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Vector Two Axis Sign Flip Tool

Compute vector two axis sign flip from explicit bounded inputs.

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Description

Negate two distinct explicitly selected vector coordinates.

A vector is an ordered set of components in a chosen basis. Its norm measures magnitude, while dot products, projections, and coordinate transformations describe different relationships. Component order, angle units, normalization, and numerical tolerances determine the meaning of a computed result.

Negate two distinct explicitly selected vector coordinates.

When to use this tool

Use Vector Two Axis Sign Flip when you need the particular coordinate operation, derivative, residual, or domain check under a known basis convention.

How to use the tool and how it works

  1. Enter vector, first, second. Keep parallel arrays aligned. Use the units and conventions below.
  2. Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
  3. Read vector. Use the output convention below.

Require first and second to be distinct zero-based indices within vector. Negate exactly those two components and preserve the others.1

Input fieldMeaning and unitsAccepted input
vectorVectorRequired. Array of Finite number.; maximum items 256.
firstFirstRequired. Safe integer; minimum 0.
secondSecondRequired. Safe integer; minimum 0.
Output fieldInterpretationReturned shape
vectorVectorRequired. Array of Finite number.; maximum items 256.
json
{
  "input": {
    "vector": [
      1,
      2,
      3
    ],
    "first": 0,
    "second": 2
  },
  "output": {
    "vector": [
      -1,
      2,
      -3
    ]
  }
}

Limitations and assumptions

  • Selecting the same index twice is rejected rather than canceling two flips. This changes coordinate signs without determining a geometric reflection plane, basis, or physical orientation.
  • The field tables state structural bounds; the mechanics also specify cross-field constraints. Malformed inputs and unsupported domains cause errors. A successful false flag, empty branch value, or zero placeholder has the meaning stated above and is distinct from an input error.
  • Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Signed zero is exported as zero.

Alternative or Complementary methods

Choose a complete vector or matrix operation when a single component or residual is insufficient. For sensitive near-zero or near-singular cases, inspect numerical conditioning and use an appropriate precision and tolerance.

References

  1. Calculation and input contract: vector/vector-two-axis-sign-flip — tool.io

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