fix(cloudwatch): period of each metric in usingMetrics for MathExpression is ignored (#30986)

### Issue # (if applicable)

Closes #<issue number here>.

### Reason for this change



The `usingMetrics` property (`Record<string, IMetric>`) in `MathExpressionProps` has Metric objects with a `period`.

On the other hand, in the `MathExpression` construct, the `period` of each metric in the `usingMetrics` is ignored and instead overridden by the `period` of the `MathExpression`. Even if the `period` of the `MathExpression` is not specified, it is overridden by its default value.

https://github.com/aws/aws-cdk/blob/main/packages/aws-cdk-lib/aws-cloudwatch/lib/metric.ts#L606-L608

However the statement is not written in the JSDoc.

https://github.com/aws/aws-cdk/blob/main/packages/aws-cdk-lib/aws-cloudwatch/lib/metric.ts#L566

```ts
new MathExpression({
  expression: "m1+m2",
  label: "AlbErrors",
  usingMetrics: {
    m1: metrics.custom("HTTPCode_ELB_500_Count", {
      period: Duration.minutes(1), // <- ignored and overridden by default value `Duration.minutes(5)` of `period` in the `MathExpressionOptions`
      statistic: "Sum",
      label: "HTTPCode_ELB_500_Count",
    }),
    m2: metrics.custom("HTTPCode_ELB_502_Count", {
      period: Duration.minutes(1), // <- ignored and overridden by default value `Duration.minutes(5)` of `period` in the `MathExpressionOptions`
      statistic: "Sum",
      label: "HTTPCode_ELB_502_Count",
    }),
  },
}),
```

### Description of changes



The current documentation could be confusing to users, so add this description. Also added warnings in the situation.

### Description of how you validated changes



### Checklist
- [x] My code adheres to the [CONTRIBUTING GUIDE](https://github.com/aws/aws-cdk/blob/main/CONTRIBUTING.md) and [DESIGN GUIDELINES](https://github.com/aws/aws-cdk/blob/main/docs/DESIGN_GUIDELINES.md)

----

*By submitting this pull request, I confirm that my contribution is made under the terms of the Apache-2.0 license*

Author: go-to-k

packages/aws-cdk-lib/aws-cloudwatch/lib/metric.ts

@@ -226,6 +226,35 @@ export interface MathExpressionProps extends MathExpressionOptions {
    * The key is the identifier that represents the given metric in the
    * expression, and the value is the actual Metric object.
    *
+   * The `period` of each metric in `usingMetrics` is ignored and instead overridden
+   * by the `period` specified for the `MathExpression` construct. Even if no `period`
+   * is specified for the `MathExpression`, it will be overridden by the default
+   * value (`Duration.minutes(5)`).
+   *
+   * Example:
+   *
+   * ```ts
+   * declare const metrics: elbv2.IApplicationLoadBalancerMetrics;
+   * new cloudwatch.MathExpression({
+   *   expression:  'm1+m2',
+   *   label: 'AlbErrors',
+   *   usingMetrics: {
+   *     m1: metrics.custom('HTTPCode_ELB_500_Count', {
+   *       period: Duration.minutes(1), // <- This period will be ignored
+   *       statistic: 'Sum',
+   *       label: 'HTTPCode_ELB_500_Count',
+   *     }),
+   *     m2: metrics.custom('HTTPCode_ELB_502_Count', {
+   *       period: Duration.minutes(1), // <- This period will be ignored
+   *       statistic: 'Sum',
+   *       label: 'HTTPCode_ELB_502_Count',
+   *     }),
+   *   },
+   *   period: Duration.minutes(3), // <- This overrides the period of each metric in `usingMetrics`
+   *                                //    (Even if not specified, it is overridden by the default value)
+   * });
+   * ```
+   *
    * @default - Empty map.
    */
   readonly usingMetrics?: Record<string, IMetric>;
@@ -605,12 +634,19 @@ export class MathExpression implements IMetric {
   constructor(props: MathExpressionProps) {
     this.period = props.period || cdk.Duration.minutes(5);
     this.expression = props.expression;
-    this.usingMetrics = changeAllPeriods(props.usingMetrics ?? {}, this.period);
     this.label = props.label;
     this.color = props.color;
     this.searchAccount = props.searchAccount;
     this.searchRegion = props.searchRegion;
 
