{ "__type": "IngestedDoc", "__tag": 4010, "_content": { "Notes": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The correlation z of two d-dimensional arrays x and y is defined as " } ] }, { "__type": "Code", "__tag": 4050, "value": "z[...,k,...] = sum[..., i_l, ...] x[..., i_l,...] * conj(y[..., i_l - k,...])", "execution_status": null }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "This way, if " }, { "__type": "InlineCode", "__tag": 4051, "value": "x" }, { "__type": "Text", "__tag": 4046, "value": " and " }, { "__type": "InlineCode", "__tag": 4051, "value": "y" }, { "__type": "Text", "__tag": 4046, "value": " are 1-D arrays and " }, { "__type": "InlineCode", "__tag": 4051, "value": "z = correlate(x, y, 'full')" }, { "__type": "Text", "__tag": 4046, "value": " then" } ] }, { "__type": "Math", "__tag": 4058, "value": "z[k] = \\sum_{l=0}^{N-1} x_l \\, y_{l-k}^{*}" }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "for " }, { "__type": "InlineMath", "__tag": 4057, "value": "k = -(M-1), \\dots, (N-1)" }, { "__type": "Text", "__tag": 4046, "value": ", where " }, { "__type": "InlineMath", "__tag": 4057, "value": "N" }, { "__type": "Text", "__tag": 4046, "value": " is the length of " }, { "__type": "InlineCode", "__tag": 4051, "value": "x" }, { "__type": "Text", "__tag": 4046, "value": ", " }, { "__type": "InlineMath", "__tag": 4057, "value": "M" }, { "__type": "Text", "__tag": 4046, "value": " is the length of " }, { "__type": "InlineCode", "__tag": 4051, "value": "y" }, { "__type": "Text", "__tag": 4046, "value": ", and " }, { "__type": "InlineMath", "__tag": 4057, "value": "y_m = 0" }, { "__type": "Text", "__tag": 4046, "value": " when " }, { "__type": "InlineMath", "__tag": 4057, "value": "m" }, { "__type": "Text", "__tag": 4046, "value": " is outside the valid range " }, { "__type": "InlineMath", "__tag": 4057, "value": "[0, M-1]" }, { "__type": "Text", "__tag": 4046, "value": ". The size of " }, { "__type": "InlineMath", "__tag": 4057, "value": "z" }, { "__type": "Text", "__tag": 4046, "value": " is " }, { "__type": "InlineMath", "__tag": 4057, "value": "N + M - 1" }, { "__type": "Text", "__tag": 4046, "value": " and " }, { "__type": "InlineMath", "__tag": 4057, "value": "y^*" }, { "__type": "Text", "__tag": 4046, "value": " denotes the complex conjugate of " }, { "__type": "InlineMath", "__tag": 4057, "value": "y" }, { "__type": "Text", "__tag": 4046, "value": "." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "InlineCode", "__tag": 4051, "value": "method='fft'" }, { "__type": "Text", "__tag": 4046, "value": " only works for numerical arrays as it relies on " }, { "__type": "CrossRef", "__tag": 4002, "value": "fftconvolve", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.signal._signaltools:fftconvolve" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": ". In certain cases (i.e., arrays of objects or when rounding integers can lose precision), " }, { "__type": "InlineCode", "__tag": 4051, "value": "method='direct'" }, { "__type": "Text", "__tag": 4046, "value": " is always used." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "When using " }, { "__type": "InlineCode", "__tag": 4051, "value": "mode='same'" }, { "__type": "Text", "__tag": 4046, "value": " with even-length inputs, the outputs of " }, { "__type": "CrossRef", "__tag": 4002, "value": "correlate", "reference": { "__type": "RefInfo", "__tag": 4000, "module": null, "version": null, "kind": "local", "path": "correlate" }, "kind": "local" }, { "__type": "Text", "__tag": 4046, "value": " and " }, { "__type": "CrossRef", "__tag": 4002, "value": "correlate2d", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.signal._signaltools:correlate2d" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " differ: There is a 1-index offset between them." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Strong", "__tag": 4048, "children": [ { "__type": "Text", "__tag": 4046, "value": "Array API Standard Support" } ] } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "CrossRef", "__tag": 4002, "value": "correlate", "reference": { "__type": "RefInfo", "__tag": 4000, "module": null, "version": null, "kind": "local", "path": "correlate" }, "kind": "local" }, { "__type": "Text", "__tag": 4046, "value": " has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable " }, { "__type": "InlineCode", "__tag": 4051, "value": "SCIPY_ARRAY_API=1" }, { "__type": "Text", "__tag": 4046, "value": " and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported." } ] }, { "__type": "Code", "__tag": 4050, "value": "==================== ==================== ====================\nLibrary CPU GPU\n==================== ==================== ====================\nNumPy ✅ n/a \nCuPy n/a ✅ \nPyTorch ✅ ⛔ \nJAX ✅ ✅ \nDask ⚠️ computes graph n/a \n==================== ==================== ====================", "execution_status": null }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "CuPy does not support inputs with " }, { "__type": "InlineCode", "__tag": 4051, "value": "ndim>1" }, { "__type": "Text", "__tag": 4046, "value": " when " }, { "__type": "InlineCode", "__tag": 4051, "value": "method=\"auto\"" }, { "__type": "Text", "__tag": 4046, "value": " but does support higher dimensional arrays for " }, { "__type": "InlineCode", "__tag": 4051, "value": "method=\"direct\"" }, { "__type": "Text", "__tag": 4046, "value": " and " }, { "__type": "InlineCode", "__tag": 4051, "value": "method=\"fft\"" }, { "__type": "Text", "__tag": 4046, "value": "." } ] }, { "__type": "Blockquote", "__tag": 4059, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "See " }, { "__type": "InlineRole", "__tag": 4003, "value": "dev-arrayapi", "domain": null, "role": "ref", "inventory": null }, { "__type": "Text", "__tag": 4046, "value": " for more information." } ] } ] } ], "title": [], "level": 0, "target": null }, "Warns": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Raises": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Yields": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Methods": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Returns": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Parameters", "__tag": 4026, "children": [ { "__type": "DocParam", "__tag": 4016, "name": "correlate", "annotation": "array", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "An N-dimensional array containing a subset of the discrete linear cross-correlation of " }, { "__type": "ParamRef", "__tag": 4071, "name": "in1" }, { "__type": "Text", "__tag": 4046, "value": " with " }, { "__type": "ParamRef", "__tag": 4071, "name": "in2" }, { "__type": "Text", "__tag": 4046, "value": "." } ] } ] } ] } ], "title": [], "level": 0, "target": null }, "Summary": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Cross-correlate two N-dimensional arrays." } ] } ], "title": [], "level": 0, "target": null }, "Receives": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Warnings": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Attributes": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Parameters": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Parameters", "__tag": 4026, "children": [ { "__type": "DocParam", "__tag": 4016, "name": "in1", "annotation": "array_like", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "First input." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "in2", "annotation": "array_like", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Second input. Should have the same number of dimensions as " }, { "__type": "ParamRef", "__tag": 4071, "name": "in1" }, { "__type": "Text", "__tag": 4046, "value": "." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "mode", "annotation": "str {'full', 'valid', 'same'}, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "A string indicating the size of the output:" } ] }, { "__type": "DefList", "__tag": 4033, "children": [ { "__type": "DefListItem", "__tag": 4037, "dt": { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "InlineCode", "__tag": 4051, "value": "full" } ] }, "dd": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The output is the full discrete linear cross-correlation of the inputs. (Default)" } ] } ] }, { "__type": "DefListItem", "__tag": 4037, "dt": { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "InlineCode", "__tag": 4051, "value": "valid" } ] }, "dd": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The output consists only of those elements that do not rely on the zero-padding. In 'valid' mode, either " }, { "__type": "ParamRef", "__tag": 4071, "name": "in1" }, { "__type": "Text", "__tag": 4046, "value": " or " }, { "__type": "ParamRef", "__tag": 4071, "name": "in2" }, { "__type": "Text", "__tag": 4046, "value": " must be at least as large as the other in every dimension." } ] } ] }, { "__type": "DefListItem", "__tag": 4037, "dt": { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "InlineCode", "__tag": 4051, "value": "same" } ] }, "dd": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The output is the same size as " }, { "__type": "ParamRef", "__tag": 4071, "name": "in1" }, { "__type": "Text", "__tag": 4046, "value": ", centered with respect to the 'full' output." } ] } ] } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "method", "annotation": "str {'auto', 'direct', 'fft'}, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "A string indicating which method to use to calculate the correlation." } ] }, { "__type": "DefList", "__tag": 4033, "children": [ { "__type": "DefListItem", "__tag": 4037, "dt": { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "InlineCode", "__tag": 4051, "value": "direct" } ] }, "dd": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The correlation is determined directly from sums, the definition of correlation." } ] } ] }, { "__type": "DefListItem", "__tag": 4037, "dt": { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "InlineCode", "__tag": 4051, "value": "fft" } ] }, "dd": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The Fast Fourier Transform is used to perform the correlation more quickly (only available for numerical arrays.)" } ] } ] }, { "__type": "DefListItem", "__tag": 4037, "dt": { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "InlineCode", "__tag": 4051, "value": "auto" } ] }, "dd": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Automatically chooses direct or Fourier method based on an estimate of which is faster (default). See " }, { "__type": "InlineRole", "__tag": 4003, "value": "convolve", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": " Notes for more detail." } ] }, { "__type": "Admonition", "__tag": 4056, "kind": "versionadded", "base_type": "neutral", "children": [ { "__type": "AdmonitionTitle", "__tag": 4055, "children": [ { "__type": "Text", "__tag": 4046, "value": "versionadded 0.19.0" } ] } ] } ] } ] } ] } ] } ], "title": [], "level": 0, "target": null }, "Extended Summary": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Cross-correlate " }, { "__type": "ParamRef", "__tag": 4071, "name": "in1" }, { "__type": "Text", "__tag": 4046, "value": " and " }, { "__type": "ParamRef", "__tag": 4071, "name": "in2" }, { "__type": "Text", "__tag": 4046, "value": ", with the output size determined by the " }, { "__type": "ParamRef", "__tag": 4071, "name": "mode" }, { "__type": "Text", "__tag": 4046, "value": " argument." } ] } ], "title": [], "level": 0, "target": null }, "Other Parameters": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null } }, "_ordered_sections": [ "Summary", "Extended Summary", "Parameters", "Attributes", "Methods", "Returns", "Yields", "Receives", "Other Parameters", "Raises", "Warns", "Warnings", "Notes" ], "item_file": "/scipy/signal/_signaltools.py", "item_line": 104, "item_type": "function", "aliases": [ "scipy.signal.correlate" ], "example_section_data": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Text", "__tag": 4046, "value": "Implement a matched filter using cross-correlation, to recover a signal\nthat has passed through a noisy channel.