The R Project SVN R

/*
 *  R : A Computer Language for Statistical Data Analysis
 *  Copyright (C) 2001--2006  The R Development Core Team.
 *  Copyright (C) 2003-5      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/
 */

/* <UTF8> All chars are ASCII */

/* Interface routines, callable from R using .Call, for Lapack code */

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

#include "Lapack.h"

static SEXP modLa_svd(SEXP jobu, SEXP jobv, SEXP x, SEXP s, SEXP u, SEXP v,
              SEXP method)
{
    int *xdims, n, p, lwork, info = 0;
    double *work, *xvals, tmp;
    SEXP val, nm;
    const char *meth;

    if (!(isString(jobu) && isString(jobv)))
    error(_("'jobu' and 'jobv' must be character strings"));
    if (!isString(method))
    error(_("'method' must be a character string"));
    meth = CHAR(STRING_ELT(method, 0));
    xdims = INTEGER(coerceVector(getAttrib(x, R_DimSymbol), INTSXP));
    n = xdims[0]; p = xdims[1];
    xvals = (double *) R_alloc(n * p, sizeof(double));
    /* work on a copy of x */
    Memcpy(xvals, REAL(x), (size_t) (n * p));

    {
    int ldu = INTEGER(getAttrib(u, R_DimSymbol))[0],
        ldvt = INTEGER(getAttrib(v, R_DimSymbol))[0];
    int *iwork= (int *) R_alloc(8*(n<p ? n : p), sizeof(int));

    /* ask for optimal size of work array */
    lwork = -1;
    F77_CALL(dgesdd)(CHAR(STRING_ELT(jobu, 0)),
             &n, &p, xvals, &n, REAL(s),
             REAL(u), &ldu,
             REAL(v), &ldvt,
             &tmp, &lwork, iwork, &info);
    if (info != 0)
        error(_("error code %d from Lapack routine '%s'"), info, "dgesdd");
    lwork = (int) tmp;
    work = (double *) R_alloc(lwork, sizeof(double));
    F77_CALL(dgesdd)(CHAR(STRING_ELT(jobu, 0)),
             &n, &p, xvals, &n, REAL(s),
             REAL(u), &ldu,
             REAL(v), &ldvt,
             work, &lwork, iwork, &info);
    if (info != 0)
        error(_("error code %d from Lapack routine '%s'"), info, "dgesdd");
    }

    val = PROTECT(allocVector(VECSXP, 3));
    nm = PROTECT(allocVector(STRSXP, 3));
    SET_STRING_ELT(nm, 0, mkChar("d"));
    SET_STRING_ELT(nm, 1, mkChar("u"));
    SET_STRING_ELT(nm, 2, mkChar("vt"));
    setAttrib(val, R_NamesSymbol, nm);
    SET_VECTOR_ELT(val, 0, s);
    SET_VECTOR_ELT(val, 1, u);
    SET_VECTOR_ELT(val, 2, v);
    UNPROTECT(2);
    return val;
}

static SEXP modLa_rs(SEXP xin, SEXP only_values)
{
    int *xdims, n, lwork, info = 0, ov;
    char jobv[1], uplo[1], range[1];
    SEXP values, ret, nm, x, z = R_NilValue;
    double *work, *rx, *rvalues, tmp, *rz = NULL;
    int liwork, *iwork, itmp, m;
    double vl = 0.0, vu = 0.0, abstol = 0.0;
    /* valgrind seems to think vu should be set, but it is documented
       not to be used if range='a' */
    int il, iu, *isuppz;

    PROTECT(x = duplicate(xin));
    rx = REAL(x);
    uplo[0] = 'L';
    xdims = INTEGER(coerceVector(getAttrib(x, R_DimSymbol), INTSXP));
    n = xdims[0];
    if (n != xdims[1])
    error(_("'x' must be a square numeric matrix"));
    ov = asLogical(only_values);
    if (ov == NA_LOGICAL) error(_("invalid 'only.values'"));
    if (ov) jobv[0] = 'N'; else jobv[0] = 'V';

    PROTECT(values = allocVector(REALSXP, n));
    rvalues = REAL(values);

    range[0] = 'A';
    if (!ov) {
    PROTECT(z = allocMatrix(REALSXP, n, n));
    rz = REAL(z);
    }
    isuppz = (int *) R_alloc(2*n, sizeof(int));
    /* ask for optimal size of work arrays */
    lwork = -1; liwork = -1;
    F77_CALL(dsyevr)(jobv, range, uplo, &n, rx, &n,
             &vl, &vu, &il, &iu, &abstol, &m, rvalues,
             rz, &n, isuppz,
             &tmp, &lwork, &itmp, &liwork, &info);
    if (info != 0)
    error(_("error code %d from Lapack routine '%s'"), info, "dsyevr");
    lwork = (int) tmp;
    liwork = itmp;

    work = (double *) R_alloc(lwork, sizeof(double));
    iwork = (int *) R_alloc(liwork, sizeof(int));
    F77_CALL(dsyevr)(jobv, range, uplo, &n, rx, &n,
             &vl, &vu, &il, &iu, &abstol, &m, rvalues,
             rz, &n, isuppz,
             work, &lwork, iwork, &liwork, &info);
    if (info != 0)
    error(_("error code %d from Lapack routine '%s'"), info, "dsyevr");

