LA_library/nonclass.cc
2004-03-17 03:07:21 +00:00

525 lines
15 KiB
C++

extern "C" {
#include "atlas_enum.h"
#include "clapack.h"
}
#include "la.h"
#ifdef FORTRAN_
#define FORNAME(x) x##_
#else
#define FORNAME(x) x
#endif
#define INSTANTIZE(T) \
template void lawritemat(FILE *file,const T *a,int r,int c,const char *form0, \
int nodim,int modulo, int issym);
INSTANTIZE(double)
INSTANTIZE(complex<double>)
template <typename T>
void lawritemat(FILE *file,const T *a,int r,int c,const char *form0,
int nodim,int modulo, int issym)
{
int i,j;
const char *f;
/*print out title before %*/
f=form0;
skiptext:
while (*f && *f !='%' ) {fputc(*f++,file);}
if (*f=='%' && f[1]=='%') {
fputc(*f,file); f+=2;
goto skiptext;
}
/* this has to be avoided when const arguments should be allowed *f=0; */
/*use the rest as a format for numbers*/
if (modulo) nodim=0;
if (nodim==2) fprintf(file,"%d %d\n",r,c);
if (nodim==1) fprintf(file,"%d\n",c);
if (modulo) {
int n1, n2, l, m;
char ff[32];
/* prepare integer format for column numbering */
if (sscanf(f+1,"%d",&l) != 1) l=128/modulo;
l -= 2;
m = l/2;
l = l-m;
sprintf(ff,"%%%ds%%3d%%%ds", l, m);
n1 = 1;
while(n1 <= c) {
n2=n1+modulo-1;
if (n2 > c) n2 = c;
/*write block between columns n1 and n2 */
fprintf(file,"\n ");
for (i=n1; i<=n2; i++) fprintf(file,ff," ",i," ");
fprintf(file,"\n\n");
for (i=1; i<=r; i++) {
fprintf(file, "%3d ", i);
for (j=n1; j<=n2; j++) {
if(issym) {
int ii,jj;
if (i >= j) {
ii=i;
jj=j;
} else {
ii=j;
jj=i;
}
fprintf(file, f, ((complex<double>)a[ii*(ii+1)/2+jj]).real(), ((complex<double>)a[ii*(ii+1)/2+jj]).imag());
} else fprintf(file, f, ((complex<double>)a[(i-1)*c+j-1]).real(), ((complex<double>)a[(i-1)*c+j-1]).imag());
if (j < n2) fputc(' ',file);
}
fprintf(file, "\n");
}
n1 = n2+1;
}
} else {
for (i=1; i<=r; i++) {
for (j=1; j<=c; j++) {
if (issym) {
int ii,jj;
if (i >= j) {
ii=i;
jj=j;
} else {
ii=j;
jj=i;
}
fprintf(file, f, ((complex<double>)a[ii*(ii+1)/2+jj]).real(), ((complex<double>)a[ii*(ii+1)/2+jj]).imag());
} else fprintf(file,f,((complex<double>)a[(i-1)*c+j-1]).real(), ((complex<double>)a[(i-1)*c+j-1]).imag());
putc(j<c?' ':'\n',file);
}
}
}
}
// LA errorr handler
void laerror(const char *s1, const char *s2, const char *s3, const char *s4)
{
std::cerr << "LA:ERROR - ";
if(!s1)
std::cerr << "udefined.";
else {
if(s1) std::cerr << s1;
if(s2) std::cerr << s2;
if(s3) std::cerr << s3;
if(s4) std::cerr << s4;
}
std::cerr << endl;
exit(1);
}
//////////////////////
// LAPACK interface //
//////////////////////
// A will be overwritten, B will contain the solutions, A is nxn, B is rhs x n
void linear_solve(NRMat<double> &A, NRMat<double> *B, double *det)
{
int r, *ipiv;
if (A.nrows() != A.ncols()) laerror("linear_solve() call for non-square matrix");
if (B && A.nrows() != B->ncols()) laerror("incompatible matrices in linear_solve()");
A.copyonwrite();
if (B) B->copyonwrite();
ipiv = new int[A.nrows()];
