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third-party-mirror / R / refs/heads/main / . / src / modules / lapack / Lapack.c
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/*
* R : A Computer Language for Statistical Data Analysis
* Copyright (C) 2001--2022 The R Core Team.
* Copyright (C) 2003--2010 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
* https://www.R-project.org/Licenses/
*/
/* Interface routines, callable from R using .Internal, for Lapack code */
#ifdef HAVE_CONFIG_H
# include <config.h>
#endif
#include <Defn.h>
#include <ctype.h> /* for toupper */
#include <limits.h> /* for PATH_MAX */
#include <stdlib.h> /* for realpath */
#ifdef HAVE_UNISTD_H
# include <unistd.h> /* for realpath on some systems */
#endif
#ifdef HAVE_DLFCN_H
# include <dlfcn.h> /* for dladdr */
#endif
#if defined(HAVE_REALPATH) && defined(HAVE_DECL_REALPATH) && !HAVE_DECL_REALPATH
extern char *realpath(const char *path, char *resolved_path);
#endif
#if defined(HAVE_DLADDR) && defined(HAVE_DECL_DLADDR) && !HAVE_DECL_DLADDR
extern int dladdr(void *addr, Dl_info *info);
#endif
#include "Lapack.h"
/* NB: the handling of dims is odd here. Most are coerced to be
* integers (which dimgets currently guarantees), but a couple were
* used unchecked.
*/
/* FIXME: MM would want to make these available to packages;
* BUT: 1) cannot be in libRlapack {since that may be external}
* 2) Pkgs cannot get it from the C-Lapack interface code {lapack.so}
* since that is R-internal
*/
static char La_norm_type(const char *typstr)
{
char typup;
if (strlen(typstr) != 1)
error(
_("argument type[1]='%s' must be a character string of string length 1"),
typstr);
typup = (char) toupper(*typstr);
if (typup == '1')
typup = 'O'; /* aliases */
else if (typup == 'E')
typup = 'F';
else if (typup != 'M' && typup != 'O' && typup != 'I' && typup != 'F')
error(_("argument type[1]='%s' must be one of 'M','1','O','I','F' or 'E'"),
typstr);
return typup;
}
/* Lapack condition number approximation: currently only supports _1 or _Inf norm : */
static char La_rcond_type(const char *typstr)
{
char typup;
if (strlen(typstr) != 1)
error(_("argument type[1]='%s' must be a character string of string length 1"),
typstr);
typup = (char) toupper(*typstr);
if (typup == '1')
typup = 'O'; /* alias */
else if (typup != 'O' && typup != 'I')
error(_("argument type[1]='%s' must be one of '1','O', or 'I'"),
typstr);
return typup; /* 'O' or 'I' */
}
/* La.svd, called from svd */
static SEXP La_svd(SEXP jobu, SEXP x, SEXP s, SEXP u, SEXP vt)
{
if (!isString(jobu))
error("'jobu' must be a character string");
int *xdims = INTEGER(coerceVector(getAttrib(x, R_DimSymbol), INTSXP)),
n = xdims[0], p = xdims[1], nprot = 2;
/* work on a copy of x */
double *xvals;
if (!isReal(x)) {
x = PROTECT(coerceVector(x, REALSXP)); nprot++;
xvals = REAL(x);
} else {
xvals = (double *) R_alloc(n * (size_t) p, sizeof(double));
Memcpy(xvals, REAL(x), n * (size_t) p);
}
SEXP dims = getAttrib(u, R_DimSymbol);
if (TYPEOF(dims) != INTSXP) error("non-integer dim(u)");
int ldu = INTEGER(dims)[0];
dims = getAttrib(vt, R_DimSymbol);
if (TYPEOF(dims) != INTSXP) error("non-integer dim(vt)");
int ldvt = INTEGER(dims)[0];
double tmp;
/* min(n,p) large is implausible, but cast to be sure */
int *iwork= (int *) R_alloc(8*(size_t)(n < p ? n : p), sizeof(int));
/* ask for optimal size of work array */
const char *ju = CHAR(STRING_ELT(jobu, 0));
int info = 0, lwork = -1;
F77_CALL(dgesdd)(ju, &n, &p, xvals, &n, REAL(s),
REAL(u), &ldu, REAL(vt), &ldvt,
&tmp, &lwork, iwork, &info FCONE);
if (info != 0)
error(_("error code %d from Lapack routine '%s'"), info, "dgesdd");
lwork = (int) tmp;
double *work = (double *) R_alloc(lwork, sizeof(double));
F77_CALL(dgesdd)(ju, &n, &p, xvals, &n, REAL(s),
REAL(u), &ldu, REAL(vt), &ldvt,
work, &lwork, iwork, &info FCONE);
if (info != 0)
error(_("error code %d from Lapack routine '%s'"), info, "dgesdd");
SEXP val = PROTECT(allocVector(VECSXP, 3));
SEXP 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, vt);
UNPROTECT(nprot);
return val;
}
/* Real, symmetric case of eigen */
static SEXP La_rs(SEXP x, SEXP only_values)
{
int *xdims, n, lwork, info = 0, ov;
char jobv[2] = "U", uplo[2] = "L", range[2] = "A";
SEXP 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;