+    const { record, overridden } = changeAllPeriods(props.usingMetrics ?? {}, this.period);
+    this.usingMetrics = record;
+
+    const warnings: { [id: string]: string } = {};
+    if (overridden) {
+      warnings['CloudWatch:Math:MetricsPeriodsOverridden'] = `Periods of metrics in 'usingMetrics' for Math expression '${this.expression}' have been overridden to ${this.period.toSeconds()} seconds.`;
+    }
+
     const invalidVariableNames = Object.keys(this.usingMetrics).filter(x => !validVariableName(x));
     if (invalidVariableNames.length > 0) {
       throw new Error(`Invalid variable names in expression: ${invalidVariableNames}. Must start with lowercase letter and only contain alphanumerics.`);
@@ -624,7 +660,6 @@ export class MathExpression implements IMetric {
     // we can add warnings.
     const missingIdentifiers = allIdentifiersInExpression(this.expression).filter(i => !this.usingMetrics[i]);
 
-    const warnings: { [id: string]: string } = {};
     if (!this.expression.toUpperCase().match('\\s*INSIGHT_RULE_METRIC|SELECT|SEARCH|METRICS\\s.*') && missingIdentifiers.length > 0) {
       warnings['CloudWatch:Math:UnknownIdentifier'] = `Math expression '${this.expression}' references unknown identifiers: ${missingIdentifiers.join(', ')}. Please add them to the 'usingMetrics' map.`;
     }
@@ -879,23 +914,33 @@ function ifUndefined<T>(x: T | undefined, def: T | undefined): T | undefined {
 /**
  * Change periods of all metrics in the map
  */
-function changeAllPeriods(metrics: Record<string, IMetric>, period: cdk.Duration): Record<string, IMetric> {
-  const ret: Record<string, IMetric> = {};
-  for (const [id, metric] of Object.entries(metrics)) {
-    ret[id] = changePeriod(metric, period);
+function changeAllPeriods(metrics: Record<string, IMetric>, period: cdk.Duration): { record: Record<string, IMetric>; overridden: boolean } {
+  const retRecord: Record<string, IMetric> = {};
+  let retOverridden = false;
+  for (const [id, m] of Object.entries(metrics)) {
+    const { metric, overridden } = changePeriod(m, period);
+    retRecord[id] = metric;
+    if (overridden) {
+      retOverridden = true;
+    }
   }
-  return ret;
+  return { record: retRecord, overridden: retOverridden };
 }
 
 /**
- * Return a new metric object which is the same type as the input object, but with the period changed
+ * Return a new metric object which is the same type as the input object but with the period changed,
+ * and a flag to indicate whether the period has been overwritten.
  *
  * Relies on the fact that implementations of `IMetric` are also supposed to have
  * an implementation of `with` that accepts an argument called `period`. See `IModifiableMetric`.
  */
-function changePeriod(metric: IMetric, period: cdk.Duration): IMetric {
+function changePeriod(metric: IMetric, period: cdk.Duration): { metric: IMetric; overridden: boolean} {
   if (isModifiableMetric(metric)) {
-    return metric.with({ period });
+    const overridden =
+      isMetricWithPeriod(metric) && // always true, as the period property is set with a default value even if it is not specified
+      metric.period.toSeconds() !== cdk.Duration.minutes(5).toSeconds() && // exclude the default value of a metric, assuming the user has not specified it
+      metric.period.toSeconds() !== period.toSeconds();
+    return { metric: metric.with({ period }), overridden };
   }
 
   throw new Error(`Metric object should also implement 'with': ${metric}`);
@@ -927,6 +972,14 @@ function isModifiableMetric(m: any): m is IModifiableMetric {
   return typeof m === 'object' && m !== null && !!m.with;
 }
 
+interface IMetricWithPeriod {
+  period: cdk.Duration;
+}
+
+function isMetricWithPeriod(m: any): m is IMetricWithPeriod {
+  return typeof m === 'object' && m !== null && !!m.period;
+}
+
 // Polyfill for string.matchAll(regexp)
 function matchAll(x: string, re: RegExp): RegExpMatchArray[] {
   const ret = new Array<RegExpMatchArray>();

packages/aws-cdk-lib/aws-cloudwatch/test/metric-math.test.ts

@@ -124,6 +124,90 @@ describe('Metric Math', () => {
     });
   });
 