r = clapack_dgesv(CblasRowMajor, A.nrows(), B ? B->nrows() : 0, A[0], A.ncols(),
ipiv, B ? B[0] : (double *)0, B ? B->ncols() : A.nrows());
if (r < 0) {
delete[] ipiv;
laerror("illegal argument in lapack_gesv");
}
if (det && r>=0) {
*det = A[0][0];
for (int i=1; i<A.nrows(); ++i) *det *= A[i][i];
//change sign of det by parity of ipiv permutation
for (int i=0; i<A.nrows(); ++i) *det = -(*det);
}
delete [] ipiv;
if (r>0 && B) laerror("singular matrix in lapack_gesv");
}
// Next routines are not available in clapack, fotran ones will b used with an
// additional swap/transpose of outputs when needed
extern "C" void FORNAME(dspsv)(const char *UPLO, const int *N, const int *NRHS,
double *AP, int *IPIV, double *B, const int *LDB, int *INFO);
void linear_solve(NRSMat<double> &a, NRMat<double> *b, double *det)
{
int r, *ipiv;
if (det) cerr << "@@@ sign of the determinant not implemented correctly yet\n";
if (b && a.nrows() != b->ncols())
laerror("incompatible matrices in symmetric linear_solve()");
a.copyonwrite();
if (b) b->copyonwrite();
ipiv = new int[a.nrows()];
char U = 'U';
int n = a.nrows();
int nrhs = 0;
if (b) nrhs = b->nrows();
int ldb = b ? b->ncols() : a.nrows();
FORNAME(dspsv)(&U, &n, &nrhs, a, ipiv, b?(*b)[0]:0, &ldb,&r);
if (r < 0) {
delete[] ipiv;
laerror("illegal argument in spsv() call of linear_solve()");
}
if (det && r >= 0) {
*det = a(0,0);
for (int i=1; i<a.nrows(); i++) *det *= a(i,i);
for (int i=0; i<a.nrows(); i++)
if (ipiv[i] != i) *det = -(*det);
}
delete[] ipiv;
if (r > 0 && b) laerror("singular matrix in linear_solve(SMat&, Mat*, double*");
}
extern "C" void FORNAME(dsyev)(const char *JOBZ, const char *UPLO, const int *N,
double *A, const int *LDA, double *W, double *WORK, const int *LWORK, int *INFO);
// a will contain eigenvectors, w eigenvalues
void diagonalize(NRMat<double> &a, NRVec<double> &w, const bool eivec,
const bool corder)
{
int n = a.nrows();
if (n != a.ncols()) laerror("diagonalize() call with non-square matrix");
if (a.nrows() != w.size())
laerror("inconsistent dimension of eigenvalue vector in diagonalize()");
a.copyonwrite();
w.copyonwrite();
int r = 0;
char U ='U';
char vectors = 'V';
if (!eivec) vectors = 'N';
int LWORK = -1;
double WORKX;
// First call is to determine size of workspace
FORNAME(dsyev)(&vectors, &U, &n, a, &n, w, (double *)&WORKX, &LWORK, &r );
LWORK = (int)WORKX;
double *WORK = new double[LWORK];
FORNAME(dsyev)(&vectors, &U, &n, a, &n, w, WORK, &LWORK, &r );
delete[] WORK;
if (vectors == 'V' && corder) a.transposeme();
if (r < 0) laerror("illegal argument in syev() of diagonalize()");
if (r > 0) laerror("convergence problem in syev() of diagonalize()");
}
extern "C" void FORNAME(dspev)(const char *JOBZ, const char *UPLO, const int *N,
double *AP, double *W, double *Z, const int *LDZ, double *WORK, int *INFO);
// v will contain eigenvectors, w eigenvalues
void diagonalize(NRSMat<double> &a, NRVec<double> &w, NRMat<double> *v,
