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Teuchos_LAPACK.hpp
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41 
42 #ifndef _TEUCHOS_LAPACK_HPP_
43 #define _TEUCHOS_LAPACK_HPP_
44 
52 #include "Teuchos_ConfigDefs.hpp"
53 #include "Teuchos_ScalarTraits.hpp"
54 
85 namespace Teuchos
86 {
87 
88  template<class T>
89  struct UndefinedLAPACKRoutine
90  {
91  // This function should not compile if there is an attempt to instantiate!
92  static inline T notDefined() { return T::LAPACK_routine_not_defined_for_this_type(); }
93  };
94 
95  template<typename OrdinalType, typename ScalarType>
96  class LAPACK
97  {
98  public:
99 
100  typedef typename Teuchos::ScalarTraits<ScalarType>::magnitudeType MagnitudeType;
101 
103 
104 
106  inline LAPACK(void) {}
107 
109  inline LAPACK(const LAPACK<OrdinalType, ScalarType>& lapack) {}
110 
112  inline virtual ~LAPACK(void) {}
114 
116 
117 
119  void PTTRF(const OrdinalType& n, ScalarType* d, ScalarType* e, OrdinalType* info) const;
120 
122  void PTTRS(const OrdinalType& n, const OrdinalType& nrhs, const ScalarType* d, const ScalarType* e, ScalarType* B, const OrdinalType& ldb, OrdinalType* info) const;
123 
125  void POTRF(const char& UPLO, const OrdinalType& n, ScalarType* A, const OrdinalType& lda, OrdinalType* info) const;
126 
128  void POTRS(const char& UPLO, const OrdinalType& n, const OrdinalType& nrhs, const ScalarType* A, const OrdinalType& lda, ScalarType* B, const OrdinalType& ldb, OrdinalType* info) const;
129 
131  void POTRI(const char& UPLO, const OrdinalType& n, ScalarType* A, const OrdinalType& lda, OrdinalType* info) const;
132 
134 
135  void POCON(const char& UPLO, const OrdinalType& n, const ScalarType* A, const OrdinalType& lda, const ScalarType& anorm, ScalarType* rcond, ScalarType* WORK, OrdinalType* IWORK, OrdinalType* info) const;
136 
138  void POSV(const char& UPLO, const OrdinalType& n, const OrdinalType& nrhs, ScalarType* A, const OrdinalType& lda, ScalarType* B, const OrdinalType& ldb, OrdinalType* info) const;
139 
141  void POEQU(const OrdinalType& n, const ScalarType* A, const OrdinalType& lda, MagnitudeType* S, MagnitudeType* scond, MagnitudeType* amax, OrdinalType* info) const;
142 
144  void PORFS(const char& UPLO, const OrdinalType& n, const OrdinalType& nrhs, const ScalarType* A, const OrdinalType& lda, const ScalarType* AF, const OrdinalType& ldaf, const ScalarType* B, const OrdinalType& ldb, ScalarType* X, const OrdinalType& ldx, ScalarType* FERR, ScalarType* BERR, ScalarType* WORK, OrdinalType* IWORK, OrdinalType* info) const;
145 
147  void POSVX(const char& FACT, const char& UPLO, const OrdinalType& n, const OrdinalType& nrhs, ScalarType* A, const OrdinalType& lda, ScalarType* AF, const OrdinalType& ldaf, char* EQUED, ScalarType* S, ScalarType* B, const OrdinalType& ldb, ScalarType* X, const OrdinalType& ldx, ScalarType* rcond, ScalarType* FERR, ScalarType* BERR, ScalarType* WORK, OrdinalType* IWORK, OrdinalType* info) const;
149 
151 
152 
154  void GELS(const char& TRANS, const OrdinalType& m, const OrdinalType& n, const OrdinalType& nrhs, ScalarType* A, const OrdinalType& lda, ScalarType* B, const OrdinalType& ldb, ScalarType* WORK, const OrdinalType& lwork, OrdinalType* info) const;
155 
189  void GELSS(const OrdinalType& m, const OrdinalType& n, const OrdinalType& nrhs, ScalarType* A, const OrdinalType& lda, ScalarType* B, const OrdinalType& ldb, MagnitudeType* S, const MagnitudeType rcond, OrdinalType* rank, ScalarType* WORK, const OrdinalType& lwork, MagnitudeType* RWORK, OrdinalType* info) const;
190 
192  void GELSS(const OrdinalType& m, const OrdinalType& n, const OrdinalType& nrhs, ScalarType* A, const OrdinalType& lda, ScalarType* B, const OrdinalType& ldb, ScalarType* S, const ScalarType& rcond, OrdinalType* rank, ScalarType* WORK, const OrdinalType& lwork, OrdinalType* info) const;
193 
195  void GGLSE(const OrdinalType& m, const OrdinalType& n, const OrdinalType& p, ScalarType* A, const OrdinalType& lda, ScalarType* B, const OrdinalType& ldb, ScalarType* C, ScalarType* D, ScalarType* X, ScalarType* WORK, const OrdinalType& lwork, OrdinalType* info) const;
196 
198  void GEQRF (const OrdinalType& m, const OrdinalType& n, ScalarType* A, const OrdinalType& lda, ScalarType* TAU, ScalarType* WORK, const OrdinalType& lwork, OrdinalType* info) const;
199 
201  void GEQR2 (const OrdinalType& m, const OrdinalType& n, ScalarType A[], const OrdinalType& lda, ScalarType TAU[], ScalarType WORK[], OrdinalType* const info) const;
202 
204  void GETRF(const OrdinalType& m, const OrdinalType& n, ScalarType* A, const OrdinalType& lda, OrdinalType* IPIV, OrdinalType* info) const;
205 
207  void GETRS(const char& TRANS, const OrdinalType& n, const OrdinalType& nrhs, const ScalarType* A, const OrdinalType& lda, const OrdinalType* IPIV, ScalarType* B, const OrdinalType& ldb, OrdinalType* info) const;
208 
210  void LASCL(const char& TYPE, const OrdinalType& kl, const OrdinalType& ku, const MagnitudeType cfrom, const MagnitudeType cto, const OrdinalType& m, const OrdinalType& n, ScalarType* A, const OrdinalType& lda, OrdinalType* info) const;
211 
213  void
214  GEQP3(const OrdinalType& m,
215  const OrdinalType& n, ScalarType* A,
216  const OrdinalType& lda,
217  OrdinalType* jpvt,
218  ScalarType* TAU,
219  ScalarType* WORK,
220  const OrdinalType& lwork,
221  MagnitudeType* RWORK,
222  OrdinalType* info ) const;
223 
225  void
226  LASWP (const OrdinalType& N,
227  ScalarType A[],
228  const OrdinalType& LDA,
229  const OrdinalType& K1,
230  const OrdinalType& K2,
231  const OrdinalType IPIV[],
232  const OrdinalType& INCX) const;
233 
235  void GBTRF(const OrdinalType& m, const OrdinalType& n, const OrdinalType& kl, const OrdinalType& ku, ScalarType* A, const OrdinalType& lda, OrdinalType* IPIV, OrdinalType* info) const;
236 
238  void GBTRS(const char& TRANS, const OrdinalType& n, const OrdinalType& kl, const OrdinalType& ku, const OrdinalType& nrhs, const ScalarType* A, const OrdinalType& lda, const OrdinalType* IPIV, ScalarType* B, const OrdinalType& ldb, OrdinalType* info) const;
239 
241  void GTTRF(const OrdinalType& n, ScalarType* dl, ScalarType* d, ScalarType* du, ScalarType* du2, OrdinalType* IPIV, OrdinalType* info) const;
242 
244  void GTTRS(const char& TRANS, const OrdinalType& n, const OrdinalType& nrhs, const ScalarType* dl, const ScalarType* d, const ScalarType* du, const ScalarType* du2, const OrdinalType* IPIV, ScalarType* B, const OrdinalType& ldb, OrdinalType* info) const;
245 
247  void GETRI(const OrdinalType& n, ScalarType* A, const OrdinalType& lda, const OrdinalType* IPIV, ScalarType* WORK, const OrdinalType& lwork, OrdinalType* info) const;
248 
253  void
254  LATRS (const char& UPLO,
255  const char& TRANS,
256  const char& DIAG,
257  const char& NORMIN,
258  const OrdinalType& N,
259  ScalarType* A,
260  const OrdinalType& LDA,
261  ScalarType* X,
262  MagnitudeType* SCALE,
263  MagnitudeType* CNORM,
264  OrdinalType* INFO) const;
265 
267  void GECON(const char& NORM, const OrdinalType& n, const ScalarType* A, const OrdinalType& lda, const ScalarType& anorm, ScalarType* rcond, ScalarType* WORK, OrdinalType* IWORK, OrdinalType* info) const;
268 
270  void GBCON(const char& NORM, const OrdinalType& n, const OrdinalType& kl, const OrdinalType& ku, const ScalarType* A, const OrdinalType& lda, OrdinalType* IPIV, const ScalarType& anorm, ScalarType* rcond, ScalarType* WORK, OrdinalType* IWORK, OrdinalType* info) const;
271 
273  typename ScalarTraits<ScalarType>::magnitudeType LANGB(const char& NORM, const OrdinalType& n, const OrdinalType& kl, const OrdinalType& ku, const ScalarType* A, const OrdinalType& lda, MagnitudeType* WORK) const;
274 
276  void GESV(const OrdinalType& n, const OrdinalType& nrhs, ScalarType* A, const OrdinalType& lda, OrdinalType* IPIV, ScalarType* B, const OrdinalType& ldb, OrdinalType* info) const;
277 
279  void GEEQU(const OrdinalType& m, const OrdinalType& n, const ScalarType* A, const OrdinalType& lda, ScalarType* R, ScalarType* C, ScalarType* rowcond, ScalarType* colcond, ScalarType* amax, OrdinalType* info) const;
280 
282  void GERFS(const char& TRANS, const OrdinalType& n, const OrdinalType& nrhs, const ScalarType* A, const OrdinalType& lda, const ScalarType* AF, const OrdinalType& ldaf, const OrdinalType* IPIV, const ScalarType* B, const OrdinalType& ldb, ScalarType* X, const OrdinalType& ldx, ScalarType* FERR, ScalarType* BERR, ScalarType* WORK, OrdinalType* IWORK, OrdinalType* info) const;
283 
285  void GBEQU(const OrdinalType& m, const OrdinalType& n, const OrdinalType& kl, const OrdinalType& ku, const ScalarType* A, const OrdinalType& lda, MagnitudeType* R, MagnitudeType* C, MagnitudeType* rowcond, MagnitudeType* colcond, MagnitudeType* amax, OrdinalType* info) const;
286 
288  void GBRFS(const char& TRANS, const OrdinalType& n, const OrdinalType& kl, const OrdinalType& ku, const OrdinalType& nrhs, const ScalarType* A, const OrdinalType& lda, const ScalarType* AF, const OrdinalType& ldaf, const OrdinalType* IPIV, const ScalarType* B, const OrdinalType& ldb, ScalarType* X, const OrdinalType& ldx, ScalarType* FERR, ScalarType* BERR, ScalarType* WORK, OrdinalType* IWORK, OrdinalType* info) const;
289 
291 
292  void GESVX(const char& FACT, const char& TRANS, const OrdinalType& n, const OrdinalType& nrhs, ScalarType* A, const OrdinalType& lda, ScalarType* AF, const OrdinalType& ldaf, OrdinalType* IPIV, char* EQUED, ScalarType* R, ScalarType* C, ScalarType* B, const OrdinalType& ldb, ScalarType* X, const OrdinalType& ldx, ScalarType* rcond, ScalarType* FERR, ScalarType* BERR, ScalarType* WORK, OrdinalType* IWORK, OrdinalType* info) const;
293 
297  void SYTRD(const char& UPLO, const OrdinalType& n, ScalarType* A, const OrdinalType& lda, ScalarType* D, ScalarType* E, ScalarType* TAU, ScalarType* WORK, const OrdinalType& lwork, OrdinalType* info) const;
298 
300  void GEHRD(const OrdinalType& n, const OrdinalType& ilo, const OrdinalType& ihi, ScalarType* A, const OrdinalType& lda, ScalarType* TAU, ScalarType* WORK, const OrdinalType& lwork, OrdinalType* info) const;
301 
303  void TRTRS(const char& UPLO, const char& TRANS, const char& DIAG, const OrdinalType& n, const OrdinalType& nrhs, const ScalarType* A, const OrdinalType& lda, ScalarType* B, const OrdinalType& ldb, OrdinalType* info) const;
304 
306  void TRTRI(const char& UPLO, const char& DIAG, const OrdinalType& n, const ScalarType* A, const OrdinalType& lda, OrdinalType* info) const;
308 
310 
311 
314  void SPEV(const char& JOBZ, const char& UPLO, const OrdinalType& n, ScalarType* AP, ScalarType* W, ScalarType* Z, const OrdinalType& ldz, ScalarType* WORK, OrdinalType* info) const;
315 
319  void SYEV(const char& JOBZ, const char& UPLO, const OrdinalType& n, ScalarType* A, const OrdinalType& lda, ScalarType* W, ScalarType* WORK, const OrdinalType& lwork, OrdinalType* info) const;
320 
324  void SYGV(const OrdinalType& itype, const char& JOBZ, const char& UPLO, const OrdinalType& n, ScalarType* A, const OrdinalType& lda, ScalarType* B, const OrdinalType& ldb, ScalarType* W, ScalarType* WORK, const OrdinalType& lwork, OrdinalType* info) const;
325 
329  void HEEV(const char& JOBZ, const char& UPLO, const OrdinalType& n, ScalarType* A, const OrdinalType& lda, MagnitudeType* W, ScalarType* WORK, const OrdinalType& lwork, MagnitudeType* RWORK, OrdinalType* info) const;
330 
334  void HEGV(const OrdinalType& itype, const char& JOBZ, const char& UPLO, const OrdinalType& n, ScalarType* A, const OrdinalType& lda, ScalarType* B, const OrdinalType& ldb, MagnitudeType* W, ScalarType* WORK, const OrdinalType& lwork, MagnitudeType *RWORK, OrdinalType* info) const;
335 
337  void STEQR(const char& COMPZ, const OrdinalType& n, MagnitudeType* D, MagnitudeType* E, ScalarType* Z, const OrdinalType& ldz, MagnitudeType* WORK, OrdinalType* info) const;
338 
340  void PTEQR(const char& COMPZ, const OrdinalType& n, MagnitudeType* D, MagnitudeType* E, ScalarType* Z, const OrdinalType& ldz, MagnitudeType* WORK, OrdinalType* info) const;
342 
344 
345  void HSEQR(const char& JOB, const char& COMPZ, const OrdinalType& n, const OrdinalType& ilo, const OrdinalType& ihi, ScalarType* H, const OrdinalType& ldh, ScalarType* WR, ScalarType* WI, ScalarType* Z, const OrdinalType& ldz, ScalarType* WORK, const OrdinalType& lwork, OrdinalType* info) const;
347 
351  void GEES(const char& JOBVS, const char& SORT, OrdinalType& (*ptr2func)(ScalarType*, ScalarType*), const OrdinalType& n, ScalarType* A, const OrdinalType& lda, OrdinalType* sdim, ScalarType* WR, ScalarType* WI, ScalarType* VS, const OrdinalType& ldvs, ScalarType* WORK, const OrdinalType& lwork, OrdinalType* BWORK, OrdinalType* info) const;
352 
356  void GEES(const char& JOBVS, const char& SORT, OrdinalType& (*ptr2func)(ScalarType*), const OrdinalType& n, ScalarType* A, const OrdinalType& lda, OrdinalType* sdim, ScalarType* W, ScalarType* VS, const OrdinalType& ldvs, ScalarType* WORK, const OrdinalType& lwork, MagnitudeType* RWORK, OrdinalType* BWORK, OrdinalType* info) const;
357 
361  void GEES(const char& JOBVS, const OrdinalType& n, ScalarType* A, const OrdinalType& lda, OrdinalType* sdim, MagnitudeType* WR, MagnitudeType* WI, ScalarType* VS, const OrdinalType& ldvs, ScalarType* WORK, const OrdinalType& lwork, MagnitudeType* RWORK, OrdinalType* BWORK, OrdinalType* info) const;
362 
