Calculating the Determinate Equation Method

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                       "selection" : "Get"
                      }
                    }
                  },
                 "stochastic" : "true",
                 "calculationPeriod" : "true",
                 "useModelPeriod" : "true",
                 "useExistingData" : "true",
                 "treatNullsAsZeros" : "true",
                 "autoName" : "true",
                 "generatedName" : "true",
                 "period" : "true",
                 "isExclusive" : "true",
                 "useAutoPeriod" : "true"
                },
               "entryKeys" : 
                {
                 "l" : "4"
                }
              }
            }
          }
        }
      },
     "execParams" : 
      {
       "k" : "0",
       "modelKeys" : 
        {
         "l" : "4"
        },
       "scenarioKeys" : "",
       "execMethod" : "true",
       "execEvaluateSeries" : "true",
       "execPairCorrelationMatrix" : "true"
      }
    }
  }
}

JSON response:

{
 "GetMsResult" : 
  {
   "id" : 
    {
     "id" : "AOGBEFLOHDNBFOAEDPIBNDGEBKEDGIEEJKBKNMPOIOPJKGIB!M!S!CDMLANFLOHDNBFOAEJJKHCEGAMOAEGLOEPKMEPMOJMOAHLALB"
    },
   "meta" : 
    {
     "item" : 
      {
       "k" : "89669",
       "id" : "MODEL_NEW",
       "n" : "MODEL_NEW",
       "vis" : "1",
       "type" : "Problem",
       "problemMd" : 
        {
         "metamodel" : 
          {
           "k" : "89670",
           "calculationChain" : 
            {
             "its" : 
              {
               "Item" : 
                {
                 "k" : "4",
                 "id" : "OBJ4",
                 "n" : "MyOutputVavable|A[t] = 10 - MyInputVavable[t] * 3.14, (From parent)-(From parent)",
                 "vis" : "1",
                 "type" : "Model",
                 "excluded" : "0",
                 "graphMeta" : "",
                 "model" : 
                  {
                   "transform" : 
                    {
                     "outputs" : 
                      {
                       "its" : 
                        {
                         "Item" : 
                          {
                           "k" : "1",
                           "id" : "VARIABLES_89670",
                           "n" : "Variables",
                           "vis" : "1",
                           "slices" : 
                            {
                             "its" : 
                              {
                               "Item" : 
                                {
                                 "k" : "0",
                                 "id" : "MyOutputVavable|A",
                                 "n" : "MyOutputVavable|A",
                                 "vis" : "1",
                                 "variableKey" : "1",
                                 "stubKey" : "89671",
                                 "selections" : 
                                  {
                                   "its" : 
                                    {
                                     "Item" : 
                                      {
                                       "id" : 
                                        {
                                         "id" : "89683"
                                        },
                                       "variant" : "2"
                                      }
                                    }
                                  },
                                 "aggregator" : "None",
                                 "parametrizedDimensions" : 
                                  {
                                   "its" : 
                                    {
                                     "Item" : 
                                      {
                                       "dimension" : "0",
                                       "parameter" : "0"
                                      }
                                    }
                                  },
                                 "unitInfo" : 
                                  {
                                   "unit" : "4294967295",
                                   "measure" : "4294967295",
                                   "baseUnit" : "4294967295",
                                   "unitsDimensionKey" : "0"
                                  },
                                 "level" : "Year"
                                }
                              }
                            },
                           "variableStubKey" : "89671",
                           "parameterID" : "",
                           "kind" : "Stub",
                           "attributeId" : "",
                           "attributeType" : "Series"
                          }
                        }
                      },
                     "formulaCount" : "1",
                     "formulas" : 
                      {
                       "its" : 
                        {
                         "it" : 
                          [
                            {
                             "k" : "0",
                             "kind" : "Deterministic",
                             "method" : 
                              {
                               "deterministic" : 
                                {
                                 "modifyType" : "Replace",
                                 "expression" : "10 - @_2:0[] * 3.14",
                                 "result" : 
                                  {
                                   "slice" : 
                                    {
                                     "k" : "0",
                                     "id" : "MyOutputVavable|A",
                                     "n" : "MyOutputVavable|A",
                                     "vis" : "1",
                                     "variableKey" : "1",
                                     "stubKey" : "89671",
                                     "selections" : 
                                      {
                                       "its" : 
                                        {
                                         "Item" : 
                                          {
                                           "id" : 
                                            {
                                             "id" : "89683"
                                            },
                                           "variant" : "2"
                                          }
                                        }
                                      },
                                     "aggregator" : "None",
                                     "parametrizedDimensions" : 
                                      {
                                       "its" : 
                                        {
                                         "Item" : 
                                          {
                                           "dimension" : "0",
                                           "parameter" : "0"
                                          }
                                        }
                                      },
                                     "unitInfo" : 
                                      {
                                       "unit" : "4294967295",
                                       "measure" : "4294967295",
                                       "baseUnit" : "4294967295",
                                       "unitsDimensionKey" : "0"
                                      },
                                     "level" : "Year"
                                    },
                                   "lag" : "",
                                   "key" : "0",
                                   "termToText" : "{MyOutputVavable|A[t]}",
                                   "termToInnerText" : "@_1:0[]",
                                   "termInfo" : 
                                    {
                                     "k" : "4294967295",
                                     "lag" : "0",
                                     "inversion" : 
                                      {
                                       "type" : "None",
                                       "lag" : "PrecidingValue",
                                       "previousLag" : "-1",
                                       "seasonality" : "None",
                                       "dependence" : "Linear",
                                       "K" : "3"
                                      },
                                     "slice" : 
                                      {
                                       "k" : "0",
                                       "id" : "MyOutputVavable|A",
                                       "n" : "MyOutputVavable|A",
                                       "vis" : "1",
                                       "variableKey" : "1",
                                       "stubKey" : "89671",
                                       "selections" : 
                                        {
                                         "its" : 
                                          {
                                           "Item" : 
                                            {
                                             "id" : 
                                              {
                                               "id" : "89683"
                                              },
                                             "variant" : "2"
                                            }
                                          }
                                        },
                                       "aggregator" : "None",
                                       "parametrizedDimensions" : 
                                        {
                                         "its" : 
                                          {
                                           "Item" : 
                                            {
                                             "dimension" : "0",
                                             "parameter" : "0"
                                            }
                                          }
                                        },
                                       "unitInfo" : 
                                        {
                                         "unit" : "4294967295",
                                         "measure" : "4294967295",
                                         "baseUnit" : "4294967295",
                                         "unitsDimensionKey" : "0"
                                        },
                                       "level" : "Year"
                                      },
                                     "date" : "1899-12-30"
                                    },
                                   "unitInfo" : 
                                    {
                                     "unit" : "4294967295",
                                     "measure" : "4294967295",
                                     "baseUnit" : "4294967295",
                                     "unitsDimensionKey" : "0"
                                    },
                                   "included" : "0"
                                  },
                                 "operands" : 
                                  {
                                   "its" : 
                                    {
                                     "Item" : 
                                      {
                                       "k" : "0",
                                       "slice" : 
                                        {
                                         "k" : "0",
                                         "id" : "1",
                                         "n" : "MyInputVavable",
                                         "vis" : "1",
                                         "variableKey" : "2",
                                         "stubKey" : "89671",
                                         "selections" : 
                                          {
                                           "its" : 
                                            {
                                             "Item" : 
                                              {
                                               "id" : 
                                                {
                                                 "id" : "89683"
                                                },
                                               "variant" : "1"
                                              }
                                            }
                                          },
                                         "aggregator" : "None",
                                         "parametrizedDimensions" : 
                                          {
                                           "its" : 
                                            {
                                             "Item" : 
                                              {
                                               "dimension" : "0",
                                               "parameter" : "0"
                                              }
                                            }
                                          },
                                         "unitInfo" : 
                                          {
                                           "unit" : "4294967295",
                                           "measure" : "4294967295",
                                           "baseUnit" : "4294967295",
                                           "unitsDimensionKey" : "0"
                                          },
                                         "level" : "Year"
                                        },
                                       "lag" : "",
                                       "key" : "1",
                                       "termToText" : "{MyInputVavable[t]}",
                                       "termToInnerText" : "@_2:0[]",
                                       "termInfo" : 
                                        {
                                         "k" : "4294967295",
                                         "lag" : "0",
                                         "inversion" : 
                                          {
                                           "type" : "None",
                                           "lag" : "PrecidingValue",
                                           "previousLag" : "-1",
                                           "seasonality" : "None",
                                           "dependence" : "Linear",
                                           "K" : "3"
                                          },
                                         "slice" : 
                                          {
                                           "k" : "0",
                                           "id" : "1",
                                           "n" : "MyInputVavable",
                                           "vis" : "1",
                                           "variableKey" : "2",
                                           "stubKey" : "89671",
                                           "selections" : 
                                            {
                                             "its" : 
                                              {
                                               "Item" : 
                                                {
                                                 "id" : 
                                                  {
                                                   "id" : "89683"
                                                  },
                                                 "variant" : "1"