const bool corder)
{
int n = a.nrows();
if (v) if (v->nrows() != v ->ncols() || n != v->nrows())
laerror("diagonalize() call with inconsistent dimensions");
if (n != w.size()) laerror("inconsistent dimension of eigenvalue vector");
a.copyonwrite();
w.copyonwrite();
int r = 0;
char U = 'U';
char job = v ? 'v' : 'n';
double *WORK = new double[3*n];
FORNAME(dspev)(&job, &U, &n, a, w, v?(*v)[0]:(double *)0, &n, WORK, &r );
delete[] WORK;
if (v && corder) v->transposeme();
if (r < 0) laerror("illegal argument in spev() of diagonalize()");
if (r > 0) laerror("convergence problem in spev() of diagonalize()");
}
extern "C" void FORNAME(dgesvd)(const char *JOBU, const char *JOBVT, const int *M,
const int *N, double *A, const int *LDA, double *S, double *U, const int *LDU,
double *VT, const int *LDVT, double *WORK, const int *LWORK, int *INFO );
void singular_decomposition(NRMat<double> &a, NRMat<double> *u, NRVec<double> &s,
NRMat<double> *v, const bool corder)
{
int m = a.nrows();
int n = a.ncols();
if (u) if (m != u->nrows() || m!= u->ncols())
laerror("inconsistent dimension of U Mat in singular_decomposition()");
if (s.size() < m && s.size() < n)
laerror("inconsistent dimension of S Vec in singular_decomposition()");
if (v) if (n != v->nrows() || n != v->ncols())
laerror("inconsistent dimension of V Mat in singular_decomposition()");
a.copyonwrite();
s.copyonwrite();
if (u) u->copyonwrite();
if (v) v->copyonwrite();
// C-order (transposed) input and swap u,v matrices,
// v should be transposed at the end
char jobu = u ? 'A' : 'N';
char jobv = v ? 'A' : 'N';
double work0;
int lwork = -1;
int r;
FORNAME(dgesvd)(&jobv, &jobu, &n, &m, a, &n, s, v?(*v)[0]:0, &n,
u?(*u)[0]:0, &m, &work0, &lwork, &r);
lwork = (int) work0;
double *work = new double[lwork];
FORNAME(dgesvd)(&jobv, &jobu, &n, &m, a, &n, s, v?(*v)[0]:0, &n,
u?(*u)[0]:0, &m, &work0, &lwork, &r);
delete[] work;
if (v && corder) v->transposeme();
if (r < 0) laerror("illegal argument in gesvd() of singular_decomposition()");
if (r > 0) laerror("convergence problem in gesvd() of ingular_decomposition()");
}
extern "C" void FORNAME(dgeev)(const char *JOBVL, const char *JOBVR, const int *N,
double *A, const int *LDA, double *WR, double *WI, double *VL, const int *LDVL,
double *VR, const int *LDVR, double *WORK, const int *LWORK, int *INFO );
void gdiagonalize(NRMat<double> &a, NRVec<double> &wr, NRVec<double> &wi,
NRMat<double> *vl, NRMat<double> *vr, const bool corder)
{
int n = a.nrows();
if (n != a.ncols()) laerror("gdiagonalize() call for a non-square matrix");
if (n != wr.size())
laerror("inconsistent dimension of eigen vector in gdiagonalize()");
if (vl) if (n != vl->nrows() || n != vl->ncols())
laerror("inconsistent dimension of vl in gdiagonalize()");
if (vr) if (n != vr->nrows() || n != vr->ncols())
laerror("inconsistent dimension of vr in gdiagonalize()");
a.copyonwrite();
wr.copyonwrite();
wi.copyonwrite();
if (vl) vl->copyonwrite();
if (vr) vr->copyonwrite();
char jobvl = vl ? 'V' : 'N';
char jobvr = vr ? 'V' : 'N';
double work0;
int lwork = -1;
int r;
FORNAME(dgeev)(&jobvr, &jobvl, &n, a, &n, wr, wi, vr?vr[0]:(double *)0,
&n, vl?vl[0]:(double *)0, &n, &work0, &lwork, &r);
lwork = (int) work0;
double *work = new double[lwork];
FORNAME(dgeev)(&jobvr, &jobvl, &n, a, &n, wr, wi, vr?vr[0]:(double *)0,
&n, vl?vl[0]:(double *)0, &n, &work0, &lwork, &r);
delete[] work;
if (corder) {
if (vl) vl->transposeme();
if (vr) vr->transposeme();
}
if (r < 0) laerror("illegal argument in geev() of gdiagonalize()");
if (r > 0) laerror("convergence problem in geev() of gdiagonalize()");
}
void gdiagonalize(NRMat<double> &a, NRVec< complex<double> > &w,
NRMat< complex<double> >*vl, NRMat< complex<double> > *vr)
{
int n = a.nrows();
if(n != a.ncols()) laerror("gdiagonalize() call for a non-square matrix");
NRVec<double> wr(n), wi(n);
NRMat<double> *rvl = 0;
NRMat<double> *rvr = 0;
if (vl) rvl = new NRMat<double>(n, n);
if (vr) rvr = new NRMat<double>(n, n);
gdiagonalize(a, wr, wi, rvl, rvr, 0);
//process the results into complex matrices
int i;
for (i=0; i<n; i++) w[i] = complex<double>(wr[i], wi[i]);
if (rvl || rvr) {
i = 0;
while (i < n) {
if (wi[i] == 0) {
if (vl) for (int j=0; j<n; j++) (*vl)[i][j] = (*rvl)[i][j];
if (vr) for (int j=0; j<n; j++) (*vr)[i][j] = (*rvr)[i][j];
i++;
} else {
if (vl)
for (int j=0; j<n; j++) {
(*vl)[i][j] = complex<double>((*rvl)[i][j], (*rvl)[i+1][j]);
(*vl)[i+1][j] = complex<double>((*rvl)[i][j], -(*rvl)[i+1][j]);
}
if (vr)
for (int j=0; j<n; j++) {
(*vr)[i][j] = complex<double>((*rvr)[i][j], (*rvr)[i+1][j]);
(*vr)[i+1][j] = complex<double>((*rvr)[i][j], -(*rvr)[i+1][j]);
}
i += 2;
}
}
}
if (rvl) delete rvl;
if (rvr) delete rvr;
}
const NRMat<double> realpart(const NRMat< complex<double> > &a)
{
NRMat<double> result(a.nrows(), a.ncols());
cblas_dcopy(a.nrows()*a.ncols(), (const double *)a[0], 2, result, 1);
return result;
}
const NRMat<double> imagpart(const NRMat< complex<double> > &a)
{
NRMat<double> result(a.nrows(), a.ncols());
cblas_dcopy(a.nrows()*a.ncols(), (const double *)a[0]+1, 2, result, 1);
return result;
}
const NRMat< complex<double> > realmatrix (const NRMat<double> &a)
{
NRMat <complex<double> > result(a.nrows(), a.ncols());
cblas_dcopy(a.nrows()*a.ncols(), a, 1, (double *)result[0], 2);
return result;
}
const NRMat< complex<double> > imagmatrix (const NRMat<double> &a)
{
NRMat< complex<double> > result(a.nrows(), a.ncols());
cblas_dcopy(a.nrows()*a.ncols(), a, 1, (double *)result[0]+1, 2);
return result;
}
NRMat<double> matrixfunction(NRMat<double> a, complex<double>
(*f)(const complex<double> &), const bool adjust)
{
int n = a.nrows();
NRMat< complex<double> > u(n, n), v(n, n);
NRVec< complex<double> > w(n);
gdiagonalize(a, w, &u, &v);
NRVec< complex<double> > z = diagofproduct(u, v, 1, 1);
for (int i=0; i<a.nrows(); i++) w[i] = (*f)(w[i]/z[i]);
u.diagmultl(w);
NRMat< complex<double> > r(n, n);
r.gemm(0.0, v, 'c', u, 'n', 1.0);
double inorm = cblas_dnrm2(n*n, (double *)r[0]+1, 2);
if (inorm > 1e-10) {
cout << "norm = " << inorm << endl;
laerror("nonzero norm of imaginary part of real matrixfunction");
}
return realpart(r);
}
NRMat<double> matrixfunction(NRSMat<double> a, double (*f) (double))
{
int n = a.nrows();
NRVec<double> w(n);
NRMat<double> v(n, n);
diagonalize(a, w, &v, 0);
for (int i=0; i<a.nrows(); i++) w[i] = (*f)(w[i]);
NRMat<double> u = v;
v.diagmultl(w);
NRMat<double> r(n, n);
r.gemm(0.0, u, 't', v, 'n', 1.0);
return r;
}
// instantize template to an addresable function
complex<double> myclog (const complex<double> &x)
{
return log(x);
}
NRMat<double> log(const NRMat<double> &a)
{
return matrixfunction(a, &myclog, 1);
}
const NRVec<double> diagofproduct(const NRMat<double> &a, const NRMat<double> &b,
bool trb, bool conjb)
{
if (trb && (a.nrows() != b.nrows() || a.ncols() != b.ncols()) ||
!trb && (a.nrows() != b.ncols() || a.ncols() != b.nrows()))
laerror("incompatible Mats in diagofproduct<double>()");
NRVec<double> result(a.nrows());
if (trb)
for(int i=0; i<a.nrows(); i++)
result[i] = cblas_ddot(a.ncols(), a[i], 1, b[i], 1);
else
for(int i=0; i<a.nrows(); i++)
result[i] = cblas_ddot(a.ncols(), a[i], 1, b[0]+i, b.ncols());
return result;
}
const NRVec< complex<double> > diagofproduct(const NRMat< complex<double> > &a,
const NRMat< complex<double> > &b, bool trb, bool conjb)
{
if (trb && (a.nrows() != b.nrows() || a.ncols() != b.ncols()) ||
!trb && (a.nrows() != b.ncols() || a.ncols() != b.nrows()))
laerror("incompatible Mats in diagofproduct<complex>()");
NRVec< complex<double> > result(a.nrows());
if (trb) {
if (conjb) {
for(int i=0; i<a.nrows(); i++)
cblas_zdotc_sub(a.ncols(), b[i], 1, a[i], 1, &result[i]);
} else {
for(int i=0; i<a.nrows(); i++)
cblas_zdotu_sub(a.ncols(), b[i], 1, a[i], 1, &result[i]);
}
} else {
if (conjb) {
for(int i=0; i<a.nrows(); i++)
cblas_zdotc_sub(a.ncols(), b[0]+i, b.ncols(), a[i], 1, &result[i]);
} else {
for(int i=0; i<a.nrows(); i++)
cblas_zdotu_sub(a.ncols(), b[0]+i, b.ncols(), a[i], 1, &result[i]);
}
}
return result;
}
double trace2(const NRMat<double> &a, const NRMat<double> &b, bool trb)
{
if (trb && (a.nrows() != b.nrows() || a.ncols() != b.ncols()) ||
!trb && (a.nrows() != b.ncols() || a.ncols() != b.nrows()))
laerror("incompatible Mats in diagofproduct<complex>()");
if (trb) return cblas_ddot(a.nrows()*a.ncols(), a, 1, b, 1);
double sum = 0.0;
for (int i=0; i<a.nrows(); i++)
sum += cblas_ddot(a.ncols(), a[i], 1, b[0]+i, b.ncols());
return sum;
}
double trace2(const NRSMat<double> &a, const NRSMat<double> &b,
const bool diagscaled)
{
if (a.nrows() != b.nrows()) laerror("incompatible SMats in trace2()");
double r = 2.0*cblas_ddot(a.nrows()*(a.nrows()+1)/2, a, 1, b, 1);
if (diagscaled) return r;
for (int i=0; i<a.nrows(); i++) r -= a(i,i)*b(i,i);
return r;
}