4.6 KiB
EigenTridiagonalBisect
Compute eigenvalues and eigenvectors of a symmetric tridiagonal matrix using the bisection algorithm (LAPACK function STEVX).
Computing for type matrix
bool matrix::EigenTridiagonalBisect(
ENUM_EIG_VALUES jobv, // compute eigenvectors or not
ENUM_BLAS_RANGE range, // subset of eigenvalues to compute
double lower, // lower bound of the subset
double upper, // Upper bound of the subset
double abstol, // absolute error tolerance
vector& eigen_values, // vector of computed eigenvectors
matrix& eigen_vectors // matrix of computed eigenvectors
);
Computing for type matrix
bool matrixf::EigenTridiagonalBisect(
ENUM_EIG_VALUES jobv, // compute eigenvectors or not
ENUM_BLAS_RANGE range, // subset of eigenvalues to compute
float lower, // lower bound of the subset
float upper, // upper bound of the subset
float abstol, // absolute error tolerance
vectorf& eigen_values, // vector of computed eigenvectors
matrixf& eigen_vectors // matrix of computed eigenvectors
);
Parameters
jobv
[in] ENUM_EIG_VALUES enumeration value which determines the method for computing eigenvectors.
range
[in] ENUM_BLAS_RANGE enumeration value that defines a subset of computable eigenvalues and vectors.
lower
[in] The lower bound of eigenvalues subset; it is specified depending on the value of the 'range' parameter.
upper
[in] The upper bound of eigenvalues subset; it is specified depending on the value of the 'range' parameter.
abstol
[in] Absolute error tolerance.
The absolute error tolerance to which each eigenvalue/eigenvector is required.
If jobv = 'V', the eigenvalues and eigenvectors output have residual norms bounded by abstol, and the dot products between different eigenvectors are bounded by abstol.
If abstol < n eps|T|, then n eps|T| is used instead, where eps is the machine precision, and |T| is the 1-norm of the matrix T. The eigenvalues are computed to an accuracy of eps*|T| irrespective of abstol.
If high relative precision is important, 'abstol' should be set to a safe minimum value X such that 1.0/X does not overflow.
eigen_values
[out] Vector of eigenvalues.
V
[out] Matrix of eigenvectors.
Return Value
Return true if successful, otherwise false in case of an error.
Note
Computation depends on the values of the jobv and range parameters.
When BLASRANGE_A is set, all eigenvalues are computed, and the lower and upper parameters are ignored.
With the BLASRANGE_V value, only those eigenvalues (and their vectors) are computed, which fall within the range of real values specified by the 'lower' and 'upper' parameters.
With the BLASRANGE_I value, only those eigenvalues (and their vectors) are computed, which fall within the range of integer indices specified by the 'lower' and 'upper' parameters. For example, with lower=0 and upper=2, only the first three eigenvalues are computed.
The input must be a symmetric matrix in the tridiagonal form.
ENUM_EIG_VALUES
An enumeration defining the need to compute eigenvectors.
| ID | Description |
|---|---|
| EIGVALUES_V | Eigenvectors and eigenvalues are calculated. |
| EIGVALUES_N | Only eigenvalues are computed, without vectors. |
ENUM_BLAS_RANGE
An enumeration defining how right singular vectors should be computed.
| ID | Description |
|---|---|
| BLASRANGE_A | All singular or eigenvalues will be found. |
| BLASRANGE_V | All singular or eigenvalues in the half-open interval (VL,VU] will be found. |
| BLASRANGE_I | The IL-th through IU-th singular or eigenvalues will be found. |