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 '%s' argument"), "only.values");
if (ov) jobv[0] = 'N'; else jobv[0] = 'V';
/* work on a copy of x, since LAPACK trashes it */
if (!isReal(x)) {
x = coerceVector(x, REALSXP);
rx = REAL(x);
} else {
rx = (double *) R_alloc(n * (size_t) n, sizeof(double));
Memcpy(rx, REAL(x), (size_t) n * n);
}
PROTECT(x);
SEXP values = PROTECT(allocVector(REALSXP, n));
rvalues = REAL(values);
if (!ov) {
z = PROTECT(allocMatrix(REALSXP, n, n));
rz = REAL(z);
}
isuppz = (int *) R_alloc(2*(size_t)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 FCONE FCONE FCONE);
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 FCONE FCONE FCONE);
if (info != 0)
error(_("error code %d from Lapack routine '%s'"), info, "dsyevr");
SEXP ret, nm;
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);
} 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(ov ? 4 : 5);
return ret;
}
static SEXP unscramble(const double* imaginary, int n,
const double* vecs)
{
int i, j;
SEXP s = allocMatrix(CPLXSXP, n, n);
size_t 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;
}
/* Real, general case of eigen */
static SEXP La_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[2] = "N", jobVR[2] = "N";
xdims = INTEGER(coerceVector(getAttrib(x, R_DimSymbol), INTSXP));
n = xdims[0];
if (n != xdims[1])
error(_("'x' must be a square numeric matrix"));
/* work on a copy of x */
if (!isReal(x)) {
x = coerceVector(x, REALSXP);
xvals = REAL(x);
} else {
xvals = (double *) R_alloc(n * (size_t)n, sizeof(double));
Memcpy(xvals, REAL(x), (size_t) n * n);
}
PROTECT(x);
ov = asLogical(only_values);
if (ov == NA_LOGICAL) error(_("invalid '%s' argument"), "only.values");
vectors = !ov;
left = right = (double *) 0;
if (vectors) {
jobVR[0] = 'V';
right = (double *) R_alloc(n * (size_t)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 FCONE FCONE);
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 FCONE FCONE);
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;
}
SEXP ret = PROTECT(allocVector(VECSXP, 2));
SEXP 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) {
SEXP 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 {
SEXP 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(3);
return ret;
}
/* norm() except for 2-norm */
static SEXP La_dlange(SEXP A, SEXP type)
{
int *xdims, m, n, nprot = 1;
double *work = NULL;
char typNorm[] = {'\0', '\0'};
if (!isMatrix(A)) error(_("'A' must be a numeric matrix"));
if (!isString(type))
error(_("'type' must be a character string"));
if (!isReal(A)) {
A = PROTECT(coerceVector(A, REALSXP)); nprot++;
}
xdims = INTEGER(coerceVector(getAttrib(A, R_DimSymbol), INTSXP));
m = xdims[0];
n = xdims[1]; /* m x n matrix {using Lapack naming convention} */
typNorm[0] = La_norm_type(CHAR(asChar(type)));
SEXP val = PROTECT(allocVector(REALSXP, 1));
if(*typNorm == 'I') work = (double *) R_alloc(m, sizeof(double));
REAL(val)[0] = F77_CALL(dlange)(typNorm, &m, &n, REAL(A), &m, work FCONE);
UNPROTECT(nprot);
return val;
}
/* ------------------------------------------------------------ */
/* Real case of rcond, for general matrices */
static SEXP La_dgecon(SEXP A, SEXP norm)
{
int *xdims, m, n, info, *iwork;
double anorm, *work;
char typNorm[] = {'\0', '\0'};
if (!isMatrix(A)) error(_("'A' must be a numeric matrix"));
if (!isString(norm))
error(_("'norm' must be a character string"));
A = PROTECT(isReal(A) ? duplicate(A) : coerceVector(A, REALSXP));
xdims = INTEGER(coerceVector(getAttrib(A, R_DimSymbol), INTSXP));
m = xdims[0]; n = xdims[1];
typNorm[0] = La_rcond_type(CHAR(asChar(norm)));
SEXP val = PROTECT(allocVector(REALSXP, 1));
work = (double *) R_alloc((*typNorm == 'I' && m > 4*(size_t)n) ? m : 4*(size_t)n,
sizeof(double));
iwork = (int *) R_alloc(m, sizeof(int));
anorm = F77_CALL(dlange)(typNorm, &m, &n, REAL(A), &m, work FCONE);
/* Compute the LU-decomposition and overwrite 'A' with result :*/
F77_CALL(dgetrf)(&m, &n, REAL(A), &m, iwork, &info);
if (info) {
if (info < 0) {
UNPROTECT(2);
error(_("error [%d] from Lapack 'dgetrf()'"), info);
}
else { /* i := info > 0: LU decomp. is completed, but U[i,i] = 0
* <==> singularity */
#if 0
warning(_("exact singularity: U[%d,%d] = 0 in LU-decomposition {Lapack 'dgetrf()'}"),
info,info);
#endif
REAL(val)[0] = 0.; /* rcond = 0 <==> singularity */
UNPROTECT(2);
return val;
}
}
