Description
Affinely map supplied reference quadrature nodes and weights to an interval.
Numerical physics calculations depend on discretization, index conventions, boundary conditions and model units. A local force kick is only part of an integration method, a stencil residual is not a solved field, and a one-sided power weight is not a spectral-density normalization. Floating-point resolution also limits grid and coordinate representations.
Affinely map supplied reference quadrature nodes and weights to an interval.
When to use this tool
Use Quadrature Node Affine Map when you already have referenceNodes, referenceWeights, lower, upper and need to affinely map supplied reference quadrature nodes and weights to an interval.
How to use the tool and how it works
- Enter referenceNodes, referenceWeights, lower, upper. Follow any array-alignment requirements below. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read nodes, weights. Use the output convention below.
Require aligned arrays, upper>lower and every node in [-1,1]; half=upper/2-lower/2, midpoint=lower/2+upper/2. Map nodes to midpoint+half*node and weights to half*weight.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| referenceNodes | Finite nodes in [-1,1], aligned with referenceWeights. | Required. Array of finite number; maximum items 256. |
| referenceWeights | Signed finite weights; no quadrature family or positivity condition is inferred. | Required. Array of finite number; maximum items 256. |
| lower | Lower | Required. Finite number. |
| upper | Upper | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| nodes | Nodes | Required. Array of finite number; maximum items 256. |
| weights | Weights | Required. Array of finite number; maximum items 256. |
{
"input": {
"referenceNodes": [
-1,
0,
1
],
"referenceWeights": [
1,
4,
1
],
"lower": 2,
"upper": 4
},
"output": {
"nodes": [
2,
3,
4
],
"weights": [
1,
4,
1
]
}
}Limitations and assumptions
- Empty arrays and signed weights are accepted. This does not choose a rule, integrate a function, establish quadrature exactness or estimate error.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- 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. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use the complete discretized model, integration algorithm and boundary treatment. Assess convergence, conservation and stability with the full calculation; individual residuals, CFL components, relaxation terms and index mappings do not establish numerical accuracy or physical validity.
References
Similar or alternative tools
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