Correlation via fft implementation

Author: AlexanderKalistratov

dpnp/dpnp_iface_statistics.py

@@ -37,6 +37,8 @@
 
 """
 
+import math
+
 import dpctl.tensor as dpt
 import dpctl.utils as dpu
 import numpy
@@ -59,6 +61,8 @@
 from .dpnp_utils.dpnp_utils_reduction import dpnp_wrap_reduction_call
 from .dpnp_utils.dpnp_utils_statistics import dpnp_cov
 
+min_ = min  # pylint: disable=used-before-assignment
+
 __all__ = [
     "amax",
     "amin",
@@ -478,17 +482,57 @@ def _get_padding(a_size, v_size, mode):
     return l_pad, r_pad
 
 
-def _run_native_sliding_dot_product1d(a, v, l_pad, r_pad):
+def _choose_conv_method(a, v, rdtype):
+    assert a.size >= v.size
+    if rdtype == dpnp.bool:
+        return "direct"
+
+    if v.size < 10**4 or a.size < 10**4:
+        return "direct"
+
+    if dpnp.issubdtype(rdtype, dpnp.integer):
+        max_a = int(dpnp.max(dpnp.abs(a)))
+        sum_v = int(dpnp.sum(dpnp.abs(v)))
+        max_value = int(max_a * sum_v)
+
+        default_float = dpnp.default_float_type(a.sycl_device)
+        if max_value > 2 ** numpy.finfo(default_float).nmant - 1:
+            return "direct"
+
+    if dpnp.issubdtype(rdtype, dpnp.number):
+        return "fft"
+
+    raise ValueError(f"Unsupported dtype: {rdtype}")
+
+
+def _run_native_sliding_dot_product1d(a, v, l_pad, r_pad, rdtype):
     queue = a.sycl_queue
+    device = a.sycl_device
+
+    supported_types = statistics_ext.sliding_dot_product1d_dtypes()
+    supported_dtype = to_supported_dtypes(rdtype, supported_types, device)
 
-    usm_type = dpu.get_coerced_usm_type([a.usm_type, v.usm_type])
-    out_size = l_pad + r_pad + a.size - v.size + 1
+    if supported_dtype is None:
+        raise ValueError(
+            f"Unsupported input types ({a.dtype}, {v.dtype}), "
+            "and the inputs could not be coerced to any "
+            f"supported types. List of supported types: {supported_types}"
+        )
+
+    a_casted = dpnp.asarray(a, dtype=supported_dtype, order="C")
+    v_casted = dpnp.asarray(v, dtype=supported_dtype, order="C")
+
+    usm_type = dpu.get_coerced_usm_type([a_casted.usm_type, v_casted.usm_type])
+    out_size = l_pad + r_pad + a_casted.size - v_casted.size + 1
     out = dpnp.empty(
-        shape=out_size, sycl_queue=queue, dtype=a.dtype, usm_type=usm_type
+        shape=out_size,
+        sycl_queue=queue,
+        dtype=supported_dtype,
+        usm_type=usm_type,
     )
 
-    a_usm = dpnp.get_usm_ndarray(a)
-    v_usm = dpnp.get_usm_ndarray(v)
+    a_usm = dpnp.get_usm_ndarray(a_casted)
+    v_usm = dpnp.get_usm_ndarray(v_casted)
     out_usm = dpnp.get_usm_ndarray(out)
 
     _manager = dpu.SequentialOrderManager[queue]
@@ -506,7 +550,30 @@ def _run_native_sliding_dot_product1d(a, v, l_pad, r_pad):
     return out
 
 
-def correlate(a, v, mode="valid"):
+def _convolve_fft(a, v, l_pad, r_pad, rtype):
+    assert a.size >= v.size
+    assert l_pad < v.size
+
+    # +1 is needed to avoid circular convolution
+    padded_size = a.size + r_pad + 1
+    fft_size = 2 ** math.ceil(math.log2(padded_size))
+
+    af = dpnp.fft.fft(a, fft_size)  # pylint: disable=no-member
+    vf = dpnp.fft.fft(v, fft_size)  # pylint: disable=no-member
+
+    r = dpnp.fft.ifft(af * vf)  # pylint: disable=no-member
+    if dpnp.issubdtype(rtype, dpnp.floating):
+        r = r.real
+    elif dpnp.issubdtype(rtype, dpnp.integer) or rtype == dpnp.bool:
+        r = r.real.round()
+
+    start = v.size - 1 - l_pad
+    end = padded_size - 1
+
+    return r[start:end]
+
+
+def correlate(a, v, mode="valid", method="auto"):
     r"""
     Cross-correlation of two 1-dimensional sequences.
 
