Mercurial > hg > octave-lyh
diff src/DLD-FUNCTIONS/qz.cc @ 10311:a217e1d74353
untabify qz.cc
| author | John W. Eaton <jwe@octave.org> |
|---|---|
| date | Thu, 11 Feb 2010 11:57:36 -0500 |
| parents | 4e4270ab70d6 |
| children | 12884915a8e4 |
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--- a/src/DLD-FUNCTIONS/qz.cc +++ b/src/DLD-FUNCTIONS/qz.cc @@ -67,26 +67,32 @@ { F77_RET_T F77_FUNC (dggbal, DGGBAL) (F77_CONST_CHAR_ARG_DECL, - const octave_idx_type& N, double* A, const octave_idx_type& LDA, - double* B, const octave_idx_type& LDB, octave_idx_type& ILO, - octave_idx_type& IHI, double* LSCALE, double* RSCALE, - double* WORK, octave_idx_type& INFO + const octave_idx_type& N, double* A, + const octave_idx_type& LDA, double* B, + const octave_idx_type& LDB, octave_idx_type& ILO, + octave_idx_type& IHI, double* LSCALE, + double* RSCALE, double* WORK, + octave_idx_type& INFO F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (zggbal, ZGGBAL) (F77_CONST_CHAR_ARG_DECL, - const octave_idx_type& N, Complex* A, const octave_idx_type& LDA, - Complex* B, const octave_idx_type& LDB, octave_idx_type& ILO, - octave_idx_type& IHI, double* LSCALE, double* RSCALE, - double* WORK, octave_idx_type& INFO - F77_CHAR_ARG_LEN_DECL); + const octave_idx_type& N, Complex* A, + const octave_idx_type& LDA, Complex* B, + const octave_idx_type& LDB, octave_idx_type& ILO, + octave_idx_type& IHI, double* LSCALE, + double* RSCALE, double* WORK, + octave_idx_type& INFO + F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (dggbak, DGGBAK) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, - const octave_idx_type& N, const octave_idx_type& ILO, - const octave_idx_type& IHI, const double* LSCALE, - const double* RSCALE, octave_idx_type& M, double* V, + const octave_idx_type& N, + const octave_idx_type& ILO, + const octave_idx_type& IHI, + const double* LSCALE, const double* RSCALE, + octave_idx_type& M, double* V, const octave_idx_type& LDV, octave_idx_type& INFO F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); @@ -94,9 +100,11 @@ F77_RET_T F77_FUNC (zggbak, ZGGBAK) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, - const octave_idx_type& N, const octave_idx_type& ILO, - const octave_idx_type& IHI, const double* LSCALE, - const double* RSCALE, octave_idx_type& M, Complex* V, + const octave_idx_type& N, + const octave_idx_type& ILO, + const octave_idx_type& IHI, + const double* LSCALE, const double* RSCALE, + octave_idx_type& M, Complex* V, const octave_idx_type& LDV, octave_idx_type& INFO F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); @@ -104,7 +112,8 @@ F77_RET_T F77_FUNC (dgghrd, DGGHRD) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, - const octave_idx_type& N, const octave_idx_type& ILO, + const octave_idx_type& N, + const octave_idx_type& ILO, const octave_idx_type& IHI, double* A, const octave_idx_type& LDA, double* B, const octave_idx_type& LDB, double* Q, @@ -116,7 +125,8 @@ F77_RET_T F77_FUNC (zgghrd, ZGGHRD) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, - const octave_idx_type& N, const octave_idx_type& ILO, + const octave_idx_type& N, + const octave_idx_type& ILO, const octave_idx_type& IHI, Complex* A, const octave_idx_type& LDA, Complex* B, const octave_idx_type& LDB, Complex* Q, @@ -129,13 +139,16 @@ F77_FUNC (dhgeqz, DHGEQZ) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, - const octave_idx_type& N, const