This Go program calculates the Exponential Moving Average (EMA) for a series of numerical data points, optionally associated with timestamps. EMA is a type of moving average that places a greater weight and significance...

The `calculateEMA` function computes the EMA for a slice of float64 values given a `period`. It first validates that the `period` is positive. If the input `values` slice is empty, it returns an empty slice. The smoothing factor `alpha` is calculated as `2 / (period + 1)`. The first EMA value is initialized with the first data point. Subsequent EMA values are calculated iteratively using the formula: `EMA_today = (Value_today * alpha) + (EMA_yesterday * (1 - alpha))`. The `calculateEMAWithTimestamps` function is a helper that sorts data points by timestamp before applying the core EMA calculation, returning the results mapped back to their original timestamps. The time complexity for `calculateEMA` is O(N), where N is the number of data points, due to a single pass. The `calculateEMAWithTimestamps` function adds O(N log N) for sorting timestamps. Space complexity for `calculateEMA` is O(N) for the result slice, and for `calculateEMAWithTimestamps` it's O(N) for storing sorted timestamps, values, and the result map.

FUNCTION calculateEMA(values, period): IF period <= 0 THEN RETURN error "Period must be positive" END IF IF values is empty THEN RETURN empty list END IF alpha = 2.0 / (period + 1). emaResults = list of same size as valu...

This Go program calculates the rate of change for a time-series metric using a dynamically adjusted time window. It aims to provide a meaningful rate by ensuring a minimum number of data points are considered, while also...

The `calculateDynamicRate` function takes metric values, their corresponding timestamps, a maximum allowed window duration, and a minimum required number of data points. It first checks for valid input. Then, it estimates the average time interval between data points and calculates a `requiredWindow` to encompass at least `minDataPoints`. The `optimalWindow` is determined by taking the minimum of `maxWindow` and `requiredWindow`, ensuring both constraints are met. It also ensures the `optimalWindow` is at least as large as the interval between the last two data points to prevent issues with very sparse data. Data points falling within this `optimalWindow`, ending at the latest timestamp, are filtered. If fewer than two data points are available in the filtered window, an error is returned. Otherwise, the rate is calculated as the difference between the last and first values in the window, divided by the time span of the window in seconds. The time complexity is O(N) due to iterating through the data points to filter the window, where N is the total number of data points. The space complexity is O(W), where W is the number of data points within the determined window, for storing `windowData` and `windowTimestamps`.

FUNCTION calculateDynamicRate(metricData, timestamps, maxWindow, minDataPoints): IF metricData is empty OR timestamps is empty OR lengths mismatch THEN RETURN error "Invalid input" END IF IF number of data points < minDa...

This scenario involves calculating a specific quantile (e.g., p95) from a histogram metric in PromQL. Histograms record observations into buckets, and this query aggregates these buckets over a time window to estimate th...

The `histogram_quantile(quantile, bucket_rate)` function in PromQL is used to calculate quantiles from histogram metrics. It requires a `quantile` value (between 0 and 1) and a `bucket_rate` series. The `bucket_rate` is typically derived by applying `rate()` to the `_bucket` metric of the histogram, aggregated by the `le` (less than or equal to) label. This calculates the per-second rate of observations falling into each bucket over the specified `duration`. The `histogram_quantile` function then interpolates between buckets to estimate the value at the desired quantile. The `sum by (le)` clause is essential to aggregate buckets correctly. Time complexity is O(N*M) where N is the number of time series and M is the number of buckets, as it iterates through buckets for each series. Space complexity is O(N) to store intermediate results. Edge cases include invalid quantile values, non-positive durations, and missing `_bucket` metrics.

function calculateHistogramQuantile(metricName, quantile, duration, labelsToSum): if metricName is empty or quantile is invalid or duration is not positive: return error message bucketQuery = "sum by (" + labelsToSum + "...

This scenario focuses on calculating the remaining budget for a Service Level Objective (SLO). It involves determining the total allowed 'bad' events (e.g., errors, downtime) over a defined period and subtracting the num...

Calculating remaining SLO budget involves understanding the total allowance and the actual consumption. For a counter metric representing violations (e.g., `slo_violations_total`), the total consumed budget over the SLO period can be found using `increase(metric[sloPeriod])`. The remaining budget is then `totalBudgetUnits - increase(metric[sloPeriod])`. This provides the absolute number of 'bad' events still permissible. To express this as a percentage, the remaining units are divided by the total budget units and multiplied by 100. Time complexity is dominated by `increase()`, which is O(N*W) where N is series and W is the window duration. Space complexity is O(N*W). Edge cases include negative or zero budget units, non-positive durations, and metrics that are not counters.

function calculateSLOBudgetRemaining(metricName, totalBudgetUnits, sloPeriod): if metricName or budget or period are invalid: return error message consumedUnits = "increase(" + metricName + "[" + sloPeriod + "])" remaini...

