NaN Propagation in Derived Data
License: restricted — no clear open-source license detected for the underlying tool; verify licensing before commercial use or redistribution.
Summary
Handle missing or invalid pixel values (NaN) consistently when evaluating per-pixel mathematical expressions across LA-ICP-MS element channels. NaN propagation ensures that pixels below detection limits, failed measurements, or invalid intermediates do not corrupt downstream derived image arrays.
When to use
When constructing derived elemental ratio images via Calculator formula evaluation in pew², and input element channels contain NaN pixels (from thresholding, signal dropout, or instrumental noise). Use this skill whenever a per-pixel arithmetic or conditional operation must decide whether to propagate NaN forward, mask the result, or apply a fallback value.
When NOT to use
- If the input element channels are already validated and contain no NaN (unlikely in real LA-ICP-MS data); NaN handling is still best practice but may be overengineering for clean synthetic data.
- If the output format or downstream tool explicitly forbids NaN (e.g., some export formats or legacy software); use
nantonum conversion as a preprocessing step instead.
- If the analysis goal requires imputation or statistical interpolation of missing pixels rather than explicit masking; consider separate imputation workflows before Calculator evaluation.
Inputs
- Open LA-ICP-MS element image arrays (in-memory, registered in the pew² image registry)
- Formula string with element references (e.g., P31, Zn66), arithmetic/logical operators, and conditionals
- Pixel arrays with potential NaN values from prior thresholding, masking, or quality filtering
Outputs
- Derived image array with NaN values propagated through arithmetic and conditional operations
- Registered image in pew² open images with user-supplied or existing name
How to apply
During element-wise evaluation of the abstract syntax tree (AST), propagate NaN through arithmetic operations (+, −, ×, ÷, ^) following IEEE 754 semantics: any operation involving a NaN operand yields NaN. For conditional branches (if/then/else or ternary ?:), evaluate the condition pixel-by-pixel; if the condition contains NaN, the pixel becomes NaN in the branch result. Use in-place masking or threshold operations (e.g., threshold(image, value)) to explicitly convert pixels below a cutoff to NaN before arithmetic, and use nantonum(array) to convert remaining NaN values to a user-specified default (typically 0) only when the downstream analysis can tolerate uniform replacement. Register the resulting derived array with NaN propagated through to the output image, or optionally apply nantonum as the final step if the output format or visualization does not support NaN.
Related tools
- Calculator (Evaluates per-pixel mathematical expressions and conditionals on element channels, with integrated NaN propagation and handling) — https://github.com/djdt/pewpew
- pewpew (GUI host and execution environment for Calculator formulas; maintains the open image registry where NaN-aware derived arrays are stored and visualized) — https://github.com/djdt/pewpew
- pewlib (Underlying Python library that implements per-pixel AST evaluation, NaN propagation semantics, and image array operations) — https://github.com/djdt/pewlib
Evaluation signals
- Output derived image contains NaN pixels exactly where any input operand was NaN (spot-check a few pixels through Calculator formula log or pixel inspector).
- Arithmetic operations involving NaN produce NaN: verify that (NaN + 5) → NaN, (NaN / 0) → NaN, and (NaN * 0) → NaN in the output.
- Conditional expressions branch correctly on NaN: e.g., in a ternary
condition ? a : b, pixels where condition is NaN should yield NaN in the result (not silently fall through to a or b).
- Histogram or statistical summary of the derived image reports the correct count of NaN pixels (can be viewed in pew² image stats panel).
- When
nantonum is applied as a final step, all NaN are replaced with the specified default value (e.g., 0 or a fill value), and the output image is exportable in standard formats (CSV, NetCDF, etc.).
Limitations
- NaN propagation follows IEEE 754 floating-point semantics; non-standard behavior in some edge cases (e.g., 0/0 or ∞ − ∞) depends on the NumPy or underlying math library version.
