The R Project SVN R

/*
 *  R : A Computer Language for Statistical Data Analysis
 *  Copyright (C) 1995, 1996, 1997  Robert Gentleman and Ross Ihaka
 *  Copyright (C) 2000          The R Development Core Team.
 *
 *  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, write to the Free Software
 *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 */

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

#include <Defn.h>       /* -> ../include/R_ext/Complex.h */
#include <Rmath.h>
#include <R_ext/Applic.h>   /* R_cpoly */

#include "arithmetic.h"     /* complex_*  */

#ifndef HAVE_HYPOT
# define hypot pythag
#endif

SEXP complex_unary(ARITHOP_TYPE code, SEXP s1)
{
    int i, n;
    Rcomplex x;
    SEXP ans;

    switch(code) {
    case PLUSOP:
    return s1;
    case MINUSOP:

    ans = duplicate(s1);
    n = LENGTH(s1);
    for (i = 0; i < n; i++) {
        x = COMPLEX(s1)[i];
        COMPLEX(ans)[i].r = -x.r;
        COMPLEX(ans)[i].i = -x.i;
    }
    return ans;
    default:
    error_return("illegal complex unary operator");
    }
}

static void complex_div(Rcomplex *c, Rcomplex *a, Rcomplex *b)
{
    double ratio, den;
    double abr, abi;

    if( (abr = b->r) < 0)
    abr = - abr;
    if( (abi = b->i) < 0)
    abi = - abi;
    if( abr <= abi ) {
    ratio = b->r / b->i ;
    den = b->i * (1 + ratio*ratio);
    c->r = (a->r*ratio + a->i) / den;
    c->i = (a->i*ratio - a->r) / den;
    }
    else {
    ratio = b->i / b->r ;
    den = b->r * (1 + ratio*ratio);
    c->r = (a->r + a->i*ratio) / den;
    c->i = (a->i - a->r*ratio) / den;
    }
}

static void complex_pow(Rcomplex *r, Rcomplex *a, Rcomplex *b)
{
/* r := a^b */
    double logr, logi, x, y;
    int ib;

    if(b->i == 0.) {        /* ^ "real" : be fast (and more accurate)*/
    if(b->r == 1.) {    /* a^1 */
        r->r = a->r; r->i = a->i; return;
    }
    if(a->i == 0. && a->r >= 0.) {
        r->r = R_pow(a->r, b->r); r->i = 0.; return;
    }
    if(a->r == 0. && b->r == (ib = (int)b->r)) {/* (|a|*i)^b */
        x = R_pow_di(a->i, ib);
        if(ib % 2) {    /* ib is odd ==> imaginary r */
        r->r = 0.;
        r->i = ((ib>0 && ib %4 == 3)||(ib<0 && (-ib)%4 == 1))? -x : x;
        } else {        /* even exponent b : real r */
        r->r = (ib %4)? -x : x; r->i = 0.;
        }
        return;
    }
    }
    logr = log(hypot(a->r, a->i) );
    logi = atan2(a->i, a->r);
    x = exp( logr * b->r - logi * b->i );
    y = logr * b->i + logi * b->r;
    r->r = x * cos(y);
    r->i = x * sin(y);
}

/* FIXME : Use the trick in arithmetic.c to eliminate "modulo" ops */

SEXP complex_binary(ARITHOP_TYPE code, SEXP s1, SEXP s2)
{
    int i, n, n1, n2;
    Rcomplex x1, x2;
    SEXP ans;

