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In this case, " }, { "__type": "InlineCode", "__tag": 4051, "value": "eigsh()" }, { "__type": "Text", "__tag": 4046, "value": " will call " }, { "__type": "InlineCode", "__tag": 4051, "value": "eigs()" }, { "__type": "Text", "__tag": 4046, "value": " and return the real parts of the eigenvalues thus obtained." } ] } ], "title": [], "level": 0, "target": null }, "Other Parameters": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Parameters", "__tag": 4026, "children": [ { "__type": "DocParam", "__tag": 4016, "name": "M", "annotation": "An N x N matrix, array, sparse matrix, or linear operator representing", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "the operation " }, { "__type": "InlineCode", "__tag": 4051, "value": "M @ x" }, { "__type": "Text", "__tag": 4046, "value": " for the generalized eigenvalue problem" } ] }, { "__type": "Blockquote", "__tag": 4059, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "A @ x = w * M @ x." } ] } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "M must represent a real symmetric matrix if A is real, and must represent a complex Hermitian matrix if A is complex. 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This is done internally via a (sparse) LU decomposition for an explicit matrix M, or via an iterative solver for a general linear operator. Alternatively, the user can supply the matrix or operator Minv, which gives " }, { "__type": "InlineCode", "__tag": 4051, "value": "x = Minv @ b = M^-1 @ b" }, { "__type": "Text", "__tag": 4046, "value": "." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "sigma", "annotation": "real", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Find eigenvalues near sigma using shift-invert mode. This requires an operator to compute the solution of the linear system " }, { "__type": "InlineCode", "__tag": 4051, "value": "[A - sigma * M] x = b" }, { "__type": "Text", "__tag": 4046, "value": ", where M is the identity matrix if unspecified. 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