X-Git-Url: https://git.donarmstrong.com/?p=mothur.git;a=blobdiff_plain;f=linearalgebra.cpp;h=e1b9470fdb218d94fd9f5fe9f36ccb23ac31ea8a;hp=2e0321e53bb8f601fcaff916db5534cc217709be;hb=a8e2df1b96a57f5f29576b08361b86a96a8eff4f;hpb=fc3b1fc4fc1c4e38fde6b0c0ee7896b5fe0b9d57 diff --git a/linearalgebra.cpp b/linearalgebra.cpp index 2e0321e..e1b9470 100644 --- a/linearalgebra.cpp +++ b/linearalgebra.cpp @@ -10,6 +10,12 @@ #include "linearalgebra.h" // This class references functions used from "Numerical Recipes in C++" // + +/*********************************************************************************************************************************/ +inline double SQR(const double a) +{ + return a*a; +} /*********************************************************************************************************************************/ inline double SIGN(const double a, const double b) @@ -17,6 +23,235 @@ inline double SIGN(const double a, const double b) return b>=0 ? (a>=0 ? a:-a) : (a>=0 ? -a:a); } /*********************************************************************************************************************************/ +//NUmerical recipes pg. 245 - Returns the complementary error function erfc(x) with fractional error everywhere less than 1.2 × 10−7. +double LinearAlgebra::erfcc(double x){ + try { + double t,z,ans; + z=fabs(x); + t=1.0/(1.0+0.5*z); + + ans=t*exp(-z*z-1.26551223+t*(1.00002368+t*(0.37409196+t*(0.09678418+ + t*(-0.18628806+t*(0.27886807+t*(-1.13520398+t*(1.48851587+ + t*(-0.82215223+t*0.17087277))))))))); + + //cout << "in erfcc " << t << '\t' << ans<< endl; + return (x >= 0.0 ? ans : 2.0 - ans); + } + catch(exception& e) { + m->errorOut(e, "LinearAlgebra", "betai"); + exit(1); + } +} +/*********************************************************************************************************************************/ +//Numerical Recipes pg. 232 +double LinearAlgebra::betai(const double a, const double b, const double x) { + try { + double bt; + double result = 0.0; + + if (x < 0.0 || x > 1.0) { m->mothurOut("[ERROR]: bad x in betai.\n"); m->control_pressed = true; return 0.0; } + + if (x == 0.0 || x == 1.0) { bt = 0.0; } + else { bt = exp(gammln(a+b)-gammln(a)-gammln(b)+a*log(x)+b*log(1.0-x)); } + + if (x < (a+1.0) / (a+b+2.0)) { result = bt*betacf(a,b,x)/a; } + else { result = 1.0-bt*betacf(b,a,1.0-x)/b; } + + return result; + } + catch(exception& e) { + m->errorOut(e, "LinearAlgebra", "betai"); + exit(1); + } +} +/*********************************************************************************************************************************/ +//Numerical Recipes pg. 219 +double LinearAlgebra::gammln(const double xx) { + try { + int j; + double x,y,tmp,ser; + static const double cof[6]={76.18009172947146,-86.50532032941677,24.01409824083091, + -1.231739572450155,0.120858003e-2,-0.536382e-5}; + + y=x=xx; + tmp=x+5.5; + tmp -= (x+0.5)*log(tmp); + ser=1.0; + for (j=0;j<6;j++) { + ser += cof[j]/++y; + } + return -tmp+log(2.5066282746310005*ser/x); + } + catch(exception& e) { + m->errorOut(e, "LinearAlgebra", "gammln"); + exit(1); + } +} +/*********************************************************************************************************************************/ +//Numerical Recipes pg. 223 +double LinearAlgebra::gammp(const double a, const double x) { + try { + double gamser,gammcf,gln; + + if (x < 0.0 || a <= 0.0) { m->mothurOut("[ERROR]: Invalid arguments in routine GAMMP\n"); m->control_pressed = true; return 