    if (!ov) {
    ret = PROTECT(allocVector(VECSXP, 2));
    nm = PROTECT(allocVector(STRSXP, 2));
    SET_STRING_ELT(nm, 1, mkChar("vectors"));
    SET_VECTOR_ELT(ret, 1, z);
    UNPROTECT_PTR(z);
    } else {
    ret = PROTECT(allocVector(VECSXP, 1));
    nm = PROTECT(allocVector(STRSXP, 1));
    }
    SET_STRING_ELT(nm, 0, mkChar("values"));
    setAttrib(ret, R_NamesSymbol, nm);
    SET_VECTOR_ELT(ret, 0, values);
    UNPROTECT(4);
    return ret;
}

static SEXP unscramble(const double* imaginary, int n,
               const double* vecs)
{
    int i, j;
    SEXP s = allocMatrix(CPLXSXP, n, n);

    for (j = 0; j < n; j++) {
    if (imaginary[j] != 0) {
        int j1 = j + 1;
        for (i = 0; i < n; i++) {
        COMPLEX(s)[i+n*j].r = COMPLEX(s)[i+n*j1].r = vecs[i + j * n];
        COMPLEX(s)[i+n*j1].i = -(COMPLEX(s)[i+n*j].i = vecs[i + j1 * n]);
        }
        j = j1;
    } else {
        for (i = 0; i < n; i++) {
        COMPLEX(s)[i+n*j].r = vecs[i + j * n];
        COMPLEX(s)[i+n*j].i = 0.0;
        }
    }
    }
    return s;
}

static SEXP modLa_rg(SEXP x, SEXP only_values)
{
    Rboolean vectors, complexValues;
    int i, n, lwork, info, *xdims, ov;
    double *work, *wR, *wI, *left, *right, *xvals, tmp;
    char jobVL[1], jobVR[1];
    SEXP ret, nm, val;

    xdims = INTEGER(coerceVector(getAttrib(x, R_DimSymbol), INTSXP));
    n = xdims[0];
    if (n != xdims[1])
    error(_("'x' must be a square numeric matrix"));

    xvals = (double *) R_alloc(n * n, sizeof(double));
    /* work on a copy of x */
    Memcpy(xvals, REAL(x), (size_t) (n * n));
    ov = asLogical(only_values);
    if (ov == NA_LOGICAL) error(_("invalid 'only.values'"));
    vectors = !ov;
    jobVL[0] = jobVR[0] = 'N';
    left = right = (double *) 0;
    if (vectors) {
    jobVR[0] = 'V';
    right = (double *) R_alloc(n * n, sizeof(double));
    }
    wR = (double *) R_alloc(n, sizeof(double));
    wI = (double *) R_alloc(n, sizeof(double));
    /* ask for optimal size of work array */
    lwork = -1;
    F77_CALL(dgeev)(jobVL, jobVR, &n, xvals, &n, wR, wI,
            left, &n, right, &n, &tmp, &lwork, &info);
    if (info != 0)
    error(_("error code %d from Lapack routine '%s'"), info, "dgeev");
    lwork = (int) tmp;
    work = (double *) R_alloc(lwork, sizeof(double));
    F77_CALL(dgeev)(jobVL, jobVR, &n, xvals, &n, wR, wI,
            left, &n, right, &n, work, &lwork, &info);
    if (info != 0)
    error(_("error code %d from Lapack routine '%s'"), info, "dgeev");

    complexValues = FALSE;
    for (i = 0; i < n; i++)
    /* This test used to be !=0 for R < 2.3.0.  This is OK for 0+0i */
    if (fabs(wI[i]) >  10 * R_AccuracyInfo.eps * fabs(wR[i])) {
        complexValues = TRUE;
        break;
    }
    ret = PROTECT(allocVector(VECSXP, 2));
    nm = PROTECT(allocVector(STRSXP, 2));
    SET_STRING_ELT(nm, 0, mkChar("values"));
    SET_STRING_ELT(nm, 1, mkChar("vectors"));
    setAttrib(ret, R_NamesSymbol, nm);
    SET_VECTOR_ELT(ret, 1, R_NilValue);
    if (complexValues) {
    val = allocVector(CPLXSXP, n);
    for (i = 0; i < n; i++) {
        COMPLEX(val)[i].r = wR[i];
        COMPLEX(val)[i].i = wI[i];
    }
    SET_VECTOR_ELT(ret, 0, val);

    if (vectors)
        SET_VECTOR_ELT(ret, 1, unscramble(wI, n, right));
    } else {
    val = allocVector(REALSXP, n);
    for (i = 0; i < n; i++)
        REAL(val)[i] = wR[i];
    SET_VECTOR_ELT(ret, 0, val);
    if(vectors) {
        val = allocMatrix(REALSXP, n, n);
        for (i = 0; i < (n * n); i++)
        REAL(val)[i] = right[i];
        SET_VECTOR_ELT(ret, 1, val);
    }
    }
    UNPROTECT(2);
    return ret;
}

