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  "Title": "Certified Partial Eigenvalue and Singular Value Computation",
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  "Description": "Computes the top-k singular triplets or eigenpairs of\nlarge sparse and structured matrices: the computation behind\nprincipal component analysis on big sparse data, spectral\nembeddings, and low-rank approximation. Every result carries a\nnumerical certificate with residuals, a backward-error bound,\northogonality loss, and a pass/fail flag, and bounds that can\nonly be estimated are reported as such rather than passed.\nCentered, scaled, and composed operators are solved through\nnative 'C++' kernels without forming dense matrices. Drop-in\nreplacements for the 'RSpectra' interface are included.",
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    "hermitian",
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    "largest_imaginary",
    "largest_magnitude",
    "largest_real",
    "left_vectors",
    "linear_operator",
    "lobpcg",
    "nearest",
    "plan_solver",
    "randomized",
    "right_vectors",
    "scale_cols",
    "scale_rows",
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    "shifted_cholesky_preconditioner",
    "shifted_diagonal_preconditioner",
    "shifted_tridiagonal_preconditioner",
    "smallest",
    "smallest_imaginary",
    "smallest_magnitude",
    "smallest_real",
    "svd_partial",
    "svd_problem",
    "svds",
    "symmetric_operator",
    "values",
    "vectors"
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      "page": "adjoint",
      "title": "Return the adjoint operator.",
      "topics": [
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      "page": "alpha_beta",
      "title": "Extract homogeneous generalized coordinates.",
      "topics": [
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      ]
    },
    {
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      "title": "Convert an object to an eigencore operator.",
      "topics": [
        "as_operator"
      ]
    },
    {
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      "title": "Automatic solver choice.",
      "topics": [
        "auto"
      ]
    },
    {
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      "title": "Extract backward-error diagnostics.",
      "topics": [
        "backward_error"
      ]
    },
    {
      "page": "both_ends",
      "title": "Target both algebraic ends.",
      "topics": [
        "both_ends"
      ]
    },
    {
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      "title": "Center an operator by rows or columns.",
      "topics": [
        "center"
      ]
    },
    {
      "page": "certificate",
      "title": "Extract a result certificate.",
      "topics": [
        "certificate"
      ]
    },
    {
      "page": "check_adjoint",
      "title": "Check an operator adjoint identity.",
      "topics": [
        "check_adjoint"
      ]
    },
    {
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      "title": "Compose two operators.",
      "topics": [
        "compose"
      ]
    },
    {
      "page": "crossprod_operator",
      "title": "Create A^* A as an operator.",
      "topics": [
        "crossprod_operator"
      ]
    },
    {
      "page": "diagnostics",
      "title": "Extract diagnostics.",
      "topics": [
        "diagnostics"
      ]
    },
    {
      "page": "eig_full",
      "title": "Compute a full dense eigendecomposition",
      "topics": [
        "eig_full"
      ]
    },
    {
      "page": "eig_partial",
      "title": "Compute a partial eigendecomposition.",
      "topics": [
        "eig_partial"
      ]
    },
    {
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      "title": "Define an eigenproblem.",
      "topics": [
        "eigen_problem"
      ]
    },
    {
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      "title": "RSpectra-compatible eigen shim.",
      "topics": [
        "eigs"
      ]
    },
    {
      "page": "eigs_sym",
      "title": "RSpectra-compatible symmetric eigen shim.",
      "topics": [
        "eigs_sym"
      ]
    },
    {
      "page": "euclidean",
      "title": "Euclidean vector space descriptor.",
      "topics": [
        "euclidean"
      ]
    },
    {
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      "title": "General operator structure descriptor.",
      "topics": [
        "general"
      ]
    },
    {
      "page": "generalized_schur",
      "title": "Compute a dense generalized Schur decomposition",
      "topics": [
        "generalized_schur"
      ]
    },
    {
      "page": "generalized_svd",
      "title": "Compute a dense generalized singular value decomposition",
      "topics": [
        "generalized_svd"
      ]
    },
    {
      "page": "golub_kahan",
      "title": "Golub-Kahan bidiagonalization method descriptor.",
      "topics": [
        "golub_kahan"
      ]
    },
    {
      "page": "hermitian",
      "title": "Hermitian/symmetric operator structure descriptor.",
      "topics": [
        "hermitian"
      ]
    },
    {
      "page": "lanczos",
      "title": "Hermitian Lanczos method descriptor.",
      "topics": [
        "lanczos"
      ]
    },
    {
      "page": "largest",
      "title": "Target the largest algebraic values.",
      "topics": [
        "largest"
      ]
    },
    {
      "page": "largest_imaginary",
      "title": "Target the largest imaginary part.",
      "topics": [
        "largest_imaginary"
      ]
    },
    {
      "page": "largest_magnitude",
      "title": "Target the largest values by magnitude.",
      "topics": [
        "largest_magnitude"
      ]
    },
    {
      "page": "largest_real",
      "title": "Target the largest real part.",
      "topics": [
        "largest_real"
      ]
    },
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      "title": "Extract left singular vectors or left eigenvectors.",
      "topics": [
        "left_vectors"
      ]
    },
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      "title": "Create a block-native linear operator.",
      "topics": [
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    },
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      "title": "LOBPCG method descriptor.",
      "topics": [
        "lobpcg"
      ]
    },
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      "topics": [
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      ]
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      "topics": [
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      "topics": [
        "randomized"
      ]
    },
    {
      "page": "residuals",
      "title": "Extract residual diagnostics.",
      "topics": [
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        "residuals.eigencore_certificate",
        "residuals.eigencore_eigen_result",
        "residuals.eigencore_svd_result"
      ]
    },
    {
      "page": "right_vectors",
      "title": "Extract right singular vectors.",
      "topics": [
        "right_vectors"
      ]
    },
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      "page": "scale_cols",
      "title": "Scale operator columns.",
      "topics": [
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      ]
    },
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      "topics": [
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      "topics": [
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      "page": "smallest",
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      "topics": [
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    {
      "page": "smallest_imaginary",
      "title": "Target the smallest imaginary part.",
      "topics": [
        "smallest_imaginary"
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    },
    {
      "page": "smallest_magnitude",
      "title": "Target the smallest values by magnitude.",
      "topics": [
        "smallest_magnitude"
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    },
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      "page": "smallest_real",
      "title": "Target the smallest real part.",
      "topics": [
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    },
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      "page": "svd_partial",
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      "topics": [
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