Mercurial > octave
diff src/DLD-FUNCTIONS/qz.cc @ 3185:9580887dd160
[project @ 1998-09-26 02:45:55 by jwe]
author | jwe |
---|---|
date | Sat, 26 Sep 1998 02:45:59 +0000 |
parents | 5edc539c2f80 |
children | 3d3eca53ecca |
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--- a/src/DLD-FUNCTIONS/qz.cc Fri Sep 25 04:35:09 1998 +0000 +++ b/src/DLD-FUNCTIONS/qz.cc Sat Sep 26 02:45:59 1998 +0000 @@ -47,61 +47,77 @@ #include "oct-map.h" #include "ov.h" #include "pager.h" -#if defined(DEBUG) || defined(DEBUG_SORT) +#if defined (DEBUG) || defined (DEBUG_SORT) #include "pr-output.h" #endif #include "symtab.h" #include "utils.h" #include "variables.h" -typedef int (*sort_function) (const int& LSIZE, const double& ALPHA, - const double& BETA, const double& S, const double& P); +typedef int (*sort_function) (const int& LSIZE, const double& ALPHA, + const double& BETA, const double& S, + const double& P); extern "C" { - int F77_FCN( dggbal, DGGBAL) (const char* JOB, const int& N, - double* A, const int& LDA, double* B, const int& LDB, - int& ILO, int & IHI, double* LSCALE, - double* RSCALE, double* WORK, int& INFO, long ); + int F77_FCN (dggbal, DGGBAL) (const char* JOB, const int& N, + double* A, const int& LDA, double* B, + const int& LDB, int& ILO, int& IHI, + double* LSCALE, double* RSCALE, + double* WORK, int& INFO, long); - int F77_FCN( dggbak, DGGBAK) (const char* JOB, const char* SIDE, - const int& N, const int& ILO, const int& IHI, - double* LSCALE, double* RSCALE, int& M, - double* V, const int& LDV, int& INFO, long, long); + int F77_FCN (dggbak, DGGBAK) (const char* JOB, const char* SIDE, + const int& N, const int& ILO, + const int& IHI, double* LSCALE, + double* RSCALE, int& M, double* V, + const int& LDV, int& INFO, long, long); - int F77_FCN( dgghrd, DGGHRD) ( const char* COMPQ, const char* COMPZ, - const int& N, const int& ILO, const int& IHI, double* A, const int& LDA, - double* B, const int& LDB, double* Q, const int& LDQ, double* Z, - const int& LDZ, int& INFO, const long, const long); + int F77_FCN (dgghrd, DGGHRD) (const char* COMPQ, const char* COMPZ, + const int& N, const int& ILO, + const int& IHI, double* A, + const int& LDA, double* B, + const int& LDB, double* Q, + const int& LDQ, double* Z, + const int& LDZ, int& INFO, long, long); - int F77_FCN( dhgeqz, DHGEQZ) ( const char* JOB, const char* COMPQ, - const char* COMPZ, const int& N, const int& ILO, const int& IHI, - double* A, const int& LDA, double* B, const int& LDB, - double* ALPHAR, double* ALPHAI, double* BETA, double* Q, - const int& LDQ, double* Z, const int& LDZ, double* WORK, - const int& LWORK, int& INFO, const long, const long, const long ); + int F77_FCN (dhgeqz, DHGEQZ) (const char* JOB, const char* COMPQ, + const char* COMPZ, const int& N, + const int& ILO, const int& IHI, + double* A, const int& LDA, double* B, + const int& LDB, double* ALPHAR, + double* ALPHAI, double* BETA, double* Q, + const int& LDQ, double* Z, + const int& LDZ, double* WORK, + const int& LWORK, int& INFO, + long, long, long); - int F77_FCN( dlag2, DLAG2) ( double* A, const int& LDA, double* B, - const int& LDB, const double& SAFMIN, double& SCALE1, double& SCALE2, - double& WR1, double& WR2, double& WI ); + int F77_FCN (dlag2, DLAG2) (double* A, const int& LDA, double* B, + const int& LDB, const double& SAFMIN, + double& SCALE1, double& SCALE2, + double& WR1, double& WR2, double& WI); // Van Dooren's code (netlib.org: toms/590) for reordering // GEP. Only processes Z, not Q. - int F77_FCN( dsubsp, DSUBSP) ( const int& NMAX, const int& N, double* A, - double* B, double* Z, sort_function, const double& EPS, - int& NDIM, int& FAIL, int* IND); + int F77_FCN (dsubsp, DSUBSP) (const int& NMAX, const int& N, double* A, + double* B, double* Z, sort_function, + const double& EPS, int& NDIM, int& FAIL, + int* IND); // documentation for DTGEVC incorrectly states that VR, VL are // complex*16; they are declared in DTGEVC as double precision // (probably a cut and paste problem fro ZTGEVC) - int F77_FCN( dtgevc, DTGEVC) ( const char* SIDE, const char* HOWMNY, - int* SELECT, const int& N, double* A, const int& LDA, double* B, - const int& LDB, double* VL, const int& LDVL, double* VR, - const int& LDVR, const int& MM, int& M, double* WORK, int& INFO, - long, long ); + int F77_FCN (dtgevc, DTGEVC) (const char* SIDE, const char* HOWMNY, + int* SELECT, const int& N, double* A, + const int& LDA, double* B, + const int& LDB, double* VL, + const int& LDVL, double* VR, + const int& LDVR, const