F77_CALL(dgecon)(typNorm, &n, REAL(A), &n, &anorm,
/* rcond = */ REAL(val),
work, iwork, &info FCONE);
UNPROTECT(2);
if (info) error(_("error [%d] from Lapack 'dgecon()'"), info);
return val;
}
/* Real case of kappa.tri (and also rcond for a triangular matrix) */
static SEXP La_dtrcon(SEXP A, SEXP norm)
{
int *xdims, n, nprot = 0, info;
char typNorm[] = {'\0', '\0'};
if (!isMatrix(A)) error(_("'A' must be a numeric matrix"));
if (!isString(norm)) error(_("'norm' must be a character string"));
if (!isReal(A)) {
nprot++;
A = PROTECT(coerceVector(A, REALSXP));
}
xdims = INTEGER(coerceVector(getAttrib(A, R_DimSymbol), INTSXP));
n = xdims[0];
if(n != xdims[1]) {
UNPROTECT(nprot);
error(_("'A' must be a *square* matrix"));
}
typNorm[0] = La_rcond_type(CHAR(asChar(norm)));
nprot++;
SEXP val = PROTECT(allocVector(REALSXP, 1));
F77_CALL(dtrcon)(typNorm, "U", "N", &n, REAL(A), &n,
REAL(val),
/* work : */ (double *) R_alloc(3*(size_t)n, sizeof(double)),
/* iwork: */ (int *) R_alloc(n, sizeof(int)),
&info FCONE FCONE FCONE);
UNPROTECT(nprot);
if (info) error(_("error [%d] from Lapack 'dtrcon()'"), info);
return val;
}
/* Complex case of rcond, for general matrices */
static SEXP La_zgecon(SEXP A, SEXP norm)
{
#ifdef HAVE_FORTRAN_DOUBLE_COMPLEX
Rcomplex *avals; /* copy of A, to be modified */
int *dims, n, info;
double anorm, *rwork;
char typNorm[] = {'\0', '\0'};
if (!isString(norm)) error(_("'norm' must be a character string"));
if (!(isMatrix(A) && isComplex(A)))
error(_("'A' must be a complex matrix"));
dims = INTEGER(coerceVector(getAttrib(A, R_DimSymbol), INTSXP));
n = dims[0];
if(n != dims[1]) error(_("'A' must be a *square* matrix"));
typNorm[0] = La_rcond_type(CHAR(asChar(norm)));
SEXP val = PROTECT(allocVector(REALSXP, 1));
rwork = (double *) R_alloc(2*(size_t)n, sizeof(Rcomplex));
anorm = F77_CALL(zlange)(typNorm, &n, &n, COMPLEX(A), &n, rwork FCONE);
/* Compute the LU-decomposition and overwrite 'x' with result;
* working on a copy of A : */
avals = (Rcomplex *) R_alloc((size_t)n * n, sizeof(Rcomplex));
Memcpy(avals, COMPLEX(A), (size_t) n * n);
F77_CALL(zgetrf)(&n, &n, avals, &n,
/* iwork: */(int *) R_alloc(n, sizeof(int)),
&info);
if (info) {
if (info < 0) {
UNPROTECT(1);
error(_("error [%d] from Lapack 'zgetrf()'"), info);
} else {
REAL(val)[0] = 0.; /* rcond = 0 <==> singularity */
UNPROTECT(1);
return val;
}
UNPROTECT(1);
error(_("error [%d] from Lapack 'zgetrf()'"), info);
}
F77_CALL(zgecon)(typNorm, &n, avals, &n, &anorm,
/* rcond = */ REAL(val),
/* work : */ (Rcomplex *) R_alloc(4*(size_t)n, sizeof(Rcomplex)),
rwork, &info FCONE);
UNPROTECT(1);
if (info) error(_("error [%d] from Lapack 'zgecon()'"), info);
return val;
#else
error(_("Fortran complex functions are not available on this platform"));
return R_NilValue; /* -Wall */
#endif
}
/* Complex case of kappa.tri (and also rcond for a triangular matrix) */
static SEXP La_ztrcon(SEXP A, SEXP norm)
{
#ifdef HAVE_FORTRAN_DOUBLE_COMPLEX
SEXP val;
int *dims, n, info;
char typNorm[] = {'\0', '\0'};
if (!isString(norm))
error(_("'norm' must be a character string"));
if (!(isMatrix(A) && isComplex(A)))
error(_("'A' must be a complex matrix"));
dims = INTEGER(coerceVector(getAttrib(A, R_DimSymbol), INTSXP));
n = dims[0];
if(n != dims[1])
error(_("'A' must be a *square* matrix"));
typNorm[0] = La_rcond_type(CHAR(asChar(norm)));
val = PROTECT(allocVector(REALSXP, 1));
F77_CALL(ztrcon)(typNorm, "U", "N", &n, COMPLEX(A), &n,
REAL(val),
/* work : */ (Rcomplex *) R_alloc(2*(size_t)n, sizeof(Rcomplex)),
/* rwork: */ (double *) R_alloc(n, sizeof(double)),
&info FCONE FCONE FCONE);
UNPROTECT(1);
if (info) error(_("error [%d] from Lapack 'ztrcon()'"), info);
return val;
#else
error(_("Fortran complex functions are not available on this platform"));
return R_NilValue; /* -Wall */
#endif
}
/* Complex case of solve.default: see the comments in La_solve */
static SEXP La_solve_cmplx(SEXP A, SEXP Bin)
{
#ifdef HAVE_FORTRAN_DOUBLE_COMPLEX
int n, p, info, *ipiv, *Adims, *Bdims;
Rcomplex *avals;
SEXP B, Adn, Bdn;
if (!isMatrix(A)) error(_("'a' must be a complex matrix"));
Adims = INTEGER(coerceVector(getAttrib(A, R_DimSymbol), INTSXP));
n = Adims[0];
if(n == 0) error(_("'a' is 0-diml"));
int n2 = Adims[1];
if(n2 != n) error(_("'a' (%d x %d) must be square"), n, n2);
Adn = getAttrib(A, R_DimNamesSymbol);
if (isMatrix(Bin)) {