368  void GEEV(const char& JOBVL, const char& JOBVR, const OrdinalType& n, ScalarType* A, const OrdinalType& lda, MagnitudeType* WR, MagnitudeType* WI, ScalarType* VL, const OrdinalType& ldvl, ScalarType* VR, const OrdinalType& ldvr, ScalarType* WORK, const OrdinalType& lwork, MagnitudeType* RWORK, OrdinalType* info) const;
369 
374  void GEEVX(const char& BALANC, const char& JOBVL, const char& JOBVR, const char& SENSE, const OrdinalType& n, ScalarType* A, const OrdinalType& lda, ScalarType* WR, ScalarType* WI, ScalarType* VL, const OrdinalType& ldvl, ScalarType* VR, const OrdinalType& ldvr, OrdinalType* ilo, OrdinalType* ihi, MagnitudeType* SCALE, MagnitudeType* abnrm, MagnitudeType* RCONDE, MagnitudeType* RCONDV, ScalarType* WORK, const OrdinalType& lwork, OrdinalType* IWORK, OrdinalType* info) const;
375 
380  void GGEVX(const char& BALANC, const char& JOBVL, const char& JOBVR, const char& SENSE, const OrdinalType& n, ScalarType* A, const OrdinalType& lda, ScalarType* B, const OrdinalType& ldb, MagnitudeType* ALPHAR, MagnitudeType* ALPHAI, ScalarType* BETA, ScalarType* VL, const OrdinalType& ldvl, ScalarType* VR, const OrdinalType& ldvr, OrdinalType* ilo, OrdinalType* ihi, MagnitudeType* lscale, MagnitudeType* rscale, MagnitudeType* abnrm, MagnitudeType* bbnrm, MagnitudeType* RCONDE, MagnitudeType* RCONDV, ScalarType* WORK, const OrdinalType& lwork, OrdinalType* IWORK, OrdinalType* BWORK, OrdinalType* info) const;
381 
385  void GGEV(const char& JOBVL, const char& JOBVR, const OrdinalType& n, ScalarType* A, const OrdinalType& lda, ScalarType* B, const OrdinalType& ldb, MagnitudeType *ALPHAR, MagnitudeType *ALPHAI, ScalarType* BETA, ScalarType* VL, const OrdinalType& ldvl, ScalarType* VR, const OrdinalType& ldvr, ScalarType* WORK, const OrdinalType& lwork, OrdinalType* info) const;
386 
387 
391  void TRSEN(const char& JOB, const char& COMPQ, const OrdinalType* SELECT, const OrdinalType& n, ScalarType* T, const OrdinalType& ldt, ScalarType* Q, const OrdinalType& ldq, MagnitudeType *WR, MagnitudeType *WI, OrdinalType* M, ScalarType* S, MagnitudeType *SEP, ScalarType* WORK, const OrdinalType& lwork, OrdinalType* IWORK, const OrdinalType& liwork, OrdinalType* info ) const;
392 
393 
397  void TGSEN(const OrdinalType& ijob, const OrdinalType& wantq, const OrdinalType& wantz, const OrdinalType* SELECT, const OrdinalType& n, ScalarType* A, const OrdinalType& lda, ScalarType* B, const OrdinalType& ldb, MagnitudeType *ALPHAR, MagnitudeType *ALPHAI, MagnitudeType *BETA, ScalarType* Q, const OrdinalType& ldq, ScalarType* Z, const OrdinalType& ldz, OrdinalType* M, MagnitudeType *PL, MagnitudeType *PR, MagnitudeType *DIF, ScalarType* WORK, const OrdinalType& lwork, OrdinalType* IWORK, const OrdinalType& liwork, OrdinalType* info ) const;
398 
399 
403  void GGES(const char& JOBVL, const char& JOBVR, const char& SORT, OrdinalType& (*ptr2func)(ScalarType* , ScalarType* , ScalarType* ), const OrdinalType& n, ScalarType* A, const OrdinalType& lda, ScalarType* B, const OrdinalType& ldb, OrdinalType* sdim, MagnitudeType *ALPHAR, MagnitudeType *ALPHAI, MagnitudeType *BETA, ScalarType* VL, const OrdinalType& ldvl, ScalarType* VR, const OrdinalType& ldvr, ScalarType* WORK, const OrdinalType& lwork, OrdinalType* BWORK, OrdinalType* info ) const;
404 
406 
407 
409 
410  void GESVD(const char& JOBU, const char& JOBVT, const OrdinalType& m, const OrdinalType& n, ScalarType* A, const OrdinalType& lda, MagnitudeType* S, ScalarType* U, const OrdinalType& ldu, ScalarType* V, const OrdinalType& ldv, ScalarType* WORK, const OrdinalType& lwork, MagnitudeType* RWORK, OrdinalType* info) const;
413 
414 
416 
417 
427  void ORMQR(const char& SIDE, const char& TRANS, const OrdinalType& m, const OrdinalType& n, const OrdinalType& k, ScalarType* A, const OrdinalType& lda, const ScalarType* TAU, ScalarType* C, const OrdinalType& ldc, ScalarType* WORK, const OrdinalType& lwork, OrdinalType* info) const;
428 
434  void ORM2R(const char& SIDE, const char& TRANS, const OrdinalType& m, const OrdinalType& n, const OrdinalType& k, const ScalarType A[], const OrdinalType& lda, const ScalarType TAU[], ScalarType C[], const OrdinalType& ldc, ScalarType WORK[], OrdinalType* const info) const;
435 
444  void UNMQR(const char& SIDE, const char& TRANS, const OrdinalType& m, const OrdinalType& n, const OrdinalType& k, ScalarType* A, const OrdinalType& lda, const ScalarType* TAU, ScalarType* C, const OrdinalType& ldc, ScalarType* WORK, const OrdinalType& lwork, OrdinalType* info) const;
445 
450  void UNM2R(const char& SIDE, const char& TRANS, const OrdinalType& M, const OrdinalType& N, const OrdinalType& K, const ScalarType A[], const OrdinalType& LDA, const ScalarType TAU[], ScalarType C[], const OrdinalType& LDC, ScalarType WORK[], OrdinalType* const INFO) const;
451 
461  void ORGQR(const OrdinalType& m, const OrdinalType& n, const OrdinalType& k, ScalarType* A, const OrdinalType& lda, const ScalarType* TAU, ScalarType* WORK, const OrdinalType& lwork, OrdinalType* info) const;
462 
471  void UNGQR(const OrdinalType& m, const OrdinalType& n, const OrdinalType& k, ScalarType* A, const OrdinalType& lda, const ScalarType* TAU, ScalarType* WORK, const OrdinalType& lwork, OrdinalType* info) const;
472 
476  void ORGHR(const OrdinalType& n, const OrdinalType& ilo, const OrdinalType& ihi, ScalarType* A, const OrdinalType& lda, const ScalarType* TAU, ScalarType* WORK, const OrdinalType& lwork, OrdinalType* info) const;
477 
481  void ORMHR(const char& SIDE, const char& TRANS, const OrdinalType& m, const OrdinalType& n, const OrdinalType& ilo, const OrdinalType& ihi, const ScalarType* A, const OrdinalType& lda, const ScalarType* TAU, ScalarType* C, const OrdinalType& ldc, ScalarType* WORK, const OrdinalType& lwork, OrdinalType* info) const;
483 
485 
486 
489  void TREVC(const char& SIDE, const char& HOWMNY, OrdinalType* select, const OrdinalType& n, const ScalarType* T, const OrdinalType& ldt, ScalarType* VL, const OrdinalType& ldvl, ScalarType* VR, const OrdinalType& ldvr, const OrdinalType& mm, OrdinalType* m, ScalarType* WORK, OrdinalType* info) const;
490 
494  void TREVC(const char& SIDE, const OrdinalType& n, const ScalarType* T, const OrdinalType& ldt, ScalarType* VL, const OrdinalType& ldvl, ScalarType* VR, const OrdinalType& ldvr, const OrdinalType& mm, OrdinalType* m, ScalarType* WORK, MagnitudeType* RWORK, OrdinalType* info) const;
495 
499  void TREXC(const char& COMPQ, const OrdinalType& n, ScalarType* T, const OrdinalType& ldt, ScalarType* Q, const OrdinalType& ldq, OrdinalType* ifst, OrdinalType* ilst, ScalarType* WORK, OrdinalType* info) const;
500 
504  void TGEVC(const char& SIDE, const char& HOWMNY, const OrdinalType* SELECT, const OrdinalType& n, ScalarType* S, const OrdinalType& lds, ScalarType* P, const OrdinalType& ldp, ScalarType* VL, const OrdinalType& ldvl, ScalarType* VR, const OrdinalType& ldvr, const OrdinalType& mm, OrdinalType* M, ScalarType* WORK, OrdinalType* info) const;
505 
506 
508 
510 
511 
513  void LARTG( const ScalarType& f, const ScalarType& g, MagnitudeType* c, ScalarType* s, ScalarType* r ) const;
514 
516  void LARFG( const OrdinalType& n, ScalarType* alpha, ScalarType* x, const OrdinalType& incx, ScalarType* tau ) const;
517 
519 
521 
522 
524 
525  void GEBAL(const char& JOBZ, const OrdinalType& n, ScalarType* A, const OrdinalType& lda, OrdinalType* ilo, OrdinalType* ihi, MagnitudeType* scale, OrdinalType* info) const;
526 
528  void GEBAK(const char& JOBZ, const char& SIDE, const OrdinalType& n, const OrdinalType& ilo, const OrdinalType& ihi, const MagnitudeType* scale , const OrdinalType& m, ScalarType* V, const OrdinalType& ldv, OrdinalType* info) const;
529 
531 
533 
534  ScalarType LARND( const OrdinalType& idist, OrdinalType* seed ) const;
536 
538  void LARNV( const OrdinalType& idist, OrdinalType* seed, const OrdinalType& n, ScalarType* v ) const;
540 
542 
543 
546  ScalarType LAMCH(const char& CMACH) const;
547 
552  OrdinalType ILAENV( const OrdinalType& ispec, const std::string& NAME, const std::string& OPTS, const OrdinalType& N1 = -1, const OrdinalType& N2 = -1, const OrdinalType& N3 = -1, const OrdinalType& N4 = -1 ) const;
554 
556 
557 
560  ScalarType LAPY2(const ScalarType& x, const ScalarType& y) const;
562  };
563 
564  // END GENERAL TEMPLATE DECLARATION //
565 
566  // BEGIN GENERAL TEMPLATE IMPLEMENTATION //
567 
568 
569  template<typename OrdinalType, typename ScalarType>
570  void LAPACK<OrdinalType, ScalarType>::PTTRF(const OrdinalType& n, ScalarType* d, ScalarType* e, OrdinalType* info) const
571  {
572  UndefinedLAPACKRoutine<ScalarType>::notDefined();
573  }
574 
575  template<typename OrdinalType, typename ScalarType>
576  void LAPACK<OrdinalType, ScalarType>::PTTRS(const OrdinalType& n, const OrdinalType& nrhs, const ScalarType* d, const ScalarType* e, ScalarType* B, const OrdinalType& ldb, OrdinalType* info) const
577  {
578  UndefinedLAPACKRoutine<ScalarType>::notDefined();
579  }
580 
581  template<typename OrdinalType, typename ScalarType>
582  void LAPACK<OrdinalType, ScalarType>::POTRF(const char& UPLO, const OrdinalType& n, ScalarType* A, const OrdinalType& lda, OrdinalType* info) const
583  {
584  UndefinedLAPACKRoutine<ScalarType>::notDefined();
585  }
586 
587  template<typename OrdinalType, typename ScalarType>
588  void LAPACK<OrdinalType, ScalarType>::POTRS(const char& UPLO, const OrdinalType& n, const OrdinalType& nrhs, const ScalarType* A, const OrdinalType& lda, ScalarType* B, const OrdinalType& ldb, OrdinalType* info) const
589  {
590  UndefinedLAPACKRoutine<ScalarType>::notDefined();
591  }
592 
593  template<typename OrdinalType, typename ScalarType>
594  void LAPACK<OrdinalType, ScalarType>::POTRI(const char& UPLO, const OrdinalType& n, ScalarType* A, const OrdinalType& lda, OrdinalType* info) const
595  {
596  UndefinedLAPACKRoutine<ScalarType>::notDefined();
597  }
598 
599  template<typename OrdinalType, typename ScalarType>
600  void LAPACK<OrdinalType, ScalarType>::POCON(const char& UPLO, const OrdinalType& n, const ScalarType* A, const OrdinalType& lda, const ScalarType& anorm, ScalarType* rcond, ScalarType* WORK, OrdinalType* IWORK, OrdinalType* info) const
601  {
602  UndefinedLAPACKRoutine<ScalarType>::notDefined();
603  }
604 
605  template<typename OrdinalType, typename ScalarType>
606  void LAPACK<OrdinalType, ScalarType>::POSV(const char& UPLO, const OrdinalType& n, const OrdinalType& nrhs, ScalarType* A, const OrdinalType& lda, ScalarType* B, const OrdinalType& ldb, OrdinalType* info) const
607  {
608  UndefinedLAPACKRoutine<ScalarType>::notDefined();
609  }
610 
611  template<typename OrdinalType, typename ScalarType>
612  void LAPACK<OrdinalType, ScalarType>::POEQU(const OrdinalType& n, const ScalarType* A, const OrdinalType& lda, MagnitudeType* S, MagnitudeType* scond, MagnitudeType* amax, OrdinalType* info) const
613  {
614  // Test the input parameters
615  *info = 0;
616  if (n < 0) {
617  *info = -1;
618  } else if (lda < TEUCHOS_MAX(1, n)) {
619  *info = -3;
620  }
621  if (*info != 0) {
622  return;
623  }
624 
625  ScalarType sZero = ScalarTraits<ScalarType>::zero();
626  ScalarType sOne = ScalarTraits<ScalarType>::one();
627  MagnitudeType mZero = ScalarTraits<ScalarType>::magnitude(sZero);
628  MagnitudeType mOne = ScalarTraits<ScalarType>::magnitude(sOne);
629 
630  // Quick return
631  if (n == 0) {
632  *scond = mOne;
633  *amax = mZero;
634  return;
635  }
636 
637  // Find the minimum and maximum diagonal elements
638  S[0] = ScalarTraits<ScalarType>::magnitude( A[0] );
639  MagnitudeType smin = S[0];
640  *amax = S[0];
641  for (OrdinalType i=0; i<n; ++i) {
642  S[i] = ScalarTraits<ScalarType>::magnitude( A[i*lda + i] );
643  smin = TEUCHOS_MIN( smin, S[i] );
644  *amax = TEUCHOS_MAX( *amax, S[i] );
645  }
646 
647  if (smin < mZero) {
648  // Find the first non-positve diagonal element and return an error code
649  for (OrdinalType i=0; i<n; ++i) {
650  if (S[i] < mZero)
651  *info = i;
652  }
653  } else {
654  // Set the scale factors to the reciprocals of the diagonal elements
655  for (OrdinalType i=0; i<n; ++i) {
656  S[i] = mOne / ScalarTraits<ScalarType>::squareroot( S[i] );
657  }
658  // Compute scond = min(S(i)) / max(S(i))
659  *scond = ScalarTraits<ScalarType>::squareroot( smin ) / ScalarTraits<ScalarType>::squareroot( *amax );
660  }
661  }
662 
663  template<typename OrdinalType, typename ScalarType>
664  void LAPACK<OrdinalType, ScalarType>::PORFS(const char& UPLO, const OrdinalType& n, const OrdinalType& nrhs, const ScalarType* A, const OrdinalType& lda, const ScalarType* AF, const OrdinalType& ldaf, const ScalarType* B, const OrdinalType& ldb, ScalarType* X, const OrdinalType& ldx, ScalarType* FERR, ScalarType* BERR, ScalarType* WORK, OrdinalType* IWORK, OrdinalType* info) const
665  {
666  UndefinedLAPACKRoutine<ScalarType>::notDefined();
667  }
668 
669  template<typename OrdinalType, typename ScalarType>
670  void LAPACK<OrdinalType, ScalarType>::POSVX(const char& FACT, const char& UPLO, const OrdinalType& n, const OrdinalType& nrhs, ScalarType* A, const OrdinalType& lda, ScalarType* AF, const OrdinalType& ldaf, char* EQUED, ScalarType* S, ScalarType* B, const OrdinalType& ldb, ScalarType* X, const OrdinalType& ldx, ScalarType* rcond, ScalarType* FERR, ScalarType* BERR, ScalarType* WORK, OrdinalType* IWORK, OrdinalType* info) const
671  {
672  UndefinedLAPACKRoutine<ScalarType>::notDefined();
673  }
674 
675  template<typename OrdinalType, typename ScalarType>