/* ------------------------------------------------------------ */

static SEXP modLa_zgesv(SEXP A, SEXP Bin)
{
#ifdef HAVE_FORTRAN_DOUBLE_COMPLEX
    int n, p, info, *ipiv, *Adims, *Bdims;
    Rcomplex *avals;
    SEXP B;

    if (!(isMatrix(A) && isComplex(A)))
    error(_("'a' must be a complex matrix"));
    if (!(isMatrix(Bin) && isComplex(Bin)))
    error(_("'b' must be a complex matrix"));
    PROTECT(B = duplicate(Bin));
    Adims = INTEGER(coerceVector(getAttrib(A, R_DimSymbol), INTSXP));
    Bdims = INTEGER(coerceVector(getAttrib(B, R_DimSymbol), INTSXP));
    n = Adims[0];
    if(n == 0) error(_("'a' is 0-diml"));
    p = Bdims[1];
    if(p == 0) error(_("no right-hand side in 'b'"));
    if(Adims[1] != n)
    error(_("'a' (%d x %d) must be square"), n, Adims[1]);
    if(Bdims[0] != n)
    error(_("'b' (%d x %d) must be compatible with 'a' (%d x %d)"),
        Bdims[0], p, n, n);
    ipiv = (int *) R_alloc(n, sizeof(int));

    avals = (Rcomplex *) R_alloc(n * n, sizeof(Rcomplex));
    /* work on a copy of x */
    Memcpy(avals, COMPLEX(A), (size_t) (n * n));
    F77_CALL(zgesv)(&n, &p, avals, &n, ipiv, COMPLEX(B), &n, &info);
    if (info < 0)
    error(_("argument %d of Lapack routine %s had invalid value"),
          -info, "zgesv");
    if (info > 0)
    error(("Lapack routine zgesv: system is exactly singular"));
    UNPROTECT(1);
    return B;
#else
    error(_("Fortran complex functions are not available on this platform"));
    return R_NilValue; /* -Wall */
#endif
}

static SEXP modLa_zgeqp3(SEXP Ain)
{
#ifdef HAVE_FORTRAN_DOUBLE_COMPLEX
    int i, m, n, *Adims, info, lwork;
    Rcomplex *work, tmp;
    double *rwork;
    SEXP val, nm, jpvt, tau, rank, A;

    if (!(isMatrix(Ain) && isComplex(Ain)))
    error(_("'a' must be a complex matrix"));
    PROTECT(A = duplicate(Ain));
    Adims = INTEGER(coerceVector(getAttrib(A, R_DimSymbol), INTSXP));
    m = Adims[0];
    n = Adims[1];
    rwork = (double *) R_alloc(2*n, sizeof(double));

    jpvt = PROTECT(allocVector(INTSXP, n));
    for (i = 0; i < n; i++) INTEGER(jpvt)[i] = 0;
    tau = PROTECT(allocVector(CPLXSXP, m < n ? m : n));
    lwork = -1;
    F77_CALL(zgeqp3)(&m, &n, COMPLEX(A), &m, INTEGER(jpvt), COMPLEX(tau),
             &tmp, &lwork, rwork, &info);
    if (info != 0)
    error(_("error code %d from Lapack routine '%s'"), info, "zgeqp3");
    lwork = (int) tmp.r;
    work = (Rcomplex *) R_alloc(lwork, sizeof(Rcomplex));
    F77_CALL(zgeqp3)(&m, &n, COMPLEX(A), &m, INTEGER(jpvt), COMPLEX(tau),
             work, &lwork, rwork, &info);
    if (info != 0)
    error(_("error code %d from Lapack routine '%s'"), info, "zgeqp3");
    val = PROTECT(allocVector(VECSXP, 4));
    nm = PROTECT(allocVector(STRSXP, 4));
    rank = PROTECT(ScalarInteger(m < n ? m : n));
    SET_STRING_ELT(nm, 0, mkChar("qr"));
    SET_STRING_ELT(nm, 1, mkChar("rank"));
    SET_STRING_ELT(nm, 2, mkChar("qraux"));
    SET_STRING_ELT(nm, 3, mkChar("pivot"));
    setAttrib(val, R_NamesSymbol, nm);
    SET_VECTOR_ELT(val, 0, A);
    SET_VECTOR_ELT(val, 1, rank);
    SET_VECTOR_ELT(val, 2, tau);
    SET_VECTOR_ELT(val, 3, jpvt);
    UNPROTECT(6);
    return val;
#else
    error(_("Fortran complex functions are not available on this platform"));
    return R_NilValue; /* -Wall */
#endif
}

static SEXP modqr_coef_cmplx(SEXP Q, SEXP Bin)
{
#ifdef HAVE_FORTRAN_DOUBLE_COMPLEX
    int n, nrhs, lwork, info, k, *Bdims, *Qdims;
    SEXP B, qr=VECTOR_ELT(Q, 0), tau=VECTOR_ELT(Q, 2);
    Rcomplex *work, tmp;

    k = LENGTH(tau);
    if (!(isMatrix(Bin) && isComplex(Bin)))
    error(_("'b' must be a complex matrix"));