- Conditional logic (if/then/else) that receives NaN in the condition branch will yield NaN for that pixel; there is no automatic fallback or imputation—users must explicitly handle with
nantonum if a deterministic result is required.
- Performance may degrade for very large image arrays (e.g., thousands of channels × millions of pixels) due to per-pixel evaluation overhead; optimize by pre-filtering or downsampling if needed.
- NaN propagation is transparent to the user; if formulas are chained across multiple derived images, NaN from early steps will accumulate, potentially leading to sparsity in final outputs; document the expected NaN fraction in the analysis plan.
Evidence
- [other] Handle NaN propagation and conditionals: pixels failing thresholds become NaN; conditionals branch per-pixel.: "Handle NaN propagation and conditionals: pixels failing thresholds become NaN; conditionals branch per-pixel."
- [other] For supported functions (threshold, mask, segment, kmeans, otsu, mean, median, percentile, normalise, nantonum, abs), apply them to specified arrays in-place within the evaluation context.: "For supported functions (threshold, mask, segment, kmeans, otsu, mean, median, percentile, normalise, nantonum, abs), apply them to specified arrays in-place within the evaluation context."
- [other] Evaluate the AST element-wise (pixel-by-pixel) over all arrays simultaneously, applying arithmetic, comparison, and logical operations in correct precedence.: "Evaluate the AST element-wise (pixel-by-pixel) over all arrays simultaneously, applying arithmetic, comparison, and logical operations in correct precedence."
- [other] Pew² provides a Calculator module that evaluates per-pixel expressions over element channels to produce new derived image arrays, supporting conditional logic and arithmetic operations on elemental data.: "Pew² provides a Calculator module that evaluates per-pixel expressions over element channels to produce new derived image arrays, supporting conditional logic and arithmetic operations on elemental"
1---2name: nan-propagation-in-derived-data3description: Use when when constructing derived elemental ratio images via Calculator formula evaluation in pew², and input element channels contain NaN pixels (from thresholding, signal dropout, or instrumental noise).4license: CC-BY-4.05---67# NaN Propagation in Derived Data89> **License: restricted** — no clear open-source license detected for the underlying tool; verify licensing before commercial use or redistribution. <!-- asb-license-banner -->10## Summary1112Handle missing or invalid pixel values (NaN) consistently when evaluating per-pixel mathematical expressions across LA-ICP-MS element channels. NaN propagation ensures that pixels below detection limits, failed measurements, or invalid intermediates do not corrupt downstream derived image arrays.1314## When to use1516When constructing derived elemental ratio images via Calculator formula evaluation in pew², and input element channels contain NaN pixels (from thresholding, signal dropout, or instrumental noise). Use this skill whenever a per-pixel arithmetic or conditional operation must decide whether to propagate NaN forward, mask the result, or apply a fallback value.1718## When NOT to use1920- If the input element channels are already validated and contain no NaN (unlikely in real LA-ICP-MS data); NaN handling is still best practice but may be overengineering for clean synthetic data.21- If the output format or downstream tool explicitly forbids NaN (e.g., some export formats or legacy software); use `nantonum` conversion as a preprocessing step instead.22- If the analysis goal requires imputation or statistical interpolation of missing pixels rather than explicit masking; consider separate imputation workflows before Calculator evaluation.2324## Inputs2526- Open LA-ICP-MS element image arrays (in-memory, registered in the pew² image registry)27- Formula string with element references (e.g., P31, Zn66), arithmetic/logical operators, and conditionals28- Pixel arrays with potential NaN values from prior thresholding, masking, or quality filtering2930## Outputs3132- Derived image array with NaN values propagated through arithmetic and conditional operations33- Registered image in pew² open images with user-supplied or existing name3435## How to apply3637During element-wise evaluation of the abstract syntax tree (AST), propagate NaN through arithmetic operations (+, −, ×, ÷, ^) following IEEE 754 