676  void LAPACK<OrdinalType,ScalarType>::GELS(const char& TRANS, const OrdinalType& m, const OrdinalType& n, const OrdinalType& nrhs, ScalarType* A, const OrdinalType& lda, ScalarType* B, const OrdinalType& ldb, ScalarType* WORK, const OrdinalType& lwork, OrdinalType* info) const
677  {
678  UndefinedLAPACKRoutine<ScalarType>::notDefined();
679  }
680 
681  template<typename OrdinalType, typename ScalarType>
682  void LAPACK<OrdinalType, ScalarType>::GELSS(const OrdinalType& m, const OrdinalType& n, const OrdinalType& nrhs, ScalarType* A, const OrdinalType& lda, ScalarType* B, const OrdinalType& ldb, MagnitudeType* S, const MagnitudeType rcond, OrdinalType* rank, ScalarType* WORK, const OrdinalType& lwork, MagnitudeType* RWORK, OrdinalType* info) const
683  {
684  UndefinedLAPACKRoutine<ScalarType>::notDefined();
685  }
686 
687  template<typename OrdinalType, typename ScalarType>
688  void LAPACK<OrdinalType,ScalarType>::GELSS(const OrdinalType& m, const OrdinalType& n, const OrdinalType& nrhs, ScalarType* A, const OrdinalType& lda, ScalarType* B, const OrdinalType& ldb, ScalarType* S, const ScalarType& rcond, OrdinalType* rank, ScalarType* WORK, const OrdinalType& lwork, OrdinalType* info) const
689  {
690  UndefinedLAPACKRoutine<ScalarType>::notDefined();
691  }
692 
693  template<typename OrdinalType, typename ScalarType>
694  void LAPACK<OrdinalType,ScalarType>::GGLSE(const OrdinalType& m, const OrdinalType& n, const OrdinalType& p, ScalarType* A, const OrdinalType& lda, ScalarType* B, const OrdinalType& ldb, ScalarType* C, ScalarType* D, ScalarType* X, ScalarType* WORK, const OrdinalType& lwork, OrdinalType* info) const
695  {
696  UndefinedLAPACKRoutine<ScalarType>::notDefined();
697  }
698 
699  template<typename OrdinalType, typename ScalarType>
700  void LAPACK<OrdinalType,ScalarType>::GEQRF( const OrdinalType& m, const OrdinalType& n, ScalarType* A, const OrdinalType& lda, ScalarType* TAU, ScalarType* WORK, const OrdinalType& lwork, OrdinalType* info) const
701  {
702  UndefinedLAPACKRoutine<ScalarType>::notDefined();
703  }
704 
705  template<typename OrdinalType, typename ScalarType>
706  void LAPACK<OrdinalType,ScalarType>::GEQR2 (const OrdinalType& m, const OrdinalType& n, ScalarType A[], const OrdinalType& lda, ScalarType TAU[], ScalarType WORK[], OrdinalType* const info) const
707  {
708  UndefinedLAPACKRoutine<ScalarType>::notDefined();
709  }
710 
711  template<typename OrdinalType, typename ScalarType>
712  void LAPACK<OrdinalType,ScalarType>::GETRF(const OrdinalType& m, const OrdinalType& n, ScalarType* A, const OrdinalType& lda, OrdinalType* IPIV, OrdinalType* info) const
713  {
714  UndefinedLAPACKRoutine<ScalarType>::notDefined();
715  }
716 
717  template<typename OrdinalType, typename ScalarType>
718  void LAPACK<OrdinalType,ScalarType>::GETRS(const char& TRANS, const OrdinalType& n, const OrdinalType& nrhs, const ScalarType* A, const OrdinalType& lda, const OrdinalType* IPIV, ScalarType* B, const OrdinalType& ldb, OrdinalType* info) const
719  {
720  UndefinedLAPACKRoutine<ScalarType>::notDefined();
721  }
722 
723  template<typename OrdinalType, typename ScalarType>
724  void LAPACK<OrdinalType,ScalarType>::LASCL(const char& TYPE, const OrdinalType& kl, const OrdinalType& ku, const MagnitudeType cfrom, const MagnitudeType cto, const OrdinalType& m, const OrdinalType& n, ScalarType* A, const OrdinalType& lda, OrdinalType* info) const
725  {
726  MagnitudeType safeMin = ScalarTraits<ScalarType>::sfmin();
727  ScalarType sZero = ScalarTraits<ScalarType>::zero();
728  ScalarType sOne = ScalarTraits<ScalarType>::one();
729  MagnitudeType mZero = ScalarTraits<ScalarType>::magnitude(sZero);
730  MagnitudeType mOne = ScalarTraits<ScalarType>::magnitude(sOne);
731 
732  MagnitudeType smlnum = ScalarTraits<ScalarType>::magnitude(safeMin);
733  MagnitudeType bignum = ScalarTraits<ScalarType>::magnitude(sOne/smlnum);
734 
735  OrdinalType i, j;
736  ScalarType* ptr;
737  MagnitudeType mul;
738  bool done = false;
739 
740  MagnitudeType cfromc = cfrom;
741  MagnitudeType ctoc = cto;
742  MagnitudeType cfrom1;
743  MagnitudeType cto1;
744 
745  while (!done) {
746 
747  cfrom1 = cfromc*smlnum;
748  if (cfrom1 == cfromc) {
749  // cfromc is an inf. Multiply by a correctly signed zero for finite ctoc, or a NaN if ctoc is infinite.
750  mul = ctoc / cfromc;
751  done = true;
752  cto1 = ctoc;
753  } else {
754  cto1 = ctoc / bignum;
755  if (cto1 == ctoc) {
756  // ctoc is either 0 or an inf. In both cases, ctoc itself serves as the correct multiplication factor.
757  mul = ctoc;
758  done = true;
759  cfromc = mOne;
760  } else if (ScalarTraits<ScalarType>::magnitude(cfrom1) > ScalarTraits<ScalarType>::magnitude(ctoc) && ctoc != mZero) {
761  mul = smlnum;
762  done = false;
763  cfromc = cfrom1;
764  } else if (ScalarTraits<ScalarType>::magnitude(cto1) > ScalarTraits<ScalarType>::magnitude(cfromc)) {
765  mul = bignum;
766  done = false;
767  ctoc = cto1;
768  } else {
769  mul = ctoc / cfromc;
770  done = true;
771  }
772  }
773 
774  for (j=0; j<n; j++) {
775  ptr = A + j*lda;
776  for (i=0; i<m; i++) { *ptr = mul * (*ptr); ptr++; }
777  }
778  }
779 
780  }
781 
782  template<typename OrdinalType, typename ScalarType>
783  void
784  LAPACK<OrdinalType,ScalarType>::
785  GEQP3 (const OrdinalType& m,
786  const OrdinalType& n,
787  ScalarType* A,
788  const OrdinalType& lda,
789  OrdinalType* jpvt,
790  ScalarType* TAU,
791  ScalarType* WORK,
792  const OrdinalType& lwork,
793  MagnitudeType* RWORK,
794  OrdinalType* info) const
795  {
796  UndefinedLAPACKRoutine<ScalarType>::notDefined();
797  }
798 
799  template<typename OrdinalType, typename ScalarType>
800  void
801  LAPACK<OrdinalType, ScalarType>::
802  LASWP (const OrdinalType& N,
803  ScalarType A[],
804  const OrdinalType& LDA,
805  const OrdinalType& K1,
806  const OrdinalType& K2,
807  const OrdinalType IPIV[],
808  const OrdinalType& INCX) const
809  {
810  UndefinedLAPACKRoutine<ScalarType>::notDefined();
811  }
812 
813  template<typename OrdinalType, typename ScalarType>
814  void LAPACK<OrdinalType,ScalarType>::GBTRF(const OrdinalType& m, const OrdinalType& n, const OrdinalType& kl, const OrdinalType& ku, ScalarType* A, const OrdinalType& lda, OrdinalType* IPIV, OrdinalType* info) const
815  {
816  UndefinedLAPACKRoutine<ScalarType>::notDefined();
817  }
818 
819  template<typename OrdinalType, typename ScalarType>
820  void LAPACK<OrdinalType,ScalarType>::GBTRS(const char& TRANS, const OrdinalType& n, const OrdinalType& kl, const OrdinalType& ku, const OrdinalType& nrhs, const ScalarType* A, const OrdinalType& lda, const OrdinalType* IPIV, ScalarType* B, const OrdinalType& ldb, OrdinalType* info) const
821  {
822  UndefinedLAPACKRoutine<ScalarType>::notDefined();
823  }
824 
825  template<typename OrdinalType, typename ScalarType>
826  void LAPACK<OrdinalType,ScalarType>::GTTRF(const OrdinalType& n, ScalarType* dl, ScalarType* d, ScalarType* du, ScalarType* du2, OrdinalType* IPIV, OrdinalType* info) const
827  {
828  UndefinedLAPACKRoutine<ScalarType>::notDefined();
829  }
830 
831  template<typename OrdinalType, typename ScalarType>
832  void LAPACK<OrdinalType,ScalarType>::GTTRS(const char& TRANS, const OrdinalType& n, const OrdinalType& nrhs, const ScalarType* dl, const ScalarType* d, const ScalarType* du, const ScalarType* du2, const OrdinalType* IPIV, ScalarType* B, const OrdinalType& ldb, OrdinalType* info) const
833  {
834  UndefinedLAPACKRoutine<ScalarType>::notDefined();
835  }
836 
837  template<typename OrdinalType, typename ScalarType>
838  void LAPACK<OrdinalType,ScalarType>::GETRI(const OrdinalType& n, ScalarType* A, const OrdinalType& lda, const OrdinalType* IPIV, ScalarType* WORK, const OrdinalType& lwork, OrdinalType* info) const
839  {
840  UndefinedLAPACKRoutine<ScalarType>::notDefined();
841  }
842 
843  template<typename OrdinalType, typename ScalarType>
844  void
845  LAPACK<OrdinalType,ScalarType>::
846  LATRS (const char& UPLO,
847  const char& TRANS,
848  const char& DIAG,
849  const char& NORMIN,
850  const OrdinalType& N,
851  ScalarType* A,
852  const OrdinalType& LDA,
853  ScalarType* X,
854  MagnitudeType* SCALE,
855  MagnitudeType* CNORM,
856  OrdinalType* INFO) const
857  {
858  UndefinedLAPACKRoutine<ScalarType>::notDefined();
859  }
860 
861  template<typename OrdinalType, typename ScalarType>
862  void LAPACK<OrdinalType,ScalarType>::GECON(const char& NORM, const OrdinalType& n, const ScalarType* A, const OrdinalType& lda, const ScalarType& anorm, ScalarType* rcond, ScalarType* WORK, OrdinalType* IWORK, OrdinalType* info) const
863  {
864  UndefinedLAPACKRoutine<ScalarType>::notDefined();
865  }
866 
867  template<typename OrdinalType, typename ScalarType>
868  void LAPACK<OrdinalType,ScalarType>::GBCON(const char& NORM, const OrdinalType& n, const OrdinalType& kl, const OrdinalType& ku, const ScalarType* A, const OrdinalType& lda, OrdinalType* IPIV, const ScalarType& anorm, ScalarType* rcond, ScalarType* WORK, OrdinalType* IWORK, OrdinalType* info) const
869  {
870  UndefinedLAPACKRoutine<ScalarType>::notDefined();
871  }
872 
873  template<typename OrdinalType, typename ScalarType>
874  typename ScalarTraits<ScalarType>::magnitudeType LAPACK<OrdinalType,ScalarType>::LANGB(const char& NORM, const OrdinalType& n, const OrdinalType& kl, const OrdinalType& ku, const ScalarType* A, const OrdinalType& lda, MagnitudeType* WORK) const
875  {
876  UndefinedLAPACKRoutine<ScalarType>::notDefined();
877  }
878 
879  template<typename OrdinalType, typename ScalarType>
880  void LAPACK<OrdinalType,ScalarType>::GESV(const OrdinalType& n, const OrdinalType& nrhs, ScalarType* A, const OrdinalType& lda, OrdinalType* IPIV, ScalarType* B, const OrdinalType& ldb, OrdinalType* info) const
881  {
882  UndefinedLAPACKRoutine<ScalarType>::notDefined();
883  }
884 
885  template<typename OrdinalType, typename ScalarType>
886  void LAPACK<OrdinalType,ScalarType>::GEEQU(const OrdinalType& m, const OrdinalType& n, const ScalarType* A, const OrdinalType& lda, ScalarType* R, ScalarType* C, ScalarType* rowcond, ScalarType* colcond, ScalarType* amax, OrdinalType* info) const
887  {
888 
889  // Test the input parameters
890  *info = 0;
891  if (m < 0) {
892  *info = -1;
893  } else if (n < 0) {
894  *info = -2;
895  } else if (lda < TEUCHOS_MAX(1, m)) {
896  *info = -4;
897  }
898  if (*info != 0) {
899  return;
900  }
901 
902  ScalarType sZero = ScalarTraits<ScalarType>::zero();
903  ScalarType sOne = ScalarTraits<ScalarType>::one();
904  MagnitudeType mZero = ScalarTraits<ScalarType>::magnitude(sZero);
905  MagnitudeType mOne = ScalarTraits<ScalarType>::magnitude(sOne);
906 
907  // Quick return
908  if (m == 0 || n == 0) {
909  *rowcond = mOne;
910  *colcond = mOne;
911  *amax = mZero;
912  return;
913  }
914 
915  MagnitudeType safeMin = ScalarTraits<ScalarType>::sfmin();
916  MagnitudeType smlnum = ScalarTraits<ScalarType>::magnitude(safeMin);
917  MagnitudeType bignum = ScalarTraits<ScalarType>::magnitude(sOne/smlnum);
918 
919  // Compute the row scale factors
920  for (OrdinalType i=0; i<m; i++) {
921  R[i] = mZero;
922  }
923 
924  // Find the maximum element in each row
925  for (OrdinalType j=0; j<n; j++) {
926  for (OrdinalType i=0; i<m; i++) {
927  R[i] = TEUCHOS_MAX( R[i], ScalarTraits<ScalarType>::magnitude( A[j*lda + i] ) );
928  }
929  }
930 
931  // Find the maximum and minimum scale factors
932  MagnitudeType rcmin = bignum;
933  MagnitudeType rcmax = mZero;
934  for (OrdinalType i=0; i<m; i++) {
935  rcmax = TEUCHOS_MAX( rcmax, R[i] );
936  rcmin = TEUCHOS_MIN( rcmin, R[i] );
937  }
938  *amax = rcmax;
939 
940  if (rcmin == mZero) {
941  // Find the first zero scale factor and return an error code
942  for (OrdinalType i=0; i<m; i++) {
943  if (R[i] == mZero)
944  *info = i;
945  }
946  } else {
947  // Invert the scale factors
948  for (OrdinalType i=0; i<m; i++) {
949  R[i] = mOne / TEUCHOS_MIN( TEUCHOS_MAX( R[i], smlnum ), bignum );
950  }
951  // Compute rowcond = min(R(i)) / max(R(i))
952  *rowcond = TEUCHOS_MAX( rcmin, smlnum ) / TEUCHOS_MIN( rcmax, bignum );
953  }
954 
955  // Compute the column scale factors
956  for (OrdinalType j=0; j<n; j++) {
957  C[j] = mZero;
958  }
959 
960  // Find the maximum element in each column, assuming the row scaling computed above
961  for (OrdinalType j=0; j<n; j++) {
962  for (OrdinalType i=0; i<m; i++) {
963  C[j] = TEUCHOS_MAX( C[j], R[i]*ScalarTraits<ScalarType>::magnitude( A[j*lda + i] ) );
964  }
965  }
966 
967  // Find the maximum and minimum scale factors
968  rcmin = bignum;
969  rcmax = mZero;
970  for (OrdinalType j=0; j<n; j++) {
971  rcmax = TEUCHOS_MAX( rcmax, C[j] );
972  rcmin = TEUCHOS_MIN( rcmin, C[j] );
973  }
974 
975  if (rcmin == mZero) {
976  // Find the first zero scale factor and return an error code
977  for (OrdinalType j=0; j<n; j++) {
978  if (C[j] == mZero)
979  *info = m+j;
980  }
981  } else {
982  // Invert the scale factors
983  for (OrdinalType j=0; j<n; j++) {
984  C[j] = mOne / TEUCHOS_MIN( TEUCHOS_MAX( C[j], smlnum ), bignum );
985  }
986  // Compute colcond = min(C(j)) / max(C(j))
987  *colcond = TEUCHOS_MAX( rcmin, smlnum ) / TEUCHOS_MIN( rcmax, bignum );
988  }
989  }
990 
991  template<typename OrdinalType, typename ScalarType>