@@ -531,6 +598,20 @@ def correlate(a, v, mode="valid"):
         is ``'valid'``, unlike :obj:`dpnp.convolve`, which uses ``'full'``.
 
         Default: ``'valid'``.
+    method : {'auto', 'direct', 'fft'}, optional
+        `'direct'`: The correlation is determined directly from sums.
+
+        `'fft'`: The Fourier Transform is used to perform the calculations.
+        This method is faster for long sequences but can have accuracy issues.
+
+        `'auto'`: Automatically chooses direct or Fourier method based on
+        an estimate of which is faster.
+
+        Note: Use of the FFT convolution on input containing NAN or INF
+        will lead to the entire output being NAN or INF.
+        Use method='direct' when your input contains NAN or INF values.
+
+        Default: ``'auto'``.
 
     Notes
     -----
@@ -556,7 +637,6 @@ def correlate(a, v, mode="valid"):
     :obj:`dpnp.convolve` : Discrete, linear convolution of two
     one-dimensional sequences.
 
-
     Examples
     --------
     >>> import dpnp as np
@@ -598,19 +678,14 @@ def correlate(a, v, mode="valid"):
             f"Received shapes: a.shape={a.shape}, v.shape={v.shape}"
         )
 
-    supported_types = statistics_ext.sliding_dot_product1d_dtypes()
+    supported_methods = ["auto", "direct", "fft"]
+    if method not in supported_methods:
+        raise ValueError(
+            f"Unknown method: {method}. Supported methods: {supported_methods}"
+        )
 
     device = a.sycl_device
     rdtype = result_type_for_device([a.dtype, v.dtype], device)
-    supported_dtype = to_supported_dtypes(rdtype, supported_types, device)
-
-    if supported_dtype is None:
-        raise ValueError(
-            f"function '{correlate}' does not support input types "
-            f"({a.dtype}, {v.dtype}), "
-            "and the inputs could not be coerced to any "
-            f"supported types. List of supported types: {supported_types}"
-        )
 
     if dpnp.issubdtype(v.dtype, dpnp.complexfloating):
         v = dpnp.conj(v)
@@ -622,13 +697,15 @@ def correlate(a, v, mode="valid"):
 
     l_pad, r_pad = _get_padding(a.size, v.size, mode)
 
-    a_casted = dpnp.asarray(a, dtype=supported_dtype, order="C")
-    v_casted = dpnp.asarray(v, dtype=supported_dtype, order="C")
-
-    if v.size > a.size:
-        a_casted, v_casted = v_casted, a_casted
+    if method == "auto":
+        method = _choose_conv_method(a, v, rdtype)
 
-    r = _run_native_sliding_dot_product1d(a_casted, v_casted, l_pad, r_pad)
+    if method == "direct":
+        r = _run_native_sliding_dot_product1d(a, v, l_pad, r_pad, rdtype)
+    elif method == "fft":
+        r = _convolve_fft(a, v[::-1], l_pad, r_pad, rdtype)
+    else:
+        raise ValueError(f"Unknown method: {method}")
 
     if revert:
         r = r[::-1]

dpnp/tests/test_statistics.py

@@ -629,26 +629,104 @@ def test_corrcoef_scalar(self):
 
 
 class TestCorrelate:
+    def setup_method(self):
+        numpy.random.seed(0)
+
     @pytest.mark.parametrize(
         "a, v", [([1], [1, 2, 3]), ([1, 2, 3], [1]), ([1, 2, 3], [1, 2])]
     )
     @pytest.mark.parametrize("mode", [None, "full", "valid", "same"])
     @pytest.mark.parametrize("dtype", get_all_dtypes(no_bool=True))
-    def test_correlate(self, a, v, mode, dtype):
+    @pytest.mark.parametrize("method", [None, "auto", "direct", "fft"])
+    def test_correlate(self, a, v, mode, dtype, method):
         an = numpy.array(a, dtype=dtype)
         vn = numpy.array(v, dtype=dtype)
         ad = dpnp.array(an)
         vd = dpnp.array(vn)
 