+  test('warn if a period is specified in usingMetrics and not equal to the value of the period for MathExpression', () => {
+    const m = new MathExpression({
+      expression: 'm1',
+      usingMetrics: {
+        m1: new Metric({ namespace: 'Test', metricName: 'ACount', period: Duration.minutes(4) }),
+      },
+      period: Duration.minutes(3),
+    });
+
+    expect(m.warningsV2).toMatchObject({
+      'CloudWatch:Math:MetricsPeriodsOverridden': 'Periods of metrics in \'usingMetrics\' for Math expression \'m1\' have been overridden to 180 seconds.',
+    });
+  });
+
+  test('warn if periods are specified in usingMetrics and one is not equal to the value of the period for MathExpression', () => {
+    const m = new MathExpression({
+      expression: 'm1 + m2',
+      usingMetrics: {
+        m1: new Metric({ namespace: 'Test', metricName: 'ACount', period: Duration.minutes(4) }),
+        m2: new Metric({ namespace: 'Test', metricName: 'BCount', period: Duration.minutes(3) }),
+      },
+      period: Duration.minutes(3),
+    });
+
+    expect(m.warningsV2).toMatchObject({
+      'CloudWatch:Math:MetricsPeriodsOverridden': 'Periods of metrics in \'usingMetrics\' for Math expression \'m1 + m2\' have been overridden to 180 seconds.',
+    });
+  });
+
+  test('warn if a period is specified in usingMetrics and not equal to the default value of the period for MathExpression', () => {
+    const m = new MathExpression({
+      expression: 'm1',
+      usingMetrics: {
+        m1: new Metric({ namespace: 'Test', metricName: 'ACount', period: Duration.minutes(4) }),
+      },
+    });
+
+    expect(m.warningsV2).toMatchObject({
+      'CloudWatch:Math:MetricsPeriodsOverridden': 'Periods of metrics in \'usingMetrics\' for Math expression \'m1\' have been overridden to 300 seconds.',
+    });
+  });
+
+  test('can raise multiple warnings', () => {
+    const m = new MathExpression({
+      expression: 'e1 + m1',
+      usingMetrics: {
+        e1: new MathExpression({
+          expression: 'n1 + n2',
+        }),
+        m1: new Metric({ namespace: 'Test', metricName: 'ACount', period: Duration.minutes(4) }),
+      },
+      period: Duration.minutes(3),
+    });
+
+    expect(m.warningsV2).toMatchObject({
+      'CloudWatch:Math:MetricsPeriodsOverridden': 'Periods of metrics in \'usingMetrics\' for Math expression \'e1 + m1\' have been overridden to 180 seconds.',
+      'CloudWatch:Math:UnknownIdentifier': expect.stringContaining("'n1 + n2' references unknown identifiers"),
+    });
+  });
+
+  test('don\'t warn if a period is not specified in usingMetrics', () => {
+    const m = new MathExpression({
+      expression: 'm1',
+      usingMetrics: {
+        m1: new Metric({ namespace: 'Test', metricName: 'ACount' }),
+      },
+      period: Duration.minutes(3),
+    });
+
+    expect(m.warningsV2).toBeUndefined();
+  });
+
+  test('don\'t warn if a period is specified in usingMetrics but equal to the value of the period for MathExpression', () => {
+    const m = new MathExpression({
+      expression: 'm1',
+      usingMetrics: {
+        m1: new Metric({ namespace: 'Test', metricName: 'ACount', period: Duration.minutes(3) }),
+      },
+      period: Duration.minutes(3),
+    });
+
+    expect(m.warningsV2).toBeUndefined();
+  });
+
   describe('in graphs', () => {
     test('MathExpressions can be added to a graph', () => {
       // GIVEN

packages/aws-cdk-lib/rosetta/aws_cloudwatch/default.ts-fixture

@@ -2,6 +2,7 @@
 import { Construct } from 'constructs';
 import { Stack, Duration } from 'aws-cdk-lib';
 import * as cloudwatch from 'aws-cdk-lib/aws-cloudwatch';
+import * as elbv2 from 'aws-cdk-lib/aws-elasticloadbalancingv2';
 import * as route53 from 'aws-cdk-lib/aws-route53';
 import * as sns from 'aws-cdk-lib/aws-sns';
 import * as lambda from 'aws-cdk-lib/aws-lambda';