Bdims = INTEGER(coerceVector(getAttrib(Bin, R_DimSymbol), INTSXP));
p = Bdims[1];
if(p == 0) error(_("no right-hand side in 'b'"));
int p2 = Bdims[0];
if(p2 != n)
error(_("'b' (%d x %d) must be compatible with 'a' (%d x %d)"),
p2, p, n, n);
PROTECT(B = allocMatrix(CPLXSXP, n, p));
SEXP Bindn = getAttrib(Bin, R_DimNamesSymbol);
if (!isNull(Adn) || !isNull(Bindn)) {
Bdn = allocVector(VECSXP, 2);
if (!isNull(Adn)) SET_VECTOR_ELT(Bdn, 0, VECTOR_ELT(Adn, 1));
if (!isNull(Bindn)) SET_VECTOR_ELT(Bdn, 1, VECTOR_ELT(Bindn, 1));
if (!isNull(VECTOR_ELT(Bdn, 0)) && !isNull(VECTOR_ELT(Bdn, 1)))
setAttrib(B, R_DimNamesSymbol, Bdn);
}
} else {
p = 1;
if(length(Bin) != n)
error(_("'b' (%d x %d) must be compatible with 'a' (%d x %d)"),
length(Bin), p, n, n);
PROTECT(B = allocVector(CPLXSXP, n));
if (!isNull(Adn)) setAttrib(B, R_NamesSymbol, VECTOR_ELT(Adn, 1));
}
Bin = PROTECT(coerceVector(Bin, CPLXSXP));
Memcpy(COMPLEX(B), COMPLEX(Bin), (size_t)n * p);
ipiv = (int *) R_alloc(n, sizeof(int));
/* work on a copy of A */
if(TYPEOF(A) != CPLXSXP) {
A = coerceVector(A, CPLXSXP);
avals = COMPLEX(A);
} else {
avals = (Rcomplex *) R_alloc((size_t)n * n, sizeof(Rcomplex));
Memcpy(avals, COMPLEX(A), (size_t) n * n);
}
PROTECT(A);
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(3); /* B, Bin, A */
return B;
#else
error(_("Fortran complex functions are not available on this platform"));
return R_NilValue; /* -Wall */
#endif
}
/* Complex case of qr.default */
static SEXP La_qr_cmplx(SEXP Ain)
{
#ifdef HAVE_FORTRAN_DOUBLE_COMPLEX
int i, m, n, *Adims, info, lwork;
Rcomplex *work, tmp;
double *rwork;
if (!(isMatrix(Ain) && isComplex(Ain)))
error(_("'a' must be a complex matrix"));
SEXP Adn = getAttrib(Ain, R_DimNamesSymbol);
Adims = INTEGER(coerceVector(getAttrib(Ain, R_DimSymbol), INTSXP));
m = Adims[0]; n = Adims[1];
SEXP A = PROTECT(allocMatrix(CPLXSXP, m, n));
Memcpy(COMPLEX(A), COMPLEX(Ain), (size_t)m * n);
rwork = (double *) R_alloc(2*(size_t)n, sizeof(double));
SEXP jpvt = PROTECT(allocVector(INTSXP, n));
for (i = 0; i < n; i++) INTEGER(jpvt)[i] = 0;
SEXP 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");
SEXP val = PROTECT(allocVector(VECSXP, 4));
SEXP nm = PROTECT(allocVector(STRSXP, 4));
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);
// Fix up dimnames(A)
if(!isNull(Adn)) {
SEXP Adn2 = duplicate(Adn);
SEXP cn = VECTOR_ELT(Adn, 1), cn2 = VECTOR_ELT(Adn2, 1);
if(!isNull(cn)) { // pivot them
for (int j = 0; j < n; j++)
SET_STRING_ELT(cn2, j, STRING_ELT(cn, INTEGER(jpvt)[j]-1));
}
setAttrib(A, R_DimNamesSymbol, Adn2);
}
SET_VECTOR_ELT(val, 0, A);
SET_VECTOR_ELT(val, 1, ScalarInteger(m < n ? m : n));
SET_VECTOR_ELT(val, 2, tau);
SET_VECTOR_ELT(val, 3, jpvt);
UNPROTECT(5);
return val;
#else
error(_("Fortran complex functions are not available on this platform"));
return R_NilValue; /* -Wall */
#endif
}
/* Complex case of qr_coef */
static SEXP qr_coef_cmplx(SEXP Q, SEXP Bin)
{
#ifdef HAVE_FORTRAN_DOUBLE_COMPLEX
int n, nrhs, lwork, info, k, *Bdims;
SEXP B, qr = VECTOR_ELT(Q, 0), tau = VECTOR_ELT(Q, 2);
Rcomplex *work, tmp;
k = LENGTH(tau);
if (!isMatrix(Bin)) error(_("'b' must be a complex matrix"));
if (!isComplex(Bin)) B = PROTECT(coerceVector(Bin, CPLXSXP));
else B = PROTECT(duplicate(Bin));
n = INTEGER(coerceVector(getAttrib(qr, R_DimSymbol), INTSXP))[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 FCONE FCONE);
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 FCONE FCONE);
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
FCONE FCONE FCONE);
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
}
/* Complex case of qr.qy and qr.qty */
static SEXP qr_qy_cmplx(SEXP Q, SEXP Bin, SEXP trans)
{
#ifdef HAVE_FORTRAN_DOUBLE_COMPLEX
int n, nrhs, lwork, info, k, *Bdims, 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 '%s' argument"), "trans");
if (!isReal(Bin)) B = PROTECT(coerceVector(Bin, CPLXSXP));
else B = PROTECT(duplicate(Bin));
n = INTEGER(coerceVector(getAttrib(qr, R_DimSymbol), INTSXP))[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 FCONE FCONE);
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 FCONE FCONE);
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 La_svd_cmplx(SEXP jobu, SEXP x, SEXP s, SEXP u, SEXP v)
{
#ifdef HAVE_FORTRAN_DOUBLE_COMPLEX
if (!(isString(jobu)))
error(_("'jobu' must be a character string"));
