 1, 5, 3, 21, 31, 75, 113, 397, 531, 747, 1081, 1841},
+  {1, 3, 1, 9, 11, 31, 109, 145, 299, 473, 223, 1097, 3045},
+  {1, 3, 1, 15, 31, 7, 119, 107, 475, 635, 1547, 2853, 3821},
+  {1, 3, 7, 15, 9, 53, 53, 233, 271, 641, 1799, 2299, 6929},
+  {1, 3, 7, 11, 25, 27, 5, 233, 249, 195, 433, 495, 4655},
+  {1, 1, 1, 15, 5, 15, 101, 43, 413, 589, 1441, 1745, 1333},
+  {1, 1, 5, 9, 1, 47, 125, 79, 233, 821, 553, 749, 6429},
+  {1, 3, 5, 15, 31, 23, 121, 23, 261, 205, 2021, 3819, 6649},
+  {1, 3, 1, 1, 13, 7, 35, 169, 495, 3, 1303, 619, 2131},
+  {1, 3, 3, 13, 29, 29, 29, 137, 171, 635, 1505, 1059, 5265},
+  {1, 1, 5, 15, 9, 53, 7, 129, 69, 371, 1735, 3559, 1051},
+  {1, 3, 1, 1, 29, 47, 63, 183, 27, 891, 1619, 183, 261},
+  {1, 1, 5, 1, 1, 9, 17, 53, 409, 249, 1065, 3743, 8057},
+  {1, 1, 3, 5, 11, 53, 63, 91, 21, 123, 1161, 723, 3379},
+  {1, 3, 5, 11, 19, 3, 13, 55, 421, 77, 2047, 949, 2179},
+  {1, 3, 3, 5, 7, 25, 69, 103, 367, 623, 347, 3501, 1993},
+  {1, 1, 3, 1, 27, 55, 15, 223, 81, 993, 867, 733, 5655},
+  {1, 3, 7, 11, 13, 45, 105, 87, 483, 401, 881, 2599, 3063},
+  {1, 3, 5, 11, 31, 63, 51, 177, 255, 525, 1447, 3983, 6381},
+  {1, 1, 7, 5, 7, 21, 127, 157, 15, 427, 329, 3961, 3587},
+  {1, 1, 3, 3, 31, 17, 105, 79, 219, 71, 781, 911, 7417},
+  {1, 1, 7, 9, 7, 23, 9, 213, 365, 655, 1065, 1899, 1579},
+  {1, 1, 3, 1, 25, 31, 57, 139, 497, 951, 219, 985, 1541},
+  {1, 1, 1, 3, 23, 27, 95, 183, 181, 357, 589, 2493, 2107},
+  {1, 3, 3, 5, 21, 27, 59, 231, 75, 851, 645, 1795, 5085},
+  {1, 1, 7, 13, 29, 43, 109, 205, 431, 899, 1257, 653, 2873},
+  {1, 1, 7, 9, 11, 63, 35, 143, 99, 535, 1833, 157, 6141},
+  {1, 3, 3, 7, 11, 55, 49, 129, 325, 493, 749, 433, 955},
+  {1, 3, 3, 7, 13, 63, 23, 243, 407, 323, 1841, 2361, 3537},
+  {1, 1, 1, 1, 11, 45, 33, 205, 229, 1003, 1733, 3093, 2157},
