{ "__type": "IngestedDoc", "__tag": 4010, "_content": { "Notes": { "__type": "Section", "__tag": 4015, "children": [ { "__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": "InlineRole", "__tag": 4003, "value": "user_guide", "domain": null, "role": "ref", "inventory": null }, { "__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. 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 ✅ n/a \n==================== ==================== ====================", "execution_status": null }, { "__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": [ { "__type": "Parameters", "__tag": 4026, "children": [ { "__type": "DocParam", "__tag": 4016, "name": "", "annotation": "ValueError", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "If the dimensions n, q, or p could not be determined or if the shapes are incompatible with each other." } ] } ] } ] } ], "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": "A, B, C, D", "annotation": "array", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "State-space matrices as two-dimensional arrays." } ] } ] } ] } ], "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: array_like, optional", "annotation": "", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Two-dimensional array of shape (n, n)." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "B: array_like, optional", "annotation": "", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Two-dimensional array of shape (n, p)." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "C: array_like, optional", "annotation": "", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Two-dimensional array of shape (q, n)." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "D: array_like, optional", "annotation": "", "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": "Converts input matrices into two-dimensional arrays as needed. Then the dimensions n, q, p are determined by investigating the non-zero entries of the array shapes. If a parameter is " }, { "__type": "InlineCode", "__tag": 4051, "value": "None" }, { "__type": "Text", "__tag": 4046, "value": ", or has shape (0, 0), it is set to a zero-array of compatible shape. Finally, it is verified that all parameter shapes are compatible to 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": 117, "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" }, { "__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" } ], "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": "scipy.signal._lti_conversion:tf2ss" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Transfer function to state-space representation." } ] } ], "type": "func" } ], "signature": { "__type": "SignatureNode", "__tag": 4029, "kind": "function", "parameters": [ { "__type": "SigParam", "__tag": 4030, "name": "A", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "B", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "C", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "D", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "None" } ], "return_annotation": { "__type": "Empty", "__tag": 4031 }, "target_name": "abcd_normalize" }, "references": null, "qa": "scipy.signal._lti_conversion:abcd_normalize", "arbitrary": [], "local_refs": [ "A", "A: array_like", "B", "B: array_like", "C", "C: array_like", "D", "D: array_like", "optional" ] }