int *xdims = INTEGER(coerceVector(getAttrib(x, R_DimSymbol), INTSXP));
int n = xdims[0], p = xdims[1];
const char *jz = CHAR(STRING_ELT(jobu, 0));
/* The underlying LAPACK, specifically ZLARF, does not work with
* long arrays */
if ((double)n * (double)p > INT_MAX)
error(_("matrices of 2^31 or more elements are not supported"));
/* work on a copy of x */
Rcomplex *xvals = (Rcomplex *) R_alloc(n * (size_t) p, sizeof(Rcomplex));
Memcpy(xvals, COMPLEX(x), n * (size_t) p);
int *iwork= (int *) R_alloc(8*(size_t)(n < p ? n : p), sizeof(int));
size_t mn0 = (n < p ? n : p), mn1 = (n > p ? n : p), lrwork;
if (strcmp(jz, "N")) {
size_t f1 = 5 * mn1 + 7, f2 = 2 * mn1 + 2 * mn0 + 1;
lrwork = (f1 > f2 ? f1 : f2) * mn0;
// 7 replaces 5: bug 111 in http://www.netlib.org/lapack/Errata/index2.html
} else lrwork = 7 * mn0;
double *rwork = (double *) R_alloc(lrwork, sizeof(double));
/* ask for optimal size of lwork array */
int lwork = -1, info;
Rcomplex tmp;
int ldu, ldv;
SEXP dims = getAttrib(u, R_DimSymbol);
if (TYPEOF(dims) != INTSXP) error("non-integer dims");
ldu = INTEGER(dims)[0];
dims = getAttrib(v, R_DimSymbol);
if (TYPEOF(dims) != INTSXP) error("non-integer dims");
ldv = INTEGER(dims)[0];
F77_CALL(zgesdd)(jz, &n, &p, xvals, &n, REAL(s),
COMPLEX(u), &ldu, COMPLEX(v), &ldv,
&tmp, &lwork, rwork, iwork, &info FCONE);
if (info != 0)
error(_("error code %d from Lapack routine '%s'"), info, "zgesdd");
lwork = (int) tmp.r;
Rcomplex *work = (Rcomplex *) R_alloc(lwork, sizeof(Rcomplex));
F77_CALL(zgesdd)(jz, &n, &p, xvals, &n, REAL(s),
COMPLEX(u), &ldu, COMPLEX(v), &ldv,
work, &lwork, rwork, iwork, &info FCONE);
if (info != 0)
error(_("error code %d from Lapack routine '%s'"), info, "zgesdd");
SEXP val = PROTECT(allocVector(VECSXP, 3));
SEXP 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;
#else
error(_("Fortran complex functions are not available on this platform"));
return R_NilValue; /* -Wall */
#endif
}
/* Complex, symmetric case of eigen */
static SEXP La_rs_cmplx(SEXP xin, SEXP only_values)
{
#ifdef HAVE_FORTRAN_DOUBLE_COMPLEX
int *xdims, n, lwork, info, ov;
char jobv[2] = "N", uplo[2] = "L";
Rcomplex *work, *rx, tmp;
double *rwork, *rvalues;
xdims = INTEGER(coerceVector(getAttrib(xin, R_DimSymbol), INTSXP));
n = xdims[0];
if (n != xdims[1]) error(_("'x' must be a square complex matrix"));
ov = asLogical(only_values);
if (ov == NA_LOGICAL) error(_("invalid '%s' argument"), "only.values");
if (ov) jobv[0] = 'N'; else jobv[0] = 'V';
SEXP x = PROTECT(allocMatrix(CPLXSXP, n, n));
rx = COMPLEX(x);
Memcpy(rx, COMPLEX(xin), (size_t) n * n);
SEXP values = PROTECT(allocVector(REALSXP, n));
rvalues = REAL(values);
rwork = (double *) R_alloc((3*(size_t)n-2) > 1 ? 3*(size_t)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 FCONE FCONE);
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 FCONE FCONE);
if (info != 0)
error(_("error code %d from Lapack routine '%s'"), info, "zheev");
SEXP ret, nm;
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
}
/* Complex, general case of eigen */
static SEXP La_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[2] = "N", jobVR[2] = "N";
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"));
/* work on a copy of x */
xvals = (Rcomplex *) R_alloc((size_t)n * n, sizeof(Rcomplex));
Memcpy(xvals, COMPLEX(x), (size_t) n * n);
ov = asLogical(only_values);
if (ov == NA_LOGICAL) error(_("invalid '%s' argument"), "only.values");
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*(size_t)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
FCONE FCONE);
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
FCONE FCONE);
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 La_chol(SEXP A, SEXP pivot, SEXP stol)
{
if (!isMatrix(A)) error(_("'a' must be a numeric matrix"));
SEXP ans = PROTECT(isReal(A) ? duplicate(A): coerceVector(A, REALSXP));
SEXP adims = getAttrib(A, R_DimSymbol);
if (TYPEOF(adims) != INTSXP) error("non-integer dims");
int m = INTEGER(adims)[0], n = INTEGER(adims)[1];
if (m != n) error(_("'a' must be a square matrix"));
if (m <= 0) error(_("'a' must have dims > 0"));
size_t N = n;
for (int j = 0; j < n; j++) /* zero the lower triangle */
for (int i = j+1; i < n; i++) REAL(ans)[i + N * j] = 0.;
int piv = asInteger(pivot);
if (piv != 0 && piv != 1) error("invalid '%s' value", "pivot");