This scenario focuses on calculating the per-second rate of increase for a counter metric in PromQL. It utilizes the `rate()` function, which is designed to handle counter resets automatically. The goal is to provide a r...

The `rate()` function in PromQL is fundamental for calculating the average per-second rate of increase of a counter over a specified time interval. It intelligently handles counter resets by detecting a decrease in value and adjusting the calculation accordingly. The function samples the counter at the given `duration` and calculates the increase, then divides by the duration to get the per-second rate. This approach ensures accurate rate measurements even when counters are reset (e.g., during service restarts). The time complexity is O(1) for each evaluation, as it operates on a fixed window. Space complexity is also O(1) as it doesn't store historical data beyond the window. Edge cases like empty metric names or non-positive durations are handled by returning an error or an empty query.

function calculateRequestRate(metricName, duration): if metricName is empty or duration is not positive: return error message or empty string query = "rate(" + metricName + "[" + duration + "])" return query function cal...

This scenario focuses on calculating the 'burn rate' of an Service Level Objective (SLO) budget. The burn rate measures how quickly the 'bad' events (violations) are occurring relative to the allowed rate defined by the...

Burn rate is a key metric for SLO management. It's typically calculated as the ratio of the current rate of violations to the average rate of violations allowed by the SLO. For instance, if an SLO allows 100 errors over 30 days, the allowed rate is `100 / (30 days)`. If the current rate of errors over a short window (e.g., 5 minutes) is higher than this allowed rate, the burn rate will be greater than 1. PromQL implementations often involve `rate()` for the current violation rate and `avg_over_time(rate(...))` for the longer-term average or allowed rate. Time complexity depends on the functions used; `rate()` and `avg_over_time()` are typically O(N*W) where N is series and W is window. Space complexity is similar. Edge cases include zero or negative durations, and metrics that are not counters.

function calculateBurnRate(metricName, budgetDuration, alertWindow): if metricName or durations are invalid: return error message currentRate = "rate(" + metricName + "[" + alertWindow + "])" averageRate = "avg_over_time...

This scenario focuses on joining two different metrics in PromQL based on a shared label. It demonstrates how to align time series from distinct sources using matching labels and then perform an arithmetic operation (lik...

PromQL's label matching and vector matching capabilities are used to join metrics. When performing binary operations between two vectors (e.g., `metricA - metricB`), PromQL requires explicit instructions on how to match the elements of these vectors. The `on(<label_list>)` clause specifies which labels must match for a pair of time series to be considered a match. The `group_left(<label_list>)` or `group_right(<label_list>)` modifiers dictate which labels from the 'unmatched' side of the operation should be preserved in the resulting time series. For instance, `metricA - metricB on(instance) group_left()` will subtract `metricB` from `metricA` for all series where the `instance` label matches, and the resulting series will retain all labels from `metricA`. Time complexity is O(N*M) where N and M are the number of series in each vector, due to pairwise comparisons. Space complexity is O(N+M) for storing intermediate results. Edge cases include missing common labels, mismatched label values, and differing numbers of series.

function joinMetricsByLabel(metricA, metricB, commonLabel): if metricA or metricB or commonLabel is empty: return error message query = metricA + " - " + metricB + " on(" + commonLabel + ") group_left()" return query fun...

This scenario focuses on performing window aggregation in PromQL, specifically calculating the sum of a metric over a sliding time window. This is useful for smoothing out noisy data, identifying trends, or calculating c...

Window aggregation functions in PromQL, like `sum_over_time`, `avg_over_time`, `max_over_time`, and `min_over_time`, operate on a sliding window of data. `sum_over_time(metric[duration])` calculates the sum of all recorded values for `metric` within the last `duration` for each point in time. This means that as time progresses, the window slides forward, and the sum is recalculated based on the new data points entering and leaving the window. This is distinct from a `sum()` aggregation which aggregates across all series at a single point in time. Time complexity is O(N*W) where N is the number of series and W is the window duration, as it needs to process data points within the window. Space complexity is O(N*W) to store data for the window. Edge cases include empty metric names, non-positive durations, and metrics with very low scrape intervals.

function calculateWindowSum(metricName, windowDuration): if metricName is empty or windowDuration is not positive: return error message query = "sum_over_time(" + metricName + "[" + windowDuration + "])" return query fun...