298 lines
8.8 KiB
C++
298 lines
8.8 KiB
C++
#include "polynomial.hpp"
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unsigned int *_Polynomial::combinatorial;
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void _Polynomial::startCombinatorialNumbers (int degree) {
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_Polynomial::combinatorial = new unsigned int [((degree+2)*(degree+1))/2];
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unsigned int *combinatorial = _Polynomial::combinatorial;
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unsigned int i; // counter for m
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unsigned int j; // counter for n
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for (i=0; i<=degree; i++) {
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combinatorial[(i*(i+1))/2] = combinatorial[(i*(i+3))/2] = 1; // FIRST AND LAST = 1
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// THE REST IS COMPUTED FROM THE RECURRENCE OF COMBINATORIAL NUMBERS.
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for (j=1; j<i; j++)
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combinatorial[(i*(i+1))/2+j] = combinatorial[((i-1)*i)/2+j-1] + combinatorial[((i-1)*i)/2+j];
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combinatorial[((i+1)*(i+2))/2-1] = 1;
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}
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}
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template <>
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IComplex Polynomial<IComplex>::evalIPolHornerXY (const IComplex &x, const IComplex &y) const {
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//evaluate polynomial as an element of K[x][y] in Horner form
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//that is, each coefficient of y is a polynomial on x
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int i; //i will represent the on x
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int j; //j will represent the degree on y
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int d = this->degree;
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IComplex coef;
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IComplex rop;
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rop = (this->coef)[(d+2)*(d+1)/2-1];
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for (j=d-1; j>=0; --j){
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coef = (this->coef)[d*(d+1)/2+j];
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for (i=d-1-j; i>=0; --i){
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coef = x * coef + (this->coef)[(j+i)*(j+i+1)/2+j];
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}
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rop = rop * y + coef;
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}
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return rop;
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}
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template <>
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IComplex Polynomial<IComplex>::evalIPolHornerYX (const IComplex &x, const IComplex &y) const {
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//evaluate polynomial as an element of K[y][x] in Horner form
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//that is, each coefficient of x is a polynomial on y
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int i; //i will represent the degree on x
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int j; //j will represent the on y
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int d = this->degree;
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IComplex coef;
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IComplex rop;
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rop = (this->coef)[(d)*(d+1)/2];
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for (i=d-1; i>=0; --i){
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coef = (this->coef)[d*(d+1)/2+d-i];
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for (j=d-i-1; j>=0; --j) {
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coef = coef * y + (this->coef)[(i+j)*(i+j+1)/2+j];
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}
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rop = rop * x + coef;
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}
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return rop;
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}
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template <>
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IComplex Polynomial<IComplex>::operator () (const IComplex &x, const IComplex &y) const{
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IComplex rop, ropx, ropy;
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ropx = this->evalIPolHornerXY (x, y);
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ropy = this->evalIPolHornerYX (x, y);
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rop = this->evalPolClassic (x, y);
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rop.r.a = MAX(MAX(ropx.r.a, ropy.r.a), rop.r.a);
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rop.r.b = MIN(MIN(ropx.r.b, ropy.r.b), rop.r.b);
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rop.i.a = MAX(MAX(ropx.i.a, ropy.i.a), rop.i.a);
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rop.i.b = MIN(MIN(ropx.i.b, ropy.i.b), rop.i.b);
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return rop;
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}
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template <>
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IComplex Polynomial<IComplex>::evalIPolYHornerXY (const IComplex &x, const IComplex &y) const {
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//evaluate polynomial as an element of K[x][y] in Horner form
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//that is, each coefficient of y is a polynomial on x
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int i; //i will represent the on x
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int j; //j will represent the degree on y
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int d = this->degree;
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IComplex coef;
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IComplex rop;
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rop = (d) * (this->coef)[(d+2)*(d+1)/2-1];
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for (j=d-2; j>=0; --j){
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coef = (this->coef)[d*(d+1)/2+j+1];