if(!piv) {
int info;
F77_CALL(dpotrf)("U", &m, REAL(ans), &m, &info FCONE);
if (info != 0) {
if (info > 0)
error(_("the leading minor of order %d is not positive definite"),
info);
error(_("argument %d of Lapack routine %s had invalid value"),
-info, "dpotrf");
}
} else {
double tol = asReal(stol);
SEXP piv = PROTECT(allocVector(INTSXP, m));
int *ip = INTEGER(piv);
double *work = (double *) R_alloc(2 * (size_t)m, sizeof(double));
int rank, info;
F77_CALL(dpstrf)("U", &m, REAL(ans), &m, ip, &rank, &tol, work, &info
FCONE);
if (info != 0) {
if (info > 0)
warning(_("the matrix is either rank-deficient or indefinite"));
else
error(_("argument %d of Lapack routine %s had invalid value"),
-info, "dpstrf");
}
setAttrib(ans, install("pivot"), piv);
SEXP s_rank = install("rank");
setAttrib(ans, s_rank, ScalarInteger(rank));
SEXP cn, dn = getAttrib(ans, R_DimNamesSymbol);
if (!isNull(dn) && !isNull(cn = VECTOR_ELT(dn, 1))) {
// need to pivot the colnames
SEXP dn2 = PROTECT(duplicate(dn));
SEXP cn2 = VECTOR_ELT(dn2, 1);
for(int i = 0; i < m; i++)
SET_STRING_ELT(cn2, i, STRING_ELT(cn, ip[i] - 1)); // base 1
setAttrib(ans, R_DimNamesSymbol, dn2);
UNPROTECT(1);
}
UNPROTECT(1); // piv
}
UNPROTECT(1); // ans
return ans;
}
static SEXP La_chol2inv(SEXP A, SEXP size)
{
int sz = asInteger(size);
if (sz == NA_INTEGER || sz < 1) {
error(_("'size' argument must be a positive integer"));
return R_NilValue; /* -Wall */
} else {
SEXP ans, Amat = A; /* -Wall: we initialize here as for the 1x1 case */
int m = 1, n = 1, nprot = 0;
if (sz == 1 && !isMatrix(A) && isReal(A)) {
/* nothing to do; m = n = 1; ... */
} else if (isMatrix(A)) {
SEXP adims = getAttrib(A, R_DimSymbol);
if (TYPEOF(adims) != INTSXP) error("non-integer dims");
Amat = PROTECT(coerceVector(A, REALSXP)); nprot++;
m = INTEGER(adims)[0]; n = INTEGER(adims)[1];
} else error(_("'a' must be a numeric matrix"));
if (sz > n) { UNPROTECT(nprot); error(_("'size' cannot exceed ncol(x) = %d"), n); }
if (sz > m) { UNPROTECT(nprot); error(_("'size' cannot exceed nrow(x) = %d"), m); }
ans = PROTECT(allocMatrix(REALSXP, sz, sz)); nprot++;
size_t M = m, SZ = sz;
for (int j = 0; j < sz; j++) {
for (int i = 0; i <= j; i++)
REAL(ans)[i + j * SZ] = REAL(Amat)[i + j * M];
}
int info;
F77_CALL(dpotri)("U", &sz, REAL(ans), &sz, &info FCONE);
if (info != 0) {
UNPROTECT(nprot);
if (info > 0)
error(_("element (%d, %d) is zero, so the inverse cannot be computed"),
info, info);
error(_("argument %d of Lapack routine %s had invalid value"),
-info, "dpotri");
}
for (int j = 0; j < sz; j++)
for (int i = j+1; i < sz; i++)
REAL(ans)[i + j * SZ] = REAL(ans)[j + i * SZ];
UNPROTECT(nprot);
return ans;
}
}
/* ------------------------------------------------------------ */
/* Real case of solve.default */
static SEXP La_solve(SEXP A, SEXP Bin, SEXP tolin)
{
int n, p;
double *avals, anorm, rcond, tol = asReal(tolin), *work;
SEXP B, Adn, Bdn;
if (!(isMatrix(A) &&
(TYPEOF(A) == REALSXP || TYPEOF(A) == INTSXP || TYPEOF(A) == LGLSXP)))
error(_("'a' must be a numeric matrix"));
int *Adims = INTEGER(coerceVector(getAttrib(A, R_DimSymbol), INTSXP));
n = Adims[0];
if(n == 0) error(_("'a' is 0-diml"));
int n2 = Adims[1];
if(n2 != n) error(_("'a' (%d x %d) must be square"), n, n2);
Adn = getAttrib(A, R_DimNamesSymbol);
if (isMatrix(Bin)) {
int *Bdims = INTEGER(coerceVector(getAttrib(Bin, R_DimSymbol), INTSXP));
p = Bdims[1];
if(p == 0) error(_("no right-hand side in 'b'"));
int p2 = Bdims[0];
if(p2 != n)
error(_("'b' (%d x %d) must be compatible with 'a' (%d x %d)"),
p2, p, n, n);
PROTECT(B = allocMatrix(REALSXP, n, p));
SEXP Bindn = getAttrib(Bin, R_DimNamesSymbol);
// This is somewhat odd, but Matrix relies on dropping NULL dimnames
if (!isNull(Adn) || !isNull(Bindn)) {
// rownames(ans) = colnames(A), colnames(ans) = colnames(Bin)
Bdn = allocVector(VECSXP, 2);
if (!isNull(Adn)) SET_VECTOR_ELT(Bdn, 0, VECTOR_ELT(Adn, 1));
if (!isNull(Bindn)) SET_VECTOR_ELT(Bdn, 1, VECTOR_ELT(Bindn, 1));
if (!isNull(VECTOR_ELT(Bdn, 0)) || !isNull(VECTOR_ELT(Bdn, 1)))
setAttrib(B, R_DimNamesSymbol, Bdn);
}
} else {
p = 1;
if(length(Bin) != n)
error(_("'b' (%d x %d) must be compatible with 'a' (%d x %d)"),
length(Bin), p, n, n);
PROTECT(B = allocVector(REALSXP, n));
if (!isNull(Adn)) setAttrib(B, R_NamesSymbol, VECTOR_ELT(Adn, 1));
}
PROTECT(Bin = coerceVector(Bin, REALSXP));
