The R Project SVN R

/*
 *  R : A Computer Language for Statistical Data Analysis
 *  Copyright (C) 1995, 1996  Robert Gentleman and Ross Ihaka
 *  Copyright (C) 1998-2013   The R Core Team
 *  Copyright (C) 2002-2008   The R Foundation
 *
 *  This program is free software; you can redistribute it and/or modify
 *  it under the terms of the GNU General Public License as published by
 *  the Free Software Foundation; either version 2 of the License, or
 *  (at your option) any later version.
 *
 *  This program is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU General Public License for more details.
 *
 *  You should have received a copy of the GNU General Public License
 *  along with this program; if not, a copy is available at
 *  http://www.r-project.org/Licenses/
 */

#ifdef HAVE_CONFIG_H
#include <config.h>
#endif

#include <Defn.h>
#include <Internal.h>
#include <Rmath.h>
#include <R_ext/RS.h>     /* for Calloc/Free */
#include <R_ext/Applic.h> /* for dgemm */

/* "GetRowNames" and "GetColNames" are utility routines which
 * locate and return the row names and column names from the
 * dimnames attribute of a matrix.  They are useful because
 * old versions of R used pair-based lists for dimnames
 * whereas recent versions use vector based lists.

 * These are now very old, plus
 * ``When the "dimnames" attribute is
 *   grabbed off an array it is always adjusted to be a vector.''

 They are used in bind.c and subset.c, and advertised in Rinternals.h
*/
SEXP GetRowNames(SEXP dimnames)
{
    if (TYPEOF(dimnames) == VECSXP)
    return VECTOR_ELT(dimnames, 0);
    else
    return R_NilValue;
}

SEXP GetColNames(SEXP dimnames)
{
    if (TYPEOF(dimnames) == VECSXP)
    return VECTOR_ELT(dimnames, 1);
    else
    return R_NilValue;
}

SEXP attribute_hidden do_matrix(SEXP call, SEXP op, SEXP args, SEXP rho)
{
    SEXP vals, ans, snr, snc, dimnames;
    int nr = 1, nc = 1, byrow, miss_nr, miss_nc;
    R_xlen_t lendat;

    checkArity(op, args);
    vals = CAR(args); args = CDR(args);
    switch(TYPEOF(vals)) {
    case LGLSXP:
    case INTSXP:
    case REALSXP:
    case CPLXSXP:
    case STRSXP:
    case RAWSXP:
    case EXPRSXP:
    case VECSXP:
        break;
    default:
        error(_("'data' must be of a vector type, was '%s'"),
        type2char(TYPEOF(vals)));
    }
    lendat = XLENGTH(vals);
    snr = CAR(args); args = CDR(args);
    snc = CAR(args); args = CDR(args);
    byrow = asLogical(CAR(args)); args = CDR(args);
    if (byrow == NA_INTEGER)
    error(_("invalid '%s' argument"), "byrow");
    dimnames = CAR(args);
    args = CDR(args);
    miss_nr = asLogical(CAR(args)); args = CDR(args);
    miss_nc = asLogical(CAR(args));

    if (!miss_nr) {
    if (!isNumeric(snr)) error(_("non-numeric matrix extent"));
    nr = asInteger(snr);
    if (nr == NA_INTEGER)
        error(_("invalid 'nrow' value (too large or NA)"));
    if (nr < 0)
        error(_("invalid 'nrow' value (< 0)"));
    }
    if (!miss_nc) {
    if (!isNumeric(snc)) error(_("non-numeric matrix extent"));
    nc = asInteger(snc);
    if (nc == NA_INTEGER)
        error(_("invalid 'ncol' value (too large or NA)"));
    if (nc < 0)
        error(_("invalid 'ncol' value (< 0)"));
    }
    if (miss_nr && miss_nc) {
    if (lendat > INT_MAX) error("data is too long");
    nr = (int) lendat;
    } else if (miss_nr) {
    if (lendat > (double) nc * INT_MAX) error("data is too long");
    // avoid division by zero
    if (nc == 0) {
        if (lendat) error(_("nc = 0 for non-null data"));
        else nr = 0;
    } else
        nr = (int) ceil((double) lendat / (double) nc);
    } else if (miss_nc) {
    if (lendat > (double) nr * INT_MAX) error("data is too long");
    // avoid division by zero
    if (nr == 0) {
        if (lendat) error(_("nr = 0 for non-null data"));
        else nc = 0;
    } else
        nc = (int) ceil((double) lendat / (double) nr);
    }

    if(lendat > 0) {
    R_xlen_t nrc = (R_xlen_t) nr * nc;
    if (lendat > 1 && nrc % lendat != 0) {
        if (((lendat > nr) && (lendat / nr) * nr != lendat) ||
        ((lendat < nr) && (nr / lendat) * lendat != nr))
        warning(_("data length [%d] is not a sub-multiple or multiple of the number of rows [%d]"), lendat, nr);
        else if (((lendat > nc) && (lendat / nc) * nc != lendat) ||
             ((lendat < nc) && (nc / lendat) * lendat != nc))
        warning(_("data length [%d] is not a sub-multiple or multiple of the number of columns [%d]"), lendat, nc);
    }
    else if ((lendat > 1) && (nrc == 0)){
        warning(_("data length exceeds size of matrix"));
    }
    }

#ifndef LONG_VECTOR_SUPPORT
    if ((double)nr * (double)nc > INT_MAX)
    error(_("too many elements specified"));
#endif

    PROTECT(ans = allocMatrix(TYPEOF(vals), nr, nc));
    if(lendat) {
    if (isVector(vals))
        copyMatrix(ans, vals, byrow);
    else
        copyListMatrix(ans, vals, byrow);
    } else if (isVector(vals)) { /* fill with NAs */
    R_xlen_t N = (R_xlen_t) nr * nc, i;
    switch(TYPEOF(vals)) {
    case STRSXP:
        for (i = 0; i < N; i++)
        SET_STRING_ELT(ans, i, NA_STRING);
        break;
    case LGLSXP:
        for (i = 0; i < N; i++)
        LOGICAL(ans)[i] = NA_LOGICAL;
        break;
    case INTSXP:
        for (i = 0; i < N; i++)
        INTEGER(ans)[i] = NA_INTEGER;
        break;
    case REALSXP:
        for (i = 0; i < N; i++)
        REAL(ans)[i] = NA_REAL;
        break;
    case CPLXSXP:
        {
        Rcomplex na_cmplx;
        na_cmplx.r = NA_REAL;
        na_cmplx.i = 0;
        for (i = 0; i < N; i++)
            COMPLEX(ans)[i] = na_cmplx;
        }
        break;
    case RAWSXP:
        memset(RAW(ans), 0, N);
        break;
    default:
        /* don't fill with anything */
        ;
    }
    }
    if(!isNull(dimnames)&& length(dimnames) > 0)
    ans = dimnamesgets(ans, dimnames);
    UNPROTECT(1);
    return ans;
}


SEXP allocMatrix(SEXPTYPE mode, int nrow, int ncol)
{
    SEXP s, t;
    R_xlen_t n;

    if (nrow < 0 || ncol < 0)
    error(_("negative extents to matrix"));
#ifndef LONG_VECTOR_SUPPORT
    if ((double)nrow * (double)ncol > INT_MAX)
    error(_("allocMatrix: too many elements specified"));
#endif
    n = ((R_xlen_t) nrow) * ncol;
    PROTECT(s = allocVector(mode, n));
    PROTECT(t = allocVector(INTSXP, 2));
    INTEGER(t)[0] = nrow;
    INTEGER(t)[1] = ncol;
    setAttrib(s, R_DimSymbol, t);
    UNPROTECT(2);
    return s;
}