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for (i=d-1; i>=j+1; --i){
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coef = x * coef + (this->coef)[(i*(i+1))/2+j+1];
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}
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rop = rop * y + (j+1.0) * coef;
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}
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return rop;
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}
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template <>
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IComplex Polynomial<IComplex>::evalIPolYHornerYX (const IComplex &x, const IComplex &y) const {
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//evaluate polynomial as an element of K[x][y] in Horner form
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//that is, each coefficient of y is a polynomial on x
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int i; //i will represent the on x
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int j; //j will represent the degree on y
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int d = this->degree;
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IComplex coef;
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IComplex rop;
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rop = (this->coef)[(d)*(d+1)/2+1];
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for (i=d-2; i>=0; --i){
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coef = ((double) d-i)*(this->coef)[(d*(d+1))/2+d-i];
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for (j=d-1; j>=i+1; --j){
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coef = y * coef + (j-i)*(this->coef)[(j*(j+1))/2+j-i];
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}
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rop = rop * x + coef;
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}
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return rop;
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}
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template <>
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IComplex Polynomial<IComplex>::diffY (const IComplex &x, const IComplex &y) const{
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IComplex rop, ropx, ropy;
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ropx = this->evalIPolYHornerXY (x, y);
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ropy = this->evalIPolYHornerYX (x, y);
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rop = this->evalPolYClassic (x, y);
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rop.r.a = MAX(MAX(ropx.r.a, ropy.r.a), rop.r.a);
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rop.r.b = MIN(MIN(ropx.r.b, ropy.r.b), rop.r.b);
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rop.i.a = MAX(MAX(ropx.i.a, ropy.i.a), rop.i.a);
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rop.i.b = MIN(MIN(ropx.i.b, ropy.i.b), rop.i.b);
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return rop;
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}
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template <>
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MPIComplex Polynomial<MPIComplex>::evalIPolHornerXY (const MPIComplex &x, const MPIComplex &y) const {
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//evaluate polynomial as an element of K[x][y] in Horner form
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//that is, each coefficient of y is a polynomial on x
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int i; //i will represent the on x
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int j; //j will represent the degree on y
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int d = this->degree;
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MPIComplex coef;
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MPIComplex rop;
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rop = (this->coef)[(d+2)*(d+1)/2-1];
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for (j=d-1; j>=0; --j){
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coef = (this->coef)[d*(d+1)/2+j];
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for (i=d-1-j; i>=0; --i){
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coef = x * coef + (this->coef)[(j+i)*(j+i+1)/2+j];
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}
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rop = rop * y + coef;
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}
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return rop;
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}
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template <>
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MPIComplex Polynomial<MPIComplex>::evalIPolHornerYX (const MPIComplex &x, const MPIComplex &y) const {
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//evaluate polynomial as an element of K[y][x] in Horner form
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//that is, each coefficient of x is a polynomial on y
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int i; //i will represent the degree on x
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int j; //j will represent the on y
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int d = this->degree;
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MPIComplex coef;
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MPIComplex rop;
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rop = (this->coef)[(d)*(d+1)/2];
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for (i=d-1; i>=0; --i){
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coef = (this->coef)[d*(d+1)/2+d-i];
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for (j=d-i-1; j>=0; --j) {
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coef = coef * y + (this->coef)[(i+j)*(i+j+1)/2+j];
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}
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rop = rop * x + coef;
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}
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return rop;
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}
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template <>
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MPIComplex Polynomial<MPIComplex>::operator () (const MPIComplex &x, const MPIComplex &y) const{
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MPIComplex rop, ropx, ropy;
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ropx = this->evalIPolHornerXY (x, y);