    PROTECT(B = duplicate(Bin));
    Qdims = INTEGER(coerceVector(getAttrib(qr, R_DimSymbol), INTSXP));
    n = Qdims[0];
    Bdims = INTEGER(coerceVector(getAttrib(Bin, R_DimSymbol), INTSXP));
    if(Bdims[0] != n)
    error(_("right-hand side should have %d not %d rows"), n, Bdims[0]);
    nrhs = Bdims[1];
    lwork = -1;
    F77_CALL(zunmqr)("L", "C", &n, &nrhs, &k,
             COMPLEX(qr), &n, COMPLEX(tau), COMPLEX(B), &n,
             &tmp, &lwork, &info);
    if (info != 0)
    error(_("error code %d from Lapack routine '%s'"), info, "zunmqr");
    lwork = (int) tmp.r;
    work = (Rcomplex *) R_alloc(lwork, sizeof(Rcomplex));
    F77_CALL(zunmqr)("L", "C", &n, &nrhs, &k,
             COMPLEX(qr), &n, COMPLEX(tau), COMPLEX(B), &n,
             work, &lwork, &info);
    if (info != 0)
    error(_("error code %d from Lapack routine '%s'"), info, "zunmqr");
    F77_CALL(ztrtrs)("U", "N", "N", &k, &nrhs,
             COMPLEX(qr), &n, COMPLEX(B), &n, &info);
    if (info != 0)
    error(_("error code %d from Lapack routine '%s'"), info, "ztrtrs");
    UNPROTECT(1);
    return B;
#else
    error(_("Fortran complex functions are not available on this platform"));
    return R_NilValue; /* -Wall */
#endif
}

static SEXP modqr_qy_cmplx(SEXP Q, SEXP Bin, SEXP trans)
{
#ifdef HAVE_FORTRAN_DOUBLE_COMPLEX
    int n, nrhs, lwork, info, k, *Bdims, *Qdims, tr;
    SEXP B, qr=VECTOR_ELT(Q, 0), tau=VECTOR_ELT(Q, 2);
    Rcomplex *work, tmp;

    k = LENGTH(tau);
    if (!(isMatrix(Bin) && isComplex(Bin)))
    error(_("'b' must be a complex matrix"));
    tr = asLogical(trans);
    if(tr == NA_LOGICAL) error(_("invalid 'trans' parameter"));

    PROTECT(B = duplicate(Bin));
    Qdims = INTEGER(coerceVector(getAttrib(qr, R_DimSymbol), INTSXP));
    n = Qdims[0];
    Bdims = INTEGER(coerceVector(getAttrib(B, R_DimSymbol), INTSXP));
    if(Bdims[0] != n)
    error(_("right-hand side should have %d not %d rows"), n, Bdims[0]);
    nrhs = Bdims[1];
    lwork = -1;
    F77_CALL(zunmqr)("L", tr ? "C" : "N", &n, &nrhs, &k,
             COMPLEX(qr), &n, COMPLEX(tau), COMPLEX(B), &n,
             &tmp, &lwork, &info);
    if (info != 0)
    error(_("error code %d from Lapack routine '%s'"), info, "zunmqr");
    lwork = (int) tmp.r;
    work = (Rcomplex *) R_alloc(lwork, sizeof(Rcomplex));
    F77_CALL(zunmqr)("L", tr ? "C" : "N", &n, &nrhs, &k,
             COMPLEX(qr), &n, COMPLEX(tau), COMPLEX(B), &n,
             work, &lwork, &info);
    if (info != 0)
    error(_("error code %d from Lapack routine '%s'"), info, "zunmqr");
    UNPROTECT(1);
    return B;
#else
    error(_("Fortran complex functions are not available on this platform"));
    return R_NilValue; /* -Wall */
#endif
}

static SEXP modLa_svd_cmplx(SEXP jobu, SEXP jobv, SEXP xin, SEXP s, SEXP u, SEXP v)
{
#ifdef HAVE_FORTRAN_DOUBLE_COMPLEX
    int *xdims, n, p, lwork, info;
    double *rwork;
    Rcomplex *work, tmp;
    SEXP x, val, nm;

    if (!(isString(jobu) && isString(jobv)))
    error(_("'jobu' and 'jobv' must be character strings"));
    PROTECT(x = duplicate(xin));
    xdims = INTEGER(coerceVector(getAttrib(x, R_DimSymbol), INTSXP));
    n = xdims[0]; p = xdims[1];
    rwork = (double *) R_alloc(5*(n < p ? n:p), sizeof(double));
    /* ask for optimal size of work array */
    lwork = -1;
    F77_CALL(zgesvd)(CHAR(STRING_ELT(jobu, 0)), CHAR(STRING_ELT(jobv, 0)),
             &n, &p, COMPLEX(x), &n, REAL(s),
             COMPLEX(u), INTEGER(getAttrib(u, R_DimSymbol)),
             COMPLEX(v), INTEGER(getAttrib(v, R_DimSymbol)),
             &tmp, &lwork, rwork, &info);
    if (info != 0)
    error(_("error code %d from Lapack routine '%s'"), info, "zgesvd");
    lwork = (int) tmp.r;
    work = (Rcomplex *) R_alloc(lwork, sizeof(Rcomplex));
    F77_CALL(zgesvd)(CHAR(STRING_ELT(jobu, 0)), CHAR(STRING_ELT(jobv, 0)),
             &n, &p, COMPLEX(x), &n, REAL(s),
             COMPLEX(u), INTEGER(getAttrib(u, R_DimSymbol)),
             COMPLEX(v), INTEGER(getAttrib(v, R_DimSymbol)),
             work, &lwork, rwork, &info);
    if (info != 0)
    error(_("error code %d from Lapack routine '%s'"), info, "zgesvd");
    val = PROTECT(allocVector(VECSXP, 3));
    nm = PROTECT(allocVector(STRSXP, 3));
    SET_STRING_ELT(nm, 0, mkChar("d"));
    SET_STRING_ELT(nm, 1, mkChar("u"));
    SET_STRING_ELT(nm, 2, mkChar("vt"));
    setAttrib(val, R_NamesSymbol, nm);
    SET_VECTOR_ELT(val, 0, s);
    SET_VECTOR_ELT(val, 1, u);
    SET_VECTOR_ELT(val, 2, v);
    UNPROTECT(3);
    return val;
#else
    error(_("Fortran complex functions are not available on this platform"));
    return R_NilValue; /* -Wall */
#endif
}