    /* Note: "s1" and "s1" are protected in the calling code. */
    n1 = LENGTH(s1);
    n2 = LENGTH(s2);
     /* S4-compatibility change: if n1 or n2 is 0, result is of length 0 */
    if (n1 == 0 || n2 == 0) return(allocVector(CPLXSXP, 0)); 

    n = (n1 > n2) ? n1 : n2;
    ans = allocVector(CPLXSXP, n);
    
    switch (code) {
    case PLUSOP:
    for (i = 0; i < n; i++) {
        x1 = COMPLEX(s1)[i % n1];
        x2 = COMPLEX(s2)[i % n2];
        COMPLEX(ans)[i].r = x1.r + x2.r;
        COMPLEX(ans)[i].i = x1.i + x2.i;
    }
    break;
    case MINUSOP:
    for (i = 0; i < n; i++) {
        x1 = COMPLEX(s1)[i % n1];
        x2 = COMPLEX(s2)[i % n2];
        COMPLEX(ans)[i].r = x1.r - x2.r;
        COMPLEX(ans)[i].i = x1.i - x2.i;
    }
    break;
    case TIMESOP:
    for (i = 0; i < n; i++) {
        x1 = COMPLEX(s1)[i % n1];
        x2 = COMPLEX(s2)[i % n2];
        COMPLEX(ans)[i].r = x1.r * x2.r - x1.i * x2.i;
        COMPLEX(ans)[i].i = x1.r * x2.i + x1.i * x2.r;
    }
    break;
    case DIVOP:
    for (i = 0; i < n; i++) {
        x1 = COMPLEX(s1)[i % n1];
        x2 = COMPLEX(s2)[i % n2];
        complex_div(&COMPLEX(ans)[i], &x1, &x2);
    }
    break;
    case POWOP:
    for (i = 0; i < n; i++) {
        x1 = COMPLEX(s1)[i % n1];
        x2 = COMPLEX(s2)[i % n2];
        complex_pow(&COMPLEX(ans)[i], &x1, &x2);
    }
    break;
    default:
    error("unimplemented complex operation");
    }

    /* quick return if there are no attributes */
    if (ATTRIB(s1) == R_NilValue && ATTRIB(s2) == R_NilValue)
    return ans;

    /* Copy attributes from longer argument. */
    if (n1 > n2)
    copyMostAttrib(s1, ans);
    else if (n1 == n2) {
    copyMostAttrib(s2, ans);
    copyMostAttrib(s1, ans);
    }
    else
    copyMostAttrib(s2, ans);
    return ans;
}

/* FIXME : Use the trick in arithmetic.c to eliminate "modulo" ops */

SEXP do_cmathfuns(SEXP call, SEXP op, SEXP args, SEXP env)
{
    SEXP x, y = R_NilValue; /* -Wall*/
    int i, n;

    checkArity(op, args);
    if (DispatchGroup("Complex", call, op, args, env, &x))
        return x;
    x = CAR(args);
    n = length(x);
    if (isComplex(x)) {
    switch(PRIMVAL(op)) {
    case 1: /* Re */
        y = allocVector(REALSXP, n);
        for(i=0 ; i<n ; i++)
        REAL(y)[i] = COMPLEX(x)[i].r;
        break;
    case 2: /* Im */
        y = allocVector(REALSXP, n);
        for(i=0 ; i<n ; i++)
        REAL(y)[i] = COMPLEX(x)[i].i;
        break;
    case 3: /* Mod */
    case 6: /* abs */
        y = allocVector(REALSXP, n);
        for(i=0 ; i<n ; i++) {
        REAL(y)[i] = hypot(COMPLEX(x)[i].r, COMPLEX(x)[i].i);
        }
        break;
    case 4: /* Arg */
        y = allocVector(REALSXP, n);
        for(i=0 ; i<n ; i++) {
        REAL(y)[i] = atan2(COMPLEX(x)[i].i, COMPLEX(x)[i].r);
        }
        break;
    case 5: /* Conj */
        y = allocVector(CPLXSXP, n);
        for(i=0 ; i<n ; i++) {
        COMPLEX(y)[i].r = COMPLEX(x)[i].r;
        COMPLEX(y)[i].i = -COMPLEX(x)[i].i;
        }
        break;
    }
    }
    else if(isNumeric(x)) {
    if(isReal(x)) PROTECT(x);
    else PROTECT(x = coerceVector(x, REALSXP));
    switch(PRIMVAL(op)) {
    case 1: /* Re */
    case 5: /* Conj */
        y = allocVector(REALSXP, n);
        for(i=0 ; i<n ; i++)
        REAL(y)[i] = REAL(x)[i];
        break;
    case 2: /* Im */
    case 4: /* Arg */
        y = allocVector(REALSXP, n);
        for(i=0 ; i<n ; i++)
        if(ISNAN(REAL(x)[i]))
            REAL(y)[i] = REAL(x)[i];
        else
            REAL(y)[i] = 0;
        break;
    case 3: /* Mod */
    case 6: /* abs */
        y = allocVector(REALSXP, n);
        for(i=0 ; i<n ; i++) {
        REAL(y)[i] = fabs(REAL(x)[i]);
        }
        break;
    }
    UNPROTECT(1);
    }
    else errorcall(call, "non-numeric argument to function");
    PROTECT(x);
    PROTECT(y);
    SET_ATTRIB(y, duplicate(ATTRIB(x)));
    SET_OBJECT(y, OBJECT(x));
    UNPROTECT(2);
    return y;
}