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ropy = this->evalIPolHornerYX (x, y);
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rop = this->evalPolClassic (x, y);
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mpfr_max (rop.r.a, rop.r.a, ropx.r.a, MPFR_RNDD);
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mpfr_max (rop.r.a, rop.r.a, ropy.r.a, MPFR_RNDD);
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mpfr_max (rop.i.a, rop.i.a, ropx.i.a, MPFR_RNDD);
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mpfr_max (rop.i.a, rop.i.a, ropy.i.a, MPFR_RNDD);
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mpfr_min (rop.r.b, rop.r.b, ropx.r.b, MPFR_RNDU);
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mpfr_min (rop.r.b, rop.r.b, ropy.r.b, MPFR_RNDU);
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mpfr_min (rop.i.b, rop.i.b, ropx.i.b, MPFR_RNDU);
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mpfr_min (rop.i.b, rop.i.b, ropy.i.b, MPFR_RNDU);
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// rop.r.a = MAX(MAX(ropx.r.a, ropy.r.a), rop.r.a);
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// rop.r.b = MIN(MIN(ropx.r.b, ropy.r.b), rop.r.b);
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// rop.i.a = MAX(MAX(ropx.i.a, ropy.i.a), rop.i.a);
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// rop.i.b = MIN(MIN(ropx.i.b, ropy.i.b), rop.i.b);
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return rop;
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}
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template <>
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MPIComplex Polynomial<MPIComplex>::evalIPolYHornerXY (const MPIComplex &x, const MPIComplex &y) const {
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//evaluate polynomial as an element of K[x][y] in Horner form
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//that is, each coefficient of y is a polynomial on x
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int i; //i will represent the on x
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int j; //j will represent the degree on y
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int d = this->degree;
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MPIComplex coef;
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MPIComplex rop;
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rop = (d) * (this->coef)[(d+2)*(d+1)/2-1];
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for (j=d-2; j>=0; --j){
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coef = (this->coef)[d*(d+1)/2+j+1];
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for (i=d-1; i>=j+1; --i){
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coef = x * coef + (this->coef)[(i*(i+1))/2+j+1];
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}
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rop = rop * y + (j+1.0) * coef;
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}
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return rop;
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}
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template <>
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MPIComplex Polynomial<MPIComplex>::evalIPolYHornerYX (const MPIComplex &x, const MPIComplex &y) const {
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//evaluate polynomial as an element of K[x][y] in Horner form
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//that is, each coefficient of y is a polynomial on x
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int i; //i will represent the on x
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int j; //j will represent the degree on y
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int d = this->degree;
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MPIComplex coef;
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MPIComplex rop;
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rop = (this->coef)[(d)*(d+1)/2+1];
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for (i=d-2; i>=0; --i){
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coef = ((double) d-i)*(this->coef)[(d*(d+1))/2+d-i];
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for (j=d-1; j>=i+1; --j){
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coef = y * coef + (j-i)*(this->coef)[(j*(j+1))/2+j-i];
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}
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rop = rop * x + coef;
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}
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return rop;
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}
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template <>
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MPIComplex Polynomial<MPIComplex>::diffY (const MPIComplex &x, const MPIComplex &y) const{
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MPIComplex rop, ropx, ropy;
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ropx = this->evalIPolYHornerXY (x, y);
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ropy = this->evalIPolYHornerYX (x, y);
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rop = this->evalPolYClassic (x, y);
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/*rop.r.a = MAX(MAX(ropx.r.a, ropy.r.a), rop.r.a);
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rop.r.b = MIN(MIN(ropx.r.b, ropy.r.b), rop.r.b);
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rop.i.a = MAX(MAX(ropx.i.a, ropy.i.a), rop.i.a);
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rop.i.b = MIN(MIN(ropx.i.b, ropy.i.b), rop.i.b);*/
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mpfr_max (rop.r.a, rop.r.a, ropx.r.a, MPFR_RNDD);
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mpfr_max (rop.r.a, rop.r.a, ropy.r.a, MPFR_RNDD);
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mpfr_max (rop.i.a, rop.i.a, ropx.i.a, MPFR_RNDD);
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mpfr_max (rop.i.a, rop.i.a, ropy.i.a, MPFR_RNDD);
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mpfr_min (rop.r.b, rop.r.b, ropx.r.b, MPFR_RNDU);
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mpfr_min (rop.r.b, rop.r.b, ropy.r.b, MPFR_RNDU);
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mpfr_min (rop.i.b, rop.i.b, ropx.i.b, MPFR_RNDU);
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mpfr_min (rop.i.b, rop.i.b, ropy.i.b, MPFR_RNDU);
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return rop;
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}
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