octave_idx_type& ILO, const octave_idx_type& IHI, + const octave_idx_type& N, + const octave_idx_type& ILO, + const octave_idx_type& IHI, double* A, const octave_idx_type& LDA, double* B, const octave_idx_type& LDB, double* ALPHAR, double* ALPHAI, double* BETA, double* Q, const octave_idx_type& LDQ, double* Z, const octave_idx_type& LDZ, double* WORK, - const octave_idx_type& LWORK, octave_idx_type& INFO + const octave_idx_type& LWORK, + octave_idx_type& INFO F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); @@ -144,55 +157,65 @@ F77_FUNC (zhgeqz, ZHGEQZ) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, - const octave_idx_type& N, const octave_idx_type& ILO, const octave_idx_type& IHI, - Complex* A, const octave_idx_type& LDA, Complex* B, - const octave_idx_type& LDB, Complex* ALPHA, Complex* BETA, Complex* CQ, const octave_idx_type& LDQ, - Complex* CZ, const octave_idx_type& LDZ, - Complex* WORK, - const octave_idx_type& LWORK, double* RWORK, - octave_idx_type& INFO + const octave_idx_type& N, + const octave_idx_type& ILO, + const octave_idx_type& IHI, + Complex* A, const octave_idx_type& LDA, + Complex* B, const octave_idx_type& LDB, + Complex* ALPHA, Complex* BETA, Complex* CQ, + const octave_idx_type& LDQ, + Complex* CZ, const octave_idx_type& LDZ, + Complex* WORK, const octave_idx_type& LWORK, + double* RWORK, octave_idx_type& INFO F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); F77_RET_T - F77_FUNC (dlag2, DLAG2) (const double* A, const octave_idx_type& LDA, const double* B, - const octave_idx_type& LDB, const double& SAFMIN, - double& SCALE1, double& SCALE2, - double& WR1, double& WR2, double& WI); + F77_FUNC (dlag2, DLAG2) (const double* A, const octave_idx_type& LDA, + const double* B, const octave_idx_type& 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. F77_RET_T - F77_FUNC (dsubsp, DSUBSP) (const octave_idx_type& NMAX, const octave_idx_type& N, double* A, + F77_FUNC (dsubsp, DSUBSP) (const octave_idx_type& NMAX, + const octave_idx_type& N, double* A, double* B, double* Z, sort_function, - const double& EPS, octave_idx_type& NDIM, octave_idx_type& FAIL, - octave_idx_type* IND); + const double& EPS, octave_idx_type& NDIM, + octave_idx_type& FAIL, octave_idx_type* IND); - // documentation for DTGEVC incorrectly states that VR, VL are + // 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) + // (probably a cut and paste problem fro ZTGEVC). F77_RET_T F77_FUNC (dtgevc, DTGEVC) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, - octave_idx_type* SELECT, const octave_idx_type& N, double* A, + octave_idx_type* SELECT, + const octave_idx_type& N, double* A, const octave_idx_type& LDA, double* B, const octave_idx_type& LDB, double* VL, const octave_idx_type& LDVL, double* VR, - const octave_idx_type& LDVR, const octave_idx_type& MM, - octave_idx_type& M, double* WORK, octave_idx_type& INFO + const octave_idx_type& LDVR, + const octave_idx_type& MM, octave_idx_type& M, + double* WORK, octave_idx_type& INFO F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (ztgevc, ZTGEVC) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, - octave_idx_type* SELECT, const octave_idx_type& N,const Complex* A, + octave_idx_type* SELECT, + const octave_idx_type& N, const Complex* A, const octave_idx_type& LDA,const Complex* B, const octave_idx_type& LDB, Complex* xVL, const octave_idx_type& LDVL, Complex* xVR, - const