992  void LAPACK<OrdinalType,ScalarType>::GERFS(const char& TRANS, const OrdinalType& n, const OrdinalType& nrhs, const ScalarType* A, const OrdinalType& lda, const ScalarType* AF, const OrdinalType& ldaf, const OrdinalType* IPIV, const ScalarType* B, const OrdinalType& ldb, ScalarType* X, const OrdinalType& ldx, ScalarType* FERR, ScalarType* BERR, ScalarType* WORK, OrdinalType* IWORK, OrdinalType* info) const
993  {
994  UndefinedLAPACKRoutine<ScalarType>::notDefined();
995  }
996 
997  template<typename OrdinalType, typename ScalarType>
998  void LAPACK<OrdinalType,ScalarType>::GBEQU(const OrdinalType& m, const OrdinalType& n, const OrdinalType& kl, const OrdinalType& ku, const ScalarType* A, const OrdinalType& lda, MagnitudeType* R, MagnitudeType* C, MagnitudeType* rowcond, MagnitudeType* colcond, MagnitudeType* amax, OrdinalType* info) const
999  {
1000 
1001  // Test the input parameters
1002  * info = 0;
1003  if (m < 0) {
1004  *info = -1;
1005  } else if (n < 0) {
1006  *info = -2;
1007  } else if (kl < 0) {
1008  *info = -3;
1009  } else if (ku < 0) {
1010  *info = -4;
1011  } else if (lda < kl+ku+1) {
1012  *info = -6;
1013  }
1014  if (*info != 0) {
1015  return;
1016  }
1017 
1018  ScalarType sZero = ScalarTraits<ScalarType>::zero();
1019  ScalarType sOne = ScalarTraits<ScalarType>::one();
1020  MagnitudeType mZero = ScalarTraits<ScalarType>::magnitude(sZero);
1021  MagnitudeType mOne = ScalarTraits<ScalarType>::magnitude(sOne);
1022 
1023  // Quick return
1024  if (m == 0 || n == 0) {
1025  *rowcond = mOne;
1026  *colcond = mOne;
1027  *amax = mZero;
1028  return;
1029  }
1030 
1031  MagnitudeType safeMin = ScalarTraits<ScalarType>::sfmin();
1032  MagnitudeType smlnum = ScalarTraits<ScalarType>::magnitude(safeMin);
1033  MagnitudeType bignum = ScalarTraits<ScalarType>::magnitude(sOne/smlnum);
1034 
1035  // Compute the row scale factors
1036  for (OrdinalType i=0; i<m; i++) {
1037  R[i] = mZero;
1038  }
1039 
1040  // Find the maximum element in each row
1041  for (OrdinalType j=0; j<n; j++) {
1042  for (OrdinalType i=TEUCHOS_MAX(j-ku,0); i<TEUCHOS_MIN(j+kl,m-1); i++) {
1043  R[i] = TEUCHOS_MAX( R[i], ScalarTraits<ScalarType>::magnitude( A[j*lda + ku+i-j] ) );
1044  }
1045  }
1046 
1047  // Find the maximum and minimum scale factors
1048  MagnitudeType rcmin = bignum;
1049  MagnitudeType rcmax = mZero;
1050  for (OrdinalType i=0; i<m; i++) {
1051  rcmax = TEUCHOS_MAX( rcmax, R[i] );
1052  rcmin = TEUCHOS_MIN( rcmin, R[i] );
1053  }
1054  *amax = rcmax;
1055 
1056  if (rcmin == mZero) {
1057  // Find the first zero scale factor and return an error code
1058  for (OrdinalType i=0; i<m; i++) {
1059  if (R[i] == mZero)
1060  *info = i;
1061  }
1062  } else {
1063  // Invert the scale factors
1064  for (OrdinalType i=0; i<m; i++) {
1065  R[i] = mOne / TEUCHOS_MIN( TEUCHOS_MAX( R[i], smlnum ), bignum );
1066  }
1067  // Compute rowcond = min(R(i)) / max(R(i))
1068  *rowcond = TEUCHOS_MAX( rcmin, smlnum ) / TEUCHOS_MIN( rcmax, bignum );
1069  }
1070 
1071  // Compute the column scale factors
1072  for (OrdinalType j=0; j<n; j++) {
1073  C[j] = mZero;
1074  }
1075 
1076  // Find the maximum element in each column, assuming the row scaling computed above
1077  for (OrdinalType j=0; j<n; j++) {
1078  for (OrdinalType i=TEUCHOS_MAX(j-ku,0); i<TEUCHOS_MIN(j+kl,m-1); i++) {
1079  C[j] = TEUCHOS_MAX( C[j], R[i]*ScalarTraits<ScalarType>::magnitude( A[j*lda + ku+i-j] ) );
1080  }
1081  }
1082 
1083  // Find the maximum and minimum scale factors
1084  rcmin = bignum;
1085  rcmax = mZero;
1086  for (OrdinalType j=0; j<n; j++) {
1087  rcmax = TEUCHOS_MAX( rcmax, C[j] );
1088  rcmin = TEUCHOS_MIN( rcmin, C[j] );
1089  }
1090 
1091  if (rcmin == mZero) {
1092  // Find the first zero scale factor and return an error code
1093  for (OrdinalType j=0; j<n; j++) {
1094  if (C[j] == mZero)
1095  *info = m+j;
1096  }
1097  } else {
1098  // Invert the scale factors
1099  for (OrdinalType j=0; j<n; j++) {
1100  C[j] = mOne / TEUCHOS_MIN( TEUCHOS_MAX( C[j], smlnum ), bignum );
1101  }
1102  // Compute colcond = min(C(j)) / max(C(j))
1103  *colcond = TEUCHOS_MAX( rcmin, smlnum ) / TEUCHOS_MIN( rcmax, bignum );
1104  }
1105  }
1106 
1107  template<typename OrdinalType, typename ScalarType>
1108  void LAPACK<OrdinalType,ScalarType>::GBRFS(const char& TRANS, const OrdinalType& n, const OrdinalType& kl, const OrdinalType& ku, const OrdinalType& nrhs, const ScalarType* A, const OrdinalType& lda, const ScalarType* AF, const OrdinalType& ldaf, const OrdinalType* IPIV, const ScalarType* B, const OrdinalType& ldb, ScalarType* X, const OrdinalType& ldx, ScalarType* FERR, ScalarType* BERR, ScalarType* WORK, OrdinalType* IWORK, OrdinalType* info) const
1109  {
1110  UndefinedLAPACKRoutine<ScalarType>::notDefined();
1111  }
1112 
1113  template<typename OrdinalType, typename ScalarType>
1114  void LAPACK<OrdinalType,ScalarType>::GESVX(const char& FACT, const char& TRANS, const OrdinalType& n, const OrdinalType& nrhs, ScalarType* A, const OrdinalType& lda, ScalarType* AF, const OrdinalType& ldaf, OrdinalType* IPIV, char* EQUED, ScalarType* R, ScalarType* C, ScalarType* B, const OrdinalType& ldb, ScalarType* X, const OrdinalType& ldx, ScalarType* rcond, ScalarType* FERR, ScalarType* BERR, ScalarType* WORK, OrdinalType* IWORK, OrdinalType* info) const
1115  {
1116  UndefinedLAPACKRoutine<ScalarType>::notDefined();
1117  }
1118 
1119  template<typename OrdinalType, typename ScalarType>
1120  void LAPACK<OrdinalType,ScalarType>::SYTRD(const char& UPLO, const OrdinalType& n, ScalarType* A, const OrdinalType& lda, ScalarType* D, ScalarType* E, ScalarType* TAU, ScalarType* WORK, const OrdinalType& lwork, OrdinalType* info) const
1121  {
1122  UndefinedLAPACKRoutine<ScalarType>::notDefined();
1123  }
1124 
1125  template<typename OrdinalType, typename ScalarType>
1126  void LAPACK<OrdinalType,ScalarType>::GEHRD(const OrdinalType& n, const OrdinalType& ilo, const OrdinalType& ihi, ScalarType* A, const OrdinalType& lda, ScalarType* TAU, ScalarType* WORK, const OrdinalType& lwork, OrdinalType* info) const
1127  {
1128  UndefinedLAPACKRoutine<ScalarType>::notDefined();
1129  }
1130 
1131  template<typename OrdinalType, typename ScalarType>
1132  void LAPACK<OrdinalType,ScalarType>::TRTRS(const char& UPLO, const char& TRANS, const char& DIAG, const OrdinalType& n, const OrdinalType& nrhs, const ScalarType* A, const OrdinalType& lda, ScalarType* B, const OrdinalType& ldb, OrdinalType* info) const
1133  {
1134  UndefinedLAPACKRoutine<ScalarType>::notDefined();
1135  }
1136 
1137  template<typename OrdinalType, typename ScalarType>
1138  void LAPACK<OrdinalType,ScalarType>::TRTRI(const char& UPLO, const char& DIAG, const OrdinalType& n, const ScalarType* A, const OrdinalType& lda, OrdinalType* info) const
1139  {
1140  UndefinedLAPACKRoutine<ScalarType>::notDefined();
1141  }
1142 
1143  template<typename OrdinalType, typename ScalarType>
1144  void LAPACK<OrdinalType,ScalarType>::SPEV(const char& JOBZ, const char& UPLO, const OrdinalType& n, ScalarType* AP, ScalarType* W, ScalarType* Z, const OrdinalType& ldz, ScalarType* WORK, OrdinalType* info) const
1145  {
1146  UndefinedLAPACKRoutine<ScalarType>::notDefined();
1147  }
1148 
1149  template<typename OrdinalType, typename ScalarType>
1150  void LAPACK<OrdinalType,ScalarType>::SYEV(const char& JOBZ, const char& UPLO, const OrdinalType& n, ScalarType* A, const OrdinalType& lda, ScalarType* W, ScalarType* WORK, const OrdinalType& lwork, OrdinalType* info) const
1151  {
1152  UndefinedLAPACKRoutine<ScalarType>::notDefined();
1153  }
1154 
1155  template<typename OrdinalType, typename ScalarType>
1156  void LAPACK<OrdinalType,ScalarType>::SYGV(const OrdinalType& itype, const char& JOBZ, const char& UPLO, const OrdinalType& n, ScalarType* A, const OrdinalType& lda, ScalarType* B, const OrdinalType& ldb, ScalarType* W, ScalarType* WORK, const OrdinalType& lwork, OrdinalType* info) const
1157  {
1158  UndefinedLAPACKRoutine<ScalarType>::notDefined();
1159  }
1160 
1161  template<typename OrdinalType, typename ScalarType>
1162  void LAPACK<OrdinalType,ScalarType>::HEEV(const char& JOBZ, const char& UPLO, const OrdinalType& n, ScalarType* A, const OrdinalType& lda, MagnitudeType* W, ScalarType* WORK, const OrdinalType& lwork, MagnitudeType* RWORK, OrdinalType* info) const
1163  {
1164  UndefinedLAPACKRoutine<ScalarType>::notDefined();
1165  }
1166 
1167  template<typename OrdinalType, typename ScalarType>
1168  void LAPACK<OrdinalType,ScalarType>::HEGV(const OrdinalType& itype, const char& JOBZ, const char& UPLO, const OrdinalType& n, ScalarType* A, const OrdinalType& lda, ScalarType* B, const OrdinalType& ldb, MagnitudeType* W, ScalarType* WORK, const OrdinalType& lwork, MagnitudeType* RWORK, OrdinalType* info) const
1169  {
1170  UndefinedLAPACKRoutine<ScalarType>::notDefined();
1171  }
1172 
1173  template<typename OrdinalType, typename ScalarType>
1174  void LAPACK<OrdinalType,ScalarType>::STEQR(const char& COMPZ, const OrdinalType& n, MagnitudeType* D, MagnitudeType* E, ScalarType* Z, const OrdinalType& ldz, MagnitudeType* WORK, OrdinalType* info) const
1175  {
1176  UndefinedLAPACKRoutine<ScalarType>::notDefined();
1177  }
1178 
1179  template<typename OrdinalType, typename ScalarType>
1180  void LAPACK<OrdinalType,ScalarType>::PTEQR(const char& COMPZ, const OrdinalType& n, MagnitudeType* D, MagnitudeType* E, ScalarType* Z, const OrdinalType& ldz, MagnitudeType* WORK, OrdinalType* info) const
1181  {
1182  UndefinedLAPACKRoutine<ScalarType>::notDefined();
1183  }
1184 
1185  template<typename OrdinalType, typename ScalarType>
1186  void LAPACK<OrdinalType, ScalarType>::HSEQR(const char& JOB, const char& COMPZ, const OrdinalType& n, const OrdinalType& ilo, const OrdinalType& ihi, ScalarType* H, const OrdinalType& ldh, ScalarType* WR, ScalarType* WI, ScalarType* Z, const OrdinalType& ldz, ScalarType* WORK, const OrdinalType& lwork, OrdinalType* info) const
1187  {
1188  UndefinedLAPACKRoutine<ScalarType>::notDefined();
1189  }
1190 
1191  template<typename OrdinalType, typename ScalarType>
1192  void LAPACK<OrdinalType, ScalarType>::GEES(const char& JOBVS, const char& SORT, OrdinalType& (*ptr2func)(ScalarType*, ScalarType*), const OrdinalType& n, ScalarType* A, const OrdinalType& lda, OrdinalType* sdim, ScalarType* WR, ScalarType* WI, ScalarType* VS, const OrdinalType& ldvs, ScalarType* WORK, const OrdinalType& lwork, OrdinalType* BWORK, OrdinalType* info) const
1193  {
1194  UndefinedLAPACKRoutine<ScalarType>::notDefined();
1195  }
1196 
1197  template<typename OrdinalType, typename ScalarType>
1198  void LAPACK<OrdinalType, ScalarType>::GEES(const char& JOBVS, const char& SORT, OrdinalType& (*ptr2func)(ScalarType*), const OrdinalType& n, ScalarType* A, const OrdinalType& lda, OrdinalType* sdim, ScalarType* W, ScalarType* VS, const OrdinalType& ldvs, ScalarType* WORK, const OrdinalType& lwork, MagnitudeType *RWORK, OrdinalType* BWORK, OrdinalType* info) const
1199  {
1200  UndefinedLAPACKRoutine<ScalarType>::notDefined();
1201  }
1202 
1203  template<typename OrdinalType, typename ScalarType>
1204  void LAPACK<OrdinalType, ScalarType>::GEES(const char& JOBVS, const OrdinalType& n, ScalarType* A, const OrdinalType& lda, OrdinalType* sdim, MagnitudeType* WR, MagnitudeType* WI, ScalarType* VS, const OrdinalType& ldvs, ScalarType* WORK, const OrdinalType& lwork, MagnitudeType *RWORK, OrdinalType* BWORK, OrdinalType* info) const
1205  {
1206  UndefinedLAPACKRoutine<ScalarType>::notDefined();
1207  }
1208 
1209  template<typename OrdinalType, typename ScalarType>
1210  void LAPACK<OrdinalType, ScalarType>::GEEV(const char& JOBVL, const char& JOBVR, const OrdinalType& n, ScalarType* A, const OrdinalType& lda, MagnitudeType* WR, MagnitudeType* WI, ScalarType* VL, const OrdinalType& ldvl, ScalarType* VR, const OrdinalType& ldvr, ScalarType* WORK, const OrdinalType& lwork, MagnitudeType* rwork, OrdinalType* info) const
1211  {
1212  UndefinedLAPACKRoutine<ScalarType>::notDefined();
1213  }
1214 
1215  template<typename OrdinalType, typename ScalarType>
1216  void LAPACK<OrdinalType, ScalarType>::GEEVX(const char& BALANC, const char& JOBVL, const char& JOBVR, const char& SENSE, const OrdinalType& n, ScalarType* A, const OrdinalType& lda, ScalarType* WR, ScalarType* WI, ScalarType* VL, const OrdinalType& ldvl, ScalarType* VR, const OrdinalType& ldvr, OrdinalType* ilo, OrdinalType* ihi, MagnitudeType* SCALE, MagnitudeType* abnrm, MagnitudeType* RCONDE, MagnitudeType* RCONDV, ScalarType* WORK, const OrdinalType& lwork, OrdinalType* IWORK, OrdinalType* info) const
1217  {
1218  UndefinedLAPACKRoutine<ScalarType>::notDefined();
1219  }
1220 
1221  template<typename OrdinalType, typename ScalarType>
1222  void LAPACK<OrdinalType, ScalarType>::GESVD(const char& JOBU, const char& JOBVT, const OrdinalType& m, const OrdinalType& n, ScalarType* A, const OrdinalType& lda, MagnitudeType* S, ScalarType* U, const OrdinalType& ldu, ScalarType* V, const OrdinalType& ldv, ScalarType* WORK, const OrdinalType& lwork, MagnitudeType* RWORK, OrdinalType* info) const
1223  {
1224  UndefinedLAPACKRoutine<ScalarType>::notDefined();
1225  }
1226 
1227  template<typename OrdinalType, typename ScalarType>
1228  void LAPACK<OrdinalType, ScalarType>::GGEVX(const char& BALANC, const char& JOBVL, const char& JOBVR, const char& SENSE, const OrdinalType& n, ScalarType* A, const OrdinalType& lda, ScalarType* B, const OrdinalType& ldb, MagnitudeType* ALPHAR, MagnitudeType* ALPHAI, ScalarType* BETA, ScalarType* VL, const OrdinalType& ldvl, ScalarType* VR, const OrdinalType& ldvr, OrdinalType* ilo, OrdinalType* ihi, MagnitudeType* lscale, MagnitudeType* rscale, MagnitudeType* abnrm, MagnitudeType* bbnrm, MagnitudeType* RCONDE, MagnitudeType* RCONDV, ScalarType* WORK, const OrdinalType& lwork, OrdinalType* IWORK, OrdinalType* BWORK, OrdinalType* info) const