+  {1, 1, 1, 9, 27, 51, 107, 93, 281, 343, 1179, 3119, 841},
+  {1, 1, 3, 9, 1, 15, 55, 59, 63, 515, 1191, 3679, 1999},
+  {1, 3, 3, 15, 23, 27, 33, 15, 83, 859, 1025, 2367, 1465},
+  {1, 1, 3, 7, 31, 5, 57, 89, 493, 1017, 1639, 1701, 5171},
+  {1, 1, 3, 5, 21, 37, 79, 9, 5, 5, 1955, 1445, 5651},
+  {1, 3, 3, 5, 23, 43, 73, 11, 113, 423, 1423, 1321, 1535},
+  {1, 3, 5, 15, 21, 11, 69, 47, 15, 315, 1685, 2397, 7235},
+  {1, 1, 5, 13, 19, 27, 59, 133, 271, 1011, 1711, 1241, 4349},
+  {1, 3, 3, 9, 31, 5, 107, 227, 37, 703, 493, 3305, 1263},
+  {1, 3, 3, 7, 5, 27, 55, 75, 87, 41, 549, 3985, 1453},
+  {1, 3, 3, 13, 31, 59, 11, 9, 451, 777, 783, 2349, 1005},
+  {1, 3, 1, 3, 25, 21, 63, 91, 299, 163, 1653, 4067, 6893},
+  {1, 3, 3, 13, 25, 7, 95, 19, 83, 95, 397, 3805, 2919},
+  {1, 3, 5, 11, 19, 39, 103, 171, 451, 831, 895, 3073, 1947},
+  {1, 3, 7, 13, 17, 27, 23, 163, 311, 79, 233, 2837, 1635},
+  {1, 3, 7, 7, 11, 63, 125, 79, 441, 975, 759, 1567, 3963},
+  {1, 1, 1, 9, 25, 35, 91, 7, 47, 235, 1505, 3783, 397},
+  {1, 1, 5, 13, 7, 47, 31, 103, 455, 633, 677, 451, 969},
+  {1, 3, 7, 13, 13, 55, 91, 5, 47, 723, 1449, 2441, 4569},
+  {1, 3, 3, 13, 1, 17, 51, 119, 253, 297, 1573, 1181, 655},
+  {1, 1, 7, 15, 29, 17, 65, 155, 13, 589, 1297, 487, 6737},
+  {1, 1, 1, 9, 17, 17, 61, 75, 109, 317, 1821, 543, 2995},
+  {1, 3, 1, 5, 23, 3, 75, 11, 369, 679, 1691, 1201, 7235},
+  {1, 1, 3, 5, 15, 19, 69, 71, 347, 981, 791, 3735, 7713},
+  {1, 3, 5, 3, 7, 21, 107, 95, 11, 195, 289, 2517, 973},
+  {1, 3, 7, 3, 29, 13, 65, 17, 409, 399, 1187, 733, 4821},
+  {1, 3, 5, 3, 17, 49, 101, 13, 275, 1003, 867, 1535, 2377},
+  {1, 3, 3, 1, 13, 61, 59, 243, 63, 121, 1535, 2175, 1673},
+  {1, 3, 3, 3, 3, 39, 35, 207, 441, 501, 575, 3613, 1},
+  {1, 1, 3, 15, 17, 15, 15, 187, 15, 155, 183, 3019, 6541}
+};