static void z_rround(Rcomplex *r, Rcomplex *x, Rcomplex *p)
{
    r->r = rround(x->r, p->r);
    r->i = rround(x->i, p->r);
}

/* Question:  This treats real and imaginary parts separately.  Should
   it do them jointly? */

static void z_prec(Rcomplex *r, Rcomplex *x, Rcomplex *p)
{
    r->r = prec(x->r, p->r);
    r->i = prec(x->i, p->r);
}

static void z_log(Rcomplex *r, Rcomplex *z)
{
    r->i = atan2(z->i, z->r);
    r->r = log(hypot( z->r, z->i ));
}

static void z_logbase(Rcomplex *r, Rcomplex *z, Rcomplex *base)
{
    Rcomplex t1, t2;
    z_log(&t1, z);
    z_log(&t2, base);
    complex_div(r, &t1, &t2);
}

static void z_exp(Rcomplex *r, Rcomplex *z)
{
    double expx;
    expx = exp(z->r);
    r->r = expx * cos(z->i);
    r->i = expx * sin(z->i);
}

static void z_sqrt(Rcomplex *r, Rcomplex *z)
{
    double mag;

    if( (mag = hypot(z->r, z->i)) == 0.0)
    r->r = r->i = 0.0;
    else if(z->r > 0) {
    r->r = sqrt(0.5 * (mag + z->r) );
    r->i = z->i / r->r / 2;
    }
    else {
    r->i = sqrt(0.5 * (mag - z->r) );
    if(z->i < 0)
        r->i = - r->i;
    r->r = z->i / r->i / 2;
    }
}

static void z_cos(Rcomplex *r, Rcomplex *z)
{
    r->r = cos(z->r) * cosh(z->i);
    r->i = - sin(z->r) * sinh(z->i);
}

static void z_sin(Rcomplex *r, Rcomplex *z)
{
    r->r = sin(z->r) * cosh(z->i);
    r->i = cos(z->r) * sinh(z->i);
}

static void z_tan(Rcomplex *r, Rcomplex *z)
{
    double x2, y2, den;
    x2 = 2.0 * z->r;
    y2 = 2.0 * z->i;
    den = cos(x2) + cosh(y2);
    r->r = sin(x2)/den;
    r->i = sinh(y2)/den;
}

    /* Complex Arcsin and Arccos Functions */
    /* Equation (4.4.37) Abramowitz and Stegun */

static void z_asin(Rcomplex *r, Rcomplex *z)
{
    double alpha, bet, t1, t2, x, y;
    x = z->r;
    y = z->i;
    t1 = 0.5 * hypot(x + 1, y);
    t2 = 0.5 * hypot(x - 1, y);
    alpha = t1 + t2;
    bet = t1 - t2;
    r->r = asin(bet);
    r->i = log(alpha + sqrt(alpha*alpha - 1));
}

static void z_acos(Rcomplex *r, Rcomplex *z)
{
    Rcomplex Asin;
    z_asin(&Asin, z);
    r->r = M_PI_2 - Asin.r;
    r->i = - Asin.i;
}

    /* Complex Arctangent Function */
    /* Equation (4.4.39) Abramowitz and Stegun */

static void z_atan(Rcomplex *r, Rcomplex *z)
{
    double x, y;
    x = z->r;
    y = z->i;
    r->r = 0.5 * atan(2 * x / ( 1 - x * x - y * y));
    r->i = 0.25 * log((x * x + (y + 1) * (y + 1)) /
              (x * x + (y - 1) * (y - 1)));
}

static void z_atan2(Rcomplex *r, Rcomplex *csn, Rcomplex *ccs)
{
    Rcomplex tmp;
    if (ccs->r == 0 && ccs->i == 0) {
    if(csn->r == 0 && csn->r == 0) {
        r->r = NA_REAL;
        r->i = NA_REAL;
    }
    else {
        r->r = fsign(M_PI_2, csn->r);
        r->i = 0;
    }
    }
    else {
    complex_div(&tmp, csn, ccs);
    z_atan(r, &tmp);
    if(ccs->r < 0) r->r += M_PI;
    if(r->r > M_PI) r->r -= 2 * M_PI;
    }
}

static void z_acosh(Rcomplex *r, Rcomplex *z)
{
    Rcomplex a;
    z_acos(&a, z);
    r->r = -a.i;
    r->i = a.r;
}

static void z_asinh(Rcomplex *r, Rcomplex *z)
{
    Rcomplex a, b;
    b.r = -z->i;
    b.i =  z->r;
    z_asin(&a, &b);
    r->r =  a.i;
    r->i = -a.r;
}

static void z_atanh(Rcomplex *r, Rcomplex *z)
{
    Rcomplex a, b;
    b.r = -z->i;
    b.i =  z->r;
    z_atan(&a, &b);
    r->r =  a.i;
    r->i = -a.r;
}

static void z_cosh(Rcomplex *r, Rcomplex *z)
{
    Rcomplex a;
    a.r = -z->i;
    a.i =  z->r;
    z_cos(r, &a);
}

static void z_sinh(Rcomplex *r, Rcomplex *z)
{
    Rcomplex a, b;
    b.r = -z->i;
    b.i =  z->r;
    z_sin(&a, &b);
    r->r =  a.i;
    r->i = -a.r;
}

static void z_tanh(Rcomplex *r, Rcomplex *z)
{
    Rcomplex a, b;
    b.r = -z->i;
    b.i =  z->r;
    z_tan(&a, &b);
    r->r =  a.i;
    r->i = -a.r;
}

static Rboolean cmath1(void (*f)(), Rcomplex *x, Rcomplex *y, int n)
{
    int i;
    Rboolean naflag = FALSE;
    for (i = 0 ; i < n ; i++) {
    if (ISNA(x[i].r) || ISNA(x[i].i)) {
        y[i].r = NA_REAL;
        y[i].i = NA_REAL;
    }
    else {
        f(&y[i], &x[i]);
    }
    }

    return(naflag);
}

SEXP complex_math1(SEXP call, SEXP op, SEXP args, SEXP env)
{
    SEXP x, y;
    int n;
    Rboolean naflag = FALSE;
    PROTECT(x = CAR(args));
    n = length(x);
    PROTECT(y = allocVector(CPLXSXP, n));

    switch (PRIMVAL(op)) {
    case 10002: naflag = cmath1(z_atan, COMPLEX(x), COMPLEX(y), n); break;
    case 10003: naflag = cmath1(z_log, COMPLEX(x), COMPLEX(y), n); break;

    case 3: naflag = cmath1(z_sqrt, COMPLEX(x), COMPLEX(y), n); break;