1229  {
1230  UndefinedLAPACKRoutine<ScalarType>::notDefined();
1231  }
1232 
1233  template<typename OrdinalType, typename ScalarType>
1234  void LAPACK<OrdinalType, ScalarType>::GGEV(const char& JOBVL, const char& JOBVR, const OrdinalType& n, ScalarType* A, const OrdinalType& lda, ScalarType* B, const OrdinalType& ldb, MagnitudeType *ALPHAR, MagnitudeType *ALPHAI, ScalarType* BETA, ScalarType* VL, const OrdinalType& ldvl, ScalarType* VR, const OrdinalType& ldvr, ScalarType* WORK, const OrdinalType& lwork, OrdinalType* info) const
1235  {
1236  UndefinedLAPACKRoutine<ScalarType>::notDefined();
1237  }
1238 
1239 
1240  template<typename OrdinalType, typename ScalarType>
1241  void LAPACK<OrdinalType,ScalarType>::TRSEN(const char& JOB, const char& COMPQ, const OrdinalType* SELECT, const OrdinalType& n, ScalarType* T, const OrdinalType& ldt, ScalarType* Q, const OrdinalType& ldq, MagnitudeType *WR, MagnitudeType *WI, OrdinalType* M, ScalarType* S, MagnitudeType *SEP, ScalarType* WORK, const OrdinalType& lwork, OrdinalType* IWORK, const OrdinalType& liwork, OrdinalType* info ) const
1242  {
1243  UndefinedLAPACKRoutine<ScalarType>::notDefined();
1244  }
1245 
1246 
1247  template<typename OrdinalType, typename ScalarType>
1248  void LAPACK<OrdinalType,ScalarType>::TGSEN(const OrdinalType& ijob, const OrdinalType& wantq, const OrdinalType& wantz, const OrdinalType* SELECT, const OrdinalType& n, ScalarType* A, const OrdinalType& lda, ScalarType* B, const OrdinalType& ldb, MagnitudeType *ALPHAR, MagnitudeType *ALPHAI, MagnitudeType *BETA, ScalarType* Q, const OrdinalType& ldq, ScalarType* Z, const OrdinalType& ldz, OrdinalType* M, MagnitudeType *PL, MagnitudeType *PR, MagnitudeType *DIF, ScalarType* WORK, const OrdinalType& lwork, OrdinalType* IWORK, const OrdinalType& liwork, OrdinalType* info ) const
1249  {
1250  UndefinedLAPACKRoutine<ScalarType>::notDefined();
1251  }
1252 
1253 
1254  template<typename OrdinalType, typename ScalarType>
1255  void LAPACK<OrdinalType, ScalarType>::GGES(const char& JOBVL, const char& JOBVR, const char& SORT, OrdinalType& (*ptr2func)(ScalarType*, ScalarType*, ScalarType*), const OrdinalType& n, ScalarType* A, const OrdinalType& lda, ScalarType* B, const OrdinalType& ldb, OrdinalType* sdim, MagnitudeType* ALPHAR, MagnitudeType* ALPHAI, MagnitudeType* BETA, ScalarType* VL, const OrdinalType& ldvl, ScalarType* VR, const OrdinalType& ldvr, ScalarType* WORK, const OrdinalType& lwork, OrdinalType* BWORK, OrdinalType* info ) const
1256  {
1257  UndefinedLAPACKRoutine<ScalarType>::notDefined();
1258  }
1259 
1260  template<typename OrdinalType, typename ScalarType>
1261  void LAPACK<OrdinalType, ScalarType>::ORMQR(const char& SIDE, const char& TRANS, const OrdinalType& m, const OrdinalType& n, const OrdinalType& k, ScalarType* A, const OrdinalType& lda, const ScalarType* TAU, ScalarType* C, const OrdinalType& ldc, ScalarType* WORK, const OrdinalType& lwork, OrdinalType* info) const
1262  {
1263  UndefinedLAPACKRoutine<ScalarType>::notDefined();
1264  }
1265 
1266  template<typename OrdinalType, typename ScalarType>
1267  void LAPACK<OrdinalType, ScalarType>::ORM2R(const char& SIDE, const char& TRANS, const OrdinalType& m, const OrdinalType& n, const OrdinalType& k, const ScalarType A[], const OrdinalType& lda, const ScalarType TAU[], ScalarType C[], const OrdinalType& ldc, ScalarType WORK[], OrdinalType* const info) const
1268  {
1269  UndefinedLAPACKRoutine<ScalarType>::notDefined();
1270  }
1271 
1272  template<typename OrdinalType, typename ScalarType>
1273  void LAPACK<OrdinalType, ScalarType>::UNMQR(const char& SIDE, const char& TRANS, const OrdinalType& m, const OrdinalType& n, const OrdinalType& k, ScalarType* A, const OrdinalType& lda, const ScalarType* TAU, ScalarType* C, const OrdinalType& ldc, ScalarType* WORK, const OrdinalType& lwork, OrdinalType* info) const
1274  {
1275  UndefinedLAPACKRoutine<ScalarType>::notDefined();
1276  }
1277 
1278  template<typename OrdinalType, typename ScalarType>
1279  void LAPACK<OrdinalType, ScalarType>::UNM2R(const char& SIDE, const char& TRANS, const OrdinalType& M, const OrdinalType& N, const OrdinalType& K, const ScalarType A[], const OrdinalType& LDA, const ScalarType TAU[], ScalarType C[], const OrdinalType& LDC, ScalarType WORK[], OrdinalType* const INFO) const
1280  {
1281  UndefinedLAPACKRoutine<ScalarType>::notDefined();
1282  }
1283 
1284  template<typename OrdinalType, typename ScalarType>
1285  void LAPACK<OrdinalType, ScalarType>::ORGQR(const OrdinalType& m, const OrdinalType& n, const OrdinalType& k, ScalarType* A, const OrdinalType& lda, const ScalarType* TAU, ScalarType* WORK, const OrdinalType& lwork, OrdinalType* info) const
1286  {
1287  UndefinedLAPACKRoutine<ScalarType>::notDefined();
1288  }
1289 
1290  template<typename OrdinalType, typename ScalarType>
1291  void LAPACK<OrdinalType, ScalarType>::UNGQR(const OrdinalType& m, const OrdinalType& n, const OrdinalType& k, ScalarType* A, const OrdinalType& lda, const ScalarType* TAU, ScalarType* WORK, const OrdinalType& lwork, OrdinalType* info) const
1292  {
1293  UndefinedLAPACKRoutine<ScalarType>::notDefined();
1294  }
1295 
1296  template<typename OrdinalType, typename ScalarType>
1297  void LAPACK<OrdinalType, ScalarType>::ORGHR(const OrdinalType& n, const OrdinalType& ilo, const OrdinalType& ihi, ScalarType* A, const OrdinalType& lda, const ScalarType* TAU, ScalarType* WORK, const OrdinalType& lwork, OrdinalType* info) const
1298  {
1299  UndefinedLAPACKRoutine<ScalarType>::notDefined();
1300  }
1301 
1302  template<typename OrdinalType, typename ScalarType>
1303  void LAPACK<OrdinalType, ScalarType>::ORMHR(const char& SIDE, const char& TRANS, const OrdinalType& m, const OrdinalType& n, const OrdinalType& ilo, const OrdinalType& ihi, const ScalarType* A, const OrdinalType& lda, const ScalarType* TAU, ScalarType* C, const OrdinalType& ldc, ScalarType* WORK, const OrdinalType& lwork, OrdinalType* info) const
1304  {
1305  UndefinedLAPACKRoutine<ScalarType>::notDefined();
1306  }
1307 
1308  template<typename OrdinalType, typename ScalarType>
1309  void LAPACK<OrdinalType, ScalarType>::TREVC(const char& SIDE, const char& HOWMNY, OrdinalType* select, const OrdinalType& n, const ScalarType* T, const OrdinalType& ldt, ScalarType* VL, const OrdinalType& ldvl, ScalarType* VR, const OrdinalType& ldvr, const OrdinalType& mm, OrdinalType* m, ScalarType* WORK, OrdinalType* info) const
1310  {
1311  UndefinedLAPACKRoutine<ScalarType>::notDefined();
1312  }
1313 
1314  template<typename OrdinalType, typename ScalarType>
1315  void LAPACK<OrdinalType, ScalarType>::TREVC(const char& SIDE, const OrdinalType& n, const ScalarType* T, const OrdinalType& ldt, ScalarType* VL, const OrdinalType& ldvl, ScalarType* VR, const OrdinalType& ldvr, const OrdinalType& mm, OrdinalType* m, ScalarType* WORK, MagnitudeType* RWORK, OrdinalType* info) const
1316  {
1317  UndefinedLAPACKRoutine<ScalarType>::notDefined();
1318  }
1319 
1320  template<typename OrdinalType, typename ScalarType>
1321  void LAPACK<OrdinalType, ScalarType>::TREXC(const char& COMPQ, const OrdinalType& n, ScalarType* T, const OrdinalType& ldt, ScalarType* Q, const OrdinalType& ldq, OrdinalType* ifst, OrdinalType* ilst, ScalarType* WORK, OrdinalType* info) const
1322  {
1323  UndefinedLAPACKRoutine<ScalarType>::notDefined();
1324  }
1325 
1326 
1327  template<typename OrdinalType, typename ScalarType>
1328  void LAPACK<OrdinalType, ScalarType>::TGEVC(const char& SIDE, const char& HOWMNY, const OrdinalType* SELECT, const OrdinalType& n, ScalarType* S, const OrdinalType& lds, ScalarType* P, const OrdinalType& ldp, ScalarType* VL, const OrdinalType& ldvl, ScalarType* VR, const OrdinalType& ldvr, const OrdinalType& mm, OrdinalType* M, ScalarType* WORK, OrdinalType* info) const
1329  {
1330  UndefinedLAPACKRoutine<ScalarType>::notDefined();
1331  }
1332 
1333 
1334  template<typename OrdinalType, typename ScalarType>
1335  ScalarType LAPACK<OrdinalType, ScalarType>::LAMCH(const char& CMACH) const
1336  {
1337  return UndefinedLAPACKRoutine<ScalarType>::notDefined();
1338  }
1339 
1340  template<typename OrdinalType, typename ScalarType>
1341  OrdinalType LAPACK<OrdinalType, ScalarType>::ILAENV( const OrdinalType& ispec, const std::string& NAME, const std::string& OPTS, const OrdinalType& N1, const OrdinalType& N2, const OrdinalType& N3, const OrdinalType& N4 ) const
1342  {
1343  return UndefinedLAPACKRoutine<OrdinalType>::notDefined();
1344  }
1345 
1346  template<typename OrdinalType, typename ScalarType>
1347  ScalarType LAPACK<OrdinalType, ScalarType>::LAPY2(const ScalarType& x, const ScalarType& y) const
1348  {
1349  return UndefinedLAPACKRoutine<ScalarType>::notDefined();
1350  }
1351 
1352  template<typename OrdinalType, typename ScalarType>
1353  void LAPACK<OrdinalType, ScalarType>::LARTG( const ScalarType& f, const ScalarType& g, MagnitudeType* c, ScalarType* s, ScalarType* r ) const
1354  {
1355  UndefinedLAPACKRoutine<ScalarType>::notDefined();
1356  }
1357 
1358  template<typename OrdinalType, typename ScalarType>
1359  void LAPACK<OrdinalType, ScalarType>::LARFG( const OrdinalType& n, ScalarType* alpha, ScalarType* x, const OrdinalType& incx, ScalarType* tau ) const
1360  {
1361  UndefinedLAPACKRoutine<ScalarType>::notDefined();
1362  }
1363 
1364  template<typename OrdinalType, typename ScalarType>
1365  void LAPACK<OrdinalType, ScalarType>::GEBAL( const char& JOBZ, const OrdinalType& n, ScalarType* A, const OrdinalType& lda, OrdinalType* ilo, OrdinalType* ihi, MagnitudeType* scale, OrdinalType* info ) const
1366  {
1367  UndefinedLAPACKRoutine<ScalarType>::notDefined();
1368  }
1369 
1370 
1371  template<typename OrdinalType, typename ScalarType>
1372  void LAPACK<OrdinalType, ScalarType>::GEBAK( const char& JOBZ, const char& SIDE, const OrdinalType& n, const OrdinalType& ilo, const OrdinalType& ihi, const MagnitudeType* scale, const OrdinalType& m, ScalarType* V, const OrdinalType& ldv, OrdinalType* info ) const
1373  {
1374  UndefinedLAPACKRoutine<ScalarType>::notDefined();
1375  }
1376 
1377  template<typename OrdinalType, typename ScalarType>
1378  ScalarType LAPACK<OrdinalType, ScalarType>::LARND( const OrdinalType& idist, OrdinalType* seed ) const
1379  {
1380  return UndefinedLAPACKRoutine<ScalarType>::notDefined();
1381  }
1382 
1383  template<typename OrdinalType, typename ScalarType>
1384  void LAPACK<OrdinalType, ScalarType>::LARNV( const OrdinalType& idist, OrdinalType* seed, const OrdinalType& n, ScalarType* v ) const
1385  {
1386  UndefinedLAPACKRoutine<ScalarType>::notDefined();
1387  }
1388 
1389  // END GENERAL TEMPLATE IMPLEMENTATION //
1390 
1391 #ifndef DOXYGEN_SHOULD_SKIP_THIS
1392 
1393  // BEGIN INT, FLOAT SPECIALIZATION DECLARATION //
1394 
1395  template<>
1396  class TEUCHOSNUMERICS_LIB_DLL_EXPORT LAPACK<int, float>
1397  {
1398  public:
1399  inline LAPACK(void) {}
1400  inline LAPACK(const LAPACK<int, float>& /*lapack*/) {}
1401  inline virtual ~LAPACK(void) {}
1402 
1403  // Symmetric positive definite linear system routines
1404  void POTRF(const char& UPLO, const int& n, float* A, const int& lda, int* info) const;
1405  void POTRS(const char& UPLO, const int& n, const int& nrhs, const float* A, const int& lda, float* B, const int& ldb, int* info) const;
1406  void PTTRF(const int& n, float* d, float* e, int* info) const;
1407  void PTTRS(const int& n, const int& nrhs, const float* d, const float* e, float* B, const int& ldb, int* info) const;
1408  void POTRI(const char& UPLO, const int& n, float* A, const int& lda, int* info) const;
1409  void POCON(const char& UPLO, const int& n, const float* A, const int& lda, const float& anorm, float* rcond, float* WORK, int* IWORK, int* info) const;
1410  void POSV(const char& UPLO, const int& n, const int& nrhs, float* A, const int& lda, float* B, const int& ldb, int* info) const;
1411  void POEQU(const int& n, const float* A, const int& lda, float* S, float* scond, float* amax, int* info) const;
1412  void PORFS(const char& UPLO, const int& n, const int& nrhs, float* A, const int& lda, const float* AF, const int& ldaf, const float* B, const int& ldb, float* X, const int& ldx, float* FERR, float* BERR, float* WORK, int* IWORK, int* info) const;
1413 
1414  void POSVX(const char& FACT, const char& UPLO, const int& n, const int& nrhs, float* A, const int& lda, float* AF, const int& ldaf, char* EQUED, float* S, float* B, const int& ldb, float* X, const int& ldx, float* rcond, float* FERR, float* BERR, float* WORK, int* IWORK, int* info) const;
1415 
1416  // General Linear System Routines
1417  void GELS(const char& TRANS, const int& m, const int& n, const int& nrhs, float* A, const int& lda, float* B, const int& ldb, float* WORK, const int& lwork, int* info) const;
1418  void GELSS(const int& m, const int& n, const int& nrhs, float* A, const int& lda, float* B, const int& ldb, float* S, const float& rcond, int* rank, float* WORK, const int& lwork, float* RWORK, int* info) const;
1419  void GELSS(const int& m, const int& n, const int& nrhs, float* A, const int& lda, float* B, const int& ldb, float* S, const float& rcond, int* rank, float* WORK, const int& lwork, int* info) const;