\n\n" }, { "__type": "Code", "__tag": 4050, "value": "import numpy as np\nfrom scipy import signal\nimport matplotlib.pyplot as plt\nrng = np.random.default_rng()\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\n" }, { "__type": "Code", "__tag": 4050, "value": "sig = np.repeat([0., 1., 1., 0., 1., 0., 0., 1.], 128)\nsig_noise = sig + rng.standard_normal(len(sig))\ncorr = signal.correlate(sig_noise, np.ones(128), mode='same') / 128\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\n" }, { "__type": "Code", "__tag": 4050, "value": "clock = np.arange(64, len(sig), 128)\nfig, (ax_orig, ax_noise, ax_corr) = plt.subplots(3, 1, sharex=True)\n", "execution_status": "success" }, { "__type": "Code", "__tag": 4050, "value": "ax_orig.plot(sig)\nax_orig.plot(clock, sig[clock], 'ro')\nax_orig.set_title('Original signal')\nax_noise.plot(sig_noise)\nax_noise.set_title('Signal with noise')\nax_corr.plot(corr)\nax_corr.plot(clock, corr[clock], 'ro')\nax_corr.axhline(0.5, ls=':')\nax_corr.set_title('Cross-correlated with rectangular pulse')\n", "execution_status": "failure" }, { "__type": "Code", "__tag": 4050, "value": "ax_orig.margins(0, 0.1)\nfig.tight_layout()\nplt.show()\n", "execution_status": "success" }, { "__type": "Figure", "__tag": 4024, "value": { "__type": "RefInfo", "__tag": 4000, "module": "scipy", "version": "1.17.1", "kind": "assets", "path": "fig-8895786552c1c9ff.png" } }, { "__type": "Text", "__tag": 4046, "value": "\nCompute the cross-correlation of a noisy signal with the original signal.\n\n" }, { "__type": "Code", "__tag": 4050, "value": "x = np.arange(128) / 128\nsig = np.sin(2 * np.pi * x)\nsig_noise = sig + rng.standard_normal(len(sig))\ncorr = signal.correlate(sig_noise, sig)\nlags = signal.correlation_lags(len(sig), len(sig_noise))\ncorr /= np.max(corr)\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\n" }, { "__type": "Code", "__tag": 4050, "value": "fig, (ax_orig, ax_noise, ax_corr) = plt.subplots(3, 1, figsize=(4.8, 4.8))\n", "execution_status": "success" }, { "__type": "Code", "__tag": 4050, "value": "ax_orig.plot(sig)\nax_orig.set_title('Original signal')\nax_orig.set_xlabel('Sample Number')\nax_noise.plot(sig_noise)\nax_noise.set_title('Signal with noise')\nax_noise.set_xlabel('Sample Number')\nax_corr.plot(lags, corr)\nax_corr.set_title('Cross-correlated signal')\nax_corr.set_xlabel('Lag')\n", "execution_status": "failure" }, { "__type": "Code", "__tag": 4050, "value": "ax_orig.margins(0, 0.1)\nax_noise.margins(0, 0.1)\nax_corr.margins(0, 0.1)\nfig.tight_layout()\nplt.show()\n", "execution_status": "success" }, { "__type": "Figure", "__tag": 4024, "value": { "__type": "RefInfo", "__tag": 4000, "module": "scipy", "version": "1.17.1", "kind": "assets", "path": "fig-bf572a16c21b274d.png" } } ], "title": [], "level": 0, "target": null }, "see_also": [ { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "choose_conv_method", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.signal._signaltools:choose_conv_method" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "contains more documentation on " }, { "__type": "InlineRole", "__tag": 4003, "value": "method", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": "." } ] } ], "type": "func" }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "correlation_lags", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.signal._signaltools:correlation_lags" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "calculates the lag / displacement indices array for 1D cross-correlation." } ] } ], "type": "func" } ], "signature": { "__type": "SignatureNode", "__tag": 4029, "kind": "function", "parameters": [ { "__type": "SigParam", "__tag": 4030, "name": "in1", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": { "__type": "Empty", "__tag": 4031 } }, { "__type": "SigParam", "__tag": 4030, "name": "in2", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": { "__type": "Empty", "__tag": 4031 } }, { "__type": "SigParam", "__tag": 4030, "name": "mode", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "full" }, { "__type": "SigParam", "__tag": 4030, "name": "method", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "auto" } ], "return_annotation": { "__type": "Empty", "__tag": 4031 }, "target_name": "correlate" }, "references": null, "qa": "scipy.signal._signaltools:correlate", "arbitrary": [], "local_refs": [ "correlate", "in1", "in2", "method", "mode" ] }