/**
 * Allocate a 3-dimensional array
 *
 * @param mode The R mode (e.g. INTSXP)
 * @param nrow number of rows
 * @param ncol number of columns
 * @param nface number of faces
 *
 * @return A 3-dimensional array of the indicated dimensions and mode
 */
SEXP alloc3DArray(SEXPTYPE mode, int nrow, int ncol, int nface)
{
    SEXP s, t;
    R_xlen_t n;

    if (nrow < 0 || ncol < 0 || nface < 0)
    error(_("negative extents to 3D array"));
#ifndef LONG_VECTOR_SUPPORT
    if ((double)nrow * (double)ncol * (double)nface > INT_MAX)
    error(_("'alloc3Darray': too many elements specified"));
#endif
    n = ((R_xlen_t) nrow) * ncol * nface;
    PROTECT(s = allocVector(mode, n));
    PROTECT(t = allocVector(INTSXP, 3));
    INTEGER(t)[0] = nrow;
    INTEGER(t)[1] = ncol;
    INTEGER(t)[2] = nface;
    setAttrib(s, R_DimSymbol, t);
    UNPROTECT(2);
    return s;
}


SEXP allocArray(SEXPTYPE mode, SEXP dims)
{
    SEXP array;
    int i;
    R_xlen_t n = 1;
    double dn = 1;

    for (i = 0; i < LENGTH(dims); i++) {
    dn *= INTEGER(dims)[i];
#ifndef LONG_VECTOR_SUPPORT
    if(dn > INT_MAX)
        error(_("'allocArray': too many elements specified by 'dims'"));
#endif
    n *= INTEGER(dims)[i];
    }

    PROTECT(dims = duplicate(dims));
    PROTECT(array = allocVector(mode, n));
    setAttrib(array, R_DimSymbol, dims);
    UNPROTECT(2);
    return array;
}

/* DropDims strips away redundant dimensioning information. */
/* If there is an appropriate dimnames attribute the correct */
/* element is extracted and attached to the vector as a names */
/* attribute.  Note that this function mutates x. */
/* Duplication should occur before this is called. */

SEXP DropDims(SEXP x)
{
    SEXP dims, dimnames, newnames = R_NilValue;
    int i, n, ndims;

    PROTECT(x);
    dims = getAttrib(x, R_DimSymbol);
    dimnames = getAttrib(x, R_DimNamesSymbol);

    /* Check that dropping will actually do something. */
    /* (1) Check that there is a "dim" attribute. */

    if (dims == R_NilValue) {
    UNPROTECT(1);
    return x;
    }
    ndims = LENGTH(dims);

    /* (2) Check whether there are redundant extents */
    n = 0;
    for (i = 0; i < ndims; i++)
    if (INTEGER(dims)[i] != 1) n++;
    if (n == ndims) {
    UNPROTECT(1);
    return x;
    }

    if (n <= 1) {
    /* We have reduced to a vector result.
       If that has length one, it is ambiguous which dimnames to use,
       so use it if there is only one (as from R 2.7.0).
     */
    if (dimnames != R_NilValue) {
        if(XLENGTH(x) != 1) {
        for (i = 0; i < LENGTH(dims); i++) {
            if (INTEGER(dims)[i] != 1) {
            newnames = VECTOR_ELT(dimnames, i);
            break;
            }
        }
        } else { /* drop all dims: keep names if unambiguous */
        int cnt;
        for(i = 0, cnt = 0; i < LENGTH(dims); i++)
            if(VECTOR_ELT(dimnames, i) != R_NilValue) cnt++;
        if(cnt == 1)
            for (i = 0; i < LENGTH(dims); i++) {
            newnames = VECTOR_ELT(dimnames, i);
            if(newnames != R_NilValue) break;
            }
        }
    }
    PROTECT(newnames);
    setAttrib(x, R_DimNamesSymbol, R_NilValue);
    setAttrib(x, R_DimSymbol, R_NilValue);
    setAttrib(x, R_NamesSymbol, newnames);
    /* FIXME: the following is desirable, but pointless as long as
       subset.c & others have a contrary version that leaves the
       S4 class in, incorrectly, in the case of vectors.  JMC
       3/3/09 */
/*  if(IS_S4_OBJECT(x)) {/\* no longer valid subclass of array or
    matrix *\/ */
/*      setAttrib(x, R_ClassSymbol, R_NilValue); */
/*      UNSET_S4_OBJECT(x); */
/*  } */
    UNPROTECT(1);
    } else {
    /* We have a lower dimensional array. */
    SEXP newdims, dnn, newnamesnames = R_NilValue;
    dnn = getAttrib(dimnames, R_NamesSymbol);
    PROTECT(newdims = allocVector(INTSXP, n));
    for (i = 0, n = 0; i < ndims; i++)
        if (INTEGER(dims)[i] != 1)
        INTEGER(newdims)[n++] = INTEGER(dims)[i];
    if (!isNull(dimnames)) {
        int havenames = 0;
        for (i = 0; i < ndims; i++)
        if (INTEGER(dims)[i] != 1 &&
            VECTOR_ELT(dimnames, i) != R_NilValue)
            havenames = 1;
        if (havenames) {
        PROTECT(newnames = allocVector(VECSXP, n));
        PROTECT(newnamesnames = allocVector(STRSXP, n));
        for (i = 0, n = 0; i < ndims; i++) {
            if (INTEGER(dims)[i] != 1) {
            if(!isNull(dnn))
                SET_STRING_ELT(newnamesnames, n,
                       STRING_ELT(dnn, i));
            SET_VECTOR_ELT(newnames, n++, VECTOR_ELT(dimnames, i));
            }
        }
        }
        else dimnames = R_NilValue;
    }
    PROTECT(dimnames);
    setAttrib(x, R_DimNamesSymbol, R_NilValue);
    setAttrib(x, R_DimSymbol, newdims);
    if (dimnames != R_NilValue)
    {
        if(!isNull(dnn))
        setAttrib(newnames, R_NamesSymbol, newnamesnames);
        setAttrib(x, R_DimNamesSymbol, newnames);
        UNPROTECT(2);
    }
    UNPROTECT(2);
    }
    UNPROTECT(1);
    return x;
}

SEXP attribute_hidden do_drop(SEXP call, SEXP op, SEXP args, SEXP rho)
{
    SEXP x, xdims;
    int i, n, shorten;

    checkArity(op, args);
    x = CAR(args);
    if ((xdims = getAttrib(x, R_DimSymbol)) != R_NilValue) {
    n = LENGTH(xdims);
    shorten = 0;
    for (i = 0; i < n; i++)
        if (INTEGER(xdims)[i] == 1) shorten = 1;
    if (shorten) {
        if (NAMED(x)) x = duplicate(x);
        x = DropDims(x);
    }
    }
    return x;
}

/* Length of Primitive Objects */

SEXP attribute_hidden do_length(SEXP call, SEXP op, SEXP args, SEXP rho)
{
    checkArity(op, args);
    check1arg(args, call, "x");

    SEXP x = CAR(args), ans;

    if (isObject(x) &&
       DispatchOrEval(call, op, "length", args, rho, &ans, 0, 1)) {
    if (length(ans) == 1 && TYPEOF(ans) == REALSXP) {
        double d = REAL(ans)[0];
        if (R_FINITE(d) && d >= 0. && d <= INT_MAX && floor(d) == d)
        return coerceVector(ans, INTSXP);
    }
    return(ans);
    }

#ifdef LONG_VECTOR_SUPPORT
    // or use IS_LONG_VEC
    R_xlen_t len = xlength(x);
    if (len > INT_MAX) return ScalarReal((double) len);
#endif
    return ScalarInteger(length(x));
}


