Hi Martin
I have changed the implementation slightly so that it now handles complex
matrices as well. Take a look and see what you think. I realise that a lot
of the if/else mode checking could be merged.
Cheers
Rory
SEXP do_matexp(SEXP call, SEXP op, SEXP args, SEXP rho)
{
int nrows, ncols;
SEXP matrix, tmp, dims, dims2;
SEXP x, y, x_, x__;
int i,j,e,mode;
// necessary?
mode = isComplex(CAR(args)) ? CPLXSXP : REALSXP;
SETCAR(args, coerceVector(CAR(args), mode));
x = CAR(args);
y = CADR(args);
dims = getAttrib(x, R_DimSymbol);
nrows = INTEGER(dims)[0];
ncols = INTEGER(dims)[1];
if (nrows != ncols)
error(_("can only raise square matrix to power"));
if (!isNumeric(y))
error(_("exponent must be a scalar integer"));
e = asInteger(y);
if (e < -1)
error(_("exponent must be >= -1"));
else if (e == 1)
return x;
else if (e == -1) { /* return matrix inverse via solve() */
SEXP p1, p2, inv;
PROTECT(p1 = p2 = allocList(2));
SET_TYPEOF(p1, LANGSXP);
CAR(p2) = install("solve.default");
p2 = CDR(p2);
CAR(p2) = x;
inv = eval(p1, rho);
UNPROTECT(1);
return inv;
}
PROTECT(matrix = allocVector(mode, nrows * ncols));
PROTECT(tmp = allocVector(mode, nrows * ncols));
PROTECT(x_ = allocVector(mode, nrows * ncols));
PROTECT(x__ = allocVector(mode, nrows * ncols));
if (mode == REALSXP)
Memcpy(REAL(x_), REAL(x), (size_t)nrows*ncols);
else
Memcpy(COMPLEX(x_), COMPLEX(x), (size_t)nrows*ncols);
// Initialize matrix to identity matrix
// Set x[i * ncols + i] = 1
if (mode == REALSXP)
for (i = 0; i < ncols*nrows; i++)
REAL(matrix)[i] = ((i % (ncols+1) == 0) ? 1 : 0);
else
for (i = 0; i < ncols*nrows;i++) {
COMPLEX(matrix)[i].i = 0.0;
COMPLEX(matrix)[i].r = ((i % (ncols+1) == 0) ? 1.0 : 0.0);
}
if (e == 0) {
; // return identity matrix
}
else
while (e > 0) {
if (e & 1) {
if (mode == REALSXP)
matprod(REAL(matrix), nrows, ncols,
REAL(x_), nrows, ncols, REAL(tmp));
else
cmatprod(COMPLEX(matrix), nrows, ncols,
COMPLEX(x_), nrows, ncols, COMPLEX(tmp));
//copyMatrixData(tmp, matrix, nrows, ncols, mode);
if (mode == REALSXP)
Memcpy(REAL(matrix), REAL(tmp), (size_t)nrows*ncols);
else
Memcpy(COMPLEX(matrix), COMPLEX(tmp), (size_t)nrows*ncols);
e--;
}
if (mode == REALSXP)
matprod(REAL(x_), nrows, ncols,
REAL(x_), nrows, ncols, REAL(x__));
else
cmatprod(COMPLEX(x_), nrows, ncols,
COMPLEX(x_), nrows, ncols, COMPLEX(x__));
//copyMatrixData(x__, x_, nrows, ncols, mode);
if (mode == REALSXP)
Memcpy(REAL(x_), REAL(x__), (size_t)nrows*ncols);
else
Memcpy(COMPLEX(x_), COMPLEX(x__), (size_t)nrows*ncols);
e >>= 1;
}
PROTECT(dims2 = allocVector(INTSXP, 2));
INTEGER(dims2)[0] = nrows;
INTEGER(dims2)[1] = ncols;
setAttrib(matrix, R_DimSymbol, dims2);
UNPROTECT(5);
return matrix;
}
On Sun, Apr 6, 2008 at 12:01 PM, Rory Winston
wrote:
> Hi Martin
>
> Thanks for the detailed reply. I had a look at the matrix power
> implementation in the actuar package and the modified version in the expm
> package. I have a couple of questions/comments:
>
> 1. Firstly, I seem to have trouble loading expm.
>
> > install.packages("expm",repos="http://R-Forge.R-project.org")
> trying URL '
> http://R-Forge.R-project.org/bin/macosx/universal/contrib/2.6/expm_0.9-1.tgz
> '
> Content type 'application/x-gzip' length 149679 bytes (146 Kb)
> opened URL
> ==================================================
> downloaded 146 Kb
> ...