int& MM, + int& M, double* WORK, int& INFO, + long, long); - int F77_FCN ( xdlamch, XDLAMCH) (const char* cmach, double& retval, long); - int F77_FCN ( xdlange, XDLANGE) (const char*, const int&, + int F77_FCN (xdlamch, XDLAMCH) (const char* cmach, double& retval, long); + + int F77_FCN (xdlange, XDLANGE) (const char*, const int&, const int&, const double*, const int&, double*, double&); } @@ -114,64 +130,79 @@ // fcrhp: real(lambda) >= 0 // folhp: real(lambda) < 0 -static int fcrhp(const int& lsize, const double& alpha, - const double& beta, const double& s, const double& p) +static int +fcrhp (const int& lsize, const double& alpha, + const double& beta, const double& s, const double&) { - if(lsize == 1) + if (lsize == 1) return (alpha*beta >= 0 ? 1 : -1); - else + else return (s >= 0 ? 1 : -1); } -static int fin(const int& lsize, const double& alpha, - const double& beta, const double& s, const double& p) + +static int +fin (const int& lsize, const double& alpha, + const double& beta, const double&, const double& p) { int retval; - if(lsize == 1) - retval = (fabs(alpha) < fabs(beta) ? 1 : -1); - else - retval = (fabs(p) < 1 ? 1 : -1); - #ifdef DEBUG + if (lsize == 1) + retval = (fabs (alpha) < fabs (beta) ? 1 : -1); + else + retval = (fabs (p) < 1 ? 1 : -1); + +#ifdef DEBUG cout << "qz: fin: retval=" << retval << endl; - #endif +#endif + return retval; } -static int folhp(const int& lsize, const double& alpha, - const double& beta, const double& s, const double& p) + +static int +folhp (const int& lsize, const double& alpha, + const double& beta, const double& s, const double&) { - if(lsize == 1) + if (lsize == 1) return (alpha*beta < 0 ? 1 : -1); - else + else return (s < 0 ? 1 : -1); } -static int fout(const int& lsize, const double& alpha, - const double& beta, const double& s, const double& p) + +static int +fout (const int& lsize, const double& alpha, + const double& beta, const double&, const double& p) { - if(lsize == 1) - return (fabs(alpha) >= fabs(beta) ? 1 : -1); - else - return (fabs(p) >= 1 ? 1 : -1); + if (lsize == 1) + return (fabs (alpha) >= fabs (beta) ? 1 : -1); + else + return (fabs (p) >= 1 ? 1 : -1); } DEFUN_DLD (qz, args, nargout, -"Usage: lambda = qz(A,B) form [1]\n\ - [AA,BB,Q,Z{,V,W,lambda}] = qz(A,B) form [2]\n\ - [AA,BB,Z{,lambda}] = qz(A,B,opt) form [3]\n\ +"Usage:\n\ + + lambda = qz (A, B) form [1]\n\ + [AA, BB, Q, Z {, V, W, lambda}] = qz (A, B) form [2]\n\ + [AA, BB, Z{, lambda}] = qz (A, B, opt) form [3]\n\ +\n\ Generalized eigenvalue problem A x = s B x \n\ - +\n\ Form [1]: Computes the generalized eigenvalues lambda of (A - sB).\n\ +\n\ Form [2]: Computes qz decomposition, generalized eigenvectors, and \n\ - generalized eigenvalues of (A - sB)\n\ - A V = B V diag(lambda)\n\ - W' A = diag(lambda) W' B\n\ - AA = Q'*A*Z, BB = Q'*B*Z with Q, Z orthogonal (unitary)= I\n\ + generalized eigenvalues of (A - sB)\n\ + A V = B V diag (lambda)\n\ + W' A = diag (lambda) W' B\n\ + AA = Q'*A*Z, BB = Q'*B*Z with Q, Z orthogonal (unitary)= I\n\ +\n\ Form [3]: As in form [2], but allows ordering of generalized eigenpairs\n\ - for (e.g.) solution of discrete time algebraic Riccati equations.\n\ - Form 3 is not available for complex matrices and does not compute\n\ - the generalized eigenvectors V, W, nor the orthogonal matrix Q.\n\ + for (e.g.) solution of discrete time algebraic Riccati equations.\n\ + Form 3 is not available for complex matrices and does not compute\n\ + the generalized eigenvectors V, W, nor the orthogonal matrix Q.\n\ \n\ - opt: for ordering eigenvalues of the GEP pencil. The leading block\n\ - of the revised pencil contains all eigenvalues that satisfy:\n\ + opt: for ordering eigenvalues of the GEP pencil. The leading block\n\ + of the revised pencil contains all eigenvalues that satisfy:\n\ +\n\ \"N\" = unordered (default) \n\ \"S\" = small: leading block has all |lambda| <=1 \n\ \"B\" = big: leading block has all |lambda >= 1 \n\ @@ -183,586 +214,705 @@ Note: Permutation balancing is performed, but not scaling (see balance)\n\ Order of output arguments was selected for compatibility with MATLAB\n\ \n\ -See also: balance, dare, eig, schur\n") +See also: balance, dare, eig, schur") { octave_value_list retval; int nargin = args.length (); - #ifdef DEBUG +#ifdef DEBUG cout << "qz: nargin = " << nargin << ", nargout = " << nargout << endl; - #endif +#endif - if (nargin < 2 || nargin > 3 || nargout > 7 ) - { - print_usage ("qz"); - return retval; - } - else if(nargin == 3 && (nargout < 3 || nargout > 4)) - { - error("qz: Illegal number of output arguments for form [3] call"); - } + if (nargin < 2 || nargin > 3 || nargout > 7) + { + print_usage ("qz"); + return retval; + } + else if (nargin == 3 && (nargout < 3 || nargout > 4)) + { + error ("qz: Illegal number of output arguments for form [3] call"); + return retval; + } - #ifdef DEBUG +#ifdef DEBUG cout << "qz: determine ordering option" << endl; - #endif +#endif // Determine ordering option string ord_job; static double safmin; - if(nargin == 2) + + if (nargin == 2) ord_job = "N"; - else if( !args(2).is_string() ) - error("qz: argument 3 must be a string"); - else - { - ord_job = args(2).string_value(); - if(ord_job[0] != 'N' && ord_job[0] != 'S' && ord_job[0] != 'B' - && ord_job[0] != '+' && ord_job[0] != '-') - error("qz: illegal order option"); + else if (!args(2).is_string ()) + { + error ("qz: argument 3 must be a string"); + return retval; + } + else + { + ord_job = args(2).string_value (); - // overflow constant required by dlag2 - F77_XFCN ( xdlamch, XDLAMCH, ("S", safmin, 1L)); - - #ifdef DEBUG_EIG - cout << "qz: initial value of safmin=" << setiosflags(ios::scientific) - << safmin << endl; - #endif + if (ord_job[0] != 'N' + && ord_job[0] != 'S' + && ord_job[0] != 'B' + && ord_job[0] != '+' + && ord_job[0] != '-') + { + error ("qz: illegal order option"); + return retval; + } + + // overflow constant required by dlag2 + F77_FCN (xdlamch, XDLAMCH) ("S", safmin, 1L); - // some machines (e.g., DEC alpha) get safmin = 0; - // for these, use eps instead to avoid problems in dlag2 - if(safmin == 0) - { - #ifdef DEBUG_EIG - cout << "qz: DANGER WILL ROBINSON: safmin is 0!" << endl; - #endif +#ifdef DEBUG_EIG + cout << "qz: initial value of safmin=" << setiosflags (ios::scientific) + << safmin << endl; +#endif - F77_XFCN ( xdlamch, XDLAMCH, ("E", safmin, 1L)); + // some machines (e.g., DEC alpha) get safmin = 0; + // for these, use eps instead to avoid problems in dlag2 + if (safmin == 0) + { +#ifdef DEBUG_EIG + cout << "qz: DANGER WILL ROBINSON: safmin is 0!" << endl; +#endif - #ifdef DEBUG_EIG - cout << "qz: safmin set to " << setiosflags(ios::scientific) - << safmin << endl; - #endif + F77_FCN (xdlamch, XDLAMCH) ("E", safmin, 1L); + +#ifdef DEBUG_EIG + cout << "qz: safmin set to " << setiosflags (ios::scientific) + << safmin << endl; +#endif + } } - } - #ifdef DEBUG +#ifdef DEBUG cout << "qz: check argument 1" << endl; - #endif +#endif // Argument 1: check if it's o.k. dimensioned - int nn = args(0).rows(); - - #ifdef DEBUG - cout << "argument 1 dimensions: (" << nn << "," << args(0).columns() << ")" - << endl; - #endif - int arg_is_empty = empty_arg ("qz", nn, args(0).columns()); + int nn = args(0).rows (); + +#ifdef DEBUG + cout << "argument 1 dimensions: (" << nn << "," << args(0).columns () << ")" + << endl; +#endif + + int arg_is_empty = empty_arg ("qz", nn, args(0).columns ()); + if (arg_is_empty < 0) - { - gripe_empty_arg("qz: parameter 1",0); - return retval; - } + { + gripe_empty_arg ("qz: parameter 1", 0); + return retval; + } else if (arg_is_empty > 0) - { - gripe_empty_arg("qz: parameter 1; continuing",0); - return octave_value_list (2, Matrix ()); - } - else if (args(0).columns() != nn) - { - gripe_square_matrix_required ("qz"); - return retval; - } + { + gripe_empty_arg ("qz: parameter 1; continuing", 0); + return octave_value_list (2, Matrix ()); + } + else if (args(0).columns () != nn) + { + gripe_square_matrix_required ("qz"); + return retval; + } // Argument 1: dimensions look good; get the value Matrix aa; ComplexMatrix caa; - if (args(0).is_complex_type ()) + + if (args(0).is_complex_type ()) caa = args(0).complex_matrix_value (); - else + else aa = args(0).matrix_value (); - if (error_state) + + if (error_state) return retval; - #ifdef DEBUG +#ifdef DEBUG cout << "qz: check argument 2" << endl; - #endif +#endif // Extract argument 2 (bb, or cbb if complex) - if( (nn != args(1).columns()) || (nn != args(1).rows() )) - { - gripe_nonconformant (); - return retval; - } + if ((nn != args(1).columns ()) || (nn != args(1).rows ())) + { + gripe_nonconformant (); + return retval; + } + Matrix bb; ComplexMatrix cbb; - if (args(1).is_complex_type ()) + + if (args(1).is_complex_type ()) cbb = args(1).complex_matrix_value (); else bb = args(1).matrix_value (); - if (error_state) + + if (error_state) return retval; // Both matrices loaded, now let's check what kind of arithmetic: //declared static to avoid compiler warnings about long jumps, vforks. - static int complex_case - = (args(0).is_complex_type() || args(1).is_complex_type()); + + static int complex_case + = (args(0).is_complex_type () || args(1).is_complex_type ()); - if(nargin == 3 && complex_case) - error("qz: cannot re-order complex qz decomposition."); + if (nargin == 3 && complex_case) + { + error ("qz: cannot re-order complex qz decomposition."); + return retval; + } // first, declare variables used in both the real and complex case Matrix QQ(nn,nn), ZZ(nn,nn), VR(nn,nn), VL(nn,nn); RowVector alphar(nn), alphai(nn), betar(nn); - ComplexMatrix CQ(nn,nn), CZ(nn,nn),CVR(nn,nn),CVL(nn,nn); + ComplexMatrix CQ(nn,nn), CZ(nn,nn), CVR(nn,nn), CVL(nn,nn); int ilo, ihi, info; - char compq = (nargout >= 3 ? 'V' : 'N'), - compz = (nargout >= 4 ? 'V' : 'N'); + char compq = (nargout >= 3 ? 'V' : 'N'); + char compz = (nargout >= 4 ? 'V' : 'N'); - // initialize Q,Z to identity if we need either of them - if(compq == 'V' || compz == 'V') - for(int ii=0; ii < nn ; ii++) - for( int jj=0; jj < nn ; jj++) + // initialize Q, Z to identity if we need either of them + if (compq == 'V' || compz == 'V') + for (int ii = 0; ii < nn; ii++) + for (int jj = 0; jj < nn; jj++) QQ(ii,jj) = ZZ(ii,jj) = (ii == jj ? 1.0 : 0.0); - // always perform permutation balancing + // always perform permutation balancing char bal_job = 'P'; RowVector lscale(nn), rscale(nn), work(6*nn); - if(complex_case) - error("Complex case not implemented yet"); + if (complex_case) + { + error ("Complex case not implemented yet"); + return retval; + } else - { - #ifdef DEBUG - if(compq == 'V') - cout << "qz: performing balancing; QQ=" << endl << QQ << endl; - #endif + { +#ifdef DEBUG + if (compq == 'V') + cout << "qz: performing balancing; QQ=" << endl << QQ << endl; +#endif - F77_XFCN( dggbal, DGGBAL, (&bal_job, nn, aa.fortran_vec(), - nn, bb.fortran_vec() , nn, ilo, ihi, lscale.fortran_vec(), - rscale.fortran_vec(), work.fortran_vec(), info , 1L)); - if(f77_exception_encountered) - (*current_liboctave_error_handler) ("unrecoverable error in qz(bal)"); - } + F77_XFCN (dggbal, DGGBAL, + (&bal_job, nn, aa.fortran_vec(), nn, bb.fortran_vec(), + nn, ilo, ihi, lscale.fortran_vec(), + rscale.fortran_vec(), work.fortran_vec(), info, 1L)); + + if (f77_exception_encountered) + { + error ("unrecoverable error in qz (bal)"); + return retval; + } + } // Since we just want the balancing matrices, we can use dggbal // for both the real and complex cases; // left first - if(compq == 'V') - { - F77_XFCN( dggbak, DGGBAK, (&bal_job, "L", - nn, ilo, ihi, lscale.fortran_vec(), - rscale.fortran_vec(), nn, QQ.fortran_vec(), - nn, info, 1L, 1L)); + + if (compq == 'V') + { + F77_XFCN (dggbak, DGGBAK, + (&bal_job, "L", nn, ilo, ihi, lscale.fortran_vec(), + rscale.fortran_vec(), nn, QQ.fortran_vec(), + nn, info, 1L, 1L)); - #ifdef DEBUG - if(compq == 'V') cout << "qz: balancing done; QQ=" << endl << QQ << endl; - #endif +#ifdef DEBUG + if (compq == 'V') + cout << "qz: balancing done; QQ=" << endl << QQ << endl; +#endif - if(f77_exception_encountered) - (*current_liboctave_error_handler) ("unrecoverable error in qz(bal-L)"); + if (f77_exception_encountered) + { + error ("unrecoverable error in qz (bal-L)"); + return retval; + } } // then right - if(compz == 'V') - { - F77_XFCN(dggbak, DGGBAK, (&bal_job, "R", - nn, ilo, ihi, lscale.fortran_vec(), - rscale.fortran_vec(), nn, ZZ.fortran_vec(), - nn, info, 1L, 1L)); + if (compz == 'V') + { + F77_XFCN (dggbak, DGGBAK, (&bal_job, "R", + nn, ilo, ihi, lscale.fortran_vec(), + rscale.fortran_vec(), nn, ZZ.fortran_vec(), + nn, info, 1L, 1L)); - #ifdef DEBUG - if(compz == 'V') cout << "qz: balancing done; ZZ=" << endl << ZZ << endl; - #endif +#ifdef DEBUG + if (compz == 'V') + cout << "qz: balancing done; ZZ=" << endl << ZZ << endl; +#endif - if(f77_exception_encountered) - (*current_liboctave_error_handler) ("unrecoverable error in qz(bal-R)"); - } + if (f77_exception_encountered) + { + error ("unrecoverable error in qz (bal-R)"); + return retval; + } + } static char qz_job; qz_job = (nargout < 2 ? 'E' : 'S'); + if (complex_case) - { - // complex case - if (args(0).is_real_type ()) caa = aa; - if (args(1).is_real_type ()) cbb = bb; - if(compq == 'V') CQ = QQ; - if(compz == 'V') CZ = ZZ; - error("complex case not done yet"); - } + { + // complex case + if (args(0).is_real_type ()) + caa = aa; + + if (args(1).is_real_type ()) + cbb = bb; + + if (compq == 'V') + CQ = QQ; + + if (compz == 'V') + CZ = ZZ; + + error ("complex case not done yet"); + return retval; + } else // real matrices case - { - #ifdef DEBUG - cout << "qz: peforming qr decomposition of bb" << endl; - #endif + { +#ifdef DEBUG + cout << "qz: peforming qr decomposition of bb" << endl; +#endif - // compute the QR factorization of bb - QR bqr(bb); + // compute the QR factorization of bb + QR bqr (bb); + +#ifdef DEBUG + cout << "qz: qr (bb) done; now peforming qz decomposition" << endl; +#endif - #ifdef DEBUG - cout << "qz: qr(bb) done; now peforming qz decomposition" << endl; - #endif + bb = bqr.R (); + +#ifdef DEBUG + cout << "qz: extracted bb" << endl; +#endif - bb = bqr.R(); - #ifdef DEBUG - cout << "qz: extracted bb" << endl; - #endif + aa = (bqr.Q ()).transpose ()*aa; + +#ifdef DEBUG + cout << "qz: updated aa " << endl; + cout << "bqr.Q () = " << endl << bqr.Q () << endl; - aa = (bqr.Q()).transpose()*aa; - #ifdef DEBUG - cout << "qz: updated aa " << endl; - cout << "bqr.Q () = " << endl << bqr.Q () << endl; - if(compq == 'V') cout << "QQ =" << QQ << endl; - #endif + if (compq == 'V') + cout << "QQ =" << QQ << endl; +#endif - if(compq == 'V') QQ = QQ*bqr.Q(); + if (compq == 'V') + QQ = QQ*bqr.Q (); - #ifdef DEBUG - cout << "qz: precursors done..." << endl; - #endif +#ifdef DEBUG + cout << "qz: precursors done..." << endl; +#endif +#ifdef DEBUG + cout << "qz: compq = " << compq << ", compz = " << compz << endl; +#endif - #ifdef DEBUG - cout << "qz: compq = " << compq << ", compz = " << compz << endl; - #endif + // reduce to generalized hessenberg form + F77_XFCN (dgghrd, DGGHRD, + (&compq, &compz, nn, ilo, ihi, aa.fortran_vec(), + nn, bb.fortran_vec(), nn, QQ.fortran_vec(), nn, + ZZ.fortran_vec(), nn, info, 1L, 1L)); - // reduce to generalized hessenberg form - F77_XFCN( dgghrd, DGGHRD, (&compq, &compz, nn, ilo, ihi, aa.fortran_vec(), - nn, bb.fortran_vec(), nn, QQ.fortran_vec(), nn, ZZ.fortran_vec(), - nn, info,1L,1L)); - if(f77_exception_encountered) - (*current_liboctave_error_handler) ("unrecoverable error in qz(dgghrd)"); + if (f77_exception_encountered) + { + error ("unrecoverable error in qz (dgghrd)"); + return retval; + } - // check if just computing generalized eigenvalues or if we're - // actually computing the decomposition + // check if just computing generalized eigenvalues or if we're + // actually computing the decomposition - // reduce to generalized Schur form - F77_XFCN( dhgeqz, DHGEQZ, ( &qz_job, &compq, &compz, nn, ilo, ihi, - aa.fortran_vec(), nn, bb.fortran_vec(), nn, alphar.fortran_vec(), - alphai.fortran_vec(), betar.fortran_vec(), QQ.fortran_vec(), - nn, ZZ.fortran_vec(), nn, work.fortran_vec(), nn, info, 1L, 1L, 1L)); - if(f77_exception_encountered) - (*current_liboctave_error_handler) ("unrecoverable error in qz(dhgeqz)"); + // reduce to generalized Schur form + F77_XFCN (dhgeqz, DHGEQZ, + (&qz_job, &compq, &compz, nn, ilo, ihi, + aa.fortran_vec(), nn, bb.fortran_vec(), nn, + alphar.fortran_vec(), alphai.fortran_vec(), + betar.fortran_vec(), QQ.fortran_vec(), nn, + ZZ.fortran_vec(), nn, work.fortran_vec(), nn, info, + 1L, 1L, 1L)); - } + if (f77_exception_encountered) + { + error ("unrecoverable error in qz (dhgeqz)"); + return retval; + } + } // order the QZ decomposition? - if(ord_job[0] != 'N') - { - if(complex_case) // probably not needed, but better be safe - error("qz: cannot re-order complex qz decomposition."); - - else + if (ord_job[0] != 'N') { - #ifdef DEBUG_SORT - cout << "qz: ordering eigenvalues: ord_job = " << ord_job[0] << endl; - #endif + if (complex_case) + { + // probably not needed, but better be safe + error ("qz: cannot re-order complex qz decomposition."); + return retval; + } + else + { +#ifdef DEBUG_SORT + cout << "qz: ordering eigenvalues: ord_job = " << ord_job[0] << endl; +#endif - // declared static to avoid vfork/long jump compiler complaints - static sort_function sort_test; - sort_test = NULL; - - switch(ord_job[0]) - { - case 'S': - sort_test = &fin; - break; - case 'B': - sort_test = &fout; - break; - case '+': - sort_test = &fcrhp; - break; - case '-': - sort_test = &folhp; - break; - default: // this should never happen - error("qz: illegal order option"); - } - - int ndim, fail, ind[nn]; - double inf_norm; - F77_XFCN (xdlange, XDLANGE, ("I", nn, nn, aa.fortran_vec (), nn, - work.fortran_vec (), inf_norm)); - - double eps = DBL_EPSILON*inf_norm*nn; - - #ifdef DEBUG_SORT - cout << "qz: calling dsubsp: aa=" << endl; - octave_print_internal(cout,aa,0); - cout << endl << "bb=" << endl; - octave_print_internal(cout,bb,0); - if(compz == 'V') - { - cout << endl << "ZZ=" << endl; - octave_print_internal(cout,ZZ,0); - } - cout << endl; - cout << "alphar = " << endl; - octave_print_internal(cout,(Matrix) alphar,0); - cout << endl << "alphai = " << endl; - octave_print_internal(cout,(Matrix) alphai,0); - cout << endl << "beta = " << endl; - octave_print_internal(cout,(Matrix) betar,0); - cout << endl; - #endif - - F77_XFCN( dsubsp, DSUBSP, (nn,nn,aa.fortran_vec(), bb.fortran_vec(), - ZZ.fortran_vec(), sort_test, eps, ndim, fail, ind)); + // declared static to avoid vfork/long jump compiler complaints + static sort_function sort_test; + sort_test = NULL; - #ifdef DEBUG - cout << "qz: back from dsubsp: aa=" << endl; - octave_print_internal(cout,aa,0); - cout << endl << "bb=" << endl; - octave_print_internal(cout,bb,0); - if(compz == 'V') - { - cout << endl << "ZZ=" << endl; - octave_print_internal(cout,ZZ,0); - } - cout << endl; - #endif + switch (ord_job[0]) + { + case 'S': + sort_test = &fin; + break; - // manually update alphar, alphai, betar - static int jj; - jj=0; - while(jj < nn) - { - #ifdef DEBUG_EIG - cout << "computing gen eig #" << jj << endl; - #endif - - static int zcnt; // number of zeros in this block - if(jj == (nn-1)) - zcnt = 1; - else if(aa(jj+1,jj) == 0) - zcnt = 1; - else zcnt = 2; - - if(zcnt == 1) // real zero - { - #ifdef DEBUG_EIG - cout << " single gen eig:" << endl; - cout << " alphar(" << jj << ") = " << aa(jj,jj) << endl; - cout << " betar( " << jj << ") = " << bb(jj,jj) << endl; - cout << " alphai(" << jj << ") = 0" << endl; - #endif + case 'B': + sort_test = &fout; + break; - alphar(jj) = aa(jj,jj); - alphai(jj) = 0; - betar(jj) = bb(jj,jj); - } - else // complex conjugate pair - { - #ifdef DEBUG_EIG - cout << "qz: calling dlag2:" << endl; - cout << "safmin=" << setiosflags(ios::scientific) << safmin << endl; - for(int idr = jj ; idr <= jj+1 ; idr++) - { - for(int idc = jj ; idc <= jj+1 ; idc++) - { - cout << "aa(" << idr << "," << idc << ")=" - << aa(idr,idc) << endl; - cout << "bb(" << idr << "," << idc << ")=" - << bb(idr,idc) << endl; - } - } - #endif - double scale1, scale2, wr1, wr2, wi; - F77_XFCN( dlag2, DLAG2, ( &aa(jj,jj), nn, &bb(jj,jj), nn, safmin, - scale1, scale2, wr1, wr2, wi)); + case '+': + sort_test = &fcrhp; + break; - #ifdef DEBUG_EIG - cout << "dlag2 returns: scale1=" << scale1 - << "\tscale2=" << scale2 << endl - << "\twr1=" << wr1 << "\twr2=" << wr2 - << "\twi=" << wi << endl; - #endif - // just to be safe, check if it's a real pair - if(wi == 0) - { - alphar(jj) = wr1; - alphai(jj) = 0; - betar(jj) = scale1; - alphar(jj+1) = wr2; - alphai(jj+1) = 0; - betar(jj+1) = scale2; - } - else - { - alphar(jj) = alphar(jj+1)=wr1; - alphai(jj) = -(alphai(jj+1) = wi); - betar(jj) = betar(jj+1) = scale1; - } - } - - jj += zcnt; // advance past this block + case '-': + sort_test = &folhp; + break; + + default: + // illegal order option (should never happen, since we + // checked the options at the top). + panic_impossible (); + break; } - #ifdef DEBUG_SORT - cout << "qz: back from dsubsp: aa=" << endl; - octave_print_internal(cout,aa,0); - cout << endl << "bb=" << endl; - octave_print_internal(cout,bb,0); - if(compz == 'V') - { - cout << endl << "ZZ=" << endl; - octave_print_internal(cout,ZZ,0); - } - cout << endl << "qz: ndim=" << ndim << endl << "fail=" << fail << endl; - cout << "alphar = " << endl; - octave_print_internal(cout,(Matrix) alphar,0); - cout << endl << "alphai = " << endl; - octave_print_internal(cout,(Matrix) alphai,0); - cout << endl << "beta = " << endl; - octave_print_internal(cout,(Matrix) betar,0); - cout << endl; - #endif + int ndim, fail, ind[nn]; + double inf_norm; + + F77_XFCN (xdlange, XDLANGE, + ("I", nn, nn, aa.fortran_vec (), nn, + work.fortran_vec (), inf_norm)); + + double eps = DBL_EPSILON*inf_norm*nn; + +#ifdef DEBUG_SORT + cout << "qz: calling dsubsp: aa=" << endl; + octave_print_internal (cout, aa, 0); + cout << endl << "bb=" << endl; + octave_print_internal (cout, bb, 0); + if (compz == 'V') + { + cout << endl << "ZZ=" << endl; + octave_print_internal (cout, ZZ, 0); + } + cout << endl; + cout << "alphar = " << endl; + octave_print_internal (cout, (Matrix) alphar, 0); + cout << endl << "alphai = " << endl; + octave_print_internal (cout, (Matrix) alphai, 0); + cout << endl << "beta = " << endl; + octave_print_internal (cout, (Matrix) betar, 0); + cout << endl; +#endif + + F77_XFCN (dsubsp, DSUBSP, + (nn, nn, aa.fortran_vec(), bb.fortran_vec(), + ZZ.fortran_vec(), sort_test, eps, ndim, fail, ind)); + +#ifdef DEBUG + cout << "qz: back from dsubsp: aa=" << endl; + octave_print_internal (cout, aa, 0); + cout << endl << "bb=" << endl; + octave_print_internal (cout, bb, 0); + if (compz == 'V') + { + cout << endl << "ZZ=" << endl; + octave_print_internal (cout, ZZ, 0); + } + cout << endl; +#endif + + // manually update alphar, alphai, betar + static int jj; + + jj=0; + while (jj < nn) + { +#ifdef DEBUG_EIG + cout << "computing gen eig #" << jj << endl; +#endif + + static int zcnt; // number of zeros in this block + + if (jj == (nn-1)) + zcnt = 1; + else if (aa(jj+1,jj) == 0) + zcnt = 1; + else zcnt = 2; + + if (zcnt == 1) // real zero + { +#ifdef DEBUG_EIG + cout << " single gen eig:" << endl; + cout << " alphar(" << jj << ") = " << aa(jj,jj) << endl; + cout << " betar( " << jj << ") = " << bb(jj,jj) << endl; + cout << " alphai(" << jj << ") = 0" << endl; +#endif + + alphar(jj) = aa(jj,jj); + alphai(jj) = 0; + betar(jj) = bb(jj,jj); + } + else + { + // complex conjugate pair +#ifdef DEBUG_EIG + cout << "qz: calling dlag2:" << endl; + cout << "safmin=" + << setiosflags (ios::scientific) << safmin << endl; + + for (int idr = jj; idr <= jj+1; idr++) + { + for (int idc = jj; idc <= jj+1; idc++) + { + cout << "aa(" << idr << "," << idc << ")=" + << aa(idr,idc) << endl; + cout << "bb(" << idr << "," << idc << ")=" + << bb(idr,idc) << endl; + } + } +#endif + + double scale1, scale2, wr1, wr2, wi; + F77_XFCN (dlag2, DLAG2, + (&aa(jj,jj), nn, &bb(jj,jj), nn, safmin, + scale1, scale2, wr1, wr2, wi)); + +#ifdef DEBUG_EIG + cout << "dlag2 returns: scale1=" << scale1 + << "\tscale2=" << scale2 << endl + << "\twr1=" << wr1 << "\twr2=" << wr2 + << "\twi=" << wi << endl; +#endif + + // just to be safe, check if it's a real pair + if (wi == 0) + { + alphar(jj) = wr1; + alphai(jj) = 0; + betar(jj) = scale1; + alphar(jj+1) = wr2; + alphai(jj+1) = 0; + betar(jj+1) = scale2; + } + else + { + alphar(jj) = alphar(jj+1)=wr1; + alphai(jj) = -(alphai(jj+1) = wi); + betar(jj) = betar(jj+1) = scale1; + } + } + + // advance past this block + jj += zcnt; + } + +#ifdef DEBUG_SORT + cout << "qz: back from dsubsp: aa=" << endl; + octave_print_internal (cout, aa, 0); + cout << endl << "bb=" << endl; + octave_print_internal (cout, bb, 0); + + if (compz == 'V') + { + cout << endl << "ZZ=" << endl; + octave_print_internal (cout, ZZ, 0); + } + cout << endl << "qz: ndim=" << ndim << endl + << "fail=" << fail << endl; + cout << "alphar = " << endl; + octave_print_internal (cout, (Matrix) alphar, 0); + cout << endl << "alphai = " << endl; + octave_print_internal (cout, (Matrix) alphai, 0); + cout << endl << "beta = " << endl; + octave_print_internal (cout, (Matrix) betar, 0); + cout << endl; +#endif + } } - } - + // compute generalized eigenvalues? ComplexColumnVector gev; - if(nargout < 2 || nargout == 7 || (nargin == 3 && nargout == 4)) - { - if(complex_case) - error("complex case not yet implemented"); - else + + if (nargout < 2 || nargout == 7 || (nargin == 3 && nargout == 4)) { - #ifdef DEBUG - cout << "qz: computing generalized eigenvalues" << endl; - #endif + if (complex_case) + { + error ("complex case not yet implemented"); + return retval; + } + else + { +#ifdef DEBUG + cout << "qz: computing generalized eigenvalues" << endl; +#endif - // return finite generalized eigenvalues - int ii, cnt = 0; - for( ii=0 ; ii < nn ; ii++) - if(betar(ii) != 0) - cnt++; - ComplexColumnVector tmp(cnt); - for( ii=0 ; ii < nn ; ii++) - if(betar(ii) != 0) - tmp(ii) = Complex(alphar(ii), alphai(ii))/betar(ii); - gev = tmp; + // return finite generalized eigenvalues + int cnt = 0; + + for (int ii = 0; ii < nn; ii++) + if (betar(ii) != 0) + cnt++; + + ComplexColumnVector tmp(cnt); + + for (int ii = 0; ii < nn; ii++) + if (betar(ii) != 0) + tmp(ii) = Complex(alphar(ii), alphai(ii))/betar(ii); + gev = tmp; + } } - } // right, left eigenvector matrices - if(nargout >= 5) - { - char side = (nargout == 5 ? 'R' : 'B'), // which side to compute? - howmny = 'B'; // compute all of them and backtransform - int *select = NULL; // dummy pointer; select is not used. - int m; - - if(complex_case) - error("complex type not yet implemented"); - else + if (nargout >= 5) { - #ifdef DEBUG - cout << "qz: computing generalized eigenvectors" << endl; - #endif + char side = (nargout == 5 ? 