0.0;} + if (x < (a+1.0)) { + gser(gamser,a,x,gln); + return gamser; + } else { + gcf(gammcf,a,x,gln); + return 1.0-gammcf; + } + + return 0; + } + catch(exception& e) { + m->errorOut(e, "LinearAlgebra", "gammp"); + exit(1); + } +} +/*********************************************************************************************************************************/ +//Numerical Recipes pg. 223 +double LinearAlgebra::gammq(const double a, const double x) { + try { + double gamser,gammcf,gln; + + if (x < 0.0 || a <= 0.0) { m->mothurOut("[ERROR]: Invalid arguments in routine GAMMQ\n"); m->control_pressed = true; return 0.0; } + if (x < (a+1.0)) { + gser(gamser,a,x,gln); + return 1.0-gamser; + } else { + gcf(gammcf,a,x,gln); + return gammcf; + } + + return 0; + } + catch(exception& e) { + m->errorOut(e, "LinearAlgebra", "gammp"); + exit(1); + } +} +/*********************************************************************************************************************************/ +//Numerical Recipes pg. 224 +double LinearAlgebra::gcf(double& gammcf, const double a, const double x, double& gln){ + try { + const int ITMAX=100; + const double EPS=numeric_limits::epsilon(); + const double FPMIN=numeric_limits::min()/EPS; + int i; + double an,b,c,d,del,h; + + gln=gammln(a); + b=x+1.0-a; + c=1.0/FPMIN; + d=1.0/b; + h=d; + for (i=1;i<=ITMAX;i++) { + an = -i*(i-a); + b += 2.0; + d=an*d+b; + if (fabs(d) < FPMIN) { d=FPMIN; } + c=b+an/c; + if (fabs(c) < FPMIN) { c=FPMIN; } + d=1.0/d; + del=d*c; + h *= del; + if (fabs(del-1.0) <= EPS) break; + } + if (i > ITMAX) { m->mothurOut("[ERROR]: a too large, ITMAX too small in gcf\n"); m->control_pressed = true; } + gammcf=exp(-x+a*log(x)-gln)*h; + + return 0.0; + } + catch(exception& e) { + m->errorOut(e, "LinearAlgebra", "gcf"); + exit(1); + } + +} +/*********************************************************************************************************************************/ +//Numerical Recipes pg. 223 +double LinearAlgebra::gser(double& gamser, const double a, const double x, double& gln) { + try { + int n; + double sum,del,ap; + const double EPS = numeric_limits::epsilon(); + + gln=gammln(a); + if (x <= 0.0) { + if (x < 0.0) { m->mothurOut("[ERROR]: x less than 0 in routine GSER\n"); m->control_pressed = true; } + gamser=0.0; return 0.0; + } else { + ap=a; + del=sum=1.0/a; + for (n=0;n<100;n++) { + ++ap; + del *= x/ap; + sum += del; + if (fabs(del) < fabs(sum)*EPS) { + gamser=sum*exp(-x+a*log(x)-gln); + return 0.0; + } + } + + m->mothurOut("[ERROR]: a too large, ITMAX too small in routine GSER\n"); + return 0.0; + } + return 0; + } + catch(exception& e) { + m->errorOut(e, "LinearAlgebra", "gser"); + exit(1); + } +} +/*********************************************************************************************************************************/ +//Numerical Recipes pg. 233 +double LinearAlgebra::betacf(const double a, const double b, const double x) { + try { + const int MAXIT = 100; + const double EPS = numeric_limits::epsilon(); + const double FPMIN = numeric_limits::min() / EPS; + int m1, m2; + double aa, c, d, del, h, qab, qam, qap; + + qab=a+b; + qap=a+1.0; + qam=a-1.0; + c=1.0; + d=1.0-qab*x/qap; + if (fabs(d) < FPMIN) d=FPMIN; + d=1.0/d; + h=d; + for (m1=1;m1<=MAXIT;m1++) { + m2=2*m1; + aa=m1*(b-m1)*x/((qam+m2)*(a+m2)); + d=1.0+aa*d; + if (fabs(d) < FPMIN) d=FPMIN; + c=1.0+aa/c; + if (fabs(c) < FPMIN) c=FPMIN; + d=1.0/d; + h *= d*c; + aa = -(a+m1)*(qab+m1)*x/((a+m2)*(qap+m2)); + d=1.0+aa*d; + if (fabs(d) < FPMIN) d=FPMIN; + c=1.0+aa/c; + if (fabs(c) < FPMIN) c=FPMIN; + d=1.0/d; + del=d*c; + h *= del; + if (fabs(del-1.0) < EPS) break; + } + + if (m1 > MAXIT) { m->mothurOut("[ERROR]: a or b too big or MAXIT too small in betacf."); m->mothurOutEndLine(); m->control_pressed = true; } + return h; + + } + catch(exception& e) { + m->errorOut(e, "LinearAlgebra", "betacf"); + exit(1); + } +} +/*********************************************************************************************************************************/ vector > LinearAlgebra::matrix_mult(vector > first, vector > second){ try { @@ -799,14 +1034,7 @@ double LinearAlgebra::calcKendall(vector& x, vector& y, double& double p = (numCoor - numDisCoor) / (float) count; - //calc signif - zA - http://en.wikipedia.org/wiki/Kendall_tau_rank_correlation_coefficient#Significance_tests - double numer = 3.0 * (numCoor - numDisCoor); - int n = xscores.size(); - double denom = n * (n-1) * (2*n + 5) / (double) 2.0; - denom = sqrt(denom); - sig = numer / denom; - - if (isnan(sig) || isinf(sig)) { sig = 0.0; } + sig = calcKendallSig(x.size(), p); return p; } @@ -815,12 +1043,200 @@ double LinearAlgebra::calcKendall(vector& x, vector& y, double& exit(1); } } +double LinearAlgebra::ran0(int& idum) +{ + const int IA=16807,IM=2147483647,IQ=127773; + const int IR=2836,MASK=123459876; + const double AM=1.0/double(IM); + int k; + double ans; + + idum ^= MASK; + k=idum/IQ; + idum=IA*(idum-k*IQ)-IR*k; + if (idum < 0) idum += IM; + ans=AM*idum; + idum ^= MASK; + return ans; +} + +double LinearAlgebra::ran1(int &idum) +{ + const int IA=16807,IM=2147483647,IQ=127773,IR=2836,NTAB=32; + const int NDIV=(1+(IM-1)/NTAB); + const double EPS=3.0e-16,AM=1.0/IM,RNMX=(1.0-EPS); + static int iy=0; + static vector iv(NTAB); + int j,k; + double temp; + + if (idum <= 0 || !iy) { + if (-idum < 1) idum=1; + else idum = -idum; + for (j=NTAB+7;j>=0;j--) { + k=idum/IQ; + idum=IA*(idum-k*IQ)-IR*k; + if (idum < 0) idum += IM; + if (j < NTAB) iv[j] = idum; + } + iy=iv[0]; + } + k=idum/IQ; + idum=IA*(idum-k*IQ)-IR*k; + if (idum < 0) idum += IM; + j=iy/NDIV; + iy=iv[j]; + iv[j] = idum; + if ((temp=AM*iy) > RNMX) return RNMX; + else return temp; +} + +double LinearAlgebra::ran2(int &idum) +{ + const int IM1=2147483563,IM2=2147483399; + const int IA1=40014,IA2=40692,IQ1=53668,IQ2=52774; + const int IR1=12211,IR2=3791,NTAB=32,IMM1=IM1-1; + const int NDIV=1+IMM1/NTAB; + const double EPS=3.0e-16,RNMX=1.0-EPS,AM=1.0/double(IM1); + static int idum2=123456789,iy=0; + static vector iv(NTAB); + int j,k; + double temp; + + if (idum <= 0) { + idum=(idum==0 ? 1 : -idum); + idum2=idum; + for (j=NTAB+7;j>=0;j--) { + k=idum/IQ1; + idum=IA1*(idum-k*IQ1)-k*IR1; + if (idum < 0) idum += IM1; + if (j < NTAB) iv[j] = idum; + } + iy=iv[0]; + } + k=idum/IQ1; + idum=IA1*(idum-k*IQ1)-k*IR1; + if (idum < 0) idum += IM1; + k=idum2/IQ2; + idum2=IA2*(idum2-k*IQ2)-k*IR2; + if (idum2 < 0) idum2 += IM2; + j=iy/NDIV; + iy=iv[j]-idum2; + iv[j] = idum; + if (iy < 1) iy += IMM1; + if ((temp=AM*iy) > RNMX) return RNMX; + else return temp; +} + +double LinearAlgebra::ran3(int &idum) +{ + static int inext,inextp; + static int iff=0; + const int MBIG=1000000000,MSEED=161803398,MZ=0; + const double FAC=(1.0/MBIG); + static vector ma(56); + int i,ii,k,mj,mk; + + if (idum < 0 || iff == 0) { + iff=1; + mj=labs(MSEED-labs(idum)); + mj %= MBIG; + ma[55]=mj; + mk=1; + for (i=1;i<=54;i++) { + ii=(21*i) % 55; + ma[ii]=mk; + mk=mj-mk; + if (mk < int(MZ)) mk += MBIG; + mj=ma[ii]; + } + for (k=0;k<4;k++) + for (i=1;i<=55;i++) { + ma[i] -= ma[1+(i+30) % 55]; + if (ma[i] < int(MZ)) ma[i] += MBIG; + } + inext=0; + inextp=31; + idum=1; + } + if (++inext == 56) inext=1; + if (++inextp == 56) inextp=1; + mj=ma[inext]-ma[inextp]; + if (mj < int(MZ)) mj += MBIG; + ma[inext]=mj; + return mj*FAC; +} + +double LinearAlgebra::ran4(int &idum) +{ +#if defined(vax) || defined(_vax_) || defined(__vax__) || defined(VAX) + static const unsigned long jflone = 0x00004080; + static const unsigned long jflmsk = 0xffff007f; +#else + static const unsigned long jflone = 0x3f800000; + static const unsigned long jflmsk = 0x007fffff; +#endif + unsigned long irword,itemp,lword; + static int idums = 0; + + if (idum < 0) { + idums = -idum; + idum=1; + } + irword=idum; + lword=idums; + psdes(lword,irword); + itemp=jflone | (jflmsk & irword); + ++idum; + return (*(float *)&itemp)-1.0; +} + +void LinearAlgebra::psdes(unsigned long &lword, unsigned long &irword) +{ + const int NITER=4; + static const unsigned long c1[NITER]={ + 0xbaa96887L, 0x1e17d32cL, 0x03bcdc3cL, 0x0f33d1b2L}; + static const unsigned long c2[NITER]={ + 0x4b0f3b58L, 0xe874f0c3L, 0x6955c5a6L, 0x55a7ca46L}; + unsigned long i,ia,ib,iswap,itmph=0,itmpl=0; + + for (i=0;i> 16; + ib=itmpl*itmpl+ ~(itmph*itmph); + irword=lword ^ (((ia = (ib >> 16) | + ((ib & 0xffff) << 16)) ^ c2[i])+itmpl*itmph); + lword=iswap; + } +} +/*********************************************************************************************************************************/ +double LinearAlgebra::calcKendallSig(double n, double r){ + try { + + double sig = 0.0; + double svar=(4.0*n+10.0)/(9.0*n*(n-1.0)); + double z= r/sqrt(svar); + sig=erfcc(fabs(z)/1.4142136); + + if (isnan(sig) || isinf(sig)) { sig = 0.0; } + + return sig; + } + catch(exception& e) { + m->errorOut(e, "LinearAlgebra", "calcKendallSig"); + exit(1); + } +} + /*********************************************************************************************************************************/ double LinearAlgebra::calcSpearman(vector& x, vector& y, double& sig){ try { if (x.size() != y.size()) { m->mothurOut("[ERROR]: vector size mismatch."); m->mothurOutEndLine(); return 0.0; } //format data + double sf = 0.0; //f^3 - f where f is the number of ties in x; + double sg = 0.0; //f^3 - f where f is the number of ties in y; map tableX; map::iterator itTable; vector xscores; @@ -865,6 +1281,8 @@ double LinearAlgebra::calcSpearman(vector& x, vector& y, double& float thisrank = rankTotal / (float) xties.size(); rankx[xties[k].name] = thisrank; } + int t = xties.size(); + sf += (t*t*t-t); xties.clear(); rankTotal = 0; } @@ -915,6 +1333,8 @@ double LinearAlgebra::calcSpearman(vector& x, vector& y, double& float thisrank = rankTotal / (float) yties.size(); rank[yties[k].name] = thisrank; } + int t = yties.size(); + sg += (t*t*t-t); yties.clear(); rankTotal = 0; } @@ -943,19 +1363,52 @@ double LinearAlgebra::calcSpearman(vector& x, vector& y, double& p = (SX2 + SY2 - di) / (2.0 * sqrt((SX2*SY2))); - //signifigance calc - http://en.wikipedia.org/wiki/Spearman%27s_rank_correlation_coefficient - double temp = (x.size()-2) / (double) (1- (p*p)); - temp = sqrt(temp); - sig = p*temp; - if (isnan(sig) || isinf(sig)) { sig = 0.0; } - + //Numerical Recipes 646 + sig = calcSpearmanSig(n, sf, sg, di); + return p; } catch(exception& e) { m->errorOut(e, "LinearAlgebra", "calcSpearman"); exit(1); } -} +} +/*********************************************************************************************************************************/ +double LinearAlgebra::calcSpearmanSig(double n, double sf, double sg, double d){ + try { + + double sig = 0.0; + double probrs = 0.0; + double en=n; + double en3n=en*en*en-en; + double aved=en3n/6.0-(sf+sg)/12.0; + double fac=(1.0-sf/en3n)*(1.0-sg/en3n); + double vard=((en-1.0)*en*en*SQR(en+1.0)/36.0)*fac; + double zd=(d-aved)/sqrt(vard); + double probd=erfcc(fabs(zd)/1.4142136); + double rs=(1.0-(6.0/en3n)*(d+(sf+sg)/12.0))/sqrt(fac); + fac=(rs+1.0)*(1.0-rs); + if (fac > 0.0) { + double t=rs*sqrt((en-2.0)/fac); + double df=en-2.0; + probrs=betai(0.5*df,0.5,df/(df+t*t)); + }else { + probrs = 0.0; + } + + //smaller of probd and probrs is sig + sig = probrs; + if (probd < probrs) { sig = probd; } + + if (isnan(sig) || isinf(sig)) { sig = 0.0; } + + return sig; + } + catch(exception& e) { + m->errorOut(e, "LinearAlgebra", "calcSpearmanSig"); + exit(1); + } +} /*********************************************************************************************************************************/ double LinearAlgebra::calcPearson(vector& x, vector& y, double& sig){ try { @@ -989,11 +1442,8 @@ double LinearAlgebra::calcPearson(vector& x, vector& y, double& r = numerator / denom; - //signifigance calc - http://faculty.vassar.edu/lowry/ch4apx.html - double temp = (1- (r*r)) / (double) (x.size()-2); - temp = sqrt(temp); - sig = r / temp; - if (isnan(sig) || isinf(sig)) { sig = 0.0; } + //Numerical Recipes pg.644 + sig = calcPearsonSig(x.size(), r); return r; } @@ -1001,33 +1451,334 @@ double LinearAlgebra::calcPearson(vector& x, vector& y, double& m->errorOut(e, "LinearAlgebra", "calcPearson"); exit(1); } -} +} +/*********************************************************************************************************************************/ +double LinearAlgebra::calcPearsonSig(double n, double r){ + try { + + double sig = 0.0; + const double TINY = 1.0e-20; + double z = 0.5*log((1.0+r+TINY)/(1.0-r+TINY)); //Fisher's z transformation + + //code below was giving an error in betacf with sop files + //int df = n-2; + //double t = r*sqrt(df/((1.0-r+TINY)*(1.0+r+TINY))); + //sig = betai(0.5+df, 0.5, df/(df+t*t)); + + //Numerical Recipes says code below gives approximately the same result + sig = erfcc(fabs(z*sqrt(n-1.0))/1.4142136); + if (isnan(sig) || isinf(sig)) { sig = 0.0; } + + return sig; + } + catch(exception& e) { + m->errorOut(e, "LinearAlgebra", "calcPearsonSig"); + exit(1); + } +} /*********************************************************************************************************************************/ vector > LinearAlgebra::getObservedEuclideanDistance(vector >& relAbundData){ + try { - int numSamples = relAbundData.size(); - int numOTUs = relAbundData[0].size(); - - vector > dMatrix(numSamples); - for(int i=0;i > dMatrix(numSamples); + for(int i=0;icontrol_pressed) { return dMatrix; } + + double d = 0; + for(int k=0;kerrorOut(e, "LinearAlgebra", "getObservedEuclideanDistance"); + exit(1); + } +} + +/*********************************************************************************************************************************/ +vector LinearAlgebra::solveEquations(vector > A, vector b){ + try { + int length = (int)b.size(); + vector x(length, 0); + vector index(length); + for(int i=0;icontrol_pressed) { return b; } + lubksb(A, index, b); + + return