> > library("expm")
> Error in namespaceExport(ns, exports) : undefined exports :matpow
> Error: package/namespace load failed for 'expm'
>
> Possibly a namespace file issue? My version is:
> platform i386-apple-darwin8.10.1
> arch i386
> os darwin8.10.1
> system i386, darwin8.10.1
> status
> major 2
> minor 6.1
> year 2007
> month 11
> day 26
> svn rev 43537
> language R
> version.string R version 2.6.1 (2007-11-26)
> >
>
> 2. On to the package implementation, I see we actually have very similar
> implementations. The main differences are:
>
> i) For an exponent equal to -1, I call back into R for the solve()
> function using eval() and CAR/CDR'ing the arguments into place. The actuar
> package calls dgesv() directly. I suspect that the direct route is more
> efficient and thus the more preferable one. I see that your implementation
> doesnt calculate the inverse for an exponent of -1,is there a specific
> reason for doing that?
> ii) Regarding complex matrices: I guess we should have support for this,
> as its not unreasonable that someone may do this, and it should be pretty
> easy to implement. My function doesnt have full support yet.
> iii) A philosophical question - where the the "right" place for the %^%
> operator? Is it in the operator list at a C level along with %*% and the
> like? Or is it in an R file as a function definition? I dont really have a
> preference either way...have you an opinion on this?
>
> Thanks
> Rory
>
>
>
> On Sat, Apr 5, 2008 at 6:52 PM, Martin Maechler <
> maechler@stat.math.ethz.ch> wrote:
>
> > >>>>> "RW" == Rory Winston
> > >>>>> on Sat, 5 Apr 2008 14:44:44 +0100 writes:
> >
> > RW> Hi all I recently started to write a matrix
> > RW> exponentiation operator for R (by adding a new operator
> > RW> definition to names.c, and adding the following code to
> > RW> arrays.c). It is not finished yet, but I would like to
> > RW> solicit some comments, as there are a few areas of R's
> > RW> internals that I am still feeling my way around.
> >
> > RW> Firstly:
> >
> > RW> 1) Would there be interest in adding a new operator %^%
> > RW> that performs the matrix equivalent of the scalar ^
> > RW> operator?
> >
> > Yes. A few weeks ago, I had investigated a bit about this and
> > found several R-help/R-devel postings with code proposals
> > and then about half dozen CRAN packages with diverse
> > implementations of the matrix power (I say "power" very much on
> > purpose, in order to not confuse it with the matrix exponential
> > which is another much more interesting topic, also recently (+-
> > two months?) talked about.
> >
> > Consequently I made a few timing tests and found that indeed,
> > the "smart matrix power" {computing m^2, m^4, ... and only those
> > multiplications needed} as you find it in many good books about
> > algorithms and e.g. also in *the* standard Golub & Van Loan
> > "Matrix Computation" is better than "the eigen" method even for
> > large powers.
> >
> > matPower <- function(X,n)
> > ## Function to calculate the n-th power of a matrix X
> > {
> > if(n != round(n)) {
> > n <- round(n)
> > warning("rounding exponent `n' to", n)
> > }
> > if(n == 0)
> > return(diag(nrow = nrow(X)))
> > n <- n - 1
> > phi <- X
> > ## pot <- X # the first power of the matrix.
> > while (n > 0)
> > {
> > if (n %% 2)
> > phi <- phi %*% X
> > if (n == 1) break
> > n <- n %/% 2
> > X <- X %*% X
> > }
> > return(phi)
> > }
> >
> > "Simultaneously" people where looking at the matrix exponential
> > expm() in the Matrix package,
> > and some of us had consequently started the 'expm' project on
> > R-forge.
> > The main goal there has been to investigate several algorithms
> > for the matrix exponential, notably the one buggy implementation
> > (in the 'Matrix' package until a couple of weeks ago, the bug
> > stemming from 'octave' implementation).
> > The authors of 'actuar', Vincent and Christophe, notably also
> > had code for the matrix *power* in a C (building on BLAS) and I
> > had added an R-interface '%^%' there as well.
> >
> > Yes, with the goal to move that (not the matrix exponential yet)
> > into standard R.
> > Even though it's not used so often (in percentage of all uses of
> > R), it's simple to *right*, and I have seen very many versions
> > of the matrix power that were much slower / inaccurate / ...
> > such that a reference implementation seems to be called for.
> >
> > So, please consider
> >
> > install.packages("expm",repos="http://R-Forge.R-project.org")
> >
> > -- but only from tomorrow for Windows (which installs a
> > pre-compiled package), since I found that we had accidentally
> > broken the package trivially by small changes two weeks ago.
> >
> > and then
> >
> > library(expm)
> > ?%^%
> >
> >
> > Best regards,
> > Martin Maechler, ETH Zurich
> >
> >
> >
> >
> > RW> operator? I am implicitly assuming that the benefits of
> > RW> a native exponentiation routine for Markov chain
> > RW> evaluation or function generation would outstrip that of
> > RW> an R solution. Based on my tests so far (comparing it to
> > RW> a couple of different pure R versions) it does, but I
> > RW> still there is much room for optimization in my method.