static SEXP modLa_rs_cmplx(SEXP xin, SEXP only_values)
{
#ifdef HAVE_FORTRAN_DOUBLE_COMPLEX
    int *xdims, n, lwork, info, ov;
    char jobv[1], uplo[1];
    SEXP values, ret, nm, x;
    Rcomplex *work, *rx, tmp;
    double *rwork, *rvalues;

    PROTECT(x = duplicate(xin));
    rx = COMPLEX(x);
    uplo[0] = 'L';
    xdims = INTEGER(coerceVector(getAttrib(x, R_DimSymbol), INTSXP));
    n = xdims[0];
    if (n != xdims[1])
    error(_("'x' must be a square numeric matrix"));
    ov = asLogical(only_values);
    if (ov == NA_LOGICAL) error(_("invalid 'only.values'"));
    if (ov) jobv[0] = 'N'; else jobv[0] = 'V';

    PROTECT(values = allocVector(REALSXP, n));
    rvalues = REAL(values);
    rwork = (double *) R_alloc((3*n-2) > 1 ? 3*n-2 : 1, sizeof(double));
    /* ask for optimal size of work array */
    lwork = -1;
    F77_CALL(zheev)(jobv, uplo, &n, rx, &n, rvalues, &tmp, &lwork, rwork,
            &info);
    if (info != 0)
    error(_("error code %d from Lapack routine '%s'"), info, "zheev");
    lwork = (int) tmp.r;
    work = (Rcomplex *) R_alloc(lwork, sizeof(Rcomplex));
    F77_CALL(zheev)(jobv, uplo, &n, rx, &n, rvalues, work, &lwork, rwork,
            &info);
    if (info != 0)
    error(_("error code %d from Lapack routine '%s'"), info, "zheev");
    if (!ov) {
    ret = PROTECT(allocVector(VECSXP, 2));
    nm = PROTECT(allocVector(STRSXP, 2));
    SET_STRING_ELT(nm, 1, mkChar("vectors"));
    SET_VECTOR_ELT(ret, 1, x);
    }
    else {
    ret = PROTECT(allocVector(VECSXP, 1));
    nm = PROTECT(allocVector(STRSXP, 1));
    }
    SET_STRING_ELT(nm, 0, mkChar("values"));
    setAttrib(ret, R_NamesSymbol, nm);
    SET_VECTOR_ELT(ret, 0, values);
    UNPROTECT(4);
    return ret;
#else
    error(_("Fortran complex functions are not available on this platform"));
    return R_NilValue; /* -Wall */
#endif
}

static SEXP modLa_rg_cmplx(SEXP x, SEXP only_values)
{
#ifdef HAVE_FORTRAN_DOUBLE_COMPLEX
    int  n, lwork, info, *xdims, ov;
    Rcomplex *work, *left, *right, *xvals, tmp;
    double *rwork;
    char jobVL[1], jobVR[1];
    SEXP ret, nm, values, val = R_NilValue;

    xdims = INTEGER(coerceVector(getAttrib(x, R_DimSymbol), INTSXP));
    n = xdims[0];
    if (n != xdims[1])
    error(_("'x' must be a square numeric matrix"));

    xvals = (Rcomplex *) R_alloc(n * n, sizeof(Rcomplex));
    /* work on a copy of x */
    Memcpy(xvals, COMPLEX(x), (size_t) (n * n));
    ov = asLogical(only_values);
    if (ov == NA_LOGICAL) error(_("invalid 'only.values'"));
    jobVL[0] = jobVR[0] = 'N';
    left = right = (Rcomplex *) 0;
    if (!ov) {
    jobVR[0] = 'V';
    PROTECT(val = allocMatrix(CPLXSXP, n, n));
    right = COMPLEX(val);
    }
    PROTECT(values = allocVector(CPLXSXP, n));
    rwork = (double *) R_alloc(2*n, sizeof(double));
    /* ask for optimal size of work array */
    lwork = -1;
    F77_CALL(zgeev)(jobVL, jobVR, &n, xvals, &n, COMPLEX(values),
            left, &n, right, &n, &tmp, &lwork, rwork, &info);
    if (info != 0)
    error(_("error code %d from Lapack routine '%s'"), info, "zgeev");
    lwork = (int) tmp.r;
    work = (Rcomplex *) R_alloc(lwork, sizeof(Rcomplex));
    F77_CALL(zgeev)(jobVL, jobVR, &n, xvals, &n, COMPLEX(values),
            left, &n, right, &n, work, &lwork, rwork, &info);
    if (info != 0)
    error(_("error code %d from Lapack routine '%s'"), info, "zgeev");

    if(!ov){
    ret = PROTECT(allocVector(VECSXP, 2));
    nm = PROTECT(allocVector(STRSXP, 2));
    SET_STRING_ELT(nm, 1, mkChar("vectors"));
    SET_VECTOR_ELT(ret, 1, val);
    } else {
    ret = PROTECT(allocVector(VECSXP, 1));
    nm = PROTECT(allocVector(STRSXP, 1));
    }
    SET_STRING_ELT(nm, 0, mkChar("values"));
    SET_VECTOR_ELT(ret, 0, values);
    setAttrib(ret, R_NamesSymbol, nm);
    UNPROTECT(ov ? 3 : 4);
    return ret;
#else
    error(_("Fortran complex functions are not available on this platform"));
    return R_NilValue; /* -Wall */
#endif
}

/* ------------------------------------------------------------ */

static SEXP modLa_chol(SEXP A)
{
    if (isMatrix(A)) {
    SEXP ans = PROTECT((TYPEOF(A) == REALSXP)?duplicate(A):
               coerceVector(A, REALSXP));
    SEXP adims = getAttrib(A, R_DimSymbol);
    int m = INTEGER(adims)[0];
    int n = INTEGER(adims)[1];
    int i, j;

    if (m != n) error(_("'a' must be a square matrix"));
    if (m <= 0) error(_("'a' must have dims > 0"));
    for (j = 0; j < n; j++) {   /* zero the lower triangle */
        for (i = j+1; i < n; i++) {
        REAL(ans)[i + j * n] = 0.;
        }
    }

    F77_CALL(dpotrf)("Upper", &m, REAL(ans), &m, &i);
    if (i != 0) {
        if (i > 0)
        error(_("the leading minor of order %d is not positive definite"),
              i);
        error(_("argument %d of Lapack routine %s had invalid value"),
          -i, "dpotrf");
    }
    unprotect(1);
    return ans;
    }
    else error(_("'a' must be a numeric matrix"));
    return R_NilValue; /* -Wall */
}

static SEXP modLa_chol2inv(SEXP A, SEXP size)
{
    int sz = asInteger(size);
    if (sz == NA_INTEGER || sz < 1)
    error(_("'size' argument must be a positive integer"));
    if (isMatrix(A)) {
    SEXP Amat = PROTECT(coerceVector(A, REALSXP));
    SEXP ans;
    SEXP adims = getAttrib(A, R_DimSymbol);
    int m = INTEGER(adims)[0];
    int n = INTEGER(adims)[1];
    int i, j;

    if (sz > n) error(_("'size' cannot exceed ncol(x) = %d"), n);
    if (sz > m) error(_("'size' cannot exceed nrow(x) = %d"), m);
    ans = PROTECT(allocMatrix(REALSXP, sz, sz));
    for (j = 0; j < sz; j++) {
        for (i = 0; i <= j; i++)
        REAL(ans)[i + j * sz] = REAL(Amat)[i + j * m];
    }
    F77_CALL(dpotri)("Upper", &sz, REAL(ans), &sz, &i);
    if (i != 0) {
        if (i > 0)
        error(_("element (%d, %d) is zero, so the inverse cannot be computed"), i, i);
        error(_("argument %d of Lapack routine %s had invalid value"),
          -i, "dpotri");
    }
    for (j = 0; j < sz; j++) {
        for (i = j+1; i < sz; i++)
        REAL(ans)[i + j * sz] = REAL(ans)[j + i * sz];
    }
    unprotect(2);
    return ans;
    }
    else error(_("'a' must be a numeric matrix"));
    return R_NilValue; /* -Wall */
}

/* ------------------------------------------------------------ */

static SEXP modLa_dgesv(SEXP A, SEXP Bin, SEXP tolin)
{
    int n, p, info, *ipiv, *Adims, *Bdims;
    double *avals, anorm, rcond, tol = asReal(tolin), *work;
    SEXP B;

    if (!(isMatrix(A) && isReal(A)))
    error(_("'a' must be a numeric matrix"));
    if (!(isMatrix(Bin) && isReal(Bin)))
    error(_("'b' must be a numeric matrix"));
    PROTECT(B = duplicate(Bin));
    Adims = INTEGER(coerceVector(getAttrib(A, R_DimSymbol), INTSXP));
    Bdims = INTEGER(coerceVector(getAttrib(B, R_DimSymbol), INTSXP));
    n = Adims[0];
    if(n == 0) error(_("'a' is 0-diml"));
    p = Bdims[1];
    if(p == 0) error(_("no right-hand side in 'b'"));
    if(Adims[1] != n)
    error(_("'a' (%d x %d) must be square"), n, Adims[1]);
    if(Bdims[0] != n)
    error(_("'b' (%d x %d) must be compatible with 'a' (%d x %d)"),
          Bdims[0], p, n, n);
    ipiv = (int *) R_alloc(n, sizeof(int));