SEXP attribute_hidden do_rowscols(SEXP call, SEXP op, SEXP args, SEXP rho)
{
    SEXP x, ans;
    int i, j, nr, nc;

    checkArity(op, args);
    /* This is the dimensions vector */
    x = CAR(args);
    if (!isInteger(x) || LENGTH(x) != 2)
    error(_("a matrix-like object is required as argument to '%s'"),
          (PRIMVAL(op) == 2) ? "col" : "row");

    nr = INTEGER(x)[0];
    nc = INTEGER(x)[1];

    ans = allocMatrix(INTSXP, nr, nc);

    R_xlen_t NR = nr;
    switch (PRIMVAL(op)) {
    case 1:
    for (i = 0; i < nr; i++)
        for (j = 0; j < nc; j++)
        INTEGER(ans)[i + j * NR] = i + 1;
    break;
    case 2:
    for (i = 0; i < nr; i++)
        for (j = 0; j < nc; j++)
        INTEGER(ans)[i + j * NR] = j + 1;
    break;
    }
    return ans;
}

static void matprod(double *x, int nrx, int ncx,
            double *y, int nry, int ncy, double *z)
{
    char *transa = "N", *transb = "N";
    double one = 1.0, zero = 0.0;
    LDOUBLE sum;
    Rboolean have_na = FALSE;
    R_xlen_t NRX = nrx, NRY = nry;

    if (nrx > 0 && ncx > 0 && nry > 0 && ncy > 0) {
    /* Don't trust the BLAS to handle NA/NaNs correctly: PR#4582
     * The test is only O(n) here.
     */
    for (R_xlen_t i = 0; i < NRX*ncx; i++)
        if (ISNAN(x[i])) {have_na = TRUE; break;}
    if (!have_na)
        for (R_xlen_t i = 0; i < NRY*ncy; i++)
        if (ISNAN(y[i])) {have_na = TRUE; break;}
    if (have_na) {
        for (int i = 0; i < nrx; i++)
        for (int k = 0; k < ncy; k++) {
            sum = 0.0;
            for (int j = 0; j < ncx; j++)
            sum += x[i + j * NRX] * y[j + k * NRY];
            z[i + k * NRX] = (double) sum;
        }
    } else
        F77_CALL(dgemm)(transa, transb, &nrx, &ncy, &ncx, &one,
                x, &nrx, y, &nry, &zero, z, &nrx);
    } else /* zero-extent operations should return zeroes */
    for(R_xlen_t i = 0; i < NRX*ncy; i++) z[i] = 0;
}

static void cmatprod(Rcomplex *x, int nrx, int ncx,
             Rcomplex *y, int nry, int ncy, Rcomplex *z)
{
#ifdef HAVE_FORTRAN_DOUBLE_COMPLEX
    char *transa = "N", *transb = "N";
    Rcomplex one, zero;

    one.r = 1.0; one.i = zero.r = zero.i = 0.0;
    if (nrx > 0 && ncx > 0 && nry > 0 && ncy > 0) {
    F77_CALL(zgemm)(transa, transb, &nrx, &ncy, &ncx, &one,
            x, &nrx, y, &nry, &zero, z, &nrx);
    } else { /* zero-extent operations should return zeroes */
    R_xlen_t NRX = nrx;
    for(R_xlen_t i = 0; i < NRX*ncy; i++) z[i].r = z[i].i = 0;
    }
#else
    int i, j, k;
    double xij_r, xij_i, yjk_r, yjk_i;
    LDOUBLE sum_i, sum_r;

    R_xlen_t NRX = nrx, NRY = nry;
    for (i = 0; i < nrx; i++)
    for (k = 0; k < ncy; k++) {
        z[i + k * NRX].r = NA_REAL;
        z[i + k * NRX].i = NA_REAL;
        sum_r = 0.0;
        sum_i = 0.0;
        for (j = 0; j < ncx; j++) {
        xij_r = x[i + j * NRX].r;
        xij_i = x[i + j * NRX].i;
        yjk_r = y[j + k * NRY].r;
        yjk_i = y[j + k * NRY].i;
        if (ISNAN(xij_r) || ISNAN(xij_i)
            || ISNAN(yjk_r) || ISNAN(yjk_i))
            goto next_ik;
        sum_r += (xij_r * yjk_r - xij_i * yjk_i);
        sum_i += (xij_r * yjk_i + xij_i * yjk_r);
        }
        z[i + k * NRX].r = sum_r;
        z[i + k * NRX].i = sum_i;
    next_ik:
        ;
    }
#endif
}

static void symcrossprod(double *x, int nr, int nc, double *z)
{
    char *trans = "T", *uplo = "U";
    double one = 1.0, zero = 0.0;
    R_xlen_t NC = nc;
    if (nr > 0 && nc > 0) {
    F77_CALL(dsyrk)(uplo, trans, &nc, &nr, &one, x, &nr, &zero, z, &nc);
    for (int i = 1; i < nc; i++)
        for (int j = 0; j < i; j++) z[i + NC *j] = z[j + NC * i];
    } else { /* zero-extent operations should return zeroes */
    for(R_xlen_t i = 0; i < NC*NC; i++) z[i] = 0;
    }

}

static void crossprod(double *x, int nrx, int ncx,
              double *y, int nry, int ncy, double *z)
{
    char *transa = "T", *transb = "N";
    double one = 1.0, zero = 0.0;
    if (nrx > 0 && ncx > 0 && nry > 0 && ncy > 0) {
    F77_CALL(dgemm)(transa, transb, &ncx, &ncy, &nrx, &one,
            x, &nrx, y, &nry, &zero, z, &ncx);
    } else { /* zero-extent operations should return zeroes */
    R_xlen_t NCX = ncx;
    for(R_xlen_t i = 0; i < NCX*ncy; i++) z[i] = 0;
    }
}

static void ccrossprod(Rcomplex *x, int nrx, int ncx,
               Rcomplex *y, int nry, int ncy, Rcomplex *z)
{
    char *transa = "T", *transb = "N";
    Rcomplex one, zero;

    one.r = 1.0; one.i = zero.r = zero.i = 0.0;
    if (nrx > 0 && ncx > 0 && nry > 0 && ncy > 0) {
    F77_CALL(zgemm)(transa, transb, &ncx, &ncy, &nrx, &one,
            x, &nrx, y, &nry, &zero, z, &ncx);
    } else { /* zero-extent operations should return zeroes */
    R_xlen_t NCX = ncx;
    for(R_xlen_t i = 0; i < NCX*ncy; i++) z[i].r = z[i].i = 0;
    }
}

static void symtcrossprod(double *x, int nr, int nc, double *z)
{
    char *trans = "N", *uplo = "U";
    double one = 1.0, zero = 0.0;
    if (nr > 0 && nc > 0) {
    F77_CALL(dsyrk)(uplo, trans, &nr, &nc, &one, x, &nr, &zero, z, &nr);
    for (int i = 1; i < nr; i++)
        for (int j = 0; j < i; j++) z[i + nr *j] = z[j + nr * i];
    } else { /* zero-extent operations should return zeroes */
    R_xlen_t NR = nr;
    for(R_xlen_t i = 0; i < NR*NR; i++) z[i] = 0;
    }

}

static void tcrossprod(double *x, int nrx, int ncx,
              double *y, int nry, int ncy, double *z)
{
    char *transa = "N", *transb = "T";
    double one = 1.0, zero = 0.0;
    if (nrx > 0 && ncx > 0 && nry > 0 && ncy > 0) {
    F77_CALL(dgemm)(transa, transb, &nrx, &nry, &ncx, &one,
            x, &nrx, y, &nry, &zero, z, &nrx);
    } else { /* zero-extent operations should return zeroes */
    R_xlen_t NRX = nrx;
    for(R_xlen_t i = 0; i < NRX*nry; i++) z[i] = 0;
    }
}

static void tccrossprod(Rcomplex *x, int nrx, int ncx,
            Rcomplex *y, int nry, int ncy, Rcomplex *z)
{
    char *transa = "N", *transb = "T";
    Rcomplex one, zero;

    one.r = 1.0; one.i = zero.r = zero.i = 0.0;
    if (nrx > 0 && ncx > 0 && nry > 0 && ncy > 0) {
    F77_CALL(zgemm)(transa, transb, &nrx, &nry, &ncx, &one,
            x, &nrx, y, &nry, &zero, z, &nrx);
    } else { /* zero-extent operations should return zeroes */
    R_xlen_t NRX = nrx;
    for(R_xlen_t i = 0; i < NRX*nry; i++) z[i].r = z[i].i = 0;
    }
}