    case 10: naflag = cmath1(z_exp, COMPLEX(x), COMPLEX(y), n); break;

    case 20: naflag = cmath1(z_cos, COMPLEX(x), COMPLEX(y), n); break;
    case 21: naflag = cmath1(z_sin, COMPLEX(x), COMPLEX(y), n); break;
    case 22: naflag = cmath1(z_tan, COMPLEX(x), COMPLEX(y), n); break;
    case 23: naflag = cmath1(z_acos, COMPLEX(x), COMPLEX(y), n); break;
    case 24: naflag = cmath1(z_asin, COMPLEX(x), COMPLEX(y), n); break;

    case 30: naflag = cmath1(z_cosh, COMPLEX(x), COMPLEX(y), n); break;
    case 31: naflag = cmath1(z_sinh, COMPLEX(x), COMPLEX(y), n); break;
    case 32: naflag = cmath1(z_tanh, COMPLEX(x), COMPLEX(y), n); break;
    case 33: naflag = cmath1(z_acosh, COMPLEX(x), COMPLEX(y), n); break;
    case 34: naflag = cmath1(z_asinh, COMPLEX(x), COMPLEX(y), n); break;
    case 35: naflag = cmath1(z_atanh, COMPLEX(x), COMPLEX(y), n); break;

#ifdef NOTYET
    MATH1(40, lgammafn);
    MATH1(41, gammafn);
#endif

    default:
    errorcall(call, "unimplemented complex function");
    }
    if (naflag)
    warning("NAs produced in function \"%s\"", PRIMNAME(op));
    SET_ATTRIB(y, duplicate(ATTRIB(x)));
    SET_OBJECT(y, OBJECT(x));
    UNPROTECT(2);
    return y;
}

/* FIXME : Use the trick in arithmetic.c to eliminate "modulo" ops */

static SEXP cmath2(SEXP op, SEXP sa, SEXP sb, void (*f)())
{
    int i, n, na, nb;
    Rcomplex ai, bi, *a, *b, *y;
    SEXP sy;
    int naflag = 0;
    na = length(sa);
    nb = length(sb);
    if ((na == 0) || (nb == 0))
    return(allocVector(CPLXSXP, 0));
    n = (na < nb) ? nb : na;
    PROTECT(sa = coerceVector(sa, CPLXSXP));
    PROTECT(sb = coerceVector(sb, CPLXSXP));
    PROTECT(sy = allocVector(CPLXSXP, n));
    a = COMPLEX(sa);
    b = COMPLEX(sb);
    y = COMPLEX(sy);
    naflag = 0;
    for (i = 0; i < n; i++) {
    ai = a[i % na];
    bi = b[i % nb];
    if(ISNA(ai.r) && ISNA(ai.i) &&
       ISNA(bi.r) && ISNA(bi.i)) {
        y[i].r = NA_REAL;
        y[i].i = NA_REAL;
    }
    else {
        f(&y[i], &ai, &bi);
    }
    }
    if (naflag)
    warning("NAs produced in function \"%s\"", PRIMNAME(op));
    if(n == na) {
    SET_ATTRIB(sy, duplicate(ATTRIB(sa)));
    SET_OBJECT(sy, OBJECT(sa));
    }
    else if(n == nb) {
    SET_ATTRIB(sy, duplicate(ATTRIB(sb)));
    SET_OBJECT(sy, OBJECT(sb));
    }
    UNPROTECT(3);
    return sy;
}

    /* Complex Functions of Two Arguments */

SEXP complex_math2(SEXP call, SEXP op, SEXP args, SEXP env)
{
    switch (PRIMVAL(op)) {
    case 10001:
    return cmath2(op, CAR(args), CADR(args), z_rround);
    case 10002:
    return cmath2(op, CAR(args), CADR(args), z_atan2);
    case 10003:
    return cmath2(op, CAR(args), CADR(args), z_logbase);
    case 10004:
    return cmath2(op, CAR(args), CADR(args), z_prec);
    case 0:
    return cmath2(op, CAR(args), CADR(args), z_atan2);
    default:
    errorcall_return(call, "unimplemented complex function");
    }
}