Memcpy(REAL(B), REAL(Bin), (size_t)n * p);
int *ipiv = (int *) R_alloc(n, sizeof(int));
/* work on a copy of A */
if (!isReal(A)) {
A = coerceVector(A, REALSXP);
avals = REAL(A);
} else {
avals = (double *) R_alloc((size_t)n * n, sizeof(double));
Memcpy(avals, REAL(A), (size_t)n * n);
}
PROTECT(A);
int info;
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 %s: system is exactly singular: U[%d,%d] = 0"),
"dgesv", info, info);
if(tol > 0) {
char one[2] = "1";
anorm = F77_CALL(dlange)(one, &n, &n, REAL(A), &n,
(double*) NULL FCONE);
work = (double *) R_alloc(4*(size_t)n, sizeof(double));
F77_CALL(dgecon)(one, &n, avals, &n, &anorm, &rcond, work, ipiv,
&info FCONE);
if (rcond < tol)
error(_("system is computationally singular: reciprocal condition number = %g"),
rcond);
}
UNPROTECT(3); /* B, Bin, A */
return B;
}
/* Real case of qr.default */
static SEXP La_qr(SEXP Ain)
{
int m, n;
if (!isMatrix(Ain)) error(_("'a' must be a numeric matrix"));
SEXP Adn = getAttrib(Ain, R_DimNamesSymbol);
int *Adims = INTEGER(coerceVector(getAttrib(Ain, R_DimSymbol), INTSXP));
m = Adims[0]; n = Adims[1];
SEXP A;
if (!isReal(Ain)) {
A = PROTECT(coerceVector(Ain, REALSXP));
} else {
A = PROTECT(allocMatrix(REALSXP, m, n));
Memcpy(REAL(A), REAL(Ain), (size_t)m * n);
}
SEXP jpvt = PROTECT(allocVector(INTSXP, n));
for (int i = 0; i < n; i++) INTEGER(jpvt)[i] = 0;
SEXP tau = PROTECT(allocVector(REALSXP, m < n ? m : n)); // qraux
int info, lwork = -1;
double tmp;
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;
double *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");
SEXP val = PROTECT(allocVector(VECSXP, 4));
SEXP nm = PROTECT(allocVector(STRSXP, 4));
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);
// Fix up dimnames(A)
if(!isNull(Adn)) {
SEXP Adn2 = duplicate(Adn);
SEXP cn = VECTOR_ELT(Adn, 1), cn2 = VECTOR_ELT(Adn2, 1);
if(!isNull(cn)) { // pivot them
for (int j = 0; j < n; j++)
SET_STRING_ELT(cn2, j, STRING_ELT(cn, INTEGER(jpvt)[j]-1));
}
setAttrib(A, R_DimNamesSymbol, Adn2);
}
SET_VECTOR_ELT(val, 0, A);
SET_VECTOR_ELT(val, 1, ScalarInteger(m < n ? m : n));
SET_VECTOR_ELT(val, 2, tau);
SET_VECTOR_ELT(val, 3, jpvt);
UNPROTECT(5);
return val;
}
/* Real case of qr.coef */
static SEXP qr_coef_real(SEXP Q, SEXP Bin)
{
if (!isMatrix(Bin)) error(_("'b' must be a numeric matrix"));
SEXP B = PROTECT(isReal(Bin) ? duplicate(Bin) : coerceVector(Bin, REALSXP)),
qr = VECTOR_ELT(Q, 0), // qr$qr
tau = VECTOR_ELT(Q, 2); // qr$qraux
int k = LENGTH(tau),
n = INTEGER(coerceVector(getAttrib(qr, R_DimSymbol), INTSXP))[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]);
int nrhs = Bdims[1],
lwork = -1, info;
double tmp;
F77_CALL(dormqr)("L", "T", &n, &nrhs, &k,
REAL(qr), &n, REAL(tau), REAL(B), &n,
&tmp, &lwork, &info FCONE FCONE);
if (info != 0)
error(_("error code %d from Lapack routine '%s'"), info, "dormqr [tmp]");
lwork = (int) tmp;
double *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 FCONE FCONE);
if (info != 0)
error(_("error code %d from Lapack routine '%s'"), info, "dormqr [work]");
F77_CALL(dtrtrs)("U", "N", "N", &k, &nrhs,
REAL(qr), &n, REAL(B), &n, &info
FCONE FCONE FCONE);
if (info != 0)
error(_("error code %d from Lapack routine '%s'"), info, "dtrtrs");
UNPROTECT(1);
return B;
}
/* Real case of qr.qy and qr.aty */
static SEXP qr_qy_real(SEXP Q, SEXP Bin, SEXP trans)
{
int n, nrhs, k, *Bdims, tr;
SEXP B, qr = VECTOR_ELT(Q, 0), tau = VECTOR_ELT(Q, 2);
double *work, tmp;
k = LENGTH(tau);
if (!isMatrix(Bin)) error(_("'b' must be a numeric matrix"));
tr = asLogical(trans);
if(tr == NA_LOGICAL) error(_("invalid '%s' argument"), "trans");
B = PROTECT(isReal(Bin) ? duplicate(Bin) : coerceVector(Bin, REALSXP));
n = INTEGER(coerceVector(getAttrib(qr, R_DimSymbol), INTSXP))[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];
int lwork = -1, info;
F77_CALL(dormqr)("L", tr ? "T" : "N", &n, &nrhs, &k,
REAL(qr), &n, REAL(tau), REAL(B), &n,
&tmp, &lwork, &info FCONE FCONE);
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 FCONE FCONE);
if (info != 0)
error(_("error code %d from Lapack routine '%s'"), info, "dormqr");
UNPROTECT(1);
return B;
}
/* TODO : add a *complex* version, using LAPACK ZGETRF() */
static SEXP det_ge_real(SEXP Ain, SEXP logarithm)
{
int info, sign = 1, useLog = asLogical(logarithm);
double modulus = 0.0; /* -Wall */