diff --git a/aten/src/ATen/native/native_functions.yaml b/aten/src/ATen/native/native_functions.yaml
index bcdb704..0793434 100644 (file)
--- a/aten/src/ATen/native/native_functions.yaml
+++ b/aten/src/ATen/native/native_functions.yaml
@@ -76,6 +76,18 @@
   dispatch:
      CUDA: masked_scale_cuda
 
+- func: _sobol_engine_draw(Tensor quasi, int n, Tensor sobolstate, int dimension, int num_generated, ScalarType? dtype) -> (Tensor, Tensor)
+  matches_jit_signature: True
+
+- func: _sobol_engine_ff_(Tensor(a!) self, int n, Tensor sobolstate, int dimension, int num_generated) -> Tensor(a!)
+  matches_jit_signature: True
+
+- func: _sobol_engine_scramble_(Tensor(a!) self, Tensor ltm, int dimension) -> Tensor(a!)
+  matches_jit_signature: True
+
+- func: _sobol_engine_initialize_state_(Tensor(a!) self, int dimension) -> Tensor(a!)
+  matches_jit_signature: True
+
 - func: _reshape_from_tensor(Tensor self, Tensor shape) -> Tensor
   matches_jit_signature: True
 

diff --git a/docs/source/torch.rst b/docs/source/torch.rst
index 782f58e..1013128 100644 (file)
--- a/docs/source/torch.rst
+++ b/docs/source/torch.rst
@@ -107,6 +107,13 @@ There are a few more in-place random sampling functions defined on Tensors as we
 - :func:`torch.Tensor.random_` - numbers sampled from the discrete uniform distribution
 - :func:`torch.Tensor.uniform_` - numbers sampled from the continuous uniform distribution
 
