feat(tabs): add method for programmatically setting focus

Adds a method that allows for focus to be moved to a particular tab. This is usually tricky, because all of the DOM elements are hidden away inside the tab group template.

Fixes angular#15007.

src/material/tabs/tab-group.spec.ts

@@ -6,7 +6,7 @@ import {By} from '@angular/platform-browser';
 import {BrowserAnimationsModule, NoopAnimationsModule} from '@angular/platform-browser/animations';
 import {CommonModule} from '@angular/common';
 import {Observable} from 'rxjs';
-import {MatTab, MatTabGroup, MatTabHeaderPosition, MatTabsModule} from './index';
+import {MatTab, MatTabGroup, MatTabHeaderPosition, MatTabsModule, MatTabHeader} from './index';
 
 
 describe('MatTabGroup', () => {
@@ -277,6 +277,21 @@ describe('MatTabGroup', () => {
         .toHaveBeenCalledWith(jasmine.objectContaining({index: 0}));
     });
 
+    it('should be able to programmatically focus a particular tab', () => {
+      fixture.detectChanges();
+      const tabGroup: MatTabGroup =
+          fixture.debugElement.query(By.css('mat-tab-group')).componentInstance;
+      const tabHeader: MatTabHeader =
+          fixture.debugElement.query(By.css('mat-tab-header')).componentInstance;
+
+      expect(tabHeader.focusIndex).not.toBe(3);
+
+      tabGroup.focusTab(3);
+      fixture.detectChanges();
+
+      expect(tabHeader.focusIndex).not.toBe(3);
+    });
+
   });
 
   describe('aria labelling', () => {

src/material/tabs/tab-group.ts

@@ -267,6 +267,18 @@ export class MatTabGroup extends _MatTabGroupMixinBase implements AfterContentIn
     }
   }
 
+  /**
+   * Sets focus to a particular tab.
+   * @param index Index of the tab to be focused.
+   */
+  focusTab(index: number) {
+    const header = this._tabHeader;
+
+    if (header) {
+      header.focusIndex = index;
+    }
+  }
+
   _focusChanged(index: number) {
     this.focusChange.emit(this._createChangeEvent(index));
   }

tools/public_api_guard/material/tabs.d.ts

@@ -95,6 +95,7 @@ export declare class MatTabGroup extends _MatTabGroupMixinBase implements AfterC
     _handleClick(tab: MatTab, tabHeader: MatTabHeader, index: number): void;
     _removeTabBodyWrapperHeight(): void;
     _setTabBodyWrapperHeight(tabHeight: number): void;
+    focusTab(index: number): void;
     ngAfterContentChecked(): void;
     ngAfterContentInit(): void;
     ngOnDestroy(): void;