semantics: any operation involving a NaN operand yields NaN. For conditional branches (if/then/else or ternary ?:), evaluate the condition pixel-by-pixel; if the condition contains NaN, the pixel becomes NaN in the branch result. Use in-place masking or threshold operations (e.g., `threshold(image, value)`) to explicitly convert pixels below a cutoff to NaN before arithmetic, and use `nantonum(array)` to convert remaining NaN values to a user-specified default (typically 0) only when the downstream analysis can tolerate uniform replacement. Register the resulting derived array with NaN propagated through to the output image, or optionally apply `nantonum` as the final step if the output format or visualization does not support NaN.3839## Related tools4041- **Calculator** (Evaluates per-pixel mathematical expressions and conditionals on element channels, with integrated NaN propagation and handling) — https://github.com/djdt/pewpew42- **pewpew** (GUI host and execution environment for Calculator formulas; maintains the open image registry where NaN-aware derived arrays are stored and visualized) — https://github.com/djdt/pewpew43- **pewlib** (Underlying Python library that implements per-pixel AST evaluation, NaN propagation semantics, and image array operations) — https://github.com/djdt/pewlib4445## Evaluation signals4647- Output derived image contains NaN pixels exactly where any input operand was NaN (spot-check a few pixels through Calculator formula log or pixel inspector).48- Arithmetic operations involving NaN produce NaN: verify that (NaN + 5) → NaN, (NaN / 0) → NaN, and (NaN * 0) → NaN in the output.49- Conditional expressions branch correctly on NaN: e.g., in a ternary `condition ? a : b`, pixels where condition is NaN should yield NaN in the result (not silently fall through to a or b).50- Histogram or statistical summary of the derived image reports the correct count of NaN pixels (can be viewed in pew² image stats panel).51- When `nantonum` is applied as a final step, all NaN are replaced with the specified default value (e.g., 0 or a fill value), and the output image is exportable in standard formats (CSV, NetCDF, etc.).5253## Limitations5455- NaN propagation follows IEEE 754 floating-point semantics; non-standard behavior in some edge cases (e.g., 0/0 or ∞ − ∞) depends on the NumPy or underlying math library version.56- Conditional logic (if/then/else) that receives NaN in the condition branch will yield NaN for that pixel; there is no automatic fallback or imputation—users must explicitly handle with `nantonum` if a deterministic result is required.57- Performance may degrade for very large image arrays (e.g., thousands of channels × millions of pixels) due to per-pixel evaluation overhead; optimize by pre-filtering or downsampling if needed.58- NaN propagation is transparent to the user; if formulas are chained across multiple derived images, NaN from early steps will accumulate, potentially leading to sparsity in final outputs; document the expected NaN fraction in the analysis plan.5960## Evidence6162- [other] Handle NaN propagation and conditionals: pixels failing thresholds become NaN; conditionals branch per-pixel.: "Handle NaN propagation and conditionals: pixels failing thresholds become NaN; conditionals branch per-pixel."63- [other] For supported functions (threshold, mask, segment, kmeans, otsu, mean, median, percentile, normalise, nantonum, abs), apply them to specified arrays in-place within the evaluation context.: "For supported functions (threshold, mask, segment, kmeans, otsu, mean, median, percentile, normalise, nantonum, abs), apply them to specified arrays in-place within the evaluation context."64- [other] Evaluate the AST element-wise (pixel-by-pixel) over all arrays simultaneously, applying arithmetic, comparison, and logical operations in correct precedence.: "Evaluate the AST element-wise (pixel-by-pixel) over all arrays simultaneously, applying arithmetic, comparison, and logical operations in correct precedence."65- [other] Pew² provides a Calculator module that evaluates per-pixel expressions over element channels to produce new derived image arrays, supporting conditional logic and arithmetic operations on elemental data.: "Pew² provides a Calculator module that evaluates per-pixel expressions over element channels to produce new derived image arrays, supporting conditional logic and arithmetic operations on elemental"
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