/* "%*%" (op = 0), crossprod (op = 1) or tcrossprod (op = 2) */
SEXP attribute_hidden do_matprod(SEXP call, SEXP op, SEXP args, SEXP rho)
{
    int ldx, ldy, nrx, ncx, nry, ncy, mode;
    SEXP x = CAR(args), y = CADR(args), xdims, ydims, ans;
    Rboolean sym;

    if (PRIMVAL(op) == 0 && /* %*% is primitive, the others are .Internal() */
       (IS_S4_OBJECT(x) || IS_S4_OBJECT(y))
       && R_has_methods(op)) {
    SEXP s, value;
    /* Remove argument names to ensure positional matching */
    for(s = args; s != R_NilValue; s = CDR(s)) SET_TAG(s, R_NilValue);
    value = R_possible_dispatch(call, op, args, rho, FALSE);
    if (value) return value;
    }

    sym = isNull(y);
    if (sym && (PRIMVAL(op) > 0)) y = x;
    if ( !(isNumeric(x) || isComplex(x)) || !(isNumeric(y) || isComplex(y)) )
    errorcall(call, _("requires numeric/complex matrix/vector arguments"));

    xdims = getAttrib(x, R_DimSymbol);
    ydims = getAttrib(y, R_DimSymbol);
    ldx = length(xdims);
    ldy = length(ydims);

    if (ldx != 2 && ldy != 2) {     /* x and y non-matrices */
    if (PRIMVAL(op) == 0) {
        nrx = 1;
        ncx = LENGTH(x);
    }
    else {
        nrx = LENGTH(x);
        ncx = 1;
    }
    nry = LENGTH(y);
    ncy = 1;
    }
    else if (ldx != 2) {        /* x not a matrix */
    nry = INTEGER(ydims)[0];
    ncy = INTEGER(ydims)[1];
    nrx = 0;
    ncx = 0;
    if (PRIMVAL(op) == 0) {
        if (LENGTH(x) == nry) { /* x as row vector */
        nrx = 1;
        ncx = nry; /* == LENGTH(x) */
        }
        else if (nry == 1) {    /* x as col vector */
        nrx = LENGTH(x);
        ncx = 1;
        }
    }
    else if (PRIMVAL(op) == 1) { /* crossprod() */
        if (LENGTH(x) == nry) { /* x is a col vector */
        nrx = nry; /* == LENGTH(x) */
        ncx = 1;
        }
        /* else if (nry == 1) ... not being too tolerant
           to treat x as row vector, as t(x) *is* row vector */
    }
    else { /* tcrossprod */
        if (LENGTH(x) == ncy) { /* x as row vector */
        nrx = 1;
        ncx = ncy; /* == LENGTH(x) */
        }
        else if (ncy == 1) {    /* x as col vector */
        nrx = LENGTH(x);
        ncx = 1;
        }
    }
    }
    else if (ldy != 2) {        /* y not a matrix */
    nrx = INTEGER(xdims)[0];
    ncx = INTEGER(xdims)[1];
    nry = 0;
    ncy = 0;
    if (PRIMVAL(op) == 0) {
        if (LENGTH(y) == ncx) { /* y as col vector */
        nry = ncx;
        ncy = 1;
        }
        else if (ncx == 1) {    /* y as row vector */
        nry = 1;
        ncy = LENGTH(y);
        }
    }
    else if (PRIMVAL(op) == 1) { /* crossprod() */
        if (LENGTH(y) == nrx) { /* y is a col vector */
        nry = nrx;
        ncy = 1;
        }
    }
    else { /* tcrossprod --     y is a col vector */
        nry = LENGTH(y);
        ncy = 1;
    }
    }
    else {              /* x and y matrices */
    nrx = INTEGER(xdims)[0];
    ncx = INTEGER(xdims)[1];
    nry = INTEGER(ydims)[0];
    ncy = INTEGER(ydims)[1];
    }
    /* nr[ow](.) and nc[ol](.) are now defined for x and y */

    if (PRIMVAL(op) == 0) {
    /* primitive, so use call */
    if (ncx != nry)
        errorcall(call, _("non-conformable arguments"));
    }
    else if (PRIMVAL(op) == 1) {
    if (nrx != nry)
        error(_("non-conformable arguments"));
    }
    else {
    if (ncx != ncy)
        error(_("non-conformable arguments"));
    }

    if (isComplex(CAR(args)) || isComplex(CADR(args)))
    mode = CPLXSXP;
    else
    mode = REALSXP;
    SETCAR(args, coerceVector(CAR(args), mode));
    SETCADR(args, coerceVector(CADR(args), mode));

    if (PRIMVAL(op) == 0) {         /* op == 0 : matprod() */

    PROTECT(ans = allocMatrix(mode, nrx, ncy));
    if (mode == CPLXSXP)
        cmatprod(COMPLEX(CAR(args)), nrx, ncx,
             COMPLEX(CADR(args)), nry, ncy, COMPLEX(ans));
    else
        matprod(REAL(CAR(args)), nrx, ncx,
            REAL(CADR(args)), nry, ncy, REAL(ans));

    PROTECT(xdims = getAttrib(CAR(args), R_DimNamesSymbol));
    PROTECT(ydims = getAttrib(CADR(args), R_DimNamesSymbol));

    if (xdims != R_NilValue || ydims != R_NilValue) {
        SEXP dimnames, dimnamesnames, dnx=R_NilValue, dny=R_NilValue;

        /* allocate dimnames and dimnamesnames */

        PROTECT(dimnames = allocVector(VECSXP, 2));
        PROTECT(dimnamesnames = allocVector(STRSXP, 2));
        if (xdims != R_NilValue) {
        if (ldx == 2 || ncx == 1) {
            SET_VECTOR_ELT(dimnames, 0, VECTOR_ELT(xdims, 0));
            dnx = getAttrib(xdims, R_NamesSymbol);
            if(!isNull(dnx))
            SET_STRING_ELT(dimnamesnames, 0, STRING_ELT(dnx, 0));
        }
        }

#define YDIMS_ET_CETERA                         \
        if (ydims != R_NilValue) {                  \
        if (ldy == 2) {                     \
            SET_VECTOR_ELT(dimnames, 1, VECTOR_ELT(ydims, 1));  \
            dny = getAttrib(ydims, R_NamesSymbol);      \
            if(!isNull(dny))                    \
            SET_STRING_ELT(dimnamesnames, 1, STRING_ELT(dny, 1)); \
        } else if (nry == 1) {                  \
            SET_VECTOR_ELT(dimnames, 1, VECTOR_ELT(ydims, 0));  \
            dny = getAttrib(ydims, R_NamesSymbol);      \
            if(!isNull(dny))                    \
            SET_STRING_ELT(dimnamesnames, 1, STRING_ELT(dny, 0)); \
        }                           \
        }                               \
                                    \
        /* We sometimes attach a dimnames attribute         \
         * whose elements are all NULL ...              \
         * This is ugly but causes no real damage.          \
         * Now (2.1.0 ff), we don't anymore: */         \
        if (VECTOR_ELT(dimnames,0) != R_NilValue ||         \
        VECTOR_ELT(dimnames,1) != R_NilValue) {         \
        if (dnx != R_NilValue || dny != R_NilValue)     \
            setAttrib(dimnames, R_NamesSymbol, dimnamesnames);  \
        setAttrib(ans, R_DimNamesSymbol, dimnames);     \
        }                               \
        UNPROTECT(2)

