I use angular CLI, angularFire and Firebase.
I have this data in realdatabase :
 I get data from firebase with an observale :
I get data from firebase with an observale : 
//Service.ts
import { Injectable } from '@angular/core';
import { Patient } from '../models/patient.model';
import {PPS } from '../models/pps.model';
import { AngularFireDatabase, AngularFireList, AngularFireObject} from 'angularfire2/database';
@Injectable({
  providedIn: 'root'
})
export class PPSsService {
ppss: AngularFireList<any>;
constructor(private database: AngularFireDatabase) {this.ppss = database.list('ppss');}
getPPSByPatientid(Patientid: string){
return this.database.list('/ppss', ref => ref.orderByChild("Patientid").equalTo(Patientid)).valueChanges();
}  
}
// component.ts
export class PpsComponent implements OnInit {
 patientid: string;
 patientToDisplay;
 diagnosticsToDisplay;
 ppssToDisplay;
 traitement: string;
 data1: any[];
 config1: GanttChartConfig;
 elementId1: string;
constructor( 
    private route: ActivatedRoute, 
    private location: Location,
    private patientsService: PatientsService,
    private diagnosticsService: DiagnosticsService,
    private ppssService: PPSsService,
    private router: Router, 
    public dialog: MatDialog, 
    ){ }
  ngOnInit() {
   this.route.params.forEach((urlParameters) => {
   this.patientid = urlParameters['id']; });
   this.patientToDisplay = this.patientsService.getSinglePatient(this.patientid);
   this.diagnosticsToDisplay = this.diagnosticsService.getDiagnosticByPatientid(this.patientid);
   this.ppssToDisplay = this.ppssService.getPPSByPatientid(this.patientid);
 console.log(this.ppssToDisplay);
 this.data1 = [[ 'traitement','start', 'end'],
   [ 'Chirurgie',  new Date(2017, 3, 29), new Date(2017, 3, 30)],
   [ 'Chimiothérapie', new Date(2017, 2, 4),  new Date(2018, 2, 4)],
   [ 'Radiothérapie',   new Date(2017, 2, 4),  new Date(2018, 2, 4)]];
    this.config1 = new GanttChartConfig('', '', '',new Date (),new Date ());
    this.elementId1 = 'myGanttChart';
}
And i can display data in my tamplate...
But now i need in my component.ts an array like that :
this.ppssToDisplay = [['typetraitement', 'traitement','datedebut', 'datefin']]
I try to replace data1 by your code but i have an error ppssToDisplay.map is not a fonction...
 
    