{ "__type": "IngestedDoc", "__tag": 4010, "_content": { "Notes": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The optional arguments defining the sequence of evenly spaced time points are compatible with the arguments of " }, { "__type": "CrossRef", "__tag": 4002, "value": "numpy.linspace", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "numpy", "version": "?", "kind": "module", "path": "numpy:linspace" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": "." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The output ndarray shape is somewhat complicated so I explain it here. The ndim of the output could be either 1, 2, or 3. It would be 1 if you are computing the expm action on a single vector at a single time point. It would be 2 if you are computing the expm action on a vector at multiple time points, or if you are computing the expm action on a matrix at a single time point. It would be 3 if you want the action on a matrix with multiple columns at multiple time points. If multiple time points are requested, expm_A_B[0] will always be the action of the expm at the first time point, regardless of whether the action is on a vector or a matrix." } ] } ], "title": [], "level": 0, "target": null }, "Warns": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Parameters", "__tag": 4026, "children": [ { "__type": "DocParam", "__tag": 4016, "name": "", "annotation": "UserWarning", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "If " }, { "__type": "ParamRef", "__tag": 4071, "name": "A" }, { "__type": "Text", "__tag": 4046, "value": " is a linear operator and " }, { "__type": "InlineCode", "__tag": 4051, "value": "traceA=None" }, { "__type": "Text", "__tag": 4046, "value": " (default)." } ] } ] } ] } ], "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": "expm_A_B", "annotation": "ndarray", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The result of the action " }, { "__type": "InlineMath", "__tag": 4057, "value": "e^{t_k A} B" }, { "__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": "Compute the action of the matrix exponential of A on B." } ] } ], "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": "transposable linear operator", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The operator whose exponential is of interest." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "B", "annotation": "ndarray, sparse array", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The matrix or vector to be multiplied by the matrix exponential of A." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "start", "annotation": "scalar, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The starting time point of the sequence." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "stop", "annotation": "scalar, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The end time point of the sequence, unless " }, { "__type": "ParamRef", "__tag": 4071, "name": "endpoint" }, { "__type": "Text", "__tag": 4046, "value": " is set to False. 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[1] Awad H. Al-Mohy and Nicholas J. Higham (2011)", " \"Computing the Action of the Matrix Exponential,", " with an Application to Exponential Integrators.\"", " SIAM Journal on Scientific Computing,", " 33 (2). pp. 488-511. ISSN 1064-8275", " http://eprints.ma.man.ac.uk/1591/", "", ".. [2] Nicholas J. Higham and Awad H. Al-Mohy (2010)", " \"Computing Matrix Functions.\"", " Acta Numerica,", " 19. 159-208. ISSN 0962-4929", " http://eprints.ma.man.ac.uk/1451/" ], "qa": "scipy.sparse.linalg._expm_multiply:expm_multiply", "arbitrary": [], "local_refs": [ "A", "B", "endpoint", "expm_A_B", "num", "start", "stop", "traceA" ] }