        YDIMS_ET_CETERA;
    }
    }

    else if (PRIMVAL(op) == 1) {    /* op == 1: crossprod() */

    PROTECT(ans = allocMatrix(mode, ncx, ncy));
    if (mode == CPLXSXP)
        if(sym)
        ccrossprod(COMPLEX(CAR(args)), nrx, ncx,
               COMPLEX(CAR(args)), nry, ncy, COMPLEX(ans));
        else
        ccrossprod(COMPLEX(CAR(args)), nrx, ncx,
               COMPLEX(CADR(args)), nry, ncy, COMPLEX(ans));
    else {
        if(sym)
        symcrossprod(REAL(CAR(args)), nrx, ncx, REAL(ans));
        else
        crossprod(REAL(CAR(args)), nrx, ncx,
              REAL(CADR(args)), nry, ncy, REAL(ans));
    }

    PROTECT(xdims = getAttrib(CAR(args), R_DimNamesSymbol));
    if (sym)
        PROTECT(ydims = xdims);
    else
        PROTECT(ydims = getAttrib(CADR(args), R_DimNamesSymbol));

    if (xdims != R_NilValue || ydims != R_NilValue) {
        SEXP dimnames, dimnamesnames, dnx=R_NilValue, dny=R_NilValue;

        /* allocate dimnames and dimnamesnames */

        PROTECT(dimnames = allocVector(VECSXP, 2));
        PROTECT(dimnamesnames = allocVector(STRSXP, 2));

        if (xdims != R_NilValue) {
        if (ldx == 2) {/* not nrx==1 : .. fixed, ihaka 2003-09-30 */
            SET_VECTOR_ELT(dimnames, 0, VECTOR_ELT(xdims, 1));
            dnx = getAttrib(xdims, R_NamesSymbol);
            if(!isNull(dnx))
            SET_STRING_ELT(dimnamesnames, 0, STRING_ELT(dnx, 1));
        }
        }

        YDIMS_ET_CETERA;
    }

    }
    else {                  /* op == 2: tcrossprod() */

    PROTECT(ans = allocMatrix(mode, nrx, nry));
    if (mode == CPLXSXP)
        if(sym)
        tccrossprod(COMPLEX(CAR(args)), nrx, ncx,
                COMPLEX(CAR(args)), nry, ncy, COMPLEX(ans));
        else
        tccrossprod(COMPLEX(CAR(args)), nrx, ncx,
                COMPLEX(CADR(args)), nry, ncy, COMPLEX(ans));
    else {
        if(sym)
        symtcrossprod(REAL(CAR(args)), nrx, ncx, REAL(ans));
        else
        tcrossprod(REAL(CAR(args)), nrx, ncx,
               REAL(CADR(args)), nry, ncy, REAL(ans));
    }

    PROTECT(xdims = getAttrib(CAR(args), R_DimNamesSymbol));
    if (sym)
        PROTECT(ydims = xdims);
    else
        PROTECT(ydims = getAttrib(CADR(args), R_DimNamesSymbol));

    if (xdims != R_NilValue || ydims != R_NilValue) {
        SEXP dimnames, dimnamesnames, dnx=R_NilValue, dny=R_NilValue;

        /* allocate dimnames and dimnamesnames */

        PROTECT(dimnames = allocVector(VECSXP, 2));
        PROTECT(dimnamesnames = allocVector(STRSXP, 2));

        if (xdims != R_NilValue) {
        if (ldx == 2) {
            SET_VECTOR_ELT(dimnames, 0, VECTOR_ELT(xdims, 0));
            dnx = getAttrib(xdims, R_NamesSymbol);
            if(!isNull(dnx))
            SET_STRING_ELT(dimnamesnames, 0, STRING_ELT(dnx, 0));
        }
        }
        if (ydims != R_NilValue) {
        if (ldy == 2) {
            SET_VECTOR_ELT(dimnames, 1, VECTOR_ELT(ydims, 0));
            dny = getAttrib(ydims, R_NamesSymbol);
            if(!isNull(dny))
            SET_STRING_ELT(dimnamesnames, 1, STRING_ELT(dny, 0));
        }
        }
        if (VECTOR_ELT(dimnames,0) != R_NilValue ||
        VECTOR_ELT(dimnames,1) != R_NilValue) {
        if (dnx != R_NilValue || dny != R_NilValue)
            setAttrib(dimnames, R_NamesSymbol, dimnamesnames);
        setAttrib(ans, R_DimNamesSymbol, dimnames);
        }

        UNPROTECT(2);
    }
    }
    UNPROTECT(3);
    return ans;
}
#undef YDIMS_ET_CETERA

SEXP attribute_hidden do_transpose(SEXP call, SEXP op, SEXP args, SEXP rho)
{
    SEXP a, r, dims, dimnames, dimnamesnames = R_NilValue,
    ndimnamesnames, rnames, cnames;
    int ldim, ncol = 0, nrow = 0;
    R_xlen_t len = 0;

    checkArity(op, args);
    a = CAR(args);

    if (isVector(a)) {
    dims = getAttrib(a, R_DimSymbol);
    ldim = length(dims);
    rnames = R_NilValue;
    cnames = R_NilValue;
    switch(ldim) {
    case 0:
        len = nrow = LENGTH(a);
        ncol = 1;
        rnames = getAttrib(a, R_NamesSymbol);
        dimnames = rnames;/* for isNull() below*/
        break;
    case 1:
        len = nrow = LENGTH(a);
        ncol = 1;
        dimnames = getAttrib(a, R_DimNamesSymbol);
        if (dimnames != R_NilValue) {
        rnames = VECTOR_ELT(dimnames, 0);
        dimnamesnames = getAttrib(dimnames, R_NamesSymbol);
        }
        break;
    case 2:
        ncol = ncols(a);
        nrow = nrows(a);
        len = XLENGTH(a);
        dimnames = getAttrib(a, R_DimNamesSymbol);
        if (dimnames != R_NilValue) {
        rnames = VECTOR_ELT(dimnames, 0);
        cnames = VECTOR_ELT(dimnames, 1);
        dimnamesnames = getAttrib(dimnames, R_NamesSymbol);
        }
        break;
    default:
        goto not_matrix;
    }
    }
    else
    goto not_matrix;
    PROTECT(r = allocVector(TYPEOF(a), len));
    R_xlen_t i, j, l_1 = len-1;
    switch (TYPEOF(a)) {
    case LGLSXP:
    case INTSXP:
    // filling in columnwise, "accessing row-wise":
        for (i = 0, j = 0; i < len; i++, j += nrow) {
            if (j > l_1) j -= l_1;
            INTEGER(r)[i] = INTEGER(a)[j];
        }
        break;
    case REALSXP:
        for (i = 0, j = 0; i < len; i++, j += nrow) {
            if (j > l_1) j -= l_1;
            REAL(r)[i] = REAL(a)[j];
        }
        break;
    case CPLXSXP:
        for (i = 0, j = 0; i < len; i++, j += nrow) {
            if (j > l_1) j -= l_1;
            COMPLEX(r)[i] = COMPLEX(a)[j];
        }
        break;
    case STRSXP:
        for (i = 0, j = 0; i < len; i++, j += nrow) {
            if (j > l_1) j -= l_1;
            SET_STRING_ELT(r, i, STRING_ELT(a,j));
        }
        break;
    case VECSXP:
        for (i = 0, j = 0; i < len; i++, j += nrow) {
            if (j > l_1) j -= l_1;
            SET_VECTOR_ELT(r, i, VECTOR_ELT(a,j));
        }
        break;
    case RAWSXP:
        for (i = 0, j = 0; i < len; i++, j += nrow) {
            if (j > l_1) j -= l_1;
            RAW(r)[i] = RAW(a)[j];
        }
        break;
    default:
        UNPROTECT(1);
        goto not_matrix;
    }
    PROTECT(dims = allocVector(INTSXP, 2));
    INTEGER(dims)[0] = ncol;
    INTEGER(dims)[1] = nrow;
    setAttrib(r, R_DimSymbol, dims);
    UNPROTECT(1);
    /* R <= 2.2.0: dropped list(NULL,NULL) dimnames :
     * if(rnames != R_NilValue || cnames != R_NilValue) */
    if(!isNull(dimnames)) {
    PROTECT(dimnames = allocVector(VECSXP, 2));
    SET_VECTOR_ELT(dimnames, 0, cnames);
    SET_VECTOR_ELT(dimnames, 1, rnames);
    if(!isNull(dimnamesnames)) {
        PROTECT(ndimnamesnames = allocVector(VECSXP, 2));
        SET_VECTOR_ELT(ndimnamesnames, 1, STRING_ELT(dimnamesnames, 0));
        SET_VECTOR_ELT(ndimnamesnames, 0,
               (ldim == 2) ? STRING_ELT(dimnamesnames, 1):
               R_BlankString);
        setAttrib(dimnames, R_NamesSymbol, ndimnamesnames);
        UNPROTECT(1);
    }
    setAttrib(r, R_DimNamesSymbol, dimnames);
    UNPROTECT(1);
    }
    copyMostAttrib(a, r);
    UNPROTECT(1);
    return r;
 not_matrix:
    error(_("argument is not a matrix"));
    return call;/* never used; just for -Wall */
}

