ts-scikit/lib/dsp/eigen-tensors3.d.ts

A scientific toolkit written in Typescript

import { Tensors3 } from './tensors3';
/**
 * An array of eigen-decomposition of tensors for 3D image processing.
 * Each tensor is a symmetric positive semi-definite 3x3 matrix.
 * <pre>
 *       | a11 a12 a13 |
 *   A = | a12 a22 a23 |
 *       | a13 a23 a33 |
 * </pre>
 * Such tensors can be used to parametrize anisotropic image processing.
 * <p>
 * The eigen-decomposition of the matrix A is
 * <pre>
 *   A = au * u * u' + av * v * v' + aw * w * w'
 *     = (au - av) * u * u' + (aw - av) * w * w' + av * I
 * </pre>
 * where, u, v, and w are orthogonal unit eigenvectors of A. (The notation
 * u' denotes the transpose of u.) The outer products of eigenvectors are
 * scaled by the non-negative eigenvalues au, av and aw. The second
 * equation exploits the identity u * u' + v * v' + w * w' = I, and makes
 * apparent the redundancy of the vector v.
 * <p>
 * Only the 1st and 2nd components of the eigenvectors u and w are stored.
 * Except for a sign, the 3rd components may be computed from the 1st and
 * 2nd. Because the tensors are independent of the choice of the sign, the
 * eigenvectors u and w are stored with an implied non-negative 3rd
 * component.
 * <p>
 * Storage may be further reduced by compression, whereby eigenvalues and
 * eigenvectors are quantized.
 */
export declare class EigenTensors3 implements Tensors3 {
    private static readonly AS_SET;
    private static readonly AS_GET;
    private _uss;
    private readonly _n1;
    private readonly _n2;
    private readonly _n3;
    private _as;
    private _au;
    private _aw;
    private _u1;
    private _u2;
    private _w1;
    private _w2;
    private static c3;
    /**
     * Constructs tensors for specified array dimensions.
     * <p>
     * All eigenvalues and eigenvectors u and w are not set and are initially
     * zero.
     * @param n1 number of tensors in 1st dimension.
     * @param n2 number of tensors in 2nd dimension.
     * @param n3 number of tensors in 3rd dimension.
     */
    constructor(n1: number, n2: number, n3: number);
    /**
     * Gets tensor elements for specified indices.
     * <p>
     * Note: If passing in an array, its values are edited in-place and
     * nothing is returned.
     * @param i1 index for 1st dimension.
     * @param i2 index for 2nd dimension.
     * @param i3 index for 3rd dimension.
     * @param a the array { a11, a12, a13, a22, a23, a33 } of tensor elements.
     * @returns the array { a11, a12, a13, a22, a23, a33 } of tensor elements.
     */
    getTensor(i1: number, i2: number, i3: number, a?: number[]): void | number[];
    /**
     * Sets the eigenvalues for the tensor with specified indices.
     * @param i1 index for the 1st dimension.
     * @param i2 index for the 2nd dimension.
     * @param i3 index for the 3rd dimension.
     * @param au eigenvalue au.
     * @param av eigenvalue av.
     * @param aw eigenvalue aw.
     */
    setEigenvalues(i1: number, i2: number, i3: number, au: number, av: number, aw: number): void;
    /**
     * Gets eigenvalues for the tensor with specified indices.
     * <p>
     * Note: If passing in an array, its values are edited in-place and
     * nothing is returned.
     * @param i1 index for 1st dimension.
     * @param i2 index for 2nd dimension.
     * @param i3 index for 3rd dimension.
     * @param a the array { au, av, aw } of eigenvalues.
     * @returns the array { au, av, aw } of eigenvalues.
     */
    getEigenvalues(i1: number, i2: number, i3: number, a?: number[]): void | number[];
    /**
     * Gets eigenvalues for all tensors.
     * @param au array of eigenvalues au.
     * @param av array of eigenvalues av.
     * @param aw array of eigenvalues aw.