-        if mode is None:
-            expected = numpy.correlate(an, vn)
-            result = dpnp.correlate(ad, vd)
-        else:
-            expected = numpy.correlate(an, vn, mode=mode)
-            result = dpnp.correlate(ad, vd, mode=mode)
+        dpnp_kwargs = {}
+        numpy_kwargs = {}
+        if mode is not None:
+            dpnp_kwargs["mode"] = mode
+            numpy_kwargs["mode"] = mode
+        if method is not None:
+            dpnp_kwargs["method"] = method
+
+        expected = numpy.correlate(an, vn, **numpy_kwargs)
+        result = dpnp.correlate(ad, vd, **dpnp_kwargs)
 
         assert_dtype_allclose(result, expected)
 
+    @pytest.mark.parametrize("a_size", [1, 100, 10000])
+    @pytest.mark.parametrize("v_size", [1, 100, 10000])
+    @pytest.mark.parametrize("mode", ["full", "valid", "same"])
+    @pytest.mark.parametrize("dtype", get_all_dtypes(no_none=True))
+    @pytest.mark.parametrize("method", ["auto", "direct", "fft"])
+    def test_correlate_random(self, a_size, v_size, mode, dtype, method):
+        if dtype == dpnp.bool:
+            an = numpy.random.rand(a_size) > 0.9
+            vn = numpy.random.rand(v_size) > 0.9
+        else:
+            an = (100 * numpy.random.rand(a_size)).astype(dtype)
+            vn = (100 * numpy.random.rand(v_size)).astype(dtype)
+
+            if dpnp.issubdtype(dtype, dpnp.complexfloating):
+                an = an + 1j * (100 * numpy.random.rand(a_size)).astype(dtype)
+                vn = vn + 1j * (100 * numpy.random.rand(v_size)).astype(dtype)
+
+        ad = dpnp.array(an)
+        vd = dpnp.array(vn)
+
+        dpnp_kwargs = {}
+        numpy_kwargs = {}
+        if mode is not None:
+            dpnp_kwargs["mode"] = mode
+            numpy_kwargs["mode"] = mode
+        if method is not None:
+            dpnp_kwargs["method"] = method
+
+        result = dpnp.correlate(ad, vd, **dpnp_kwargs)
+        expected = numpy.correlate(an, vn, **numpy_kwargs)
+
+        rdtype = result.dtype
+        if dpnp.issubdtype(rdtype, dpnp.integer):
+            rdtype = dpnp.default_float_type(ad.device)
+
+        if method != "fft" and (
+            dpnp.issubdtype(dtype, dpnp.integer) or dtype == dpnp.bool
+        ):
+            # For 'direct' and 'auto' methods, we expect exact results for integer types
+            assert_array_equal(result, expected)
+        else:
+            result = result.astype(rdtype)
+            if method == "direct":
+                expected = numpy.correlate(an, vn, **numpy_kwargs)
+                # For 'direct' method we can use standard validation
+                assert_dtype_allclose(result, expected, factor=30)
+            else:
+                rtol = 1e-3
+                atol = 1e-10
+
+                if rdtype == dpnp.float64 or rdtype == dpnp.complex128:
+                    rtol = 1e-6
+                    atol = 1e-12
+                elif rdtype == dpnp.bool:
+                    result = result.astype(dpnp.int32)
+                    rdtype = result.dtype
+
+                expected = expected.astype(rdtype)
+
+                diff = numpy.abs(result.asnumpy() - expected)
+                invalid = diff > atol + rtol * numpy.abs(expected)
+
+                # When using the 'fft' method, we might encounter outliers.
+                # This usually happens when the resulting array contains values close to zero.
+                # For these outliers, the relative error can be significant.
+                # We can tolerate a few such outliers.
+                max_outliers = 8 if expected.size > 1 else 0
+                if invalid.sum() > max_outliers:
+                    assert_dtype_allclose(result, expected, factor=1000)
+
     def test_correlate_mode_error(self):
         a = dpnp.arange(5)
         v = dpnp.arange(3)
@@ -689,7 +767,7 @@ def test_correlate_different_sizes(self, size):
         vd = dpnp.array(v)
 
         expected = numpy.correlate(a, v)
-        result = dpnp.correlate(ad, vd)
+        result = dpnp.correlate(ad, vd, method="direct")
 
         assert_dtype_allclose(result, expected, factor=20)
 
@@ -700,6 +778,13 @@ def test_correlate_another_sycl_queue(self):
         with pytest.raises(ValueError):
             dpnp.correlate(a, v)
 
+    def test_correlate_unkown_method(self):
+        a = dpnp.arange(5)
+        v = dpnp.arange(3)
+
+        with pytest.raises(ValueError):
+            dpnp.correlate(a, v, method="unknown")
+
 
 @pytest.mark.parametrize(
     "dtype", get_all_dtypes(no_bool=True, no_none=True, no_complex=True)