1420  void GGLSE(const int& m, const int& n, const int& p, float* A, const int& lda, float* B, const int& ldb, float* C, float* D, float* X, float* WORK, const int& lwork, int* info) const;
1421  void GEQRF(const int& m, const int& n, float* A, const int& lda, float* TAU, float* WORK, const int& lwork, int* info) const;
1422  void GEQR2(const int& m, const int& n, float A[], const int& lda, float TAU[], float WORK[], int* const info) const;
1423 
1424  void GETRF(const int& m, const int& n, float* A, const int& lda, int* IPIV, int* info) const;
1425  void GETRS(const char& TRANS, const int& n, const int& nrhs, const float* A, const int& lda, const int* IPIV, float* B, const int& ldb, int* info) const;
1426  void LASCL(const char& TYPE, const int& kl, const int& ku, const float& cfrom, const float& cto, const int& m, const int& n, float* A, const int& lda, int* info) const;
1427 
1428  void
1429  GEQP3 (const int& m,
1430  const int& n,
1431  float* A,
1432  const int& lda,
1433  int* jpvt,
1434  float* TAU,
1435  float* WORK,
1436  const int& lwork,
1437  float* RWORK,
1438  int* info) const;
1439 
1440  void LASWP (const int& N,
1441  float A[],
1442  const int& LDA,
1443  const int& K1,
1444  const int& K2,
1445  const int IPIV[],
1446  const int& INCX) const;
1447 
1448  void GBTRF(const int& m, const int& n, const int& kl, const int& ku, float* A, const int& lda, int* IPIV, int* info) const;
1449  void GBTRS(const char& TRANS, const int& n, const int& kl, const int& ku, const int& nrhs, const float* A, const int& lda, const int* IPIV, float* B, const int& ldb, int* info) const;
1450  void GTTRF(const int& n, float* dl, float* d, float* du, float* du2, int* IPIV, int* info) const;
1451  void GTTRS(const char& TRANS, const int& n, const int& nrhs, const float* dl, const float* d, const float* du, const float* du2, const int* IPIV, float* B, const int& ldb, int* info) const;
1452 
1453 
1454  void GETRI(const int& n, float* A, const int& lda, const int* IPIV, float* WORK, const int& lwork, int* info) const;
1455  void LATRS (const char& UPLO, const char& TRANS, const char& DIAG, const char& NORMIN, const int& N, float* A, const int& LDA, float* X, float* SCALE, float* CNORM, int* INFO) const;
1456  void GECON(const char& NORM, const int& n, const float* A, const int& lda, const float& anorm, float* rcond, float* WORK, int* IWORK, int* info) const;
1457  void GBCON(const char& NORM, const int& n, const int& kl, const int& ku, const float* A, const int& lda, int* IPIV, const float& anorm, float* rcond, float* WORK, int* IWORK, int* info) const;
1458  float LANGB(const char& NORM, const int& n, const int& kl, const int& ku, const float* A, const int& lda, float* WORK) const;
1459  void GESV(const int& n, const int& nrhs, float* A, const int& lda, int* IPIV, float* B, const int& ldb, int* info) const;
1460  void GEEQU(const int& m, const int& n, const float* A, const int& lda, float* R, float* C, float* rowcond, float* colcond, float* amax, int* info) const;
1461  void GERFS(const char& TRANS, const int& n, const int& nrhs, const float* A, const int& lda, const float* AF, const int& ldaf, const int* IPIV, const float* B, const int& ldb, float* X, const int& ldx, float* FERR, float* BERR, float* WORK, int* IWORK, int* info) const;
1462  void GBEQU(const int& m, const int& n, const int& kl, const int& ku, const float* A, const int& lda, float* R, float* C, float* rowcond, float* colcond, float* amax, int* info) const;
1463  void GBRFS(const char& TRANS, const int& n, const int& kl, const int& ku, const int& nrhs, const float* A, const int& lda, const float* AF, const int& ldaf, const int* IPIV, const float* B, const int& ldb, float* X, const int& ldx, float* FERR, float* BERR, float* WORK, int* IWORK, int* info) const;
1464 
1465  void GESVX(const char& FACT, const char& TRANS, const int& n, const int& nrhs, float* A, const int& lda, float* AF, const int& ldaf, int* IPIV, char* EQUED, float* R, float* C, float* B, const int& ldb, float* X, const int& ldx, float* rcond, float* FERR, float* BERR, float* WORK, int* IWORK, int* info) const;
1466 
1467  void SYTRD(const char& UPLO, const int& n, float* A, const int& lda, float* D, float* E, float* TAU, float* WORK, const int& lwork, int* info) const;
1468  void GEHRD(const int& n, const int& ilo, const int& ihi, float* A, const int& lda, float* TAU, float* WORK, const int& lwork, int* info) const;
1469  void TRTRS(const char& UPLO, const char& TRANS, const char& DIAG, const int& n, const int& nrhs, const float* A, const int& lda, float* B, const int& ldb, int* info) const;
1470  void TRTRI(const char& UPLO, const char& DIAG, const int& n, const float* A, const int& lda, int* info) const;
1471 
1472  // Symmetric eigenvalue routines.
1473  void STEQR(const char& COMPZ, const int& n, float* D, float* E, float* Z, const int& ldz, float* WORK, int* info) const;
1474  void PTEQR(const char& COMPZ, const int& n, float* D, float* E, float* Z, const int& ldz, float* WORK, int* info) const;
1475  void SPEV(const char& JOBZ, const char& UPLO, const int& n, float* AP, float* W, float* Z, const int& ldz, float* WORK, int* info) const;
1476  void SYEV(const char& JOBZ, const char& UPLO, const int& n, float* A, const int& lda, float* W, float* WORK, const int& lwork, int* info) const;
1477  void SYGV(const int& itype, const char& JOBZ, const char& UPLO, const int& n, float* A, const int& lda, float* B, const int& ldb, float* W, float* WORK, const int& lwork, int* info) const;
1478  void HEEV(const char& JOBZ, const char& UPLO, const int& n, float* A, const int& lda, float* W, float* WORK, const int& lwork, float* RWORK, int* info) const;
1479  void HEGV(const int& itype, const char& JOBZ, const char& UPLO, const int& n, float* A, const int& lda, float* B, const int& ldb, float* W, float* WORK, const int& lwork, float* RWORK, int* info) const;
1480 
1481  // Non-Hermitian eigenvalue routines.
1482  void HSEQR(const char& JOB, const char& COMPZ, const int& n, const int& ilo, const int& ihi, float* H, const int& ldh, float* WR, float* WI, float* Z, const int& ldz, float* WORK, const int& lwork, int* info) const;
1483  void GEES(const char& JOBVS, const char& SORT, int (*ptr2func)(float*, float*), const int& n, float* A, const int& lda, int* sdim, float* WR, float* WI, float* VS, const int& ldvs, float* WORK, const int& lwork, int* BWORK, int* info) const;
1484  void GEES(const char& JOBVS, const int& n, float* A, const int& lda, int* sdim, float* WR, float* WI, float* VS, const int& ldvs, float* WORK, const int& lwork, float* RWORK, int* BWORK, int* info) const;
1485 
1486  void GEEV(const char& JOBVL, const char& JOBVR, const int& n, float* A, const int& lda, float* WR, float* WI, float* VL, const int& ldvl, float* VR, const int& ldvr, float* WORK, const int& lwork, int* info) const;
1487  void GEEV(const char& JOBVL, const char& JOBVR, const int& n, float* A, const int& lda, float* WR, float* WI, float* VL, const int& ldvl, float* VR, const int& ldvr, float* WORK, const int& lwork, float* rwork, int* info) const;
1488 
1489  void GEEVX(const char& BALANC, const char& JOBVL, const char& JOBVR, const char& SENSE, const int& n, float* A, const int& lda, float* WR, float* WI, float* VL, const int& ldvl, float* VR, const int& ldvr, int* ilo, int* ihi, float* SCALE, float* abnrm, float* RCONDE, float* RCONDV, float* WORK, const int& lwork, int* IWORK, int* info) const;
1490  void GGEVX(const char& BALANC, const char& JOBVL, const char& JOBVR, const char& SENSE, const int& n, float* A, const int& lda, float* B, const int& ldb, float* ALPHAR, float* ALPHAI, float* BETA, float* VL, const int& ldvl, float* VR, const int& ldvr, int* ilo, int* ihi, float* lscale, float* rscale, float* abnrm, float* bbnrm, float* RCONDE, float* RCONDV, float* WORK, const int& lwork, int* IWORK, int* BWORK, int* info) const;
1491  void GGEVX(const char& BALANC, const char& JOBVL, const char& JOBVR, const char& SENSE, const int& n, float* A, const int& lda, float* B, const int& ldb, float* ALPHAR, float* ALPHAI, float* BETA, float* VL, const int& ldvl, float* VR, const int& ldvr, int* ilo, int* ihi, float* lscale, float* rscale, float* abnrm, float* bbnrm, float* RCONDE, float* RCONDV, float* WORK, const int& lwork, float* rwork, int* IWORK, int* BWORK, int* info) const;
1492  void GGEV(const char& JOBVL, const char& JOBVR, const int& n, float* A, const int& lda, float* B, const int& ldb, float* ALPHAR, float* ALPHAI, float* BETA, float* VL, const int& ldvl, float* VR, const int& ldvr, float* WORK, const int& lwork, int* info) const;
1493  void TRSEN(const char& JOB, const char& COMPQ, const int* SELECT, const int& n, float* T, const int& ldt, float* Q, const int& ldq, float* WR, float* WI, int* M, float* S, float* SEP, float* WORK, const int& lwork, int* IWORK, const int& liwork, int* info ) const;
1494  void TGSEN(const int& ijob, const int& wantq, const int& wantz, const int* SELECT, const int& n, float* A, const int& lda, float* B, const int& ldb, float* ALPHAR, float* ALPHAI, float* BETA, float* Q, const int& ldq, float* Z, const int& ldz, int* M, float* PL, float* PR, float* DIF, float* WORK, const int& lwork, int* IWORK, const int& liwork, int* info ) const;
1495  void GGES(const char& JOBVL, const char& JOBVR, const char& SORT, int (*ptr2func)(float*, float*, float*), const int& n, float* A, const int& lda, float* B, const int& ldb, int* sdim, float* ALPHAR, float* ALPHAI, float* BETA, float* VL, const int& ldvl, float* VR, const int& ldvr, float* WORK, const int& lwork, int* bwork, int* info ) const;
1496 
1497  // SVD routine
1498  void GESVD(const char& JOBU, const char& JOBVT, const int& m, const int& n, float* A, const int& lda, float* S, float* U, const int& ldu, float* V, const int& ldv, float* WORK, const int& lwork, float* RWORK, int* info) const;
1499 
1500  // Orthogonal matrix routines.
1501  void ORMQR(const char& SIDE, const char& TRANS, const int& m, const int& n, const int& k, float* A, const int& lda, const float* TAU, float* C, const int& ldc, float* WORK, const int& lwork, int* info) const;
1502  void ORM2R(const char& SIDE, const char& TRANS, const int& m, const int& n, const int& k, const float A[], const int& lda, const float TAU[], float C[], const int& ldc, float WORK[], int* const info) const;
1503  void UNMQR(const char& SIDE, const char& TRANS, const int& m, const int& n, const int& k, float* A, const int& lda, const float* TAU, float* C, const int& ldc, float* WORK, const int& lwork, int* info) const;
1504  void UNM2R(const char& SIDE, const char& TRANS, const int& M, const int& N, const int& K, const float A[], const int& LDA, const float TAU[], float C[], const int& LDC, float WORK[], int* const INFO) const;
1505  void ORGQR(const int& m, const int& n, const int& k, float* A, const int& lda, const float* TAU, float* WORK, const int& lwork, int* info) const;
1506  void UNGQR(const int& m, const int& n, const int& k, float* A, const int& lda, const float* TAU, float* WORK, const int& lwork, int* info) const;
1507  void ORGHR(const int& n, const int& ilo, const int& ihi, float* A, const int& lda, const float* TAU, float* WORK, const int& lwork, int* info) const;
1508  void ORMHR(const char& SIDE, const char& TRANS, const int& m, const int& n, const int& ilo, const int& ihi, const float* A, const int& lda, const float* TAU, float* C, const int& ldc, float* WORK, const int& lwork, int* info) const;
1509 
1510  // Triangular matrix routines.
1511  void TREVC(const char& SIDE, const char& HOWMNY, int* select, const int& n, const float* T, const int& ldt, float* VL, const int& ldvl, float* VR, const int& ldvr, const int& mm, int* m, float* WORK, int* info) const;
1512  void TREVC(const char& SIDE, const int& n, const float* T, const int& ldt, float* VL, const int& ldvl, float* VR, const int& ldvr, const int& mm, int* m, float* WORK, float* RWORK, int* info) const;
1513 
1514  void TREXC(const char& COMPQ, const int& n, float* T, const int& ldt, float* Q, const int& ldq, int* ifst, int* ilst, float* WORK, int* info) const;
1515 
1516  void TGEVC(const char& SIDE, const char& HOWMNY, const int* SELECT, const int& n, float* S, const int& lds, float* P, const int& ldp, float* VL, const int& ldvl, float* VR, const int& ldvr, const int& mm, int* M, float* WORK, int* info) const;
1517 
1518  // Rotation/reflection generators
1519  void LARTG( const float& f, const float& g, float* c, float* s, float* r ) const;
1520  void LARFG( const int& n, float* alpha, float* x, const int& incx, float* tau ) const;
1521 
1522  // Matrix balancing routines.
1523 
1524  void GEBAL(const char& JOBZ, const int& n, float* A, const int& lda, int* ilo, int* ihi, float* scale, int* info) const;
1525 
1526  void GEBAK(const char& JOBZ, const char& SIDE, const int& n, const int& ilo, const int& ihi, const float* scale, const int& m, float* V, const int& ldv, int* info) const;
1527 
1528  // Random number generators
1529  float LARND( const int& idist, int* seed ) const;
1530  void LARNV( const int& idist, int* seed, const int& n, float* v ) const;
1531 
1532  // Machine characteristics.
1533  float LAMCH(const char& CMACH) const;
1534  int ILAENV( const int& ispec, const std::string& NAME, const std::string& OPTS, const int& N1 = -1, const int& N2 = -1, const int& N3 = -1, const int& N4 = -1 ) const;
1535 
1536  // Miscellaneous routines.