+Quasi-random sampling
+~~~~~~~~~~~~~~~~~~~~~
+
+.. autoclass:: torch.quasirandom.SobolEngine
+    :members:
+    :exclude-members: MAXBIT, MAXDIM
+    :undoc-members:
 
 Serialization
 ----------------------------------

diff --git a/test/test_torch.py b/test/test_torch.py
index e337797..6b6c2a2 100644 (file)
--- a/test/test_torch.py
+++ b/test/test_torch.py
@@ -8682,6 +8682,87 @@ class _TestTorchMixin(object):
         self.assertEqual(r[:, :50].std(), 4, 0.3)
         self.assertEqual(r[:, 50:].std(), 1, 0.2)
 
+    def test_sobolengine_unscrambled_lowdim(self):
+        engine_1d = torch.quasirandom.SobolEngine(1)
+        expected_1d = torch.tensor([0.5, 0.75, 0.25, 0.375, 0.875, 0.625, 0.125, 0.1875, 0.6875, 0.9375])
+        actual_1d = engine_1d.draw(10)
+        self.assertEqual(actual_1d.view(-1), expected_1d)
+        self.assertEqual(actual_1d.size(), torch.Size([10, 1]))
+
+        # Test out kwarg
+        engine_1d.reset()
+        actual_1d_out = torch.Tensor().float()
+        engine_1d.draw(10, out=actual_1d_out)
+        self.assertEqual(actual_1d.view(-1), expected_1d)
+
+        engine_3d = torch.quasirandom.SobolEngine(3)
+        expected_3d = torch.tensor([0.5, 0.75, 0.25, 0.625, 0.125, 0.375, 0.875, 0.3125, 0.8125, 0.5625])
+        actual_3d = engine_3d.draw(10)
+        self.assertEqual(actual_3d[:, 2], expected_3d)
+        self.assertEqual(actual_3d[:, 0], expected_1d)
+        self.assertEqual(actual_3d.size(), torch.Size([10, 3]))
+
+        engine_3d = torch.quasirandom.SobolEngine(3)
+        draws = torch.cat([engine_3d.draw() for _ in range(0, 10)])
+        self.assertEqual(draws, actual_3d)
+
+        engine_3d = torch.quasirandom.SobolEngine(3).fast_forward(5)
+        draws = engine_3d.draw(5)
+        self.assertEqual(draws, actual_3d[5:])
+        engine_3d.reset()
+        self.assertEqual(engine_3d.draw(3), actual_3d[:3])
+        engine_3d.fast_forward(2)
+        self.assertEqual(engine_3d.draw(5), actual_3d[5:])
+
+    def test_sobolengine_unscrambled_highdim(self):
+        from collections import Counter
+        engine = torch.quasirandom.SobolEngine(1111)
+        count1 = dict(Counter(engine.draw().view(-1).tolist()))
+        count2 = dict(Counter(engine.draw().view(-1).tolist()))
+        count3 = dict(Counter(engine.draw().view(-1).tolist()))
+        self.assertTrue(count1 == {0.5: 1111})
+        self.assertTrue(count2 == {0.25: 580, 0.75: 531})
+        self.assertTrue(count3 == {0.25: 531, 0.75: 580})
+
+        engine = torch.quasirandom.SobolEngine(1111)
+        draws = engine.draw(1000)
+        self.assertTrue(torch.all(draws <= 1))
+        self.assertTrue(torch.all(draws >= 0))
+
+    def test_sobolengine_scrambled_lowdim(self):
+        engine_1d = torch.quasirandom.SobolEngine(1, scramble=True, seed=1729)
+        expected_1d = [0.16478512, 0.43221009, 0.84261382, 0.99750268, 0.27460563,
+                       0.01084163, 0.73373985, 0.65039611, 0.12329865, 0.35587373]
+        actual_1d = engine_1d.draw(10)
+        self.assertEqual(actual_1d.flatten(), torch.tensor(expected_1d))
+        self.assertEqual(actual_1d.size(), torch.Size([10, 1]))
+
+        engine_3d = torch.quasirandom.SobolEngine(3, scramble=True, seed=1729)
+        expected_3d = [0.32642800, 0.17881306, 0.68837059, 0.46492538, 0.91789097,
+                       0.58075899, 0.03642474, 0.68229187, 0.20051685, 0.30083340]
+        actual_3d = engine_3d.draw(10)
+        self.assertEqual(actual_3d[:, 2], torch.tensor(expected_3d))
+        self.assertEqual(actual_3d.size(), torch.Size([10, 3]))
+
+        engine_3d = torch.quasirandom.SobolEngine(3, scramble=True, seed=1729)
+        draws = torch.cat([engine_3d.draw() for _ in range(0, 10)])
+        self.assertEqual(draws, actual_3d)
+
+        engine_3d = torch.quasirandom.SobolEngine(3, scramble=True, seed=1729)
+        engine_3d.fast_forward(5)
+        draws = engine_3d.draw(5)
+        self.assertEqual(draws, actual_3d[5:])
+        engine_3d.reset()
+        self.assertEqual(engine_3d.draw(3), actual_3d[:3])
+        engine_3d.fast_forward(2)
+        self.assertEqual(engine_3d.draw(5), actual_3d[5:])
+
+    def test_sobolengine_scrambled_highdim(self):
+        engine = torch.quasirandom.SobolEngine(1111, scramble=True)
+        draws = engine.draw(1000)
+        self.assertTrue(torch.all(draws <= 1))
+        self.assertTrue(torch.all(draws >= 0))
+
     def test_parsing_int64(self):
         # accepts integer arguments
         x = torch.cumsum(torch.ones(5, 5), 0)

