Vector Sparse Explicit Zero Policy Tool

Description

Preserve or remove explicit zero entries from a sorted sparse vector under a supplied policy.

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.

Preserve or remove explicit zero entries from a sorted sparse vector under a supplied policy.

When to use this tool

Use Vector Sparse Explicit Zero Policy 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

Enter indices, values, dropZeros. Keep parallel arrays aligned. Use the units and conventions below.
Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
Read indices, values. Use the output convention below.

Require aligned indices and values, with nonnegative strictly increasing integer indices. When dropZeros is true remove entries whose value is exactly zero from both arrays; otherwise preserve all entries.^[1]

Input field	Meaning and units	Accepted input
indices	Indices	Required. Array of Safe integer.; maximum items 256.
values	Values	Required. Array of Finite number.; maximum items 256.
dropZeros	Drop Zeros	Required. Boolean.

Output field	Interpretation	Returned shape
indices	Indices	Required. Array of Safe integer.; maximum items 256.
values	Values	Required. Array of Finite number.; maximum items 256.

json

{
  "input": {
    "indices": [
      0,
      2,
      4
    ],
    "values": [
      3,
      0,
      5
    ],
    "dropZeros": true
  },
  "output": {
    "indices": [
      0,
      4
    ],
    "values": [
      3,
      5
    ]
  }
}

Limitations and assumptions

Indices are zero-based sparse coordinates without a supplied maximum dimension. No tolerance is used for small nonzero values, and duplicate or unsorted indices are rejected rather than merged.
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

Calculation and input contract: vector/vector-sparse-explicit-zero-policy — tool.io

Similar or alternative tools

Vector Homogeneous Weight Zero Tag
Divide homogeneous coordinates by a nonzero final weight or flag the zero-weight branch.
GS1 AI Date Day Zero Policy
Validate a supplied-century YYMMDD token and optionally interpret day 00 as the final day of its month.