    avals = (double *) R_alloc(n * n, sizeof(double));
                /* work on a copy of A */
    Memcpy(avals, REAL(A), (size_t) (n * n));
    F77_CALL(dgesv)(&n, &p, avals, &n, ipiv, REAL(B), &n, &info);
    if (info < 0)
    error(_("argument %d of Lapack routine %s had invalid value"),
          -info, "dgesv");
    if (info > 0)
    error(_("Lapack routine dgesv: system is exactly singular"));
    anorm = F77_CALL(dlange)("1", &n, &n, REAL(A), &n, (double*) NULL);
    work = (double *) R_alloc(4*n, sizeof(double));
    F77_CALL(dgecon)("1", &n, avals, &n, &anorm, &rcond, work, ipiv, &info);
    if (rcond < tol)
    error(_("system is computationally singular: reciprocal condition number = %g"),
          rcond);
    UNPROTECT(1);
    return B;
}

static SEXP modLa_dgeqp3(SEXP Ain)
{
    int i, m, n, *Adims, info, lwork;
    double *work, tmp;
    SEXP val, nm, jpvt, tau, rank, A;

    if (!(isMatrix(Ain) && isReal(Ain)))
    error(_("'a' must be a numeric matrix"));
    PROTECT(A = duplicate(Ain));
    Adims = INTEGER(coerceVector(getAttrib(A, R_DimSymbol), INTSXP));
    m = Adims[0];
    n = Adims[1];

    jpvt = PROTECT(allocVector(INTSXP, n));
    for (i = 0; i < n; i++) INTEGER(jpvt)[i] = 0;
    tau = PROTECT(allocVector(REALSXP, m < n ? m : n));
    lwork = -1;
    F77_CALL(dgeqp3)(&m, &n, REAL(A), &m, INTEGER(jpvt), REAL(tau),
             &tmp, &lwork, &info);
    if (info < 0)
    error(_("error code %d from Lapack routine '%s'"), info, "dgeqp3");
    lwork = (int) tmp;
    work = (double *) R_alloc(lwork, sizeof(double));
    F77_CALL(dgeqp3)(&m, &n, REAL(A), &m, INTEGER(jpvt), REAL(tau),
             work, &lwork, &info);
    if (info < 0)
    error(_("error code %d from Lapack routine '%s'"), info, "dgeqp3");
    val = PROTECT(allocVector(VECSXP, 4));
    nm = PROTECT(allocVector(STRSXP, 4));
    rank = PROTECT(ScalarInteger(m < n ? m : n));
    SET_STRING_ELT(nm, 0, mkChar("qr"));
    SET_STRING_ELT(nm, 1, mkChar("rank"));
    SET_STRING_ELT(nm, 2, mkChar("qraux"));
    SET_STRING_ELT(nm, 3, mkChar("pivot"));
    setAttrib(val, R_NamesSymbol, nm);
    SET_VECTOR_ELT(val, 0, A);
    SET_VECTOR_ELT(val, 1, rank);
    SET_VECTOR_ELT(val, 2, tau);
    SET_VECTOR_ELT(val, 3, jpvt);
    UNPROTECT(6);
    return val;
}

static SEXP modqr_coef_real(SEXP Q, SEXP Bin)
{
    int n, nrhs, lwork, info, k, *Bdims, *Qdims;
    SEXP B, qr=VECTOR_ELT(Q, 0), tau=VECTOR_ELT(Q, 2);
    double *work, tmp;

    k = LENGTH(tau);
    if (!(isMatrix(Bin) && isReal(Bin)))
    error(_("'b' must be a numeric matrix"));

    PROTECT(B = duplicate(Bin));
    Qdims = INTEGER(coerceVector(getAttrib(qr, R_DimSymbol), INTSXP));
    n = Qdims[0];
    Bdims = INTEGER(coerceVector(getAttrib(B, R_DimSymbol), INTSXP));
    if(Bdims[0] != n)
    error(_("right-hand side should have %d not %d rows"), n, Bdims[0]);
    nrhs = Bdims[1];
    lwork = -1;
    F77_CALL(dormqr)("L", "T", &n, &nrhs, &k,
             REAL(qr), &n, REAL(tau), REAL(B), &n,
             &tmp, &lwork, &info);
    if (info != 0)
    error(_("error code %d from Lapack routine '%s'"), info, "dormqr");
    lwork = (int) tmp;
    work = (double *) R_alloc(lwork, sizeof(double));
    F77_CALL(dormqr)("L", "T", &n, &nrhs, &k,
             REAL(qr), &n, REAL(tau), REAL(B), &n,
             work, &lwork, &info);
    if (info != 0)
    error(_("error code %d from Lapack routine '%s'"), info, "dormqr");
    F77_CALL(dtrtrs)("U", "N", "N", &k, &nrhs,
             REAL(qr), &n, REAL(B), &n, &info);
    if (info != 0)
    error(_("error code %d from Lapack routine '%s'"), info, "dtrtrs");
    UNPROTECT(1);
    return B;
}

static SEXP modqr_qy_real(SEXP Q, SEXP Bin, SEXP trans)
{
    int n, nrhs, lwork, info, k, *Bdims, *Qdims, tr;
    SEXP B, qr=VECTOR_ELT(Q, 0), tau=VECTOR_ELT(Q, 2);
    double *work, tmp;

    k = LENGTH(tau);
    if (!(isMatrix(Bin) && isReal(Bin)))
    error(_("'b' must be a numeric matrix"));
    tr = asLogical(trans);
    if(tr == NA_LOGICAL) error(_("invalid 'trans' parameter"));