diff --git a/tools/autograd/gen_variable_type.py b/tools/autograd/gen_variable_type.py
index 2cd53a6..777c9c0 100644 (file)
--- a/tools/autograd/gen_variable_type.py
+++ b/tools/autograd/gen_variable_type.py
@@ -75,6 +75,9 @@ DONT_REQUIRE_DERIVATIVE = {
     # These are only implemented on integral types
     '__and__', '__iand__', '__ilshift__', '__ior__', '__irshift__', '__ixor__',
     '__lshift__', '__or__', '__rshift__', '__xor__',
+    # These work on integral data types, and hence don't require derivative
+    '_sobol_engine_draw', '_sobol_engine_ff', '_sobol_engine_scramble_',
+    '_sobol_engine_initialize_state_',
     # This is an unsafe method that is meant to be out of reach of autograd.
     '_coalesced_',
 }

diff --git a/torch/__init__.py b/torch/__init__.py
index a7503b9..b4c50e9 100644 (file)
--- a/torch/__init__.py
+++ b/torch/__init__.py
@@ -310,3 +310,6 @@ def compiled_with_cxx11_abi():
 
 # Import the ops "namespace"
 from torch._ops import ops
+
+# Import the quasi random sampler
+import torch.quasirandom

diff --git a/torch/quasirandom.py b/torch/quasirandom.py
new file mode 100644 (file)
index 0000000..615d79d
--- /dev/null
+++ b/torch/quasirandom.py
@@ -0,0 +1,122 @@
+import torch
+
+
+class SobolEngine(object):
+    r"""
+    The :class:`torch.quasirandom.SobolEngine` is an engine for generating
+    (scrambled) Sobol sequences. Sobol sequences are an example of low
+    discrepancy quasi-random sequences.
+
+    This implementation of an engine for Sobol sequences is capable of
+    sampling sequences up to a maximum dimension of 1111. It uses direction
+    numbers to generate these sequences, and these numbers have been adapted
+    from `here <http://web.maths.unsw.edu.au/~fkuo/sobol/joe-kuo-old.1111>`_.
+
+    References:
+      - Art B. Owen. Scrambling Sobol and Niederreiter-Xing points.
+        Journal of Complexity, 14(4):466-489, December 1998.
+
+      - I. M. Sobol. The distribution of points in a cube and the accurate
+        evaluation of integrals.
+        Zh. Vychisl. Mat. i Mat. Phys., 7:784-802, 1967.
+
+    Args:
+        dimension (Int): The dimensionality of the sequence to be drawn
+        scramble (bool, optional): Setting this to ``True`` will produce
+                                   scrambled Sobol sequences. Scrambling is
+                                   capable of producing better Sobol
+                                   sequences. Default: ``False``.
+        seed (Int, optional): This is the seed for the scrambling. The seed
+                              of the random number generator is set to this,
+                              if specified. Default: ``None``
+
+    Examples::
+
+        >>> soboleng = torch.quasirandom.SobolEngine(dimension=5)
+        >>> soboleng.draw(3)
+        tensor([[0.5000, 0.5000, 0.5000, 0.5000, 0.5000],
+                [0.7500, 0.2500, 0.7500, 0.2500, 0.7500],
+                [0.2500, 0.7500, 0.2500, 0.7500, 0.2500]])
+    """
+    MAXBIT = 30
+    MAXDIM = 1111
+
+    def __init__(self, dimension, scramble=False, seed=None):
+        if dimension > self.MAXDIM or dimension < 1:
+            raise ValueError("Supported range of dimensionality "
+                             "for SobolEngine is [1, {}]".format(self.MAXDIM))
+
+        self.seed = seed
+        self.scramble = scramble
+        self.dimension = dimension
+
+        self.sobolstate = torch.zeros(dimension, self.MAXBIT, dtype=torch.long)
+        torch._sobol_engine_initialize_state_(self.sobolstate, self.dimension)
+
+        if self.scramble:
+            g = torch.Generator()
+            if self.seed is not None:
+                g.manual_seed(self.seed)
+
+            self.shift = torch.mv(torch.randint(2, (self.dimension, self.MAXBIT), generator=g),
+                                  torch.pow(2, torch.arange(0, self.MAXBIT)))
+
+            ltm = torch.randint(2, (self.dimension, self.MAXBIT, self.MAXBIT), generator=g).tril()
+
+            torch._sobol_engine_scramble_(self.sobolstate, ltm, self.dimension)
+        else:
+            self.shift = torch.zeros(self.dimension, dtype=torch.long)
+
+        self.quasi = self.shift.clone()
+        self.num_generated = 0
+
+    def draw(self, n=1, out=None, dtype=torch.float32):
+        r"""
+        Function to draw a sequence of :attr:`n` points from a Sobol sequence.
+        Note that the samples are dependent on the previous samples. The size
+        of the result is :math:`(n, dimension)`.
+
+        Args:
+            n (Int, optional): The length of sequence of points to draw.
+                               Default: 1
+            out (Tensor, optional): The output tensor
+            dtype (:class:`torch.dtype`, optional): the desired data type of the
+                                                    returned tensor.
+                                                    Default: ``torch.float32``
+        """
+        result, self.quasi = torch._sobol_engine_draw(self.quasi, n, self.sobolstate,
+                                                      self.dimension, self.num_generated, dtype=dtype)
+        self.num_generated += n
+        if out is not None:
+            out.resize_as_(result).copy_(result)
+            return out
+        return result
+
+    def reset(self):
+        r"""
+        Function to reset the ``SobolEngine`` to base state.
+        """
+        self.quasi.copy_(self.shift)
+        self.num_generated = 0
+        return self
+
+    def fast_forward(self, n):
+        r"""
+        Function to fast-forward the state of the ``SobolEngine`` by
+        :attr:`n` steps. This is equivalent to drawing :attr:`n` samples
+        without using the samples.
+
+        Args:
+            n (Int): The number of steps to fast-forward by.
+        """
+        torch._sobol_engine_ff_(self.quasi, n, self.sobolstate, self.dimension, self.num_generated)
+        self.num_generated += n
+        return self
+
+    def __repr__(self):
+        fmt_string = ['dimension={}'.format(self.dimension)]
+        if self.scramble:
+            fmt_string += ['scramble=True']
+        if self.seed is not None:
+            fmt_string += ['seed={}'.format(self.seed)]
+        return self.__class__.__name__ + '(' + ', '.join(fmt_string) + ')'