b; + } + catch(exception& e) { + m->errorOut(e, "LinearAlgebra", "solveEquations"); + exit(1); + } +} +/*********************************************************************************************************************************/ +vector LinearAlgebra::solveEquations(vector > A, vector b){ + try { + int length = (int)b.size(); + vector x(length, 0); + vector index(length); + for(int i=0;icontrol_pressed) { return b; } + lubksb(A, index, b); + + return b; + } + catch(exception& e) { + m->errorOut(e, "LinearAlgebra", "solveEquations"); + exit(1); + } +} + +/*********************************************************************************************************************************/ + +void LinearAlgebra::ludcmp(vector >& A, vector& index, double& d){ + try { + double tiny = 1e-20; + + int n = (int)A.size(); + vector vv(n, 0.0); + double temp; + int imax; + + d = 1.0; + + for(int i=0;i big ) big=temp; } + if(big==0.0){ m->mothurOut("Singular matrix in routine ludcmp\n"); } + vv[i] = 1.0/big; + } + + for(int j=0;jcontrol_pressed) { break; } + for(int i=0;i= big){ + big = dum; + imax = i; + } + } + if(j != imax){ + for(int k=0;kerrorOut(e, "LinearAlgebra", "ludcmp"); + exit(1); + } +} + +/*********************************************************************************************************************************/ + +void LinearAlgebra::lubksb(vector >& A, vector& index, vector& b){ + try { + double total; + int n = (int)A.size(); + int ii = 0; + + for(int i=0;icontrol_pressed) { break; } + int ip = index[i]; + total = b[ip]; + b[ip] = b[i]; + + if (ii != 0) { + for(int j=ii-1;j=0;i--){ + total = b[i]; + for(int j=i+1;jerrorOut(e, "LinearAlgebra", "lubksb"); + exit(1); + } +} +/*********************************************************************************************************************************/ + +void LinearAlgebra::ludcmp(vector >& A, vector& index, float& d){ + try { + double tiny = 1e-20; + + int n = (int)A.size(); + vector vv(n, 0.0); + double temp; + int imax; + + d = 1.0; + + for(int i=0;i big ) big=temp; } + if(big==0.0){ m->mothurOut("Singular matrix in routine ludcmp\n"); } + vv[i] = 1.0/big; + } + + for(int j=0;jcontrol_pressed) { break; } + for(int i=0;i= big){ + big = dum; + imax = i; + } + } + if(j != imax){ + for(int k=0;kerrorOut(e, "LinearAlgebra", "ludcmp"); + exit(1); + } +} + +/*********************************************************************************************************************************/ + +void LinearAlgebra::lubksb(vector >& A, vector& index, vector& b){ + try { + float total; + int n = (int)A.size(); + int ii = 0; + + for(int i=0;icontrol_pressed) { break; } + int ip = index[i]; + total = b[ip]; + b[ip] = b[i]; + + if (ii != 0) { + for(int j=ii-1;j=0;i--){ + total = b[i]; + for(int j=i+1;jerrorOut(e, "LinearAlgebra", "lubksb"); + exit(1); + } +} + + +/*********************************************************************************************************************************/ + +vector > LinearAlgebra::getInverse(vector > matrix){ + try { + int n = (int)matrix.size(); + + vector > inverse(n); + for(int i=0;i column(n, 0.0000); + vector index(n, 0); + double dummy; + + ludcmp(matrix, index, dummy); + + for(int j=0;jcontrol_pressed) { break; } + + column.assign(n, 0); + + column[j] = 1.0000; + + lubksb(matrix, index, column); + + for(int i=0;ierrorOut(e, "LinearAlgebra", "getInverse"); + exit(1); } - return dMatrix; - } /*********************************************************************************************************************************/