     */
    getAllEigenvalues(au: number[][][], av: number[][][], aw: number[][][]): void;
    /**
     * Sets the eigenvector u for the tensor with specified indices.
     * <p>
     * The specified vector is assumed to have length one. If the 3rd
     * component is negative, this method stores the negative of the
     * specified vector, so that the 3rd component is positive.
     * @param i1 index for 1st dimension.
     * @param i2 index for 2nd dimension.
     * @param i3 index for 3rd dimension.
     * @param u1 1st component of u.
     * @param u2 2nd component of u.
     * @param u3 3rd component of u.
     */
    setEigenvectorU(i1: number, i2: number, i3: number, u1: number, u2: number, u3: number): void;
    /**
     * Gets the eigenvector u for the tensor with specified indices.
     * <p>
     * Note: If passing in an array, its values are edited in-place and
     * nothing is returned.
     * @param i1 index for 1st dimension.
     * @param i2 index for 2nd dimension.
     * @param i3 index for 3rd dimension.
     * @param u array { u1, u2, u3 } of eigenvector components.
     */
    getEigenvectorU(i1: number, i2: number, i3: number, u?: number[]): void | number[];
    /**
     * Sets the eigenvector w for the tensor with specified indices.
     * <p>
     * The specified vector is assumed to have length one. If the 3rd
     * component is negative, this method stores the negative of the
     * specified vector, so that the 3rd component is positive.
     * @param i1 index for 1st dimension.
     * @param i2 index for 2nd dimension.
     * @param i3 index for 3rd dimension.
     * @param w1 1st component of w.
     * @param w2 2nd component of w.
     * @param w3 3rd component of w.
     */
    setEigenvectorW(i1: number, i2: number, i3: number, w1: number, w2: number, w3: number): void;
    /**
     * Gets the eigenvector w for the tensor with specified indices.
     * <p>
     * Note: If passing in an array, its values are edited in-place and
     * nothing is returned.
     * @param i1 index for 1st dimension.
     * @param i2 index for 2nd dimension.
     * @param i3 index for 3rd dimension.
     * @param w array { w1, w2, w3 } of eigenvector components.
     */
    getEigenvectorW(i1: number, i2: number, i3: number, w?: number[]): void | number[];
    /**
     * Gets the eigenvector v for the tensor with specified indices.
     * <p>
     * Note: If passing in an array, its values are edited in-place and
     * nothing is returned.
     * @param i1 index for 1st dimension.
     * @param i2 index for 2nd dimension.
     * @param i3 index for 3rd dimension.
     * @param v array { v1, v2, v3 } of eigenvector components.
     */
    getEigenvectorV(i1: number, i2: number, i3: number, v?: number[]): void | number[];
    /**
     * Sets tensor elements for specified indices.
     * <p>
     * This method first computes an eigen-decomposition of the specified
     * tensor, and then stores the computed eigenvectors and eigenvalues.
     * The eigenvalues are ordered such that au &gt;= av &gt;= aw &gt;= 0.
     * @param i1 index for 1st dimension.
     * @param i2 index for 2nd dimension.
     * @param i3 index for 3rd dimension.
     * @param a array { a11, a12, a13, a22, a23, a33 } of tensor elements.
     */
    setTensor(i1: number, i2: number, i3: number, a: number): any;
    /**
     * Sets tensor elements for specified indices.
     * <p>
     * This method first computes an eigen-decomposition of the specified
     * tensor, and then stores the computed eigenvectors and eigenvalues.
     * The eigenvalues are ordered such that au &gt;= av &gt;= aw &gt;= 0.
     * @param i1 index for the 1st dimension.
     * @param i2 index for the 2nd dimension.
     * @param i3 index for the 3rd dimension.
     * @param a11 tensor element a11.
     * @param a12 tensor element a12.
     * @param a13 tensor element a13.
     * @param a22 tensor element a22.
     * @param a23 tensor element a23.
     * @param a33 tensor element a33.
     */
    setTensor(i1: number, i2: number, i3: number, a11: number, a12: number, a13: number, a22: number, a23: number, a33: number): any;
}