SEXP do_complex(SEXP call, SEXP op, SEXP args, SEXP rho)
{
    /* complex(length, real, imaginary) */
    SEXP ans, re, im;
    int i, na, nr, ni;
    na = asInteger(CAR(args));
    if(na == NA_INTEGER || na < 0)
    errorcall(call, "invalid length");
    PROTECT(re = coerceVector(CADR(args), REALSXP));
    PROTECT(im = coerceVector(CADDR(args), REALSXP));
    nr = length(re);
    ni = length(im);
    /* is always true: if (na >= 0) {*/
    na = (nr > na) ? nr : na;
    na = (ni > na) ? ni : na;
    /* }*/
    ans = allocVector(CPLXSXP, na);
    for(i=0 ; i<na ; i++) {
    COMPLEX(ans)[i].r = 0;
    COMPLEX(ans)[i].i = 0;
    }
    UNPROTECT(2);
    if(na > 0 && nr > 0) {
    for(i=0 ; i<na ; i++)
        COMPLEX(ans)[i].r = REAL(re)[i%nr];
    }
    if(na > 0 && ni > 0) {
    for(i=0 ; i<na ; i++)
        COMPLEX(ans)[i].i = REAL(im)[i%ni];
    }
    return ans;
}


SEXP do_polyroot(SEXP call, SEXP op, SEXP args, SEXP rho)
{
    SEXP z, zr, zi, r, rr, ri;
    Rboolean fail;
    int degree, i, n;

    checkArity(op, args);
    z = CAR(args);
    switch(TYPEOF(z)) {
    case CPLXSXP:
    PROTECT(z);
    break;
    case REALSXP:
    case INTSXP:
    case LGLSXP:
    PROTECT(z = coerceVector(z, CPLXSXP));
    break;
    default:
    errorcall(call, "invalid argument type");
    }
    n = length(z);
    degree = 0;
    for(i = 0; i < n; i++) {
    if(COMPLEX(z)[i].r!= 0.0 || COMPLEX(z)[i].i != 0.0) degree = i;
    }
    n = degree + 1; /* omit trailing zeroes */
    if(degree >= 1) {
    if(n > 49) errorcall(call, "polynomial degree too high (49 max)");
    /* <==>  #define NMAX 50  in  ../appl/cpoly.c */

    /* if(COMPLEX(z)[n-1].r == 0.0 && COMPLEX(z)[n-1].i == 0.0)
       errorcall(call, "highest power has coefficient 0");*/

    PROTECT(rr = allocVector(REALSXP, n));
    PROTECT(ri = allocVector(REALSXP, n));
    PROTECT(zr = allocVector(REALSXP, n));
    PROTECT(zi = allocVector(REALSXP, n));

    for(i=0 ; i<n ; i++) {
        if(!R_FINITE(COMPLEX(z)[i].r) || !R_FINITE(COMPLEX(z)[i].i))
        errorcall(call, "invalid polynomial coefficient");
        REAL(zr)[degree-i] = COMPLEX(z)[i].r;
        REAL(zi)[degree-i] = COMPLEX(z)[i].i;
    }
    R_cpolyroot(REAL(zr), REAL(zi), &degree, REAL(rr), REAL(ri), &fail);
    if(fail) errorcall(call, "root finding code failed");
    UNPROTECT(2);
    r = allocVector(CPLXSXP, degree);
    for(i=0 ; i<degree ; i++) {
        COMPLEX(r)[i].r = REAL(rr)[i];
        COMPLEX(r)[i].i = REAL(ri)[i];
    }
    UNPROTECT(3);
    }
    else {
    UNPROTECT(1);
    r = allocVector(CPLXSXP, 0);
    }
    return r;
}