Struct MatsubaraSamplingPositiveOnly 

pub struct MatsubaraSamplingPositiveOnly<S: StatisticsType> { /* private fields */ }

Matsubara sampling for positive frequencies only

Exploits the symmetry G(-iωn) = conj(G(iωn)) of physical Green’s functions to fit real coefficients from values at non-negative frequencies. Supports: {0, 1, 2, 3, …} (no negative frequencies)

Implementations

impl<S: StatisticsType> MatsubaraSamplingPositiveOnly<S>

pub fn new(basis: &impl Basis<S>) -> Result<Self>

where S: 'static,

Create Matsubara sampling with default positive-only sampling points

Uses the default sampling points of the basis (non-negative frequencies only). Exploits symmetry to reconstruct real coefficients.

Errors

The errors of Basis::default_matsubara_sampling_points (NotSupported for a DLR or for basis functions without a definite parity, #183)

pub fn with_sampling_points( basis: &impl Basis<S>, sampling_points: Vec<MatsubaraFreq<S>>, ) -> Result<Self>

where S: 'static,

Create Matsubara sampling with custom positive-only sampling points

The points may be in any order, and are kept in the given order: Self::sampling_points returns them unchanged, and index i along the sampling-point axis of evaluate and fit refers to sampling_points[i].

Duplicate points are accepted; they only raise the condition number.

Errors

• Error::EmptyInput if sampling_points is empty
• Error::InvalidMatsubaraIndex if a point is negative
• The errors of Basis::evaluate_matsubara

pub fn from_matrix( sampling_points: Vec<MatsubaraFreq<S>>, matrix: &Matrix<Complex<f64>>, ) -> Result<Self>

Create Matsubara sampling (positive-only) with custom sampling points and pre-computed matrix

This constructor is useful when the sampling matrix is already computed. Uses symmetry to fit real coefficients from complex values at non-negative frequencies.

Arguments

• sampling_points - Matsubara frequency sampling points (must be non-negative), in any order
• matrix - Pre-computed sampling matrix (n_points × basis_size); row i belongs to sampling_points[i]

The points are kept in the given order: Self::sampling_points returns them unchanged, and index i along the sampling-point axis of evaluate and fit refers to sampling_points[i].

Duplicate points are accepted; they only raise the condition number.

Errors

• Error::EmptyInput if sampling_points is empty, or matrix has no columns
• Error::ShapeMismatch of the input if matrix does not have one row per point
• Error::InvalidMatsubaraIndex for the first negative point
• Error::NonFiniteInput for the first entry of matrix with a NaN or infinite part

pub fn sampling_points(&self) -> &[MatsubaraFreq<S>]

Get sampling points

pub fn n_sampling_points(&self) -> usize

Number of sampling points

pub fn basis_size(&self) -> usize

Basis size

pub fn matrix(&self) -> &Matrix<Complex<f64>>

Get the original complex sampling matrix

pub fn condition_number(&self) -> Result<f64>

Condition number of the real least-squares problem that fitting solves

Fitting real coefficients x to complex values g at non-negative frequencies solves [Re A; Im A] x = [Re g; Im g], where A is the complex n_sampling_points × basis_size matrix Self::matrix. This returns σ_max / σ_min, the ratio of the largest to the smallest of the min(2 n_sampling_points, basis_size) singular values of that real 2 n_sampling_points × basis_size matrix; it bounds how much Self::fit can amplify relative errors in the values. It is not the condition number of A: with n_sampling_points ≈ basis_size / 2, A is wide, and its condition number can understate that amplification by orders of magnitude.

Returns f64::INFINITY if the smallest singular value is below 1e-15 (numerically singular matrix). The singular value decomposition is the one fitting uses: it is computed by the first call to this method or to a fit, then cached.

Errors

Error::DecompositionFailed if the singular value decomposition fails, which a matrix of finite entries does not cause in practice (the constructors reject non-finite entries)

pub fn evaluate(&self, coeffs: &[f64]) -> Result<Vec<Complex<f64>>>

Evaluate basis coefficients at sampling points

Errors

• Error::ShapeMismatch of the input if coeffs does not have length basis_size

pub fn fit(&self, values: &[Complex<f64>]) -> Result<Vec<f64>>

Fit basis coefficients from values at sampling points

Errors

• Error::ShapeMismatch of the input if values does not have length n_sampling_points
• Error::DecompositionFailed if the singular value decomposition fails

pub fn evaluate_nd( &self, backend: Option<&GemmBackendHandle>, coeffs: &TypedTensor<f64>, dim: usize, ) -> Result<TypedTensor<Complex<f64>>>

Evaluate N-dimensional array of real basis coefficients at sampling points

Arguments

• coeffs - N-dimensional tensor of real basis coefficients
• dim - Dimension along which to evaluate (must have size = basis_size)

Returns

N-dimensional tensor of complex values at Matsubara frequencies

Errors

• Error::AxisOutOfRange if dim is not an axis of coeffs
• Error::ShapeMismatch of the input if coeffs does not have basis_size along dim

pub fn fit_nd( &self, backend: Option<&GemmBackendHandle>, values: &TypedTensor<Complex<f64>>, dim: usize, ) -> Result<TypedTensor<f64>>