/*
 New version of aperm, using strides for speed.
 Jonathan Rougier <J.C.Rougier@durham.ac.uk>

 v1.0 30.01.01

 M.Maechler : expanded  all ../include/Rdefines.h macros
 */

/* this increments iip and sets j using strides */

#define CLICKJ                      \
    for (itmp = 0; itmp < n; itmp++)            \
    if (iip[itmp] == isr[itmp]-1) iip[itmp] = 0;    \
    else {                      \
        iip[itmp]++;                \
        break;                  \
    }                       \
    for (lj = 0, itmp = 0; itmp < n; itmp++)            \
    lj += iip[itmp] * stride[itmp];

/* aperm (a, perm, resize = TRUE) */
SEXP attribute_hidden do_aperm(SEXP call, SEXP op, SEXP args, SEXP rho)
{
    SEXP a, perm, r, dimsa, dimsr, dna;
    int i, j, n, itmp;

    checkArity(op, args);

    a = CAR(args);
    if (!isArray(a))
    error(_("invalid first argument, must be an array"));

    PROTECT(dimsa = getAttrib(a, R_DimSymbol));
    n = LENGTH(dimsa);
    int *isa = INTEGER(dimsa);

    /* check the permutation */

    int *pp = (int *) R_alloc((size_t) n, sizeof(int));
    perm = CADR(args);
    if (length(perm) == 0) {
    for (i = 0; i < n; i++) pp[i] = n-1-i;
    } else {
    if (LENGTH(perm) != n)
        error(_("'perm' is of wrong length %d (!= %d)"),
          LENGTH(perm), n);
    if (isString(perm)) {
        SEXP dna = getAttrib(a, R_DimNamesSymbol);
        if (isNull(dna))
        error(_("'a' does not have named dimnames"));
        SEXP dnna = getAttrib(dna, R_NamesSymbol);
        if (isNull(dnna))
        error(_("'a' does not have named dimnames"));
        for (i = 0; i < n; i++) {
        const char *this = translateChar(STRING_ELT(perm, i));
        for (j = 0; j < n; j++)
            if (streql(translateChar(STRING_ELT(dnna, j)),
                   this)) {pp[i] = j; break;}
        if (j >= n)
            error(_("'perm[%d]' does not match a dimension name"), i+1);
        }
    } else {
        PROTECT(perm = coerceVector(perm, INTSXP));
        for (i = 0; i < n; i++) pp[i] = INTEGER(perm)[i] - 1;
        UNPROTECT(1);
    }
    }

    R_xlen_t *iip = (R_xlen_t *) R_alloc((size_t) n, sizeof(R_xlen_t));
    for (i = 0; i < n; iip[i++] = 0);
    for (i = 0; i < n; i++)
    if (pp[i] >= 0 && pp[i] < n) iip[pp[i]]++;
    else error(_("value out of range in 'perm'"));
    for (i = 0; i < n; i++)
    if (iip[i] == 0) error(_("invalid '%s' argument"), "perm");

    /* create the stride object and permute */

    R_xlen_t *stride = (R_xlen_t *) R_alloc((size_t) n, sizeof(R_xlen_t));
    for (iip[0] = 1, i = 1; i<n; i++) iip[i] = iip[i-1] * isa[i-1];
    for (i = 0; i < n; i++) stride[i] = iip[pp[i]];

    /* also need to have the dimensions of r */

    PROTECT(dimsr = allocVector(INTSXP, n));
    int *isr = INTEGER(dimsr);
    for (i = 0; i < n; i++) isr[i] = isa[pp[i]];

    /* and away we go! iip will hold the incrementer */

    R_xlen_t len = XLENGTH(a);
    PROTECT(r = allocVector(TYPEOF(a), len));

    for (i = 0; i < n; iip[i++] = 0);

    R_xlen_t li, lj;
    switch (TYPEOF(a)) {

    case INTSXP:
    for (lj = 0, li = 0; li < len; li++) {
        INTEGER(r)[li] = INTEGER(a)[lj];
        CLICKJ;
    }
    break;

    case LGLSXP:
    for (lj = 0, li = 0; li < len; li++) {
        LOGICAL(r)[li] = LOGICAL(a)[lj];
        CLICKJ;
    }
    break;

    case REALSXP:
    for (lj = 0, li = 0; li < len; li++) {
        REAL(r)[li] = REAL(a)[lj];
        CLICKJ;
    }
    break;

    case CPLXSXP:
    for (lj = 0, li = 0; li < len; li++) {
        COMPLEX(r)[li].r = COMPLEX(a)[lj].r;
        COMPLEX(r)[li].i = COMPLEX(a)[lj].i;
        CLICKJ;
    }
    break;

    case STRSXP:
    for (lj = 0, li = 0; li < len; li++) {
        SET_STRING_ELT(r, li, STRING_ELT(a, lj));
        CLICKJ;
    }
    break;

    case VECSXP:
    for (lj = 0, li = 0; li < len; li++) {
        SET_VECTOR_ELT(r, li, VECTOR_ELT(a, lj));
        CLICKJ;
    }
    break;

    case RAWSXP:
    for (lj = 0, li = 0; li < len; li++) {
        RAW(r)[li] = RAW(a)[lj];
        CLICKJ;
    }
    break;

    default:
    UNIMPLEMENTED_TYPE("aperm", a);
    }

    /* handle the resize */
    int resize = asLogical(CADDR(args));
    if (resize == NA_LOGICAL) error(_("'resize' must be TRUE or FALSE"));
    setAttrib(r, R_DimSymbol, resize ? dimsr : dimsa);

    /* and handle the dimnames, if any */
    if (resize) {
    PROTECT(dna = getAttrib(a, R_DimNamesSymbol));
    if (dna != R_NilValue) {
        SEXP dnna, dnr, dnnr;