1537  float LAPY2(const float& x, const float& y) const;
1538 
1539  };
1540 
1541  // END INT, FLOAT SPECIALIZATION DECLARATION //
1542 
1543  // BEGIN INT, DOUBLE SPECIALIZATION DECLARATION //
1544 
1545  template<>
1546  class TEUCHOSNUMERICS_LIB_DLL_EXPORT LAPACK<int, double>
1547  {
1548  public:
1549  inline LAPACK(void) {}
1550  inline LAPACK(const LAPACK<int, double>& /*lapack*/) {}
1551  inline virtual ~LAPACK(void) {}
1552 
1553  // Symmetric positive definite linear system routines
1554  void PTTRF(const int& n, double* d, double* e, int* info) const;
1555  void PTTRS(const int& n, const int& nrhs, const double* d, const double* e, double* B, const int& ldb, int* info) const;
1556  void POTRF(const char& UPLO, const int& n, double* A, const int& lda, int* info) const;
1557  void POTRS(const char& UPLO, const int& n, const int& nrhs, const double* A, const int& lda, double* B, const int& ldb, int* info) const;
1558  void POTRI(const char& UPLO, const int& n, double* A, const int& lda, int* info) const;
1559  void POCON(const char& UPLO, const int& n, const double* A, const int& lda, const double& anorm, double* rcond, double* WORK, int* IWORK, int* info) const;
1560  void POSV(const char& UPLO, const int& n, const int& nrhs, double* A, const int& lda, double* B, const int& ldb, int* info) const;
1561  void POEQU(const int& n, const double* A, const int& lda, double* S, double* scond, double* amax, int* info) const;
1562  void PORFS(const char& UPLO, const int& n, const int& nrhs, double* A, const int& lda, const double* AF, const int& ldaf, const double* B, const int& ldb, double* X, const int& ldx, double* FERR, double* BERR, double* WORK, int* IWORK, int* info) const;
1563 
1564  void POSVX(const char& FACT, const char& UPLO, const int& n, const int& nrhs, double* A, const int& lda, double* AF, const int& ldaf, char* EQUED, double* S, double* B, const int& ldb, double* X, const int& ldx, double* rcond, double* FERR, double* BERR, double* WORK, int* IWORK, int* info) const;
1565 
1566  // General linear system routines
1567  void GELS(const char& TRANS, const int& m, const int& n, const int& nrhs, double* A, const int& lda, double* B, const int& ldb, double* WORK, const int& lwork, int* info) const;
1568  void GELSS(const int& m, const int& n, const int& nrhs, double* A, const int& lda, double* B, const int& ldb, double* S, const double& rcond, int* rank, double* WORK, const int& lwork, double* RWORK, int* info) const;
1569  void GELSS(const int& m, const int& n, const int& nrhs, double* A, const int& lda, double* B, const int& ldb, double* S, const double& rcond, int* rank, double* WORK, const int& lwork, int* info) const;
1570  void GGLSE(const int& m, const int& n, const int& p, double* A, const int& lda, double* B, const int& ldb, double* C, double* D, double* X, double* WORK, const int& lwork, int* info) const;
1571  void GEQRF(const int& m, const int& n, double* A, const int& lda, double* TAU, double* WORK, const int& lwork, int* info) const;
1572  void GEQR2(const int& m, const int& n, double A[], const int& lda, double TAU[], double WORK[], int* const info) const;
1573  void GETRF(const int& m, const int& n, double* A, const int& lda, int* IPIV, int* info) const;
1574  void GETRS(const char& TRANS, const int& n, const int& nrhs, const double* A, const int& lda, const int* IPIV, double* B, const int& ldb, int* info) const;
1575  void LASCL(const char& TYPE, const int& kl, const int& ku, const double& cfrom, const double& cto, const int& m, const int& n, double* A, const int& lda, int* info) const;
1576 
1577  void
1578  GEQP3 (const int& m,
1579  const int& n,
1580  double* A,
1581  const int& lda,
1582  int* jpvt,
1583  double* TAU,
1584  double* WORK,
1585  const int& lwork,
1586  double* RWORK,
1587  int* info) const;
1588 
1589  void LASWP (const int& N,
1590  double A[],
1591  const int& LDA,
1592  const int& K1,
1593  const int& K2,
1594  const int IPIV[],
1595  const int& INCX) const;
1596 
1597  void GBTRF(const int& m, const int& n, const int& kl, const int& ku, double* A, const int& lda, int* IPIV, int* info) const;
1598  void GBTRS(const char& TRANS, const int& n, const int& kl, const int& ku, const int& nrhs, const double* A, const int& lda, const int* IPIV, double* B, const int& ldb, int* info) const;
1599  void GTTRF(const int& n, double* dl, double* d, double* du, double* du2, int* IPIV, int* info) const;
1600  void GTTRS(const char& TRANS, const int& n, const int& nrhs, const double* dl, const double* d, const double* du, const double* du2, const int* IPIV, double* B, const int& ldb, int* info) const;
1601  void GETRI(const int& n, double* A, const int& lda, const int* IPIV, double* WORK, const int& lwork, int* info) const;
1602  void LATRS (const char& UPLO, const char& TRANS, const char& DIAG, const char& NORMIN, const int& N, double* A, const int& LDA, double* X, double* SCALE, double* CNORM, int* INFO) const;
1603  void GECON(const char& NORM, const int& n, const double* A, const int& lda, const double& anorm, double* rcond, double* WORK, int* IWORK, int* info) const;
1604  void GBCON(const char& NORM, const int& n, const int& kl, const int& ku, const double* A, const int& lda, int* IPIV, const double& anorm, double* rcond, double* WORK, int* IWORK, int* info) const;
1605  double LANGB(const char& NORM, const int& n, const int& kl, const int& ku, const double* A, const int& lda, double* WORK) const;
1606  void GESV(const int& n, const int& nrhs, double* A, const int& lda, int* IPIV, double* B, const int& ldb, int* info) const;
1607  void GEEQU(const int& m, const int& n, const double* A, const int& lda, double* R, double* C, double* rowcond, double* colcond, double* amax, int* info) const;
1608  void GERFS(const char& TRANS, const int& n, const int& nrhs, const double* A, const int& lda, const double* AF, const int& ldaf, const int* IPIV, const double* B, const int& ldb, double* X, const int& ldx, double* FERR, double* BERR, double* WORK, int* IWORK, int* info) const;
1609  void GBEQU(const int& m, const int& n, const int& kl, const int& ku, const double* A, const int& lda, double* R, double* C, double* rowcond, double* colcond, double* amax, int* info) const;
1610  void GBRFS(const char& TRANS, const int& n, const int& kl, const int& ku, const int& nrhs, const double* A, const int& lda, const double* AF, const int& ldaf, const int* IPIV, const double* B, const int& ldb, double* X, const int& ldx, double* FERR, double* BERR, double* WORK, int* IWORK, int* info) const;
1611 
1612  void GESVX(const char& FACT, const char& TRANS, const int& n, const int& nrhs, double* A, const int& lda, double* AF, const int& ldaf, int* IPIV, char* EQUED, double* R, double* C, double* B, const int& ldb, double* X, const int& ldx, double* rcond, double* FERR, double* BERR, double* WORK, int* IWORK, int* info) const;
1613 
1614  void SYTRD(const char& UPLO, const int& n, double* A, const int& lda, double* D, double* E, double* TAU, double* WORK, const int& lwork, int* info) const;
1615  void GEHRD(const int& n, const int& ilo, const int& ihi, double* A, const int& lda, double* TAU, double* WORK, const int& lwork, int* info) const;
1616  void TRTRS(const char& UPLO, const char& TRANS, const char& DIAG, const int& n, const int& nrhs, const double* A, const int& lda, double* B, const int& ldb, int* info) const;
1617  void TRTRI(const char& UPLO, const char& DIAG, const int& n, const double* A, const int& lda, int* info) const;
1618 
1619  // Symmetric eigenproblem routines.
1620  void STEQR(const char& COMPZ, const int& n, double* D, double* E, double* Z, const int& ldz, double* WORK, int* info) const;
1621  void PTEQR(const char& COMPZ, const int& n, double* D, double* E, double* Z, const int& ldz, double* WORK, int* info) const;
1622  void SPEV(const char& JOBZ, const char& UPLO, const int& n, double* AP, double* W, double* Z, const int& ldz, double* WORK, int* info) const;
1623  void SYEV(const char& JOBZ, const char& UPLO, const int& n, double* A, const int& lda, double* W, double* WORK, const int& lwork, int* info) const;
1624  void SYGV(const int& itype, const char& JOBZ, const char& UPLO, const int& n, double* A, const int& lda, double* B, const int& ldb, double* W, double* WORK, const int& lwork, int* info) const;
1625  void HEEV(const char& JOBZ, const char& UPLO, const int& n, double* A, const int& lda, double* W, double* WORK, const int& lwork, double* RWORK, int* info) const;
1626  void HEGV(const int& itype, const char& JOBZ, const char& UPLO, const int& n, double* A, const int& lda, double* B, const int& ldb, double* W, double* WORK, const int& lwork, double* RWORK, int* info) const;
1627 
1628  // Non-Hermitian eigenproblem routines.
1629  void HSEQR(const char& JOB, const char& COMPZ, const int& n, const int& ilo, const int& ihi, double* H, const int& ldh, double* WR, double* WI, double* Z, const int& ldz, double* WORK, const int& lwork, int* info) const;
1630  void GEES(const char& JOBVS, const char& SORT, int (*ptr2func)(double*, double*), const int& n, double* A, const int& lda, int* sdim, double* WR, double* WI, double* VS, const int& ldvs, double* WORK, const int& lwork, int* BWORK, int* info) const;
1631  void GEES(const char& JOBVS, const int& n, double* A, const int& lda, int* sdim, double* WR, double* WI, double* VS, const int& ldvs, double* WORK, const int& lwork, double* RWORK, int* BWORK, int* info) const;
1632 
1633  void GEEV(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) const;
1634  void GEEV(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, double* RWORK, int* info) const;
1635 
1636  void GEEVX(const char& BALANC, const char& JOBVL, const char& JOBVR, const char& SENSE, const int& n, double* A, const int& lda, double* WR, double* WI, double* VL, const int& ldvl, double* VR, const int& ldvr, int* ilo, int* ihi, double* SCALE, double* abnrm, double* RCONDE, double* RCONDV, double* WORK, const int& lwork, int* IWORK, int* info) const;
1637  void GGEVX(const char& BALANC, const char& JOBVL, const char& JOBVR, const char& SENSE, const int& n, double* A, const int& lda, double* B, const int& ldb, double* ALPHAR, double* ALPHAI, double* BETA, double* VL, const int& ldvl, double* VR, const int& ldvr, int* ilo, int* ihi, double* lscale, double* rscale, double* abnrm, double* bbnrm, double* RCONDE, double* RCONDV, double* WORK, const int& lwork, int* IWORK, int* BWORK, int* info) const;
1638  void GGEVX(const char& BALANC, const char& JOBVL, const char& JOBVR, const char& SENSE, const int& n, double* A, const int& lda, double* B, const int& ldb, double* ALPHAR, double* ALPHAI, double* BETA, double* VL, const int& ldvl, double* VR, const int& ldvr, int* ilo, int* ihi, double* lscale, double* rscale, double* abnrm, double* bbnrm, double* RCONDE, double* RCONDV, double* WORK, const int& lwork, double* rwork, int* IWORK, int* BWORK, int* info) const;
1639  void GGEV(const char& JOBVL, const char& JOBVR, const int& n, double* A, const int& lda, double* B, const int& ldb, double* ALPHAR, double* ALPHAI, double* BETA, double* VL, const int& ldvl, double* VR, const int& ldvr, double* WORK, const int& lwork, int* info) const;
1640  void TRSEN(const char& JOB, const char& COMPQ, const int* SELECT, const int& n, double* T, const int& ldt, double* Q, const int& ldq, double* WR, double* WI, int* M, double* S, double* SEP, double* WORK, const int& lwork, int* IWORK, const int& liwork, int* info ) const;
1641  void TGSEN(const int& ijob, const int& wantq, const int& wantz, const int* SELECT, const int& n, 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, int* M, double* PL, double* PR, double* DIF, double* WORK, const int& lwork, int* IWORK, const int& liwork, int* info ) const;
1642  void GGES(const char& JOBVL, const char& JOBVR, const char& SORT, int (*ptr2func)(double*, double*, double*), const int& n, double* A, const int& lda, double* B, const int& ldb, int* sdim, double* ALPHAR, double* ALPHAI, double* BETA, double* VL, const int& ldvl, double* VR, const int& ldvr, double* WORK, const int& lwork, int* bwork, int* info ) const;
1643 
1644 
1645  // SVD routine
1646  void GESVD(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* V, const int& ldv, double* WORK, const int& lwork, double* RWORK, int* info) const;
1647 
1648  // Orthogonal matrix routines.
1649  void ORMQR(const char& SIDE, const char& TRANS, const int& m, const int& n, const int& k, double* A, const int& lda, const double* TAU, double* C, const int& ldc, double* WORK, const int& lwork, int* info) const;
1650  void ORM2R(const char& SIDE, const char& TRANS, const int& m, const int& n, const int& k, const double A[], const int& lda, const double TAU[], double C[], const int& ldc, double WORK[], int* const info) const;
1651  void UNMQR(const char& SIDE, const char& TRANS, const int& m, const int& n, const int& k, double* A, const int& lda, const double* TAU, double* C, const int& ldc, double* WORK, const int& lwork, int* info) const;
1652  void UNM2R(const char& SIDE, const char& TRANS, const int& M, const int& N, const int& K, const double A[], const int& LDA, const double TAU[], double C[], const int& LDC, double WORK[], int* const INFO) const;
1653  void ORGQR(const int& m, const int& n, const int& k, double* A, const int& lda, const double* TAU, double* WORK, const int& lwork, int* info) const;
1654  void UNGQR(const int& m, const int& n, const int& k, double* A, const int& lda, const double* TAU, double* WORK, const int& lwork, int* info) const;
1655  void ORGHR(const int& n, const int& ilo, const int& ihi, double* A, const int& lda, const double* TAU, double* WORK, const int& lwork, int* info) const;
1656  void ORMHR(const char& SIDE, const char& TRANS, const int& m, const int& n, const int& ilo, const int& ihi, const double* A, const int& lda, const double* TAU, double* C, const int& ldc, double* WORK, const int& lwork, int* info) const;
1657 
1658  // Triangular matrix routines.
1659  void TREVC(const char& SIDE, const char& HOWMNY, int* select, const int& n, const double* T, const int& ldt, double* VL, const int& ldvl, double* VR, const int& ldvr, const int& mm, int* m, double* WORK, int* info) const;
1660  void TREVC(const char& SIDE, const int& n, const double* T, const int& ldt, double* VL, const int& ldvl, double* VR, const int& ldvr, const int& mm, int* m, double* WORK, double* RWORK, int* info) const;
1661 
1662  void TREXC(const char& COMPQ, const int& n, double* T, const int& ldt, double* Q, const int& ldq, int* ifst, int* ilst, double* WORK, int* info) const;
1663 
1664  void TGEVC(const char& SIDE, const char& HOWMNY, const int* SELECT, const int& n, double* S, const int& lds, double* P, const int& ldp, double* VL, const int& ldvl, double* VR, const int& ldvr, const int& mm, int* M, double* WORK, int* info) const;
1665 
1666  // Rotation/reflection generators
1667  void LARTG( const double& f, const double& g, double* c, double* s, double* r ) const;
1668  void LARFG( const int& n, double* alpha, double* x, const int& incx, double* tau ) const;
1669 
1670  // Matrix balancing routines.
1671 
1672  void GEBAL(const char& JOBZ, const int& n, double* A, const int& lda, int* ilo, int* ihi, double* scale, int* info) const;
1673 
1674  void GEBAK(const char& JOBZ, const char& SIDE, const int& n, const int& ilo, const int& ihi, const double* scale, const int& m, double* V, const int& ldv, int* info) const;
1675 
1676  // Random number generators
1677  double LARND( const int& idist, int* seed ) const;
1678  void LARNV( const int& idist, int* seed, const int& n, double* v ) const;
1679 
1680  // Machine characteristic routines.
1681  double LAMCH(const char& CMACH) const;
1682  int ILAENV( const int& ispec, const std::string& NAME, const std::string& OPTS, const int& N1 = -1, const int& N2 = -1, const int& N3 = -1, const int& N4 = -1 ) const;
1683 
1684  // Miscellaneous routines.