                                                }
                                              }
                                            },
                                           "aggregator" : "None",
                                           "parametrizedDimensions" : 
                                            {
                                             "its" : 
                                              {
                                               "Item" : 
                                                {
                                                 "dimension" : "0",
                                                 "parameter" : "0"
                                                }
                                              }
                                            },
                                           "unitInfo" : 
                                            {
                                             "unit" : "4294967295",
                                             "measure" : "4294967295",
                                             "baseUnit" : "4294967295",
                                             "unitsDimensionKey" : "0"
                                            },
                                           "level" : "Year"
                                          },
                                         "date" : "1899-12-30"
                                        },
                                       "unitInfo" : 
                                        {
                                         "unit" : "4294967295",
                                         "measure" : "4294967295",
                                         "baseUnit" : "4294967295",
                                         "unitsDimensionKey" : "0"
                                        },
                                       "included" : "1"
                                      }
                                    }
                                  },
                                 "pairCorrelationMatrix" : 
                                  {
                                   "data" : 
                                    {
                                     "d" : "1"
                                    }
                                  }
                                },
                               "name" : "10 - X1 * 3.14",
                               "series" : 
                                {
                                 "addFactor" : 
                                  {
                                   "k" : "4294967295"
                                  }
                                },
                               "evaluateSeries" : 
                                {
                                 "its" : 
                                  {
                                   "Item" : 
                                    {
                                     "scenarioKey" : "4294967295",
                                     "fact" : 
                                      {
                                       "d" : 
                                        [
                                          "3",
                                          "7",
                                          "2",
                                          "6",
                                          "4",
                                          "1",
                                          "5",
                                          "3.42857143",
                                          "3.28571429",
                                          "3.14285714",
                                          "3",
                                          "2.85714286",
                                          "2.71428571",
                                          "2.57142857",
                                          "2.42857143",
                                          "2.28571429",
                                          "2.14285714",
                                          "2",
                                          "1.85714286",
                                          "1.71428571",
                                          "1.57142857",
                                          "1.42857143",
                                          "1.28571429",
                                          "1.14285714",
                                          "1",
                                          "0.85714286",
                                          "0.71428571",
                                          "0.57142857",
                                          "NaN"
                                        ]
                                      },
                                     "modelling" : 
                                      {
                                       "d" : 
                                        [
                                          "6.859999999999999",
                                          "-2.56",
                                          "3.72",
                                          "-11.98",
                                          "-13.55",
                                          "-18.574",
                                          "-23.598",
                                          "-28.62200000000001",
                                          "-33.646",
                                          "-38.67",
                                          "-43.69400000000001",
                                          "-48.718",
                                          "-53.742",
                                          "-58.76600000000001",
                                          "-63.79000000000001",
                                          "-68.81400000000001",
                                          "-73.83800000000001",
                                          "-78.86200000000001",
                                          "-83.886",
                                          "-88.91000000000001",
                                          "-93.93400000000001",
                                          "-98.95800000000001",
                                          "-103.982",
                                          "-109.006",
                                          "-114.03",
                                          "-119.054",
                                          "NaN",
                                          "NaN",
                                          "NaN"
                                        ]
                                      },
                                     "residuals" : 
                                      {
                                       "d" : 
                                        [
                                          "-3.859999999999999",
                                          "9.56",
                                          "-1.72",
                                          "17.98",
                                          "17.55",
                                          "19.574",
                                          "28.598",
                                          "32.05057143000001",
                                          "36.93171429",
                                          "41.81285714",
                                          "46.69400000000001",
                                          "51.57514286000001",
                                          "56.45628571",
                                          "61.33742857000001",
                                          "66.21857143000001",
                                          "71.09971429000001",
                                          "75.98085714000001",
                                          "80.86200000000001",
                                          "85.74314285999999",
                                          "90.62428571000001",
                                          "95.50542857000001",
