gallery

Generate commonly used test matrices and data for numerical experiments

📝 Syntax

• [A1,A2,...,Am] = gallery(matrixname,P1,P2,...,Pn)

• [A1,A2,...,Am] = gallery(matrixname,P1,P2,...,Pn,typename)

• A = gallery(k)

• A = gallery("circul", v)

• [v,beta] = gallery("house", x)

• [A,beta] = gallery("ipjfact", n, k)

• A = gallery("cauchy", x, y)

📥 Input argument

• matrixname - name of the matrix family to generate (string or character vector), e.g. "circul", "cauchy", "grcar", "minij", "dramadah", "house", "ipjfact"

• P1, P2, ..., Pn - family-dependent parameters: scalars, vectors or matrices that determine size and entries (for example n, vectors v, x, y, or option flags)

• n - positive integer specifying matrix order or size

• v, x, y - vectors used as parameters (for example first row for circulant, point locations for chebvand, or Cauchy parameters)

• k - option or small integer parameter controlling family behaviour (for example number of superdiagonals for grcar or variant selectors for dramadah)

• typename - optional output data type: "double" (default) or "single"

📤 Output argument

• A1,A2,...,Am - one or more matrices or arrays produced by the chosen family

• A - single matrix or multidimensional array when one output is requested

• v,beta,s - Householder outputs: v (vector), beta (scalar), and optional s returned by house

• beta - determinant or scalar output for families that return it explicitly (for example ipjfact returns determinant beta)

📄 Description

The gallery function returns a collection of standard test matrices and generated data used to illustrate numerical linear algebra concepts, test algorithms, and reproduce textbook examples.

Use the matrixname argument to select a family; additional parameters (sizes, vectors, options) depend on the chosen family.

Typical uses: study eigenvalue sensitivity and conditioning, exercise solvers with structured matrices (Toeplitz, Hankel, circulant), generate random or specially structured matrices with prescribed singular/eigenvalue properties, or obtain canonical examples for teaching and tests.

The optional typename forces the numeric output type.

If omitted, the output type is inferred from the inputs: presence of a single input yields single, otherwise outputs are double.

📚 Bibliography

See references in Higham, N. J., Accuracy and Stability of Numerical Algorithms for Gallery of Test Matrices.

💡 Examples

Simple ill-conditioned 3-by-3 test matrix

A = gallery(3)

Create and display a circulant matrix

C = gallery("circul",120);
imagesc(C);
axis square;
colorbar;

🔗 See also

hankel, hilb, magic, pascal, toeplitz.

🕔 History

Version	📄 Description
1.15.0	initial version