        PROTECT(dnr  = allocVector(VECSXP, n));
        PROTECT(dnna = getAttrib(dna, R_NamesSymbol));
        if (dnna != R_NilValue) {
        PROTECT(dnnr = allocVector(STRSXP, n));
        for (i = 0; i < n; i++) {
            SET_VECTOR_ELT(dnr, i, VECTOR_ELT(dna, pp[i]));
            SET_STRING_ELT(dnnr, i, STRING_ELT(dnna, pp[i]));
        }
        setAttrib(dnr, R_NamesSymbol, dnnr);
        UNPROTECT(1);
        } else {
        for (i = 0; i < n; i++)
            SET_VECTOR_ELT(dnr, i, VECTOR_ELT(dna, pp[i]));
        }
        setAttrib(r, R_DimNamesSymbol, dnr);
        UNPROTECT(2);
    }
    UNPROTECT(1);
    }

    UNPROTECT(3); /* dimsa, r, dimsr */
    return r;
}

/* colSums(x, n, p, na.rm) and friends */
SEXP attribute_hidden do_colsum(SEXP call, SEXP op, SEXP args, SEXP rho)
{
    SEXP x, ans = R_NilValue;
    int type;
    Rboolean NaRm, keepNA;

    checkArity(op, args);
    x = CAR(args); args = CDR(args);
    int n = asInteger(CAR(args)); args = CDR(args);
    int p = asInteger(CAR(args)); args = CDR(args);
    NaRm = asLogical(CAR(args));
    if (n == NA_INTEGER || n < 0)
    error(_("invalid '%s' argument"), "n");
    if (p == NA_INTEGER || p < 0)
    error(_("invalid '%s' argument"), "p");
    if (NaRm == NA_LOGICAL) error(_("invalid '%s' argument"), "na.rm");
    keepNA = !NaRm;

    int OP = PRIMVAL(op);
    switch (type = TYPEOF(x)) {
    case LGLSXP: break;
    case INTSXP: break;
    case REALSXP: break;
    default:
    error(_("'x' must be numeric"));
    }

    if (OP == 0 || OP == 1) { /* columns */
    PROTECT(ans = allocVector(REALSXP, p));
#ifdef _OPENMP
    int nthreads;
    /* This gives a spurious -Wunused-but-set-variable error */
    if (R_num_math_threads > 0)
        nthreads = R_num_math_threads;
    else
        nthreads = 1; /* for now */
#pragma omp parallel for num_threads(nthreads) default(none) \
    firstprivate(x, ans, n, p, type, NaRm, keepNA, R_NaReal, R_NaInt, OP)
#endif
    for (int j = 0; j < p; j++) {
        int cnt = n, i;
        LDOUBLE sum = 0.0;
        switch (type) {
        case REALSXP:
        {
        double *rx = REAL(x) + (R_xlen_t)n*j;
        if (keepNA)
            for (sum = 0., i = 0; i < n; i++) sum += *rx++;
        else {
            for (cnt = 0, sum = 0., i = 0; i < n; i++, rx++)
            if (!ISNAN(*rx)) {cnt++; sum += *rx;}
            else if (keepNA) {sum = NA_REAL; break;} // unused
        }
        break;
        }
        case INTSXP:
        {
        int *ix = INTEGER(x) + (R_xlen_t)n*j;
        for (cnt = 0, sum = 0., i = 0; i < n; i++, ix++)
            if (*ix != NA_INTEGER) {cnt++; sum += *ix;}
            else if (keepNA) {sum = NA_REAL; break;}
        break;
        }
        case LGLSXP:
        {
        int *ix = LOGICAL(x) + (R_xlen_t)n*j;
        for (cnt = 0, sum = 0., i = 0; i < n; i++, ix++)
            if (*ix != NA_LOGICAL) {cnt++; sum += *ix;}
            else if (keepNA) {sum = NA_REAL; break;}
        break;
        }
        }
        if (OP == 1) sum /= cnt; /* gives NaN for cnt = 0 */
        REAL(ans)[j] = (double) sum;
    }
    }
    else { /* rows */
    PROTECT(ans = allocVector(REALSXP, n));

    /* allocate scratch storage to allow accumulating by columns
       to improve cache hits */
    int *Cnt = NULL;
    LDOUBLE *rans;
    if(n <= 10000) {
        R_CheckStack2(n * sizeof(LDOUBLE));
        rans = (LDOUBLE *) alloca(n * sizeof(LDOUBLE));
        Memzero(rans, n);
    } else rans = Calloc(n, LDOUBLE);
    if (!keepNA && OP == 3) Cnt = Calloc(n, int);

    for (int j = 0; j < p; j++) {
        LDOUBLE *ra = rans;
        switch (type) {
        case REALSXP:
        {
        double *rx = REAL(x) + (R_xlen_t)n * j;
        if (keepNA)
            for (int i = 0; i < n; i++) *ra++ += *rx++;
        else
            for (int i = 0; i < n; i++, ra++, rx++)
            if (!ISNAN(*rx)) {
                *ra += *rx;
                if (OP == 3) Cnt[i]++;
            }
        break;
        }
        case INTSXP:
        {
        int *ix = INTEGER(x) + (R_xlen_t)n * j;
        for (int i = 0; i < n; i++, ra++, ix++)
            if (keepNA) {
            if (*ix != NA_INTEGER) *ra += *ix;
            else *ra = NA_REAL;
            }
            else if (*ix != NA_INTEGER) {
            *ra += *ix;
            if (OP == 3) Cnt[i]++;
            }
        break;
        }
        case LGLSXP:
        {
        int *ix = LOGICAL(x) + (R_xlen_t)n * j;
        for (int i = 0; i < n; i++, ra++, ix++)
            if (keepNA) {
            if (*ix != NA_LOGICAL) *ra += *ix;
            else *ra = NA_REAL;
            }
            else if (*ix != NA_LOGICAL) {
            *ra += *ix;
            if (OP == 3) Cnt[i]++;
            }
        break;
        }
        }
    }
    if (OP == 3) {
        if (keepNA)
        for (int i = 0; i < n; i++) rans[i] /= p;
        else
        for (int i = 0; i < n; i++) rans[i] /= Cnt[i];
    }
    for (int i = 0; i < n; i++) REAL(ans)[i] = (double) rans[i];

    if (!keepNA && OP == 3) Free(Cnt);
    if(n > 10000) Free(rans);
    }

    UNPROTECT(1);
    return ans;
}

/*
{
    data <- as.vector(data)
    dim <- as.integer(dim)
    vl <- prod(dim)
    if (length(data) != vl) {
        if (vl > .Machine$integer.max)
            stop("'dim' specifies too large an array")
        data <- rep(data, length.out = vl)
    }
    if (length(dim))
        dim(data) <- dim
    if (is.list(dimnames) && length(dimnames))
        dimnames(data) <- dimnames
    data
}
*/

/* array(data, dim, dimnames) */
SEXP attribute_hidden do_array(SEXP call, SEXP op, SEXP args, SEXP rho)
{
    SEXP vals, ans, dims, dimnames;
    R_xlen_t lendat, i, nans;

    checkArity(op, args);
    vals = CAR(args);
    /* at least NULL can get here */
    switch(TYPEOF(vals)) {
    case LGLSXP:
    case INTSXP:
    case REALSXP:
    case CPLXSXP:
    case STRSXP:
    case RAWSXP:
    case EXPRSXP:
    case VECSXP:
        break;
    default:
        error(_("'data' must be of a vector type, was '%s'"),
        type2char(TYPEOF(vals)));
    }
    lendat = XLENGTH(vals);
    dims = CADR(args);
    dimnames = CADDR(args);
    PROTECT(dims = coerceVector(dims, INTSXP));
    int nd = LENGTH(dims);
    if (nd == 0) error(_("'dims' cannot be of length 0"));
    double d = 1.0;
    for (int j = 0; j < nd; j++) d *= INTEGER(dims)[j];
#ifndef LONG_VECTOR_SUPPORT
    if (d > INT_MAX) error(_("too many elements specified"));
#endif
    nans = (R_xlen_t) d;

