{ "__type": "IngestedDoc", "__tag": 4010, "_content": { "Notes": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "If a matrix is not modified, the original matrix (not a copy) is returned." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The " }, { "__type": "InlineRole", "__tag": 4003, "value": "tutorial_signal_state_space_representation", "domain": null, "role": "ref", "inventory": null }, { "__type": "Text", "__tag": 4046, "value": " section of the " }, { "__type": "CrossRef", "__tag": 4002, "value": "user_guide", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "docs", "path": "tutorial:index" }, "kind": "exists" }, { "__type": "Text", "__tag": 4046, "value": " presents the corresponding definitions of continuous-time and disrcete time state space systems." } ] }, { "__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": "abcd_normalize", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.signal._lti_conversion:abcd_normalize" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " has experimental support for Python Array API Standard compatible backends in addition to NumPy. 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The result dtype is determined based on the standard " }, { "__type": "Link", "__tag": 4049, "children": [ { "__type": "Text", "__tag": 4046, "value": "dtype promotion rules" } ], "url": "https://numpy.org/doc/2.3/reference/arrays.promotion.html", "title": "" }, { "__type": "Text", "__tag": 4046, "value": " except for when the inputs are all of integer dtype, in which case the returned arrays will have the default floating point dtype of " }, { "__type": "InlineCode", "__tag": 4051, "value": "float64" }, { "__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": "Check state-space matrices compatibility and ensure they are 2d 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": "A", "annotation": "array_like, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Two-dimensional array of shape (n, n)." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "B", "annotation": "array_like, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Two-dimensional array of shape (n, p)." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "C", "annotation": "array_like, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Two-dimensional array of shape (q, n)." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "D", "annotation": "array_like, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Two-dimensional array of shape (q, p)." } ] } ] } ] } ], "title": [], "level": 0, "target": null }, "Extended Summary": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "First, the input matrices are converted into two-dimensional arrays with appropriate dtype as needed. Then the dimensions n, q, p are determined by investigating the array shapes. If an input is " }, { "__type": "InlineCode", "__tag": 4051, "value": "None" }, { "__type": "Text", "__tag": 4046, "value": ", or has size zero, it is set to an array of zeros of compatible shape. Finally, it is verified that all parameter shapes are compatible with each other. If that fails, a " }, { "__type": "InlineCode", "__tag": 4051, "value": "ValueError" }, { "__type": "Text", "__tag": 4046, "value": " is raised. Note that the dimensions n, q, p are allowed to be zero." } ] } ], "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/_lti_conversion.py", "item_line": 118, "item_type": "function", "aliases": [ "scipy.signal.abcd_normalize" ], "example_section_data": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Text", "__tag": 4046, "value": "The following example demonstrates that the passed lists are converted into\ntwo-dimensional arrays:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "from scipy.signal import abcd_normalize\nAA, BB, CC, DD = abcd_normalize(A=[[1, 2], [3, 4]], B=[[-1], [5]],\n C=[[4, 5]], D=2.5)\nAA.shape, BB.shape, CC.shape, DD.shape\n", "execution_status": "success", "out": "((2, 2), (2, 1), (1, 2), (1, 1))\n" }, { "__type": "Text", "__tag": 4046, "value": "\nIn the following, the missing parameter C is assumed to be an array of zeros\nwith shape (1, 2):\n\n" }, { "__type": "Code", "__tag": 4050, "value": "from scipy.signal import abcd_normalize\nAA, BB, CC, DD = abcd_normalize(A=[[1, 2], [3, 4]], B=[[-1], [5]], D=2.5)\nAA.shape, BB.shape, CC.shape, DD.shape\nCC\n", "execution_status": "success", "out": "array([[0., 0.]])\n" } ], "title": [], "level": 0, "target": null }, "see_also": [ { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "StateSpace", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.signal._ltisys:StateSpace" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Linear Time Invariant system in state-space form." } ] } ], "type": "func" }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "cont2discrete", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.signal._lti_conversion:cont2discrete" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Transform a continuous to a discrete state-space system." } ] } ], "type": "func" }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "dlti", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.signal._ltisys:dlti" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Discrete-time linear time invariant system base class." } ] } ], "type": "func" }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "ss2tf", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.signal._lti_conversion:ss2tf" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "State-space to transfer function." } ] } ], "type": "func" }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "ss2zpk", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.signal._lti_conversion:ss2zpk" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "State-space representation to zero-pole-gain representation." } ] } ], "type": "func" }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "tf2ss", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": 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