squareform — Convert between condensed distance vectors and square distance matrices.
squareform converts a condensed pairwise-distance vector into a square symmetric matrix, or converts a square symmetric distance matrix back into condensed form.
Syntax
Y = squareform(Z)
Y = squareform(Z, Force)Inputs
| Name | Type | Required | Default | Description |
|---|---|---|---|---|
Z | NumericArray | Yes | — | Condensed distance vector or square distance matrix. |
force | StringScalar | No | — | Conversion force option: 'tomatrix' or 'tovector'. |
Returns
| Name | Type | Description |
|---|---|---|
Z | NumericArray | Square symmetric matrix or condensed distance vector. |
Errors
| Identifier | When | Message |
|---|---|---|
RunMat:distance:InvalidArgument | Inputs, dimensions, metrics, metric parameters, or selection options are malformed. | distance helper: invalid argument |
RunMat:distance:Internal | RunMat cannot allocate or construct a distance output. | distance helper: internal error |
How squareform works
- Vector inputs must have length
n*(n-1)/2for an integern. - Matrix inputs must be square, symmetric, and have a zero diagonal.
squareform(Z,"tomatrix")forces vector-to-matrix conversion.squareform(Z,"tovector")forces matrix-to-vector conversion.- Condensed vectors use the same pair ordering as
pdist. - The conversion preserves native single, double, and RunMat-extension integer storage exactly; it does not route structural values through double.
Examples
Expand a condensed vector
D = [5 4 7];
M = squareform(D)Expected output:
M is a 3-by-3 symmetric matrix with zeros on the diagonal.Convert back to condensed form
D2 = squareform(M)Expected output:
D2 is [5 4 7].Force output mode
M = squareform(D, "tomatrix")Expected output:
The input is interpreted as a condensed distance vector.Using squareform with coding agents
Open a RunMat example with live inputs, then ask the agent to explain how squareform changes the result.
Run a small squareform example, explain the result, then change one input and compare the output.
FAQ
Why does a matrix input need a zero diagonal?⌄
A distance matrix represents distance from each observation to itself on the diagonal, which must be zero for condensed conversion.
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Hist
Open-source implementation
Unlike proprietary runtimes, every RunMat function is open-source. Read exactly how squareform is executed, line by line, in Rust.
- View the source for squareform in Rust on GitHub
- Learn how the RunMat runtime works
- Found a bug? Open an issue with a minimal reproduction.
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