                                          "100.38657143",
                                          "105.26771429",
                                          "110.14885714",
                                          "115.03",
                                          "119.91114286",
                                          "NaN",
                                          "NaN",
                                          "NaN"
                                        ]
                                      },
                                     "input" : 
                                      {
                                       "d" : 
                                        [
                                          "3",
                                          "7",
                                          "2",
                                          "6",
                                          "4",
                                          "1",
                                          "5",
                                          "3.42857143",
                                          "3.28571429",
                                          "3.14285714",
                                          "3",
                                          "2.85714286",
                                          "2.71428571",
                                          "2.57142857",
                                          "2.42857143",
                                          "2.28571429",
                                          "2.14285714",
                                          "2",
                                          "1.85714286",
                                          "1.71428571",
                                          "1.57142857",
                                          "1.42857143",
                                          "1.28571429",
                                          "1.14285714",
                                          "1",
                                          "0.85714286",
                                          "0.71428571",
                                          "0.57142857",
                                          "NaN",
                                          "NaN",
                                          "NaN"
                                        ]
                                      },
                                     "factors" : 
                                      {
                                       "its" : 
                                        {
                                         "it" : 
                                          [
                                            {
                                             "termToText" : "{MyInputVavable[t]}",
                                             "serie" : 
                                              {
                                               "d" : 
                                                [
                                                  "1",
                                                  "4",
                                                  "2",
                                                  "7",
                                                  "7.5",
                                                  "9.1",
                                                  "10.7",
                                                  "12.3",
                                                  "13.9",
                                                  "15.5",
                                                  "17.1",
                                                  "18.7",
                                                  "20.3",
                                                  "21.9",
                                                  "23.5",
                                                  "25.1",
                                                  "26.7",
                                                  "28.3",
                                                  "29.9",
                                                  "31.5",
                                                  "33.1",
                                                  "34.7",
                                                  "36.3",
                                                  "37.9",
                                                  "39.5",
                                                  "41.1",
                                                  "NaN",
                                                  "NaN",
                                                  "NaN",
                                                  "NaN",
                                                  "NaN"
                                                ]
                                              },
                                             "inversion" : 
                                              {
                                               "type" : "None",
                                               "lag" : "PrecidingValue",
                                               "previousLag" : "-1",
                                               "seasonality" : "None",
                                               "dependence" : "Linear",
                                               "K" : "3"
                                              },
                                             "entryKey" : "1"
                                            }
                                          ]
                                        }
                                      }
                                    }
                                  },
                                 "dates" : 
                                  {
                                   "it" : 
                                    [
                                      "1990A1",
                                      "1991A1",
                                      "1992A1",
                                      "1993A1",
                                      "1994A1",
                                      "1995A1",
                                      "1996A1",
                                      "1997A1",
                                      "1998A1",
                                      "1999A1",
                                      "2000A1",
                                      "2001A1",
                                      "2002A1",
                                      "2003A1",
                                      "2004A1",
                                      "2005A1",
                                      "2006A1",
                                      "2007A1",
                                      "2008A1",
                                      "2009A1",
                                      "2010A1",
                                      "2011A1",
                                      "2012A1",
                                      "2013A1",
                                      "2014A1",
                                      "2015A1",
                                      "2016A1",
                                      "2017A1",
                                      "2018A1",
                                      "2019A1",
                                      "2020A1"
                                    ]
                                  }
                                },
                               "inversionInfo" : 
                                {
                                 "type" : "None",
                                 "lag" : "PrecidingValue",
                                 "previousLag" : "-1",
                                 "seasonality" : "None",
                                 "dependence" : "Linear",
                                 "K" : "3"
                                },
                               "doUseR" : "0",
                               "supportsR" : "0"
                              },
