### Generalized eigen decomposition in complex*16 precision.
#
# Call "src/R_zggev.c" wrap "src/zggev.f".
# See "src/zggev.f" for details notations.
#
# The right generalized eigenvector v(j) corresponding to the
# generalized eigenvalue lambda(j) of (A,B) satisfies
#
# A * v(j) = lambda(j) * B * v(j).
#
# The left generalized eigenvector u(j) corresponding to the
# generalized eigenvalues lambda(j) of (A,B) satisfies
#
# u(j)**H * A = lambda(j) * u(j)**H * B
#
# where u(j)**H is the conjugate-transpose of u(j).
#
qz.zggev <- function(A, B, vl = TRUE, vr = TRUE, LWORK = NULL){
# Check
if(!(is.complex(A) && is.complex(B))){
stop("A and B should be in complex.")
}
if(!(is.matrix(A) && is.matrix(B))){
stop("A and B should be in matrix.")
}
if(any(dim(A) != dim(B))){
stop("Dimensions of A and B should be equal.")
}
if(dim(A)[1] != dim(A)[2]){
stop("Squared matrices are required.")
}
# Prepare
JOBVL <- ifelse(vl, "V", "N")
JOBVR <- ifelse(vr, "V", "N")
N <- as.integer(ncol(A))
# S <- A # WCC: memory copy, done in C.
LDA <- as.integer(N)
# T <- B # WCC: memory copy, done in C.
LDB <- as.integer(N)
ALPHA <- complex(N)
BETA <- complex(N)
if(vl){
LDVL <- as.integer(N)
VL <- complex(LDVL * N)
dim(VL) <- c(LDVL, N)
} else{
LDVL <- as.integer(1)
VL <- complex(1)
}
if(vr){
LDVR <- as.integer(N)
VR <- complex(LDVR * N)
dim(VR) <- c(LDVR, N)
} else{
LDVR <- as.integer(1)
VR <- complex(1)
}
if(is.null(LWORK) || LWORK < 2 * N){
LWORK <- as.integer(2 * N)
} else{
LWORK <- as.integer(LWORK)
}
WORK <- complex(LWORK)
RWORK <- double(8 * N)
INFO <- integer(1)
# Run
ret <- .Call("R_zggev",
JOBVL, JOBVR, N,
A, LDA, B, LDB,
ALPHA, BETA, VL, LDVL, VR, LDVR,
WORK, LWORK, RWORK, INFO,
PACKAGE = "QZ")
# Return
ret$ALPHA <- ALPHA
ret$BETA <- BETA
if(vl){
ret$VL <- VL
} else{
ret$VL <- NULL
}
if(vr){
ret$VR <- VR
} else{
ret$VR <- NULL
}
ret$WORK <- WORK[1]
ret$INFO <- INFO
# Extra returns
if(vl){
ret$U <- VL
} else{
ret$U <- NULL
}
if(vr){
ret$V <- VR
} else{
ret$V <- NULL
}
class(ret) <- "zggev"
ret
} # End of qz.zggev().
### S3 method.
print.zggev <- function(x, digits = max(4, getOption("digits") - 3), ...){
op.org <- options()
options(digits = digits)
cat("ALPHA:\n")
print(x$ALPHA)
cat("\nBETA:\n")
print(x$BETA)
if(! is.null(x$U)){
cat("\nU:\n")
print(x$U)
}
if(! is.null(x$V)){
cat("\nV:\n")
print(x$V)
}
options(op.org)
invisible()
} # end of print.zggev().
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