if (!isMatrix(Ain)) error(_("'a' must be a numeric matrix"));
if (useLog == NA_LOGICAL) error(_("argument 'logarithm' must be logical"));
SEXP A = PROTECT(isReal(Ain) ? duplicate(Ain): coerceVector(Ain, REALSXP));
int *Adims = INTEGER(coerceVector(getAttrib(Ain, R_DimSymbol), INTSXP));
int n = Adims[0];
if (Adims[1] != n) error(_("'a' must be a square matrix"));
int *jpvt = (int *) R_alloc(n, sizeof(int));
F77_CALL(dgetrf)(&n, &n, REAL(A), &n, jpvt, &info);
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 =
#ifdef _not_quite_/* unfortunately does not work -- FIXME */
(ISNAN(REAL(A)[(info-1)*n + (info-1)])) /* pivot is NA/NaN */
? R_NaN :
#endif
(useLog ? R_NegInf : 0.);
}
else {
for (int i = 0; i < n; i++) if (jpvt[i] != (i + 1)) sign = -sign;
if (useLog) {
modulus = 0.0;
size_t N1 = n+1;
for (int i = 0; i < n; i++) {
double dii = REAL(A)[i * N1]; /* ith diagonal element */
modulus += log(dii < 0 ? -dii : dii);
if (dii < 0) sign = -sign;
}
} else {
modulus = 1.0;
size_t N1 = n+1;
for (int i = 0; i < n; i++) modulus *= REAL(A)[i * N1];
if (modulus < 0) {
modulus = -modulus;
sign = -sign;
}
}
}
SEXP val = PROTECT(allocVector(VECSXP, 2));
SEXP 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));
SEXP s_logarithm = install("logarithm");
setAttrib(VECTOR_ELT(val, 0), s_logarithm, ScalarLogical(useLog));
SET_VECTOR_ELT(val, 1, ScalarInteger(sign));
setAttrib(val, R_ClassSymbol, ScalarString(mkChar("det")));
UNPROTECT(3);
return val;
}
static SEXP mod_do_lapack(SEXP call, SEXP op, SEXP args, SEXP env)
{
SEXP ans = R_NilValue;
switch(PRIMVAL(op)) {
case 0: ans = La_qr_cmplx(CAR(args)); break;
case 1: ans = La_rs(CAR(args), CADR(args)); break;
case 2: ans = La_rs_cmplx(CAR(args), CADR(args)); break;
case 3: ans = La_rg(CAR(args), CADR(args)); break;
case 41: ans = La_rg_cmplx(CAR(args), CADR(args)); break;
case 5: ans = La_rs(CAR(args), CADR(args)); break;
case 51: ans = La_rs_cmplx(CAR(args), CADR(args)); break;
case 6: ans = La_dlange(CAR(args), CADR(args)); break;
case 7: ans = La_dgecon(CAR(args), CADR(args)); break;
case 8: ans = La_dtrcon(CAR(args), CADR(args)); break;
case 9: ans = La_zgecon(CAR(args), CADR(args)); break;
case 10: ans = La_ztrcon(CAR(args), CADR(args)); break;
case 11: ans = La_solve_cmplx(CAR(args), CADR(args)); break;
case 100: ans = La_solve(CAR(args), CADR(args), CADDR(args)); break;
case 101: ans = La_qr(CAR(args)); break;
case 200: ans = La_chol(CAR(args), CADR(args), CADDR(args)); break;
case 201: ans = La_chol2inv(CAR(args), CADR(args)); break;
case 300: ans = qr_coef_real(CAR(args), CADR(args)); break;
case 301: ans = qr_qy_real(CAR(args), CADR(args), CADDR(args)); break;
case 302: ans = det_ge_real(CAR(args), CADR(args)); break;
case 303: ans = qr_coef_cmplx(CAR(args), CADR(args)); break;
case 304: ans = qr_qy_cmplx(CAR(args), CADR(args), CADDR(args)); break;
case 400:
{
SEXP a1, a2, a3, a4;
a1 = CAR(args); args = CDR(args);
a2 = CAR(args); args = CDR(args);
a3 = CAR(args); args = CDR(args);
a4 = CAR(args); args = CDR(args);
ans = La_svd(a1, a2, a3, a4, CAR(args));
break;
}
case 401:
{
SEXP a1, a2, a3, a4;
a1 = CAR(args); args = CDR(args);
a2 = CAR(args); args = CDR(args);
a3 = CAR(args); args = CDR(args);
a4 = CAR(args); args = CDR(args);
ans = La_svd_cmplx(a1, a2, a3, a4, CAR(args));
break;
}
case 1000:
{
int major, minor, patch;
char str[20];
F77_CALL(ilaver)(&major, &minor, &patch);
snprintf(str, 20, "%d.%d.%d", major, minor, patch);
ans = mkString(str);
break;
}
case 1001:
{
#if defined(HAVE_DLADDR) && defined(HAVE_REALPATH)
Dl_info dl_info;
/* the call to dladdr() converts a function pointer to an object
pointer, which is not allowed by ISO C, but there is no compliant
alternative to using dladdr() */
// dladdr has first arg void * on Solaris. This is not POSIX.
if (dladdr((void *) F77_NAME(ilaver), &dl_info)) {
char buf[PATH_MAX+1];
char *res = realpath(dl_info.dli_fname, buf);
if (res) {
ans = mkString(res);
break;
}
}
#endif
ans = mkString(""); /* LAPACK library not known */
break;
}
}// switch
return ans;
}
/* ------------------------------------------------------------ */
#include <Rmodules/Rlapack.h>
#include <R_ext/Rdynload.h>
void
R_init_lapack(DllInfo *info)
{
R_LapackRoutines *tmp;
tmp = R_Calloc(1, R_LapackRoutines);
tmp->do_lapack = mod_do_lapack;
R_setLapackRoutines(tmp);
}