    PROTECT(B = duplicate(Bin));
    Qdims = INTEGER(coerceVector(getAttrib(qr, R_DimSymbol), INTSXP));
    n = Qdims[0];
    Bdims = INTEGER(coerceVector(getAttrib(B, R_DimSymbol), INTSXP));
    if(Bdims[0] != n)
    error(_("right-hand side should have %d not %d rows"), n, Bdims[0]);
    nrhs = Bdims[1];
    lwork = -1;
    F77_CALL(dormqr)("L", tr ? "T" : "N", &n, &nrhs, &k,
             REAL(qr), &n, REAL(tau), REAL(B), &n,
             &tmp, &lwork, &info);
    if (info != 0)
    error(_("error code %d from Lapack routine '%s'"), info, "dormqr");
    lwork = (int) tmp;
    work = (double *) R_alloc(lwork, sizeof(double));
    F77_CALL(dormqr)("L", tr ? "T" : "N", &n, &nrhs, &k,
             REAL(qr), &n, REAL(tau), REAL(B), &n,
             work, &lwork, &info);
    if (info != 0)
    error(_("error code %d from Lapack routine '%s'"), info, "dormqr");
    UNPROTECT(1);
    return B;
}

static SEXP moddet_ge_real(SEXP Ain, SEXP logarithm)
{
    int i, n, *Adims, info, *jpvt, sign, useLog;
    double modulus = 0.0; /* -Wall */
    SEXP val, nm, A;

    if (!(isMatrix(Ain) && isReal(Ain)))
    error(_("'a' must be a numeric matrix"));
    useLog = asLogical(logarithm);
    if (useLog == NA_LOGICAL) error(_("argument 'logarithm' must be logical"));
    PROTECT(A = duplicate(Ain));
    Adims = INTEGER(coerceVector(getAttrib(A, R_DimSymbol), INTSXP));
    n = Adims[0];
    if (Adims[1] != n)
    error(_("'a' must be a square matrix"));
    jpvt = (int *) R_alloc(n, sizeof(int));
    F77_CALL(dgetrf)(&n, &n, REAL(A), &n, jpvt, &info);
    sign = 1;
    if (info < 0)
    error(_("error code %d from Lapack routine '%s'"), info, "dgetrf");
    else if (info > 0) { /* Singular matrix:  U[i,i] (i := info) is 0 */
    /*warning("Lapack dgetrf(): singular matrix: U[%d,%d]=0", info,info);*/
    modulus = (useLog ? R_NegInf : 0.);
    }
    else {
    for (i = 0; i < n; i++) if (jpvt[i] != (i + 1))
        sign = -sign;
    if (useLog) {
        modulus = 0.0;
        for (i = 0; i < n; i++) {
        double dii = REAL(A)[i*(n + 1)]; /* ith diagonal element */
        modulus += log(dii < 0 ? -dii : dii);
        if (dii < 0) sign = -sign;
        }
    } else {
        modulus = 1.0;
        for (i = 0; i < n; i++)
        modulus *= REAL(A)[i*(n + 1)];
        if (modulus < 0) {
        modulus = -modulus;
        sign = -sign;
        }
    }
    }
    val = PROTECT(allocVector(VECSXP, 2));
    nm = PROTECT(allocVector(STRSXP, 2));
    SET_STRING_ELT(nm, 0, mkChar("modulus"));
    SET_STRING_ELT(nm, 1, mkChar("sign"));
    setAttrib(val, R_NamesSymbol, nm);
    SET_VECTOR_ELT(val, 0, ScalarReal(modulus));
    setAttrib(VECTOR_ELT(val, 0), install("logarithm"), ScalarLogical(useLog));
    SET_VECTOR_ELT(val, 1, ScalarInteger(sign));
    setAttrib(val, R_ClassSymbol, ScalarString(mkChar("det")));
    UNPROTECT(3);
    return val;
}

/* ------------------------------------------------------------ */

#include <Rmodules/Rlapack.h>
#include <R_ext/Rdynload.h>

void
R_init_lapack(DllInfo *info)
{
    R_LapackRoutines *tmp;
    tmp = Calloc(1, R_LapackRoutines);

    tmp->svd = modLa_svd;
    tmp->rs = modLa_rs;
    tmp->rg = modLa_rg;
    tmp->zgesv = modLa_zgesv;
    tmp->zgeqp3 = modLa_zgeqp3;
    tmp->qr_coef_cmplx = modqr_coef_cmplx;
    tmp->qr_qy_cmplx = modqr_qy_cmplx;
    tmp->svd_cmplx = modLa_svd_cmplx;
    tmp->rs_cmplx = modLa_rs_cmplx;
    tmp->rg_cmplx = modLa_rg_cmplx;
    tmp->chol = modLa_chol;
    tmp->chol2inv = modLa_chol2inv;
    tmp->dgesv = modLa_dgesv;
    tmp->dgeqp3 = modLa_dgeqp3;
    tmp->qr_coef_real = modqr_coef_real;
    tmp->qr_qy_real = modqr_qy_real;
    tmp->det_ge_real = moddet_ge_real;
    R_setLapackRoutines(tmp);
}