Vector projection

vector-projection · version 1.0.0 · Vectors & matrices · free, no key needed

Compute the vector projection of a finite-number vector onto another.

Use when you need to: vector projection · project a vector onto another vector.

Supported

• vector projection
• project a vector onto another vector

Not supported

• scalar projection only (this returns the full vector projection)
• projecting onto a zero vector

Behavior

• Inputs a and onto are arrays of finite JSON numbers with the same length, from 1 to 64 entries, magnitude bounded to at most 1000000.
• The result is the vector projection proj_onto(a) = ((a . onto) / (onto . onto)) * onto, computed in IEEE-754 double precision.
• Optional input tolerance (default 1e-9, range 0 to 1) is the minimum value of (onto . onto) accepted; smaller values are rejected as projecting onto a zero (or effectively zero) vector.
• A result entry of -0 is normalized to 0.
• Every result entry is checked to be a finite number before it is returned; a non-finite intermediate is rejected as invalid input rather than silently serialized.

Input

• a (array of number, required): min items 1; max items 64
• onto (array of number, required): min items 1; max items 64
• tolerance (number, optional): min 0; max 1

Output

• result (array of number, required)

Limits

• max dim: 64
• max abs value: 1000000

Example

Request input:

{
  "a": [
    3,
    4
  ],
  "onto": [
    1,
    0
  ]
}

Response:

{
  "result": {
    "result": [
      3,
      0
    ]
  }
}

How to call it

MCP

Connect https://computefirst.net/mcp (setup), then call execute with:

{
  "id": "vector-projection",
  "version": "1.0.0",
  "input": {
    "a": [
      3,
      4
    ],
    "onto": [
      1,
      0
    ]
  }
}

HTTP (no key)

curl -X POST https://computefirst.net/v1/tools/vector-projection/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"a":[3,4],"onto":[1,0]}'

The machine-readable contract is at /v1/tools/vector-projection/versions/1.0.0.

CLI

node cli.mjs run vector-projection 1.0.0 --input input.json --base-url https://computefirst.net

Get the client at /clients/cli/.

Related tools

• Matrix vector multiply: Multiply an MxN finite-number matrix by a length-N finite-number vector, producing a length-M vector.
• Vector scale: Multiply every entry of a finite-number vector by a scalar.
• Vector subtract: Subtract two equal-length finite-number vectors elementwise (a minus b).
• Matrix determinant: Compute the determinant of a small square finite-number matrix.
• Matrix inverse: Compute the inverse of a small square finite-number matrix.
• Matrix scale: Multiply every entry of a finite-number matrix by a scalar.