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mat: update documentation for Eigen

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This commit is contained in:
Vladimir Chalupecky
2019-02-13 15:15:31 +01:00
committed by Vladimír Chalupecký
parent 66532af93a
commit c5cc4a2357
1 changed files with 13 additions and 13 deletions
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26
mat/eigen.go
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@@ -127,7 +127,7 @@ func (e *Eigen) succFact() bool {
// A right eigenvalue/eigenvector combination is defined by // A right eigenvalue/eigenvector combination is defined by
// A * x_r = λ * x_r // A * x_r = λ * x_r
// where x_r is the column vector called an eigenvector, and λ is the corresponding // where x_r is the column vector called an eigenvector, and λ is the corresponding
// eigenvector. // eigenvalue.
// //
// Similarly, a left eigenvalue/eigenvector combination is defined by // Similarly, a left eigenvalue/eigenvector combination is defined by
// x_l * A = λ * x_l // x_l * A = λ * x_l
@@ -135,7 +135,7 @@ func (e *Eigen) succFact() bool {
// //
// Typically eigenvectors refer to right eigenvectors. // Typically eigenvectors refer to right eigenvectors.
// //
// In all cases, Eigen computes the eigenvalues of the matrix. If right and left // In all cases, Factorize computes the eigenvalues of the matrix. If right and left
// are true, then the right and left eigenvectors will be computed, respectively. // are true, then the right and left eigenvectors will be computed, respectively.
// Eigen panics if the input matrix is not square. // Eigen panics if the input matrix is not square.
// //
@@ -228,17 +228,17 @@ func (e *Eigen) Values(dst []complex128) []complex128 {
return dst return dst
} }
// complexEigenTo extracts the complex eigenvectors from the Dense matrix r and // complexEigenTo extracts the complex eigenvectors from the real matrix d
// stores them into the complex matrix c. // and stores them into the complex matrix dst.
// //
// The returned dense matrix contains the eigenvectors of the decomposition // The columns of the returned n×n dense matrix contain the eigenvectors of the
// in the columns of the n×n matrix in the same order as their eigenvalues. // decomposition in the same order as the eigenvalues.
// If the j-th eigenvalue is real, then // If the j-th eigenvalue is real, then
// dst_j = d[:,j], // dst[:,j] = d[:,j],
// and if it is not real, then j and j+1 form a complex conjugate pair and the // and if it is not real, then the elements of the j-th and (j+1)-th columns of d
// eigenvectors can be recovered as // form complex conjugate pairs and the eigenvectors are recovered as
// dst_j = d[:,j] + i*d[:,j+1], // dst[:,j] = d[:,j] + i*d[:,j+1],
// dst_{j+1} = d[:,j] - i*d[:,j+1], // dst[:,j+1] = d[:,j] - i*d[:,j+1],
// where i is the imaginary unit. // where i is the imaginary unit.
func (e *Eigen) complexEigenTo(dst *CDense, d *Dense) { func (e *Eigen) complexEigenTo(dst *CDense, d *Dense) {
r, c := d.Dims() r, c := d.Dims()
@@ -266,7 +266,7 @@ func (e *Eigen) complexEigenTo(dst *CDense, d *Dense) {
} }
} }
// Vectors returns the right eigenvectors of the decomposition. Vectors // VectorsTo returns the right eigenvectors of the decomposition. VectorsTo
// will panic if the right eigenvectors were not computed during the factorization, // will panic if the right eigenvectors were not computed during the factorization,
// or if the factorization was not successful. // or if the factorization was not successful.
// //
@@ -288,7 +288,7 @@ func (e *Eigen) VectorsTo(dst *CDense) *CDense {
return dst return dst
} }
// LeftVectors returns the left eigenvectors of the decomposition. Vectors // LeftVectorsTo returns the left eigenvectors of the decomposition. LeftVectorsTo
// will panic if the left eigenvectors were not computed during the factorization, // will panic if the left eigenvectors were not computed during the factorization,
// or if the factorization was not successful. // or if the factorization was not successful.
// //