#
#   Copyright 2007-2010 The OpenMx Project
#
#   Licensed under the Apache License, Version 2.0 (the "License");
#   you may not use this file except in compliance with the License.
#   You may obtain a copy of the License at
# 
#        http://www.apache.org/licenses/LICENSE-2.0
# 
#   Unless required by applicable law or agreed to in writing, software
#   distributed under the License is distributed on an "AS IS" BASIS,
#   WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
#   See the License for the specific language governing permissions and
#   limitations under the License.

# -----------------------------------------------------------------------
# Program: LatentGrowthModel_MatrixRaw.R  
#  Author: Ryne Estabrook
#    Date: 08 01 2009 
#
# Latent Growth model to estimate means and (co)variances of slope and intercept
# Matrix style model input - Raw data input
#
# Revision History
#   Hermine Maes -- 10 08 2009 updated & reformatted
# -----------------------------------------------------------------------

require(OpenMx)

#Prepare Data
# -----------------------------------------------------------------------
data(myLongitudinalData)

#Create an MxModel object
# -----------------------------------------------------------------------
#PHIL: matrix model that uses raw data, works just fine

growthCurveModel <- mxModel("Linear Growth Curve Model Matrix Specification", 
    mxData(
    	observed=myLongitudinalData, 
        type="raw"
    ),
    mxMatrix(
        type="Full",
        nrow=7, 
        ncol=7,
        free=F,
        values=c(0,0,0,0,0,1,0,
                 0,0,0,0,0,1,1,
                 0,0,0,0,0,1,2,
                 0,0,0,0,0,1,3,
                 0,0,0,0,0,1,4,
                 0,0,0,0,0,0,0,
                 0,0,0,0,0,0,0),
        byrow=TRUE,
        name="A"
    ),
    mxMatrix(
        type="Symm",
        nrow=7,
        ncol=7,
        free=c(T, F, F, F, F, F, F,
               F, T, F, F, F, F, F,
               F, F, T, F, F, F, F,
               F, F, F, T, F, F, F,
               F, F, F, F, T, F, F,
               F, F, F, F, F, T, T,
               F, F, F, F, F, T, T),
        values=c(0,0,0,0,0,  0,  0,
                 0,0,0,0,0,  0,  0,
                 0,0,0,0,0,  0,  0,
                 0,0,0,0,0,  0,  0,
                 0,0,0,0,0,  0,  0,
                 0,0,0,0,0,  1,0.5,
                 0,0,0,0,0,0.5,  1),
        labels=c("residual", NA, NA, NA, NA, NA, NA,
                 NA, "residual", NA, NA, NA, NA, NA,
                 NA, NA, "residual", NA, NA, NA, NA,
                 NA, NA, NA, "residual", NA, NA, NA,
                 NA, NA, NA, NA, "residual", NA, NA,
                 NA, NA, NA, NA, NA, "vari", "cov",
                 NA, NA, NA, NA, NA, "cov", "vars"),
        byrow= TRUE,
        name="S"
    ),
    mxMatrix(
        type="Full",
        nrow=5,
        ncol=7,
        free=F,
        values=c(1,0,0,0,0,0,0,
                 0,1,0,0,0,0,0,
                 0,0,1,0,0,0,0,
                 0,0,0,1,0,0,0,
                 0,0,0,0,1,0,0),
        byrow=T,
        dimnames=list(NULL, c(names(myLongitudinalData), "intercept", "slope")),
        name="F"
    ),
    mxMatrix(
    	type="Full",
    	nrow=1, 
    	ncol=7,
        values=c(0,0,0,0,0,1,1),
        free=c(F,F,F,F,F,T,T),
        labels=c(NA,NA,NA,NA,NA,"meani","means"),
        name="M"
    ),
    mxRAMObjective("A","S","F","M")
)
      
growthCurveFit<-mxRun(growthCurveModel, suppressWarnings=TRUE)

summary(growthCurveFit)
growthCurveFit@output$estimate

#-------------------------------------------------------------------
####PHIL: This next run block fails, even after tinkering with the failing messages by 
####	 manually adding dimnames and other things
require(OpenMx)

#Prepare Data
# -----------------------------------------------------------------------
data(myLongitudinalData)
covMat<-cov(myLongitudinalData)
means<-colMeans(myLongitudinalData)
N<-nrow(myLongitudinalData)

#Create an MxModel object
# -----------------------------------------------------------------------
#PHIL: Specify input as a covariance, means, and sample size
growthCurveModel <- mxModel("Linear Growth Curve Model Matrix Specification", 
    mxData(
    	observed=covMat, 
        type='cov', means=means, numObs=N
    ),
    mxMatrix(
        type="Full",
        nrow=7, 
        ncol=7,
        free=F,
        values=c(0,0,0,0,0,1,0,
                 0,0,0,0,0,1,1,
                 0,0,0,0,0,1,2,
                 0,0,0,0,0,1,3,
                 0,0,0,0,0,1,4,
                 0,0,0,0,0,0,0,
                 0,0,0,0,0,0,0),
        byrow=TRUE,
        name="A"
    ),
    mxMatrix(
        type="Symm",
        nrow=7,
        ncol=7,
        free=c(T, F, F, F, F, F, F,
               F, T, F, F, F, F, F,
               F, F, T, F, F, F, F,
               F, F, F, T, F, F, F,
               F, F, F, F, T, F, F,
               F, F, F, F, F, T, T,
               F, F, F, F, F, T, T),
        values=c(0,0,0,0,0,  0,  0,
                 0,0,0,0,0,  0,  0,
                 0,0,0,0,0,  0,  0,
                 0,0,0,0,0,  0,  0,
                 0,0,0,0,0,  0,  0,
                 0,0,0,0,0,  1,0.5,
                 0,0,0,0,0,0.5,  1),
        labels=c("residual", NA, NA, NA, NA, NA, NA,
                 NA, "residual", NA, NA, NA, NA, NA,
                 NA, NA, "residual", NA, NA, NA, NA,
                 NA, NA, NA, "residual", NA, NA, NA,
                 NA, NA, NA, NA, "residual", NA, NA,
                 NA, NA, NA, NA, NA, "vari", "cov",
                 NA, NA, NA, NA, NA, "cov", "vars"),
        byrow= TRUE,
        name="S"
    ),
    mxMatrix(
        type="Full",
        nrow=5,
        ncol=7,
        free=F,
        values=c(1,0,0,0,0,0,0,
                 0,1,0,0,0,0,0,
                 0,0,1,0,0,0,0,
                 0,0,0,1,0,0,0,
                 0,0,0,0,1,0,0),
        byrow=T,
        dimnames=list(NULL, c(names(myLongitudinalData), "intercept", "slope")),
        name="F"
    ),
    mxMatrix(
    	type="Full",
    	nrow=1, 
    	ncol=7,
        values=c(0,0,0,0,0,1,1),
        free=c(F,F,F,F,F,T,T),
        labels=c(NA,NA,NA,NA,NA,"meani","means"),
        name="M"
    ),
    mxRAMObjective("A","S","F","M")
)
      
growthCurveFit<-mxRun(growthCurveModel, suppressWarnings=TRUE) #Error

############################################################################
###PHIL: My solution was to create arbitrary raw data that perfectly fit
# the first and second moments and use that instead

#Function to synthesize raw data from Cov and means with N observations
 momentGen<-function(C,M,N)
{      
	#C = covariance Matrix, M= means vector, N = sample size
    U<-eigen(C)$vectors
    L<-eigen(C)$values
    L.sqrt<-diag(sqrt(L))
    C.sqrt<-U%*%L.sqrt%*%t(U)
    n<-nrow(C)            
    Y.s<-scale(matrix(rnorm(N*n),nrow=N,ncol=n))
    C.y<-cor(Y.s)
    Q<-eigen(C.y)$vectors
    D<-eigen(C.y)$values
    D.invSqrt<-diag(1/sqrt(D))
    Z<-Y.s%*%Q%*%D.invSqrt
    X<-Z%*%C.sqrt
	raw<-t(t(X)+M)
	colnames(raw)<-colnames(C)
	raw
} 

#create data
require(OpenMx)
data(myLongitudinalData)

covMat<-cov(myLongitudinalData)
means<-colMeans(myLongitudinalData)
N<-nrow(myLongitudinalData)

system.time(rawData<-momentGen(covMat,means,N))

#check
cov(rawData)
colMeans(rawData)

#rerun using synthesized data

growthCurveModel <- mxModel("Linear Growth Curve Model Matrix Specification", 
    mxData(
    	observed=rawData, 
        type="raw"
    ),
    mxMatrix(
        type="Full",
        nrow=7, 
        ncol=7,
        free=F,
        values=c(0,0,0,0,0,1,0,
                 0,0,0,0,0,1,1,
                 0,0,0,0,0,1,2,
                 0,0,0,0,0,1,3,
                 0,0,0,0,0,1,4,
                 0,0,0,0,0,0,0,
                 0,0,0,0,0,0,0),
        byrow=TRUE,
        name="A"
    ),
    mxMatrix(
        type="Symm",
        nrow=7,
        ncol=7,
        free=c(T, F, F, F, F, F, F,
               F, T, F, F, F, F, F,
               F, F, T, F, F, F, F,
               F, F, F, T, F, F, F,
               F, F, F, F, T, F, F,
               F, F, F, F, F, T, T,
               F, F, F, F, F, T, T),
        values=c(0,0,0,0,0,  0,  0,
                 0,0,0,0,0,  0,  0,
                 0,0,0,0,0,  0,  0,
                 0,0,0,0,0,  0,  0,
                 0,0,0,0,0,  0,  0,
                 0,0,0,0,0,  1,0.5,
                 0,0,0,0,0,0.5,  1),
        labels=c("residual", NA, NA, NA, NA, NA, NA,
                 NA, "residual", NA, NA, NA, NA, NA,
                 NA, NA, "residual", NA, NA, NA, NA,
                 NA, NA, NA, "residual", NA, NA, NA,
                 NA, NA, NA, NA, "residual", NA, NA,
                 NA, NA, NA, NA, NA, "vari", "cov",
                 NA, NA, NA, NA, NA, "cov", "vars"),
        byrow= TRUE,
        name="S"
    ),
    mxMatrix(
        type="Full",
        nrow=5,
        ncol=7,
        free=F,
        values=c(1,0,0,0,0,0,0,
                 0,1,0,0,0,0,0,
                 0,0,1,0,0,0,0,
                 0,0,0,1,0,0,0,
                 0,0,0,0,1,0,0),
        byrow=T,
        dimnames=list(NULL, c(names(myLongitudinalData), "intercept", "slope")),
        name="F"
    ),
    mxMatrix(
    	type="Full",
    	nrow=1, 
    	ncol=7,
        values=c(0,0,0,0,0,1,1),
        free=c(F,F,F,F,F,T,T),
        labels=c(NA,NA,NA,NA,NA,"meani","means"),
        name="M"
    ),
    mxRAMObjective("A","S","F","M")
)
      
growthCurveFitSim<-mxRun(growthCurveModel, suppressWarnings=TRUE) #Works just fine

#Identical to first run with acutal raw data
summary(growthCurveFitSim)
summary(growthCurveFit)