    PROTECT(ans = allocVector(TYPEOF(vals), nans));
    switch(TYPEOF(vals)) {
    case LGLSXP:
    if (nans && lendat)
        for (i = 0; i < nans; i++)
        LOGICAL(ans)[i] = LOGICAL(vals)[i % lendat];
    else
        for (i = 0; i < nans; i++) LOGICAL(ans)[i] = NA_LOGICAL;
    break;
    case INTSXP:
    if (nans && lendat)
        for (i = 0; i < nans; i++)
        INTEGER(ans)[i] = INTEGER(vals)[i % lendat];
    else
        for (i = 0; i < nans; i++) INTEGER(ans)[i] = NA_INTEGER;
    break;
    case REALSXP:
    if (nans && lendat)
        for (i = 0; i < nans; i++) REAL(ans)[i] = REAL(vals)[i % lendat];
    else
        for (i = 0; i < nans; i++) REAL(ans)[i] = NA_REAL;
    break;
    case CPLXSXP:
    if (nans && lendat)
        for (i = 0; i < nans; i++)
        COMPLEX(ans)[i] = COMPLEX(vals)[i % lendat];
    else {
        Rcomplex na_cmplx;
        na_cmplx.r = NA_REAL;
        na_cmplx.i = 0;
        for (i = 0; i < nans; i++) COMPLEX(ans)[i] = na_cmplx;
    }
    break;
    case RAWSXP:
    if (nans && lendat)
        for (i = 0; i < nans; i++) RAW(ans)[i] = RAW(vals)[i % lendat];
    else
        for (i = 0; i < nans; i++) RAW(ans)[i] = 0;
    break;
    /* Rest are already initialized */
    case STRSXP:
    if (nans && lendat)
        for (i = 0; i < nans; i++)
        SET_STRING_ELT(ans, i, STRING_ELT(vals, i % lendat));
    break;
    case VECSXP:
    case EXPRSXP:
    if (nans && lendat)
        for (i = 0; i < nans; i++)
        SET_VECTOR_ELT(ans, i, VECTOR_ELT(vals, i % lendat));
    break;
    default:
    // excluded above
    break;
    }

    ans = dimgets(ans, dims);
    if (TYPEOF(dimnames) == VECSXP && LENGTH(dimnames)) {
    PROTECT(ans);
    ans = dimnamesgets(ans, dimnames);
    UNPROTECT(1);
    }

    UNPROTECT(2);
    return ans;
}

SEXP attribute_hidden do_diag(SEXP call, SEXP op, SEXP args, SEXP rho)
{
    SEXP ans, x, snr, snc;
    int nr = 1, nc = 1, nprotect = 1;

    checkArity(op, args);
    x = CAR(args);
    snr = CADR(args);
    snc = CADDR(args);
    nr = asInteger(snr);
    if (nr == NA_INTEGER)
    error(_("invalid 'nrow' value (too large or NA)"));
    if (nr < 0)
    error(_("invalid 'nrow' value (< 0)"));
    nc = asInteger(snc);
    if (nc == NA_INTEGER)
    error(_("invalid 'ncol' value (too large or NA)"));
    if (nc < 0)
    error(_("invalid 'ncol' value (< 0)"));
    int mn = (nr < nc) ? nr : nc;
    if (mn > 0 && LENGTH(x) == 0)
    error(_("'x' must have positive length"));

 #ifndef LONG_VECTOR_SUPPORT
   if ((double)nr * (double)nc > INT_MAX)
    error(_("too many elements specified"));
#endif

   if (TYPEOF(x) == CPLXSXP) {
       PROTECT(ans = allocMatrix(CPLXSXP, nr, nc));
       int nx = LENGTH(x);
       R_xlen_t NR = nr;
       Rcomplex *rx = COMPLEX(x), *ra = COMPLEX(ans), zero;
       zero.r = zero.i = 0.0;
       for (R_xlen_t i = 0; i < NR*nc; i++) ra[i] = zero;
       for (int j = 0; j < mn; j++) ra[j * (NR+1)] = rx[j % nx];
  } else {
       if(TYPEOF(x) != REALSXP) {
       PROTECT(x = coerceVector(x, REALSXP));
       nprotect++;
       }
       PROTECT(ans = allocMatrix(REALSXP, nr, nc));
       int nx = LENGTH(x);
       R_xlen_t NR = nr;
       double *rx = REAL(x), *ra = REAL(ans);
       for (R_xlen_t i = 0; i < NR*nc; i++) ra[i] = 0.0;
       for (int j = 0; j < mn; j++) ra[j * (NR+1)] = rx[j % nx];
   }
   UNPROTECT(nprotect);
   return ans;
}


/* backsolve(r, b, k, upper.tri, transpose) */
SEXP attribute_hidden do_backsolve(SEXP call, SEXP op, SEXP args, SEXP rho)
{
    int nprot = 1;
    checkArity(op, args);

    SEXP r = CAR(args); args = CDR(args);
    SEXP b = CAR(args); args = CDR(args);
    int nrr = nrows(r), nrb = nrows(b), ncb = ncols(b);
    int k = asInteger(CAR(args)); args = CDR(args);
    /* k is the number of rows to be used: there must be at least that
       many rows and cols in the rhs and at least that many rows on
       the rhs.
    */
    if (k == NA_INTEGER || k <= 0 || k > nrr || k > ncols(r) || k > nrb)
    error(_("invalid '%s' argument"), "k");
    int upper = asLogical(CAR(args)); args = CDR(args);
    if (upper == NA_INTEGER) error(_("invalid '%s' argument"), "upper.tri");
    int trans = asLogical(CAR(args));
    if (trans == NA_INTEGER) error(_("invalid '%s' argument"), "transpose");
    if (TYPEOF(r) != REALSXP) {PROTECT(r = coerceVector(r, REALSXP)); nprot++;}
    if (TYPEOF(b) != REALSXP) {PROTECT(b = coerceVector(b, REALSXP)); nprot++;}
    double *rr = REAL(r);

    /* check for zeros on diagonal of r: only k row/cols are used. */
    size_t incr = nrr + 1;
    for(int i = 0; i < k; i++) { /* check for zeros on diagonal */
    if (rr[i * incr] == 0.0)
        error(_("singular matrix in 'backsolve'. First zero in diagonal [%d]"),
          i + 1);
    }

    SEXP ans = PROTECT(allocMatrix(REALSXP, k, ncb));
    if (k > 0 && ncb > 0) {
       /* copy (part) cols of b to ans */
    for(R_xlen_t j = 0; j < ncb; j++)
        memcpy(REAL(ans) + j*k, REAL(b) + j*nrb, (size_t)k *sizeof(double));
    double one = 1.0;
    F77_CALL(dtrsm)("L", upper ? "U" : "L", trans ? "T" : "N", "N",
            &k, &ncb, &one, rr, &nrr, REAL(ans), &k);
    }
    UNPROTECT(nprot);
    return ans;
}

/* max.col(m, ties.method) */
SEXP attribute_hidden do_maxcol(SEXP call, SEXP op, SEXP args, SEXP rho)
{
    checkArity(op, args);
    SEXP m = CAR(args);
    int method = asInteger(CADR(args));
    int nr = nrows(m), nc = ncols(m), nprot = 1;
    if (TYPEOF(m) != REALSXP) {PROTECT(m = coerceVector(m, REALSXP)); nprot++;}
    SEXP ans = PROTECT(allocVector(INTSXP, nr));
    R_max_col(REAL(m), &nr, &nc, INTEGER(ans), &method);
    UNPROTECT(nprot);
    return ans;
}