octave_idx_type& LDVR, const octave_idx_type& MM, - octave_idx_type& M, Complex* CWORK, double* RWORK, octave_idx_type& INFO + const octave_idx_type& LDVR, + const octave_idx_type& MM, octave_idx_type& M, + Complex* CWORK, double* RWORK, + octave_idx_type& INFO F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); @@ -203,7 +226,8 @@ F77_RET_T F77_FUNC (xdlange, XDLANGE) (F77_CONST_CHAR_ARG_DECL, - const octave_idx_type&, const octave_idx_type&, const double*, + const octave_idx_type&, + const octave_idx_type&, const double*, const octave_idx_type&, double*, double& F77_CHAR_ARG_LEN_DECL); } @@ -221,7 +245,7 @@ const double& beta, const double& s, const double&) { if (lsize == 1) - return (alpha*beta >= 0 ? 1 : -1); + return (alpha * beta >= 0 ? 1 : -1); else return (s >= 0 ? 1 : -1); } @@ -249,7 +273,7 @@ const double& beta, const double& s, const double&) { if (lsize == 1) - return (alpha*beta < 0 ? 1 : -1); + return (alpha * beta < 0 ? 1 : -1); else return (s < 0 ? 1 : -1); } @@ -293,9 +317,9 @@ @example\n\ @group\n\ \n\ - A*V = B*V*diag(lambda)\n\ - W'*A = diag(lambda)*W'*B\n\ - AA = Q*A*Z, BB = Q*B*Z\n\ + A * V = B * V * diag (lambda)\n\ + W' * A = diag (lambda) * W' * B\n\ + AA = Q * A * Z, BB = Q * B * Z\n\ \n\ @end group\n\ @end example\n\ @@ -361,7 +385,7 @@ std::cout << "qz: determine ordering option" << std::endl; #endif - // Determine ordering option + // Determine ordering option. volatile char ord_job = 0; static double safmin; @@ -398,8 +422,8 @@ << safmin << std::endl; #endif - // some machines (e.g., DEC alpha) get safmin = 0; - // for these, use eps instead to avoid problems in dlag2 + // 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 @@ -421,7 +445,7 @@ std::cout << "qz: check argument 1" << std::endl; #endif - // Argument 1: check if it's o.k. dimensioned + // Argument 1: check if it's o.k. dimensioned. octave_idx_type nn = args(0).rows (); #ifdef DEBUG @@ -447,7 +471,7 @@ return retval; } - // Argument 1: dimensions look good; get the value + // Argument 1: dimensions look good; get the value. Matrix aa; ComplexMatrix caa; @@ -463,7 +487,7 @@ std::cout << "qz: check argument 2" << std::endl; #endif - // Extract argument 2 (bb, or cbb if complex) + // Extract argument 2 (bb, or cbb if complex). if ((nn != args(1).columns ()) || (nn != args(1).rows ())) { gripe_nonconformant (); @@ -482,18 +506,19 @@ return retval; // Both matrices loaded, now let's check what kind of arithmetic: - //declared static to avoid compiler warnings about long jumps, vforks. + // declared volatile to avoid compiler warnings about long jumps, + // vforks. - int complex_case + volatile int complex_case = (args(0).is_complex_type () || args(1).is_complex_type ()); - // static complex_case causing random segfault, so it is removed + 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 + // 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); ComplexRowVector xalpha(nn), xbeta(nn); @@ -502,7 +527,7 @@ char compq = (nargout >= 3 ? 'V' : 'N'); char compz = (nargout >= 4 ? 'V' : 'N'); - // initialize Q, Z to identity if we need either of them + // Initialize Q, Z to identity if we need either of them. if (compq == 'V' || compz == 'V') for (octave_idx_type ii = 0; ii < nn; ii++) for (octave_idx_type jj = 0; jj < nn; jj++) @@ -511,34 +536,34 @@ QQ(ii,jj) = ZZ(ii,jj) = (ii == jj ? 