'R' : 'B'); // which side to compute? + char howmny = 'B'; // compute all of them and backtransform + int *select = NULL; // dummy pointer; select is not used. + int m; + + if (complex_case) + { + error ("complex type not yet implemented"); + return retval; + } + else + { +#ifdef DEBUG + cout << "qz: computing generalized eigenvectors" << endl; +#endif + + VL = QQ; + VR = ZZ; + + F77_XFCN (dtgevc, DTGEVC, + (&side, &howmny, select, nn, aa.fortran_vec(), + nn, bb.fortran_vec(), nn, VL.fortran_vec(), nn, + VR.fortran_vec(), nn, nn, m, work.fortran_vec(), + info, 1L, 1L)); + + if (f77_exception_encountered) + { + error ("unrecoverable error in qz (dtgevc)"); + return retval; + } - VL = QQ; - VR = ZZ; - - F77_XFCN( dtgevc, DTGEVC, ( &side, &howmny, select, nn, aa.fortran_vec(), - nn, bb.fortran_vec(), nn, VL.fortran_vec(), nn, VR.fortran_vec(), - nn, nn, m, work.fortran_vec(), info, 1L, 1L )); - if(f77_exception_encountered) - (*current_liboctave_error_handler) - ("unrecoverable error in qz(dtgevc)"); + // now construct the complex form of VV, WW + int jj = 0; + + while (jj < nn) + { + // see if real or complex eigenvalue + int cinc = 2; // column increment; assume complex eigenvalue + + if (jj == (nn-1)) + cinc = 1; // single column + else if (aa(jj+1,jj) == 0) + cinc = 1; + + // now copy the eigenvector (s) to CVR, CVL + if (cinc == 1) + { + for (int ii = 0; ii < nn; ii++) + CVR(ii,jj) = VR(ii,jj); + + if (side == 'B') + for (int ii = 0; ii < nn; ii++) + CVL(ii,jj) = VL(ii,jj); + } + else + { + // double column; complex vector + + for (int ii = 0; ii < nn; ii++) + { + CVR(ii,jj) = Complex (VR(ii,jj), VR(ii,jj+1)); + CVR(ii,jj+1) = Complex (VR(ii,jj), -VR(ii,jj+1)); + } - // now construct the complex form of VV, WW - int jj = 0; - while(jj < nn) - { - // see if real or complex eigenvalue - int cinc = 2; // column increment; assume complex eigenvalue - if(jj == (nn-1)) - cinc = 1; // single column - else if(aa(jj+1,jj) == 0) - cinc = 1; - - // now copy the eigenvector(s) to CVR, CVL - if(cinc == 1) - { - int ii; - for(ii = 0; ii < nn ; ii++) - CVR(ii,jj) = VR(ii,jj); - if(side == 'B') - for(ii = 0; ii < nn ; ii++) - CVL(ii,jj) = VL(ii,jj); - } - else // double column; complex vector - { - int ii; - for(ii = 0; ii < nn ; ii++) - { - CVR(ii,jj) = Complex(VR(ii,jj),VR(ii,jj+1)); - CVR(ii,jj+1) = Complex(VR(ii,jj),-VR(ii,jj+1)); - } - if(side == 'B') - for(ii = 0; ii < nn ; ii++) - { - CVL(ii,jj) = Complex(VL(ii,jj),VL(ii,jj+1)); - CVL(ii,jj+1) = Complex(VL(ii,jj),-VL(ii,jj+1)); - } - } - jj += cinc; // advance to next eigenvectors (if any) - } + if (side == 'B') + for (int ii = 0; ii < nn; ii++) + { + CVL(ii,jj) = Complex (VL(ii,jj), VL(ii,jj+1)); + CVL(ii,jj+1) = Complex (VL(ii,jj), -VL(ii,jj+1)); + } + } + + // advance to next eigenvectors (if any) + jj += cinc; + } + } } + + switch (nargout) + { + case 7: + retval(6) = gev; + + case 6: // return eigenvectors + retval(5) = CVL; + + case 5: // return eigenvectors + retval(4) = CVR; + + case 4: + if (nargin == 3) + { +#ifdef DEBUG + cout << "qz: sort: retval(3) = gev = " << endl; + octave_print_internal (cout, gev); + cout << endl; +#endif + retval(3) = gev; + } + else + retval(3) = ZZ; + + case 3: + if (nargin == 3) + retval(2) = ZZ; + else + retval(2) = QQ; + + case 2: +#ifdef DEBUG + cout << "qz: retval (1) = bb = " << endl; + octave_print_internal (cout, bb, 0); + cout << endl << "qz: retval(0) = aa = " <<endl; + octave_print_internal (cout, aa, 0); + cout << endl; +#endif + retval(1) = bb; + retval(0) = aa; + break; + + case 1: + case 0: +#ifdef DEBUG + cout << "qz: retval(0) = gev = " << gev << endl; +#endif + retval(0) = gev; + break; + + default: + error ("qz: too many return arguments."); + break; } - switch(nargout) - { - case 7: - retval(6) = gev; - case 6: // return eigenvectors - retval(5) = CVL; - case 5: // return eigenvectors - retval(4) = CVR; - case 4: - if(nargin == 3) - { - #ifdef DEBUG - cout << "qz: sort: retval(3) = gev = " << endl; - octave_print_internal(cout,gev); - cout << endl; - #endif - retval(3) = gev; - } - else retval(3) = ZZ; - case 3: - if(nargin == 3) - retval(2) = ZZ; - else - retval(2) = QQ; - case 2: - #ifdef DEBUG - cout << "qz: retval(1) = bb = " << endl; - octave_print_internal(cout,bb,0); - cout << endl << "qz: retval(0) = aa = " <<endl; - octave_print_internal(cout,aa,0); - cout << endl; - #endif - retval(1) = bb; - retval(0) = aa; - break; - case 1: - case 0: - #ifdef DEBUG - cout << "qz: retval(0) = gev = " << gev << endl; - #endif - retval(0) = gev; - break; - default: - error("qz: too many return arguments. Sorry. "); - } +#ifdef DEBUG + cout << "qz: exiting (at long last)" << endl; +#endif - #ifdef DEBUG - cout << "qz: exiting (at long last)" << endl; - #endif - return retval; }