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All functions on this page live under the linalg namespace. Access them as np.linalg.solve(...), np.linalg.inv(...), etc.

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linalg.solve

Solve the linear matrix equation Ax = b for x. The matrix a must be square and non-singular. 
function linalg.solve(a: ArrayLike, b: ArrayLike): NDArray
NameTypeDefaultDescription
aArrayLike—Coefficient matrix of shape [N, N].
bArrayLike—Right-hand side vector or matrix. Shape [N] for a single system or [N, M] for multiple right-hand sides.
Returns: NDArray — Solution x such that A @ x = b. Throws: Error if a is singular or not square. 
import * as np from 'numpy-ts';

// Solve: 2x + y = 5, x + 3y = 7
const A = np.array([[2, 1], [1, 3]]);
const b = np.array([5, 7]);

const x = np.linalg.solve(A, b);
// array([1.6, 1.8])

// Verify: A @ x ≈ b
console.log(np.matmul(A, x).toArray());  // [5, 7]

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linalg.lstsq

Compute the least-squares solution to a linear matrix equation. Finds x that minimizes ||b - Ax||^2. Works for overdetermined and underdetermined systems. 
function linalg.lstsq(
  a: ArrayLike,
  b: ArrayLike,
  rcond?: number | null
): { x: NDArray; residuals: NDArray; rank: number; s: NDArray; }
NameTypeDefaultDescription
aArrayLike—Coefficient matrix of shape [M, N].
bArrayLike—Right-hand side of shape [M] or [M, K].
rcondnumber-1Cut-off ratio for small singular values. Singular values less than rcond * largest_sv are treated as zero. A value of -1 uses machine precision.
Returns: { x, residuals, rank, s } where:
  • x — Least-squares solution of shape [N] or [N, K].
  • residuals — Sum of squared residuals (empty if rank < N or M <= N).
  • rank — Effective rank of a.
  • s — Singular values of a in descending order.
import * as np from 'numpy-ts';

// Overdetermined system (3 equations, 2 unknowns)
const A = np.array([[1, 1], [1, 2], [1, 3]]);
const b = np.array([1, 2, 2]);

const { x, residuals, rank, s } = np.linalg.lstsq(A, b);
console.log(x.toArray());  // least-squares fit
console.log(rank);          // 2
console.log(s.toArray());   // singular values

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linalg.inv

Compute the multiplicative inverse of a square matrix. The result satisfies A @ A_inv = I. 
function linalg.inv(a: ArrayLike): NDArray
NameTypeDefaultDescription
aArrayLike—Input square matrix of shape [N, N].
Returns: NDArray — The inverse matrix of shape [N, N]. Throws: Error if the matrix is singular. 
import * as np from 'numpy-ts';

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

const A_inv = np.linalg.inv(A);
// array([[-2  ,  1  ],
//        [ 1.5, -0.5]])

// Verify: A @ A_inv ≈ identity
const I = np.matmul(A, A_inv);
// array([[1, 0],
//        [0, 1]])

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linalg.pinv

Compute the Moore-Penrose pseudo-inverse of a matrix. This generalizes the inverse to non-square and singular matrices. 
function linalg.pinv(a: ArrayLike, rcond?: number): NDArray
NameTypeDefaultDescription
aArrayLike—Input matrix of shape [M, N].
rcondnumber1e-15Cutoff for small singular values. Singular values less than rcond * max(sv) are set to zero.
Returns: NDArray — The pseudo-inverse of shape [N, M]. 
import * as np from 'numpy-ts';

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

const A_pinv = np.linalg.pinv(A);
console.log(A_pinv.shape);  // [2, 3]

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

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linalg.tensorinv

Compute the inverse of an N-dimensional array. The inverse is defined such that tensordot(a_inv, a, ind) = I, where I is the identity operator. 
function linalg.tensorinv(a: ArrayLike, ind?: number): NDArray
NameTypeDefaultDescription
aArrayLike—Input tensor to invert.
indnumber2Number of first indices that are involved in the inverse sum. Must satisfy prod(a.shape[:ind]) == prod(a.shape[ind:]).
Returns: NDArray — The tensor inverse. 
import * as np from 'numpy-ts';

const a = np.eye(4).reshape([2, 2, 2, 2]);

const a_inv = np.linalg.tensorinv(a);
console.log(a_inv.shape);  // [2, 2, 2, 2]

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linalg.tensorsolve

Solve the tensor equation a x = b for x. This is the tensor generalization of linalg.solve. 
function linalg.tensorsolve(a: ArrayLike, b: ArrayLike, axes?: number[]): NDArray
NameTypeDefaultDescription
aArrayLike—Coefficient tensor.
bArrayLike—Right-hand side tensor.
axesnumber[]undefinedAxes in a to reorder to the right before solving.
Returns: NDArray — The solution tensor x. 
import * as np from 'numpy-ts';

const a = np.eye(6).reshape([2, 3, 2, 3]);
const b = np.array([[1, 0, 0], [0, 1, 0]]);

const x = np.linalg.tensorsolve(a, b);
console.log(x.shape);  // [2, 3]

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linalg.multi_dot

Compute the dot product of two or more arrays in a single call, automatically optimizing the order of multiplications (using the optimal parenthesization) to minimize the number of scalar multiplications. 
function linalg.multi_dot(arrays: ArrayLike[]): NDArray
NameTypeDefaultDescription
arraysArrayLike[]—Array of matrices to multiply. The first and last can be 1-D (treated as row/column vectors).
Returns: NDArray — The dot product of all the input arrays. 
import * as np from 'numpy-ts';

const A = np.random.rand([10, 100]);
const B = np.random.rand([100, 5]);
const C = np.random.rand([5, 50]);

// Efficiently computes A @ B @ C with optimal ordering
const result = np.linalg.multi_dot([A, B, C]);
console.log(result.shape);  // [10, 50]

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linalg.matrix_power

Raise a square matrix to an integer power. For positive n, this computes a @ a @ ... @ a (n times). For n = 0, returns the identity. For negative n, computes the inverse raised to |n|. 
function linalg.matrix_power(a: ArrayLike, n: number): NDArray
NameTypeDefaultDescription
aArrayLike—Input square matrix.
nnumber—Integer exponent. Can be positive, zero, or negative.
Returns: NDArray — The matrix a raised to the power n. 
import * as np from 'numpy-ts';

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

// Square the matrix
const A2 = np.linalg.matrix_power(A, 2);
// array([[ 7, 10],
//        [15, 22]])

// Identity (n=0)
const I = np.linalg.matrix_power(A, 0);
// array([[1, 0],
//        [0, 1]])

// Inverse (n=-1)
const A_inv = np.linalg.matrix_power(A, -1);
// equivalent to np.linalg.inv(A)