1.0 : 0.0); } - // always perform permutation balancing + // Always perform permutation balancing. const char bal_job = 'P'; - RowVector lscale(nn), rscale(nn), work(6*nn), rwork(nn); + RowVector lscale (nn), rscale (nn), work (6 * nn), rwork (nn); if (complex_case) { #ifdef DEBUG if (compq == 'V') - std::cout << "qz: performing balancing; CQ=" << std::endl << CQ << std::endl; + std::cout << "qz: performing balancing; CQ=" << std::endl << CQ << std::endl; #endif if (args(0).is_real_type ()) - caa = ComplexMatrix (aa); + caa = ComplexMatrix (aa); if (args(1).is_real_type ()) - cbb = ComplexMatrix (bb); + cbb = ComplexMatrix (bb); if (compq == 'V') - CQ = ComplexMatrix (QQ); + CQ = ComplexMatrix (QQ); if (compz == 'V') - CZ = ComplexMatrix (ZZ); + CZ = ComplexMatrix (ZZ); - F77_XFCN (zggbal, ZGGBAL, - (F77_CONST_CHAR_ARG2 (&bal_job, 1), - nn, caa.fortran_vec (), nn, cbb.fortran_vec (), - nn, ilo, ihi, lscale.fortran_vec (), - rscale.fortran_vec (), work.fortran_vec (), info - F77_CHAR_ARG_LEN (1))); + F77_XFCN (zggbal, ZGGBAL, + (F77_CONST_CHAR_ARG2 (&bal_job, 1), + nn, caa.fortran_vec (), nn, cbb.fortran_vec (), + nn, ilo, ihi, lscale.fortran_vec (), + rscale.fortran_vec (), work.fortran_vec (), info + F77_CHAR_ARG_LEN (1))); } else { @@ -556,10 +581,10 @@ } // Since we just want the balancing matrices, we can use dggbal - // for both the real and complex cases; - // left first + // for both the real and complex cases; left first - /* if (compq == 'V') +#if 0 + if (compq == 'V') { F77_XFCN (dggbak, DGGBAK, (F77_CONST_CHAR_ARG2 (&bal_job, 1), @@ -590,19 +615,24 @@ if (compz == 'V') std::cout << "qz: balancing done; ZZ=" << std::endl << ZZ << std::endl; #endif - } */ + } +#endif static char qz_job; qz_job = (nargout < 2 ? 'E' : 'S'); if (complex_case) { - // complex case - ComplexQR cbqr (cbb); // declare cbqr as the QR decomposition of cbb - cbb = cbqr.R (); // the R matrix of QR decomposition for cbb - caa = (cbqr.Q ().hermitian ())*caa; // (Q*)caa for following work - //if (compq == 'V') - CQ = CQ*cbqr.Q (); + // Complex case. + + // The QR decomposition of cbb. + ComplexQR cbqr (cbb); + // The R matrix of QR decomposition for cbb. + cbb = cbqr.R (); + // (Q*)caa for following work. + caa = (cbqr.Q ().hermitian ()) * caa; + CQ = CQ * cbqr.Q (); + F77_XFCN (zgghrd, ZGGHRD, (F77_CONST_CHAR_ARG2 (&compq, 1), F77_CONST_CHAR_ARG2 (&compz, 1), @@ -611,7 +641,9 @@ CZ.fortran_vec (), nn, info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); - ComplexRowVector cwork(1*nn); + + ComplexRowVector cwork (1 * nn); + F77_XFCN (zhgeqz, ZHGEQZ, (F77_CONST_CHAR_ARG2 (&qz_job, 1), F77_CONST_CHAR_ARG2 (&compq, 1), @@ -629,7 +661,7 @@ if (compq == 'V') { - // Left eigenvector + // Left eigenvector. F77_XFCN (zggbak, ZGGBAK, (F77_CONST_CHAR_ARG2 (&bal_job, 1), F77_CONST_CHAR_ARG2 ("L", 1), @@ -639,7 +671,7 @@ F77_CHAR_ARG_LEN (1))); } - // then right + // Right eigenvector. if (compz == 'V') { F77_XFCN (zggbak, ZGGBAK, @@ -652,13 +684,13 @@ } } - else // real matrices case + else { #ifdef DEBUG std::cout << "qz: peforming qr decomposition of bb" << std::endl; #endif - // compute the QR factorization of bb + // Compute the QR factorization of bb. QR bqr (bb); #ifdef DEBUG @@ -671,7 +703,7 @@ std::cout << "qz: extracted bb" << std::endl; #endif - aa = (bqr.Q ()).transpose ()*aa; + aa = (bqr.Q ()).transpose () * aa; #ifdef DEBUG std::cout << "qz: updated aa " << std::endl; @@ -682,7 +714,7 @@ #endif if (compq == 'V') - QQ = QQ*bqr.Q (); + QQ = QQ * bqr.Q (); #ifdef DEBUG std::cout << "qz: precursors done..." << std::endl; @@ -692,7 +724,7 @@ std::cout << "qz: compq = " << compq << ", compz = " << compz << std::endl; #endif - // reduce to generalized hessenberg form + // Reduce to generalized hessenberg form. F77_XFCN (dgghrd, DGGHRD, (F77_CONST_CHAR_ARG2 (&compq, 1), F77_CONST_CHAR_ARG2 (&compz, 1), @@ -702,10 +734,10 @@ F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); - // 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 + // Reduce to generalized Schur form. F77_XFCN (dhgeqz, DHGEQZ, (F77_CONST_CHAR_ARG2 (&qz_job, 1), F77_CONST_CHAR_ARG2 (&compq, 1), @@ -717,19 +749,20 @@ F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); + if (compq == 'V') - { - F77_XFCN (dggbak, DGGBAK, - (F77_CONST_CHAR_ARG2 (&bal_job, 1), - F77_CONST_CHAR_ARG2 ("L", 1), - nn, ilo, ihi, lscale.data (), rscale.data (), - nn, QQ.fortran_vec (), nn, info - F77_CHAR_ARG_LEN (1) - F77_CHAR_ARG_LEN (1))); + { + F77_XFCN (dggbak, DGGBAK, + (F77_CONST_CHAR_ARG2 (&bal_job, 1), + F77_CONST_CHAR_ARG2 ("L", 1), + nn, ilo, ihi, lscale.data (), rscale.data (), + nn, QQ.fortran_vec (), nn, info + F77_CHAR_ARG_LEN (1) + F77_CHAR_ARG_LEN (1))); #ifdef DEBUG - if (compq == 'V') - std::cout << "qz: balancing done; QQ=" << std::endl << QQ << std::endl; + if (compq == 'V') + std::cout << "qz: balancing done; QQ=" << std::endl << QQ << std::endl; #endif } @@ -737,12 +770,12 @@ if (compz == 'V') { F77_XFCN (dggbak, DGGBAK, - (F77_CONST_CHAR_ARG2 (&bal_job, 1), - F77_CONST_CHAR_ARG2 ("R", 1), - nn, ilo, ihi, lscale.data (), rscale.data (), - nn, ZZ.fortran_vec (), nn, info - F77_CHAR_ARG_LEN (1) - F77_CHAR_ARG_LEN (1))); + (F77_CONST_CHAR_ARG2 (&bal_job, 1), + F77_CONST_CHAR_ARG2 ("R", 1), + nn, ilo, ihi, lscale.data (), rscale.data (), + nn, ZZ.fortran_vec (), nn, info + F77_CHAR_ARG_LEN (1) + F77_CHAR_ARG_LEN (1))); #ifdef DEBUG if (compz == 'V') @@ -752,12 +785,12 @@ } - // order the QZ decomposition? + // Order the QZ decomposition? if (! (ord_job == 'N' || ord_job == 'n')) { if (complex_case) { - // probably not needed, but better be safe + // Probably not needed, but better be safe. error ("qz: cannot re-order complex qz decomposition."); return retval; } @@ -768,7 +801,7 @@ << ord_job << std::endl; #endif - // declared static to avoid vfork/long jump compiler complaints + // Declared static to avoid vfork/long jump compiler complaints. static sort_function sort_test; sort_test = 0; @@ -793,7 +826,7 @@ break; default: - // invalid order option (should never happen, since we + // Invalid order option (should never happen, since we // checked the options at the top). panic_impossible (); break; @@ -807,7 +840,7 @@ nn, nn, aa.data (), nn, work.fortran_vec (), inf_norm F77_CHAR_ARG_LEN (1))); - double eps = DBL_EPSILON*inf_norm*nn; + double eps = DBL_EPSILON * inf_norm * nn; #ifdef DEBUG_SORT std::cout << "qz: calling dsubsp: aa=" << std::endl; @@ -849,17 +882,18 @@ std::cout << std::endl; #endif - // manually update alphar, alphai, betar + // Manually update alphar, alphai, betar. static int jj; - jj=0; + jj = 0; while (jj < nn) { #ifdef DEBUG_EIG std::cout << "computing gen eig #" << jj << std::endl; #endif - static int zcnt; // number of zeros in this block + // Number of zeros in this block. + static int zcnt; if (jj == (nn-1)) zcnt = 1; @@ -867,8 +901,9 @@ zcnt = 1; else zcnt = 2; - if (zcnt == 1) // real zero + if (zcnt == 1) { + // Real zero. #ifdef DEBUG_EIG std::cout << " single gen eig:" << std::endl; std::cout << " alphar(" << jj << ") = " << aa(jj,jj) << std::endl; @@ -882,7 +917,7 @@ } else { - // complex conjugate pair + // Complex conjugate pair. #ifdef DEBUG_EIG std::cout << "qz: calling dlag2:" << std::endl; std::cout << "safmin=" @@ -904,8 +939,8 @@ // fortran_vec instead of &aa(jj,jj) here. double scale1, scale2, wr1, wr2, wi; - const double *aa_ptr = aa.data () + jj*nn+jj; - const double *bb_ptr = bb.data () + jj*nn+jj; + const double *aa_ptr = aa.data () + jj * nn + jj; + const double *bb_ptr = bb.data () + jj * nn + jj; F77_XFCN (dlag2, DLAG2, (aa_ptr, nn, bb_ptr, nn, safmin, scale1, scale2, wr1, wr2, wi)); @@ -917,7 +952,7 @@ << "\twi=" << wi << std::endl; #endif - // just to be safe, check if it's a real pair + // Just to be safe, check if it's a real pair. if (wi == 0) { alphar(jj) = wr1; @@ -929,13 +964,13 @@ } else { - alphar(jj) = alphar(jj+1)=wr1; + alphar(jj) = alphar(jj+1) = wr1; alphai(jj) = -(alphai(jj+1) = wi); betar(jj) = betar(jj+1) = scale1; } } - // advance past this block + // Advance past this block. jj += zcnt; } @@ -963,26 +998,25 @@ } } - // compute generalized eigenvalues? + // Compute generalized eigenvalues? ComplexColumnVector gev; if (nargout < 2 || nargout == 7 || (nargin == 3 && nargout == 4)) { if (complex_case) { - int cnt = 0; + int cnt = 0; - for (int ii = 0; ii < nn; ii++) - // if (cbetar(ii) != 0) - cnt++; + for (int ii = 0; ii < nn; ii++) + cnt++; - ComplexColumnVector tmp(cnt); + ComplexColumnVector tmp (cnt); - cnt = 0; - for (int ii = 0; ii < nn; ii++) - // if (cbetar(ii) != 0) - tmp(cnt++) = xalpha(ii)/xbeta(ii); - gev = tmp; + cnt = 0; + for (int ii = 0; ii < nn; ii++) + tmp(cnt++) = xalpha(ii) / xbeta(ii); + + gev = tmp; } else { @@ -990,47 +1024,50 @@ std::cout << "qz: computing generalized eigenvalues" << std::endl; #endif - // return finite generalized eigenvalues + // Return finite generalized eigenvalues. int cnt = 0; for (int ii = 0; ii < nn; ii++) if (betar(ii) != 0) cnt++; - ComplexColumnVector tmp(cnt); + ComplexColumnVector tmp (cnt); cnt = 0; for (int ii = 0; ii < nn; ii++) if (betar(ii) != 0) tmp(cnt++) = Complex(alphar(ii), alphai(ii))/betar(ii); + gev = tmp; } } - // right, left eigenvector matrices + // Right, left eigenvector matrices. if (nargout >= 5) { - char side = (nargout == 5 ? 'R' : 'B'); // which side to compute? - char howmny = 'B'; // compute all of them and backtransform - octave_idx_type *select = 0; // dummy pointer; select is not used. + // Which side to compute? + char side = (nargout == 5 ? 'R' : 'B'); + // Compute all of them and backtransform + char howmny = 'B'; + // Dummy pointer; select is not used. + octave_idx_type *select = 0; if (complex_case) { + CVL = CQ; + CVR = CZ; + ComplexRowVector cwork2 (2 * nn); + RowVector rwork2 (8 * nn); octave_idx_type m; - CVL=CQ; - CVR=CZ; - ComplexRowVector cwork2(2*nn); - RowVector rwork2(8*nn); - //octave_idx_type n=nn; - F77_XFCN (ztgevc, ZTGEVC, - (F77_CONST_CHAR_ARG2 (&side, 1), - F77_CONST_CHAR_ARG2 (&howmny, 1), - select, nn, caa.fortran_vec (), nn, cbb.fortran_vec (), - nn, CVL.fortran_vec (), nn, CVR.fortran_vec (), nn, nn, - m, cwork2.fortran_vec (), rwork2.fortran_vec (), info - F77_CHAR_ARG_LEN (1) - F77_CHAR_ARG_LEN (1))); + F77_XFCN (ztgevc, ZTGEVC, + (F77_CONST_CHAR_ARG2 (&side, 1), + F77_CONST_CHAR_ARG2 (&howmny, 1), + select, nn, caa.fortran_vec (), nn, cbb.fortran_vec (), + nn, CVL.fortran_vec (), nn, CVR.fortran_vec (), nn, nn, + m, cwork2.fortran_vec (), rwork2.fortran_vec (), info + F77_CHAR_ARG_LEN (1) + F77_CHAR_ARG_LEN (1))); } else { @@ -1040,7 +1077,8 @@ VL = QQ; VR = ZZ; - octave_idx_type m; + octave_idx_type m; + F77_XFCN (dtgevc, DTGEVC, (F77_CONST_CHAR_ARG2 (&side, 1), F77_CONST_CHAR_ARG2 (&howmny, 1), @@ -1050,22 +1088,25 @@ F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); - // now construct the complex form of VV, WW + // Now construct the complex form of VV, WW. int jj = 0; while (jj < nn) { OCTAVE_QUIT; - // see if real or complex eigenvalue - int cinc = 2; // column increment; assume complex eigenvalue + // See if real or complex eigenvalue. + + // Column increment; assume complex eigenvalue. + int cinc = 2; if (jj == (nn-1)) - cinc = 1; // single column + // Single column. + cinc = 1; else if (aa(jj+1,jj) == 0) cinc = 1; - // now copy the eigenvector (s) to CVR, CVL + // Now copy the eigenvector (s) to CVR, CVL. if (cinc == 1) { for (int ii = 0; ii < nn; ii++) @@ -1077,7 +1118,7 @@ } else { - // double column; complex vector + // Double column; complex vector. for (int ii = 0; ii < nn; ii++) { @@ -1093,7 +1134,7 @@ } } - // advance to next eigenvectors (if any) + // Advance to next eigenvectors (if any). jj += cinc; } } @@ -1104,10 +1145,12 @@ case 7: retval(6) = gev; - case 6: // return eigenvectors + case 6: + // Return eigenvectors. retval(5) = CVL; - case 5: // return eigenvectors + case 5: + // Return eigenvectors. retval(4) = CVR; case 4: @@ -1121,47 +1164,52 @@ retval(3) = gev; } else - {if (complex_case) - retval(3) = CZ; - else - retval(3) = ZZ; - } + { + if (complex_case) + retval(3) = CZ; + else + retval(3) = ZZ; + } case 3: if (nargin == 3) - retval(2) = CZ; + retval(2) = CZ; else - {if (complex_case) - retval(2) = CQ.hermitian(); // compabible with MATLAB output - else - retval(2) = QQ.transpose(); - } + { + if (complex_case) + retval(2) = CQ.hermitian (); + else + retval(2) = QQ.transpose (); + } + case 2: - {if (complex_case) { + if (complex_case) + { #ifdef DEBUG - std::cout << "qz: retval (1) = cbb = " << std::endl; - octave_print_internal (std::cout, cbb, 0); - std::cout << std::endl << "qz: retval(0) = caa = " <<std::endl; - octave_print_internal (std::cout, caa, 0); - std::cout << std::endl; -#endif - retval(1) = cbb; - retval(0) = caa; - } + std::cout << "qz: retval (1) = cbb = " << std::endl; + octave_print_internal (std::cout, cbb, 0); + std::cout << std::endl << "qz: retval(0) = caa = " <<std::endl; + octave_print_internal (std::cout, caa, 0); + std::cout << std::endl; +#endif + retval(1) = cbb; + retval(0) = caa; + } else - { // real case + { #ifdef DEBUG - std::cout << "qz: retval (1) = bb = " << std::endl; - octave_print_internal (std::cout, bb, 0); - std::cout << std::endl << "qz: retval(0) = aa = " <<std::endl; - octave_print_internal (std::cout, aa, 0); - std::cout << std::endl; + std::cout << "qz: retval (1) = bb = " << std::endl; + octave_print_internal (std::cout, bb, 0); + std::cout << std::endl << "qz: retval(0) = aa = " <<std::endl; + octave_print_internal (std::cout, aa, 0); + std::cout << std::endl; #endif - retval(1) = bb; - retval(0) = aa; - } - break;} + retval(1) = bb; + retval(0) = aa; + } + } + break; case 1: