# This function produces an intraspecific F-matrix for x phenotypic traits and y performance traits 
# using multiple regression.
# It also runs a number of calculations to help interpret the F-matrix.

fmat <- function(pheno,perf) {

# pheno should be a data frame containing only phenotypic vars in columns, where rows are individuals.
# perf should be a data frame with performance traits in columns, rows are individuals.
# Individuals must be in the same order in pheno and perf.

# Calculate how many phenotypic and performance traits there are.
	npheno <- length(pheno)
	nperf <- length(perf)
	perf_pheno <- cbind(perf,pheno)

# Scale all of the perf and pheno variables to mean zero and SD 1 so that regression gives standardized coeffs.
	perf_pheno <- as.data.frame(scale(perf_pheno))
	attach(perf_pheno)

# Do a multiple regression on each perf variable using all pheno variables, place coefficients
# and r-squares into objects.
	mreg_coefs <- NULL
	mreg_rsq <- rep(NA,nperf)
	for (i in 1:nperf) {
		frm <- as.formula(paste(names(perf)[i],paste(" ~ ",paste(names(pheno),collapse= "+"))))
		mreg_coefs[[i]] <- summary(lm(frm))$coefficients
		mreg_rsq[i] <- summary(lm(frm))$r.squared
	}
	names(mreg_coefs) <- names(perf)
	names(mreg_rsq) <- names(perf)
	detach()

# Combine multiple regression slopes into an F-matrix, omitting the intercepts and label variables.
	F <- NULL
	for (i in 1:nperf) {
		F <- cbind(F,mreg_coefs[[i]][2:(npheno+1),1])
	}
	colnames(F) <- names(perf)

# Calculate row and col sums, row var, col var of abs values, FTF and FFT matrices
	Fabs <- abs(F)
	rsum <- apply(F,1,sum)
	csum <- apply(Fabs,2,sum)

	rvar <- apply(F,1,var)
	cvar <- apply(Fabs,2,var)

	FTF <- (t(F)) %*% F
	FFT <- F %*% (t(F))

	rstats <- rbind(rsum,rvar)
	cstats <- rbind(csum,cvar)

	rgsum <- sum(abs(rsum))
	cgsum <- sum(abs(csum))
	gsum <- c(rgsum,cgsum)
	names(gsum) <- c("row","col")

# Combine all the results into a list
	results <- list(mreg_coefs,mreg_rsq,F,FTF,FFT,rstats,cstats,gsum)
	names(results)<-c("mregs","rsq","F","FTF","FFT","row.stats","col.stats","grand.sum")
	results
}