> > RW> 2) Regarding the code below: Is there a better way to do
> > RW> the matrix multiplication? I am creating quite a few
> > RW> copies for this implementation of exponentiation by
> > RW> squaring. Is there a way to cut down on the number of
> > RW> copies I am making here (I am assuming that the lhs and
> > RW> rhs of matprod() must be different instances).
> >
> > RW> Any feedback appreciated ! Thanks Rory
> >
> > RW>
> >
> > RW> /* Convenience function */ static void
> > RW> copyMatrixData(SEXP a, SEXP b, int nrows, int ncols, int
> > RW> mode) { for (int i=0; i < ncols; ++i) for (int j=0; j <
> > RW> nrows; ++j) REAL(b)[i * nrows + j] = REAL(a)[i * nrows +
> > RW> j]; }
> >
> > RW> SEXP do_matexp(SEXP call, SEXP op, SEXP args, SEXP rho)
> > RW> { int nrows, ncols; SEXP matrix, tmp, dims, dims2; SEXP
> > RW> x, y, x_, x__; int i,j,e,mode;
> >
> > RW> // Still need to fix full complex support mode =
> > RW> isComplex(CAR(args)) ? CPLXSXP : REALSXP;
> >
> > RW> SETCAR(args, coerceVector(CAR(args), mode)); x =
> > RW> CAR(args); y = CADR(args);
> >
> > RW> dims = getAttrib(x, R_DimSymbol); nrows =
> > RW> INTEGER(dims)[0]; ncols = INTEGER(dims)[1];
> >
> >
> > RW> if (nrows != ncols) error(_("can only raise square
> > RW> matrix to power"));
> >
> > RW> if (!isNumeric(y)) error(_("exponent must be a
> > RW> scalar integer"));
> >
> > RW> e = asInteger(y);
> >
> > RW> if (e < -1) error(_("exponent must be >= -1")); else
> > RW> if (e == 1) return x;
> >
> > RW> else if (e == -1) { /* return matrix inverse via
> > RW> solve() */ SEXP p1, p2, inv; PROTECT(p1 = p2 =
> > RW> allocList(2)); SET_TYPEOF(p1, LANGSXP); CAR(p2) =
> > RW> install("solve.default"); p2 = CDR(p2); CAR(p2) = x; inv
> > RW> = eval(p1, rho); UNPROTECT(1); return inv; }
> >
> > RW> PROTECT(matrix = allocVector(mode, nrows * ncols));
> > RW> PROTECT(tmp = allocVector(mode, nrows * ncols));
> > RW> PROTECT(x_ = allocVector(mode, nrows * ncols));
> > RW> PROTECT(x__ = allocVector(mode, nrows * ncols));
> >
> > RW> copyMatrixData(x, x_, nrows, ncols, mode);
> >
> > RW> // Initialize matrix to identity matrix // Set x[i *
> > RW> ncols + i] = 1 for (i = 0; i < ncols*nrows; i++)
> > RW> REAL(matrix)[i] = ((i % (ncols+1) == 0) ? 1 : 0);
> >
> > RW> if (e == 0) { ; // return identity matrix } else
> > RW> while (e > 0) { if (e & 1) { if (mode == REALSXP)
> > RW> matprod(REAL(matrix), nrows, ncols, REAL(x_), nrows,
> > RW> ncols, REAL(tmp)); else cmatprod(COMPLEX(tmp), nrows,
> > RW> ncols, COMPLEX(x_), nrows, ncols, COMPLEX(matrix));
> >
> > RW> copyMatrixData(tmp, matrix, nrows, ncols,
> > RW> mode); e--; }
> >
> > RW> if (mode == REALSXP) matprod(REAL(x_), nrows,
> > RW> ncols, REAL(x_), nrows, ncols, REAL(x__)); else
> > RW> cmatprod(COMPLEX(x_), nrows, ncols, COMPLEX(x_), nrows,
> > RW> ncols, COMPLEX(x__));
> >
> > RW> copyMatrixData(x__, x_, nrows, ncols, mode); e
> > RW> /= 2; }
> >
> > RW> PROTECT(dims2 = allocVector(INTSXP, 2));
> > RW> INTEGER(dims2)[0] = nrows; INTEGER(dims2)[1] = ncols;
> > RW> setAttrib(matrix, R_DimSymbol, dims2);
> >
> > RW> UNPROTECT(5); return matrix; }
> >
> > RW> [[alternative HTML version deleted]]
> >
> > RW> ______________________________________________
> > RW> R-devel@r-project.org mailing list
> > RW> https://stat.ethz.ch/mailman/listinfo/r-devel
> >
>
>
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