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Documentation Index

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All decomposition functions live under the linalg namespace. Access them as np.linalg.eig(...), np.linalg.svd(...), etc.

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linalg.eig

Compute the eigenvalues and right eigenvectors of a square matrix. For each eigenvalue w[i], the corresponding eigenvector is the column v[:, i]. 
function linalg.eig(a: ArrayLike): { w: NDArray; v: NDArray; }
NameTypeDefaultDescription
aArrayLike—Input square matrix.
Returns: { w, v } — Object where w has shape [n] (eigenvalues) and v has shape [n, n] (eigenvectors). The column v[:, i] is the eigenvector corresponding to w[i]. 
import * as np from 'numpy-ts';

const A = np.array([[1, -1], [1, 1]]);

const { w, v } = np.linalg.eig(A);
console.log(w.shape);    // [2]
console.log(v.shape);    // [2, 2]

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linalg.eigh

Compute eigenvalues and eigenvectors of a symmetric (Hermitian) matrix. The eigenvalues are returned in ascending order. This is faster than eig for symmetric matrices and guarantees real eigenvalues. 
function linalg.eigh(a: ArrayLike, UPLO?: 'L' | 'U'): { w: NDArray; v: NDArray; }
NameTypeDefaultDescription
aArrayLike—Input symmetric matrix.
UPLO'L' | 'U''L'Whether to use the lower ('L') or upper ('U') triangle of a.
Returns: { w, v } — Object where w contains eigenvalues in ascending order and v contains orthonormal eigenvectors. 
import * as np from 'numpy-ts';

const A = np.array([[2, 1], [1, 3]]);

const { w, v } = np.linalg.eigh(A);
console.log(w.toArray());  // eigenvalues in ascending order
console.log(v.shape);      // [2, 2]

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linalg.eigvals

Compute the eigenvalues of a square matrix. This is equivalent to linalg.eig but only returns eigenvalues, which can be more efficient when eigenvectors are not needed. 
function linalg.eigvals(a: ArrayLike): NDArray
NameTypeDefaultDescription
aArrayLike—Input square matrix.
Returns: NDArray — 1-D array of eigenvalues (may be complex-valued). 
import * as np from 'numpy-ts';

const A = np.array([[1, 2], [3, 4]]);

const w = np.linalg.eigvals(A);
console.log(w.shape);  // [2]

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linalg.eigvalsh

Compute the eigenvalues of a symmetric (Hermitian) matrix. Returns eigenvalues only, sorted in ascending order. 
function linalg.eigvalsh(a: ArrayLike, UPLO?: 'L' | 'U'): NDArray
NameTypeDefaultDescription
aArrayLike—Input symmetric matrix.
UPLO'L' | 'U''L'Whether to use the lower or upper triangle.
Returns: NDArray — 1-D array of real eigenvalues in ascending order. 
import * as np from 'numpy-ts';

const A = np.array([[5, 2], [2, 8]]);

const w = np.linalg.eigvalsh(A);
console.log(w.toArray());  // eigenvalues in ascending order

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linalg.svd

Compute the singular value decomposition (SVD) of a matrix. Factors the matrix a as U @ diag(S) @ Vh. 
function linalg.svd(
  a: ArrayLike,
  full_matrices?: boolean,
  compute_uv?: boolean
): { u: NDArray; s: NDArray; vt: NDArray; } | NDArray
NameTypeDefaultDescription
aArrayLike—Input matrix of shape [M, N].
full_matricesbooleantrueIf true, U is [M, M] and Vh is [N, N]. If false, U is [M, K] and Vh is [K, N] where K = min(M, N).
compute_uvbooleantrueIf false, return only singular values.
Returns: { u, s, vt } when compute_uv is true, where u contains left singular vectors, s contains singular values (descending), and vt contains right singular vectors (conjugate-transposed). Returns NDArray of singular values when compute_uv is false. 
import * as np from 'numpy-ts';

const A = np.array([[1, 0, 0], [0, 2, 0], [0, 0, 3]]);

const { u, s, vt } = np.linalg.svd(A);
console.log(s.toArray());  // [3, 2, 1]

// Reduced SVD
const { u: ur, s: sr, vt: vtr } = np.linalg.svd(A, false);
console.log(ur.shape);   // [3, 3]
console.log(sr.shape);   // [3]
console.log(vtr.shape);  // [3, 3]

const sOnly = np.linalg.svd(A, true, false);
console.log(sOnly.shape); // [3]

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linalg.svdvals

Compute the singular values of a matrix. This is equivalent to linalg.svd but only returns the singular values, which can be more efficient. 
function linalg.svdvals(a: ArrayLike): NDArray
NameTypeDefaultDescription
aArrayLike—Input matrix.
Returns: NDArray — 1-D array of singular values in descending order. 
import * as np from 'numpy-ts';

const A = np.array([[1, 2], [3, 4]]);

const s = np.linalg.svdvals(A);
console.log(s.shape);  // [2]

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linalg.qr

Compute the QR decomposition of a matrix. Factors the matrix a as Q @ R, where Q is orthogonal and R is upper triangular. 
function linalg.qr(
  a: ArrayLike,
  mode?: 'reduced' | 'complete' | 'r' | 'raw'
): { q: NDArray; r: NDArray; } | NDArray | { h: NDArray; tau: NDArray; }
NameTypeDefaultDescription
aArrayLike—Input matrix of shape [M, N].
mode'reduced' | 'complete' | 'r' | 'raw''reduced'If 'reduced'/'complete', returns { q, r }. If 'r', returns only R. If 'raw', returns { h, tau }.
Returns: { q, r } for 'reduced'/'complete', NDArray for 'r', and { h, tau } for 'raw'. 
import * as np from 'numpy-ts';

const A = np.array([[1, 2], [3, 4], [5, 6]]);

// Reduced QR (default)
const { q, r } = np.linalg.qr(A);
console.log(q.shape);  // [3, 2]
console.log(r.shape);  // [2, 2]

// Complete QR
const { q: qf, r: rf } = np.linalg.qr(A, 'complete');
console.log(qf.shape);  // [3, 3]
console.log(rf.shape);  // [3, 2]

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linalg.cholesky

Compute the Cholesky decomposition of a positive-definite symmetric matrix. Returns the lower-triangular matrix L such that a = L @ L.T. 
function linalg.cholesky(a: ArrayLike, upper?: boolean): NDArray
NameTypeDefaultDescription
aArrayLike—Input positive-definite symmetric matrix.
upperbooleanfalseIf true, compute upper-triangular factor instead of lower-triangular.
Returns: NDArray — Lower-triangular Cholesky factor L. Throws: Error if the matrix is not positive definite. 
import * as np from 'numpy-ts';

const A = np.array([[4, 2], [2, 3]]);

const L = np.linalg.cholesky(A);
// array([[2, 0],
//        [1, 1.41421356]])

// Verify: L @ L.T ≈ A
const reconstructed = np.matmul(L, L.T);