                             "calendarLevel" : "Year",
                             "outputSliceKey" : "0"
                            }
                          ]
                        }
                      },
                     "displayId" : "0",
                     "series" : 
                      {
                       "its" : ""
                      },
                     "kind" : "Simple",
                     "displaySettings" : 
                      {
                       "displayTermsAs" : "Derive"
                      },
                     "additionalAttributes" : "",
                     "calculationType" : "Serie",
                     "calculationDirection" : "Forward"
                    },
                   "stochastic" : "0",
                   "calculationPeriod" : "Forecast",
                   "useModelPeriod" : "1",
                   "useExistingData" : "0",
                   "treatNullsAsZeros" : "0",
                   "autoName" : "1",
                   "period" : 
                    {
                     "identificationStartDate" : "1990-01-01",
                     "identificationEndDate" : "2018-04-24",
                     "forecastStartDate" : "2018-04-25",
                     "forecastEndDate" : "2020-01-01",
                     "identificationStartDateParamID" : "",
                     "identificationEndDateParamID" : "",
                     "forecastStartDateParamID" : "",
                     "forecastEndDateParamID" : "",
                     "autoPeriod" : "28672",
                     "identificationStartOffset" : "0",
                     "identificationEndOffset" : "0",
                     "forecastEndOffset" : "0",
                     "isIdentStartCorrect" : "1",
                     "isIdentEndCorrect" : "1",
                     "isForecastEndCorrect" : "1"
                    },
                   "isExclusive" : "1",
                   "useAutoPeriod" : "1",
                   "generatedName" : "MyOutputVavable|A[t] = 10 - MyInputVavable[t] * 3.14",
                   "warnings" : "",
                   "readOnly" : "0"
                  }
                }
              }
            },
           "visualController" : 
            {
             "userRPath" : "",
             "isRExist" : "0"
            },
           "suppressEmptyFilter" : 
            {
             "suppressEmpty" : "0",
             "suppressEmptyArea" : "SerieBounds"
            },
           "readOnly" : "0",
           "variableTestUseR" : "0",
           "calculateIdentOnFact" : "0"
          },
         "useScenarios" : "0",
         "readOnly" : "0"
        }
      }
    }
  }
}

public static MsCalculationChainEntry GetMsDeterm(MsId ms, ulong modelKey, ulong eqKey)
{
    var getMsOp = new GetMs();
    // Set operation execution parameters
    getMsOp.tMs = ms;
    getMsOp.tArg = new GetMsArg()
    {  // Set data extraction pattern
        pattern = new MsMdPattern()
        {
            obInst = false,
            all = false,
            item = new MsItemPattern()
            {  // Specify calculated model key
                key = modelKey,
                problem = new MsProblemPattern()
                {
                    metamodel = new MsMetaModelPattern()
                    {
                        calculationChain = ListOperation.Get,
                        calcChainPattern = new MsCalculationChainPattern()
                        {
                            // Specify calculated equation key
                            entryKeys = new long[] { (long)eqKey },
                            modelPattern = new MsModelPattern()
                            {
                                autoName = true,
                                calculationPeriod = true,
                                generatedName = true,
                                isExclusive = true,
                                period = true,
                                stochastic = true,
                                treatNullsAsZeros = true,
                                useAutoPeriod = true,
                                useExistingData = true,
                                useModelPeriod = true,
                                transform = new MsFormulaTransformPattern()
                                {
                                    additionalAttributes = true,
                                    calculationDirection = true,
                                    calculationType = true,
                                    displayId = true,
                                    displaySettings = true,
                                    formulaCount = true,
                                    outputs = ListOperation.Get,
                                    series = ListOperation.Get,
                                    kind = true,
                                    formulas = new TsFormulaPattern()
                                    {
                                        method = new TsMethodPattern()
                                        {
                                            series = true
                                        }
                                    },
                                    equationsFormula = new TsFormulaPattern()
                                    {
                                        method = new TsMethodPattern() { }
                                    },
                                    transformVariable = new MsFormulaTransformVariablePattern()
                                    {
                                        slices = ListOperation.Get,
                                        transformSlice = new MsFormulaTransformSlicePattern()
                                        {
                                            selection = ListOperation.Get
                                        }
                                    }
                                }
                            }
                        }
                    }
                }
            }
        }, // Set equation calculation parameters
        execParams = new MsMdExecParams()
        {
            k = 0,
            execMethod = true,
            execEvaluateSeries = true,
            execPairCorrelationMatrix = true,
            scenarioKeys = new long[] { },
            modelKeys = new long[] { (long)eqKey }
        }
    };
            // Create a proxy object for operation execution
            var somClient = new SomPortTypeClient();
    GetMsResult getMsResult = somClient.GetMs(getMsOp);
    MsMetaModel meta = getMsResult.meta.item.problemMd.metamodel;
    MsCalculationChainEntry chainEntry = meta.calculationChain.its.GetValue(0) as MsCalculationChainEntry;
    // Display errors and warnings
    MsModel eq = chainEntry.model;
    if (eq.warnings != null)
    {
        Console.WriteLine("-- Warnings --");
        Console.WriteLine("".PadRight(3) + printArray(eq.warnings));
    }
    if (eq.error == null) //Check if errors occurred on equation calculation
    {   // Equation is calculated without errors, get calculation results   
        TsFormula formula = eq.transform.formulas.its.GetValue(0) as TsFormula;
        TsDeterministicMethod determ = formula.method.deterministic;       
        Console.WriteLine("-- Input factors --");       
        Console.WriteLine("".PadRight(3) + printArray(determ.factsMatrix));
        Console.WriteLine("-- Correlation matrix --");
        MsPairCorrelationMatrix pm = determ.pairCorrelationMatrix;
        if (pm.error != null) {Console.WriteLine("".PadRight(3) + "error: " + pm.error);}       
        Console.WriteLine("".PadRight(3) + printArray(pm.data));
        // Get calculated values and display into console window
        MsEvaluateSeriesResult seriesRes = formula.method.evaluateSeries;
        printSeries(seriesRes);
    }
    else // Errors occurred on equation calculation
    {
        Console.WriteLine("-- Errors --");
        Console.WriteLine(eq.error);
    }
    // Return the model that contains equation
    return chainEntry;
}