Fit N-dimensional array of complex values to real basis coefficients

Arguments

• backend - Optional GEMM backend handle (None uses default)
• values - N-dimensional tensor of complex values at Matsubara frequencies
• dim - Dimension along which to fit (must have size = n_sampling_points)

Returns

N-dimensional tensor of real basis coefficients

Errors

• Error::AxisOutOfRange if dim is not an axis of values
• Error::ShapeMismatch of the input if values does not have n_sampling_points along dim
• Error::DecompositionFailed if the singular value decomposition fails

pub fn evaluate_nd_to( &self, backend: Option<&GemmBackendHandle>, coeffs: &TypedTensorView<'_, f64>, dim: usize, out: &mut TypedTensorViewMut<'_, Complex<f64>>, ) -> Result<()>

Evaluate real basis coefficients at Matsubara sampling points (N-dimensional) with in-place output

Arguments

• coeffs - N-dimensional tensor of real coefficients with coeffs.shape().dim(dim) == basis_size
• dim - Dimension along which to evaluate (0-indexed)
• out - Output tensor with out.shape().dim(dim) == n_sampling_points (Complex)

Errors

• Error::AxisOutOfRange if dim is not an axis of coeffs
• Error::ShapeMismatch of the input if coeffs does not have basis_size along dim, and of the output if out does not have the shape of coeffs with n_sampling_points along dim

Nothing is written to out then.

pub fn fit_nd_to( &self, backend: Option<&GemmBackendHandle>, values: &TypedTensorView<'_, Complex<f64>>, dim: usize, out: &mut TypedTensorViewMut<'_, f64>, ) -> Result<()>

Fit N-dimensional complex values to real coefficients with in-place output

Arguments

• values - N-dimensional tensor with values.shape().dim(dim) == n_sampling_points
• dim - Dimension along which to fit (0-indexed)
• out - Output tensor with out.shape().dim(dim) == basis_size (f64)

Errors

• Error::AxisOutOfRange if dim is not an axis of values
• Error::ShapeMismatch of the input if values does not have n_sampling_points along dim, and of the output if out does not have the shape of values with basis_size along dim
• Error::DecompositionFailed if the singular value decomposition fails

Nothing is written to out then.

Trait Implementations

impl<S: StatisticsType> InplaceFitter for MatsubaraSamplingPositiveOnly<S>

fn n_points(&self) -> usize

Number of sampling points.

fn basis_size(&self) -> usize

Number of basis functions.

fn evaluate_nd_dz_to( &self, backend: Option<&GemmBackendHandle>, coeffs: &TypedTensorView<'_, f64>, dim: usize, out: &mut TypedTensorViewMut<'_, Complex<f64>>, ) -> Result<()>

Evaluate: f64 coefficients to Complex<f64> values.

fn evaluate_nd_zz_to( &self, backend: Option<&GemmBackendHandle>, coeffs: &TypedTensorView<'_, Complex<f64>>, dim: usize, out: &mut TypedTensorViewMut<'_, Complex<f64>>, ) -> Result<()>

Evaluate: Complex<f64> coefficients to Complex<f64> values.

fn fit_nd_zd_to( &self, backend: Option<&GemmBackendHandle>, values: &TypedTensorView<'_, Complex<f64>>, dim: usize, out: &mut TypedTensorViewMut<'_, f64>, ) -> Result<()>

Fit: Complex<f64> values to f64 coefficients.

fn fit_nd_zz_to( &self, backend: Option<&GemmBackendHandle>, values: &TypedTensorView<'_, Complex<f64>>, dim: usize, out: &mut TypedTensorViewMut<'_, Complex<f64>>, ) -> Result<()>

Fit: Complex<f64> values to Complex<f64> coefficients.

fn evaluate_nd_dd_to( &self, backend: Option<&GemmBackendHandle>, coeffs: &TypedTensorView<'_, f64>, dim: usize, out: &mut TypedTensorViewMut<'_, f64>, ) -> Result<()>

Evaluate: f64 coefficients to f64 values.

fn evaluate_nd_zd_to( &self, backend: Option<&GemmBackendHandle>, coeffs: &TypedTensorView<'_, Complex<f64>>, dim: usize, out: &mut TypedTensorViewMut<'_, f64>, ) -> Result<()>

Evaluate: Complex<f64> coefficients to f64 values.

fn fit_nd_dd_to( &self, backend: Option<&GemmBackendHandle>, values: &TypedTensorView<'_, f64>, dim: usize, out: &mut TypedTensorViewMut<'_, f64>, ) -> Result<()>

Fit: f64 values to f64 coefficients.

fn fit_nd_dz_to( &self, backend: Option<&GemmBackendHandle>, values: &TypedTensorView<'_, f64>, dim: usize, out: &mut TypedTensorViewMut<'_, Complex<f64>>, ) -> Result<()>

Fit: f64 values to Complex<f64> coefficients.