1685  double LAPY2(const double& x, const double& y) const;
1686 
1687  };
1688 
1689  // END INT, DOUBLE SPECIALIZATION DECLARATION //
1690 
1691 #ifdef HAVE_TEUCHOS_COMPLEX
1692 
1693  // BEGIN INT, COMPLEX<FLOAT> SPECIALIZATION DECLARATION //
1694 
1695  template<>
1696  class TEUCHOSNUMERICS_LIB_DLL_EXPORT LAPACK<int, std::complex<float> >
1697  {
1698  public:
1699  inline LAPACK(void) {}
1700  inline LAPACK(const LAPACK<int, std::complex<float> >& lapack) {}
1701  inline virtual ~LAPACK(void) {}
1702 
1703  // Symmetric positive definite linear system routines
1704  void PTTRF(const int& n, std::complex<float>* d, std::complex<float>* e, int* info) const;
1705  void PTTRS(const int& n, const int& nrhs, const std::complex<float>* d, const std::complex<float>* e, std::complex<float>* B, const int& ldb, int* info) const;
1706  void POTRF(const char& UPLO, const int& n, std::complex<float>* A, const int& lda, int* info) const;
1707  void POTRS(const char& UPLO, const int& n, const int& nrhs, const std::complex<float>* A, const int& lda, std::complex<float>* B, const int& ldb, int* info) const;
1708  void POTRI(const char& UPLO, const int& n, std::complex<float>* A, const int& lda, int* info) const;
1709  void POCON(const char& UPLO, const int& n, const std::complex<float>* A, const int& lda, const float& anorm, float* rcond, std::complex<float>* WORK, float* rwork, int* info) const;
1710  void POSV(const char& UPLO, const int& n, const int& nrhs, std::complex<float>* A, const int& lda, std::complex<float>* B, const int& ldb, int* info) const;
1711  void POEQU(const int& n, const std::complex<float>* A, const int& lda, float* S, float* scond, float* amax, int* info) const;
1712  void PORFS(const char& UPLO, const int& n, const int& nrhs, std::complex<float>* A, const int& lda, const std::complex<float>* AF, const int& ldaf, const std::complex<float>* B, const int& ldb, std::complex<float>* X, const int& ldx, float* FERR, float* BERR, std::complex<float>* WORK, float* RWORK, int* info) const;
1713 
1714  void POSVX(const char& FACT, const char& UPLO, const int& n, const int& nrhs, std::complex<float>* A, const int& lda, std::complex<float>* AF, const int& ldaf, char* EQUED, float* S, std::complex<float>* B, const int& ldb, std::complex<float>* X, const int& ldx, float* rcond, float* FERR, float* BERR, std::complex<float>* WORK, float* RWORK, int* info) const;
1715 
1716  // General Linear System Routines
1717  void GELS(const char& TRANS, const int& m, const int& n, const int& nrhs, std::complex<float>* A, const int& lda, std::complex<float>* B, const int& ldb, std::complex<float>* WORK, const int& lwork, int* info) const;
1718  void GELSS(const int& m, const int& n, const int& nrhs, std::complex<float>* A, const int& lda, std::complex<float>* B, const int& ldb, float* S, const float& rcond, int* rank, std::complex<float>* WORK, const int& lwork, float* RWORK, int* info) const;
1719  void GEQRF(const int& m, const int& n, std::complex<float>* A, const int& lda, std::complex<float>* TAU, std::complex<float>* WORK, const int& lwork, int* info) const;
1720  void GEQR2(const int& m, const int& n, std::complex<float> A[], const int& lda, std::complex<float> TAU[], std::complex<float> WORK[], int* const info) const;
1721  void UNGQR(const int& m, const int& n, const int& k, std::complex<float>* A, const int& lda, const std::complex<float>* TAU, std::complex<float>* WORK, const int& lwork, int* info) const;
1722  void UNMQR(const char& SIDE, const char& TRANS, const int& m, const int& n, const int& k, std::complex<float>* A, const int& lda, const std::complex<float>* TAU, std::complex<float>* C, const int& ldc, std::complex<float>* WORK, const int& lwork, int* info) const;
1723  void UNM2R(const char& SIDE, const char& TRANS, const int& M, const int& N, const int& K, const std::complex<float> A[], const int& LDA, const std::complex<float> TAU[], std::complex<float> C[], const int& LDC, std::complex<float> WORK[], int* const INFO) const;
1724  void GETRF(const int& m, const int& n, std::complex<float>* A, const int& lda, int* IPIV, int* info) const;
1725  void GETRS(const char& TRANS, const int& n, const int& nrhs, const std::complex<float>* A, const int& lda, const int* IPIV, std::complex<float>* B, const int& ldb, int* info) const;
1726  void LASCL(const char& TYPE, const int& kl, const int& ku, const float& cfrom, const float& cto, const int& m, const int& n, std::complex<float>* A, const int& lda, int* info) const;
1727 
1728  void
1729  GEQP3 (const int& m,
1730  const int& n,
1731  std::complex<float>* A,
1732  const int& lda,
1733  int* jpvt,
1734  std::complex<float>* TAU,
1735  std::complex<float>* WORK,
1736  const int& lwork,
1737  float* RWORK,
1738  int* info) const;
1739 
1740  void LASWP (const int& N,
1741  std::complex<float> A[],
1742  const int& LDA,
1743  const int& K1,
1744  const int& K2,
1745  const int IPIV[],
1746  const int& INCX) const;
1747 
1748  void GBTRF(const int& m, const int& n, const int& kl, const int& ku, std::complex<float>* A, const int& lda, int* IPIV, int* info) const;
1749  void GBTRS(const char& TRANS, const int& n, const int& kl, const int& ku, const int& nrhs, const std::complex<float>* A, const int& lda, const int* IPIV, std::complex<float>* B, const int& ldb, int* info) const;
1750  void GTTRF(const int& n, std::complex<float>* dl, std::complex<float>* d, std::complex<float>* du, std::complex<float>* du2, int* IPIV, int* info) const;
1751  void GTTRS(const char& TRANS, const int& n, const int& nrhs, const std::complex<float>* dl, const std::complex<float>* d, const std::complex<float>* du, const std::complex<float>* du2, const int* IPIV, std::complex<float>* B, const int& ldb, int* info) const;
1752  void GETRI(const int& n, std::complex<float>* A, const int& lda, const int* IPIV, std::complex<float>* WORK, const int& lwork, int* info) const;
1753  void LATRS (const char& UPLO, const char& TRANS, const char& DIAG, const char& NORMIN, const int& N, std::complex<float>* A, const int& LDA, std::complex<float>* X, float* SCALE, float* CNORM, int* INFO) const;
1754  void GECON(const char& NORM, const int& n, const std::complex<float>* A, const int& lda, const float& anorm, float* rcond, std::complex<float>* WORK, float* RWORK, int* info) const;
1755  void GBCON(const char& NORM, const int& n, const int& kl, const int& ku, const std::complex<float>* A, const int& lda, int* IPIV, const float& anorm, float* rcond, std::complex<float>* WORK, float* RWORK, int* info) const;
1756  float LANGB(const char& NORM, const int& n, const int& kl, const int& ku, const std::complex<float>* A, const int& lda, float* WORK) const;
1757  void GESV(const int& n, const int& nrhs, std::complex<float>* A, const int& lda, int* IPIV, std::complex<float>* B, const int& ldb, int* info) const;
1758  void GEEQU(const int& m, const int& n, const std::complex<float>* A, const int& lda, float* R, float* C, float* rowcond, float* colcond, float* amax, int* info) const;
1759  void GERFS(const char& TRANS, const int& n, const int& nrhs, const std::complex<float>* A, const int& lda, const std::complex<float>* AF, const int& ldaf, const int* IPIV, const std::complex<float>* B, const int& ldb, std::complex<float>* X, const int& ldx, float* FERR, float* BERR, std::complex<float>* WORK, float* RWORK, int* info) const;
1760  void GBEQU(const int& m, const int& n, const int& kl, const int& ku, const std::complex<float>* A, const int& lda, float* R, float* C, float* rowcond, float* colcond, float* amax, int* info) const;
1761  void GBRFS(const char& TRANS, const int& n, const int& kl, const int& ku, const int& nrhs, const std::complex<float>* A, const int& lda, const std::complex<float>* AF, const int& ldaf, const int* IPIV, const std::complex<float>* B, const int& ldb, std::complex<float>* X, const int& ldx, float* FERR, float* BERR, std::complex<float>* WORK, float* RWORK, int* info) const;
1762 
1763  void GESVX(const char& FACT, const char& TRANS, const int& n, const int& nrhs, std::complex<float>* A, const int& lda, std::complex<float>* AF, const int& ldaf, int* IPIV, char* EQUED, float* R, float* C, std::complex<float>* B, const int& ldb, std::complex<float>* X, const int& ldx, float* rcond, float* FERR, float* BERR, std::complex<float>* WORK, float* RWORK, int* info) const;
1764 
1765  void GEHRD(const int& n, const int& ilo, const int& ihi, std::complex<float>* A, const int& lda, std::complex<float>* TAU, std::complex<float>* WORK, const int& lwork, int* info) const;
1766  void TRTRS(const char& UPLO, const char& TRANS, const char& DIAG, const int& n, const int& nrhs, const std::complex<float>* A, const int& lda, std::complex<float>* B, const int& ldb, int* info) const;
1767  void TRTRI(const char& UPLO, const char& DIAG, const int& n, const std::complex<float>* A, const int& lda, int* info) const;
1768 
1769  // Symmetric eigenvalue routines.
1770  void STEQR(const char& COMPZ, const int& n, float* D, float* E, std::complex<float>* Z, const int& ldz, float* WORK, int* info) const;
1771  void PTEQR(const char& COMPZ, const int& n, float* D, float* E, std::complex<float>* Z, const int& ldz, float* WORK, int* info) const;
1772  void HEEV(const char& JOBZ, const char& UPLO, const int& n, std::complex<float>* A, const int& lda, float* W, std::complex<float>* WORK, const int& lwork, float* RWORK, int* info) const;
1773  void HEGV(const int& itype, const char& JOBZ, const char& UPLO, const int& n, std::complex<float>* A, const int& lda, std::complex<float>* B, const int& ldb, float* W, std::complex<float>* WORK, const int& lwork, float* RWORK, int* info) const;
1774 
1775  // Non-Hermitian eigenvalue routines.
1776  void HSEQR(const char& JOB, const char& COMPZ, const int& n, const int& ilo, const int& ihi, std::complex<float>* H, const int& ldh, std::complex<float>* W, std::complex<float>* Z, const int& ldz, std::complex<float>* WORK, const int& lwork, int* info) const;
1777  void GEES(const char& JOBVS, const char& SORT, int (*ptr2func)(std::complex<float>*), const int& n, std::complex<float>* A, const int& lda, int* sdim, std::complex<float>* W, std::complex<float>* VS, const int& ldvs, std::complex<float>* WORK, const int& lwork, float* RWORK, int* BWORK, int* info) const;
1778  void GEES(const char& JOBVS, const int& n, std::complex<float>* A, const int& lda, int* sdim, float* WR, float* WI, std::complex<float>* VS, const int& ldvs, std::complex<float>* WORK, const int& lwork, float* RWORK, int* BWORK, int* info) const;
1779 
1780  void GEEV(const char& JOBVL, const char& JOBVR, const int& n, std::complex<float>* A, const int& lda, std::complex<float>* W, std::complex<float>* VL, const int& ldvl, std::complex<float>* VR, const int& ldvr, std::complex<float>* WORK, const int& lwork, float* RWORK, int* info) const;
1781  void GEEV(const char& JOBVL, const char& JOBVR, const int& n, std::complex<float>* A, const int& lda, float* WR, float* WI, std::complex<float>* VL, const int& ldvl, std::complex<float>* VR, const int& ldvr, std::complex<float>* WORK, const int& lwork, float* RWORK, int* info) const;
1782 
1783  void GEEVX(const char& BALANC, const char& JOBVL, const char& JOBVR, const char& SENSE, const int& n, std::complex<float>* A, const int& lda, std::complex<float>* W, std::complex<float>* VL, const int& ldvl, std::complex<float>* VR, const int& ldvr, int* ilo, int* ihi, float* SCALE, float* abnrm, float* RCONDE, float* RCONDV, std::complex<float>* WORK, const int& lwork, float* RWORK, int* info) const;
1784 
1785  void GGEVX(const char& BALANC, const char& JOBVL, const char& JOBVR, const char& SENSE, const int& n, std::complex<float>* A, const int& lda, std::complex<float>* B, const int& ldb, std::complex<float>* ALPHA, std::complex<float>* BETA, std::complex<float>* VL, const int& ldvl, std::complex<float>* VR, const int& ldvr, int* ilo, int* ihi, float* lscale, float* rscale, float* abnrm, float* bbnrm, float* RCONDE, float* RCONDV, std::complex<float>* WORK, const int& lwork, float* RWORK, int* IWORK, int* BWORK, int* info) const;
1786  void GGEVX(const char& BALANC, const char& JOBVL, const char& JOBVR, const char& SENSE, const int& n, std::complex<float>* A, const int& lda, std::complex<float>* B, const int& ldb, float* ALPHAR, float* ALPHAI, std::complex<float>* BETA, std::complex<float>* VL, const int& ldvl, std::complex<float>* VR, const int& ldvr, int* ilo, int* ihi, float* lscale, float* rscale, float* abnrm, float* bbnrm, float* RCONDE, float* RCONDV, std::complex<float>* WORK, const int& lwork, float* RWORK, int* IWORK, int* BWORK, int* info) const;
1787  void GGEV(const char& JOBVL, const char& JOBVR, const int& n, std::complex<float> *A, const int& lda, std::complex<float> *B, const int& ldb, std::complex<float>* ALPHA, std::complex<float>* BETA, std::complex<float>* VL, const int& ldvl, std::complex<float>* VR, const int& ldvr, std::complex<float> *WORK, const int& lwork, float* RWORK, int* info) const;
1788 
1789  // SVD routine
1790  void GESVD(const char& JOBU, const char& JOBVT, const int& m, const int& n, std::complex<float>* A, const int& lda, float* S, std::complex<float>* U, const int& ldu, std::complex<float>* V, const int& ldv, std::complex<float>* WORK, const int& lwork, float* RWORK, int* info) const;
1791 
1792  // Triangular matrix routines.
1793  void TREVC(const char& SIDE, const char& HOWMNY, int* select, const int& n, const std::complex<float>* T, const int& ldt, std::complex<float>* VL, const int& ldvl, std::complex<float>* VR, const int& ldvr, const int& mm, int* m, std::complex<float>* WORK, float* RWORK, int* info) const;
1794  void TREVC(const char& SIDE, const int& n, const std::complex<float>* T, const int& ldt, std::complex<float>* VL, const int& ldvl, std::complex<float>* VR, const int& ldvr, const int& mm, int* m, std::complex<float>* WORK, float* RWORK, int* info) const;
1795 
1796  void TREXC(const char& COMPQ, const int& n, std::complex<float>* T, const int& ldt, std::complex<float>* Q, const int& ldq, int* ifst, int* ilst, std::complex<float>* WORK, int* info) const;
1797 
1798  // Rotation/reflection generators
1799  void LARTG( const std::complex<float> f, const std::complex<float> g, float* c, std::complex<float>* s, std::complex<float>* r ) const;
1800  void LARFG( const int& n, std::complex<float>* alpha, std::complex<float>* x, const int& incx, std::complex<float>* tau ) const;
1801 
1802  // Matrix balancing routines.
1803 
1804  void GEBAL(const char& JOBZ, const int& n, std::complex<float>* A, const int& lda, int* ilo, int* ihi, float* scale, int* info) const;
1805 
1806  void GEBAK(const char& JOBZ, const char& SIDE, const int& n, const int& ilo, const int& ihi, const float* scale, const int& m, std::complex<float>* V, const int& ldv, int* info) const;
1807 
1808  // Random number generators
1809  std::complex<float> LARND( const int& idist, int* seed ) const;
1810  void LARNV( const int& idist, int* seed, const int& n, std::complex<float>* v ) const;
1811 
1812  // Machine characteristics
1813  int ILAENV( const int& ispec, const std::string& NAME, const std::string& OPTS, const int& N1 = -1, const int& N2 = -1, const int& N3 = -1, const int& N4 = -1 ) const;
1814 
1815  };
1816 
1817  // END INT, COMPLEX<FLOAT> SPECIALIZATION DECLARATION //
1818 
1819  // BEGIN INT, COMPLEX<DOUBLE> SPECIALIZATION DECLARATION //
1820 
1821  template<>
1822  class TEUCHOSNUMERICS_LIB_DLL_EXPORT LAPACK<int, std::complex<double> >
1823  {
1824  public:
1825  inline LAPACK(void) {}
1826  inline LAPACK(const LAPACK<int, std::complex<double> >& lapack) {}
1827  inline virtual ~LAPACK(void) {}
1828 
1829  // Symmetric positive definite linear system routines
1830  void PTTRF(const int& n, std::complex<double>* d, std::complex<double>* e, int* info) const;
1831  void PTTRS(const int& n, const int& nrhs, const std::complex<double>* d, const std::complex<double>* e, std::complex<double>* B, const int& ldb, int* info) const;
1832  void POTRF(const char& UPLO, const int& n, std::complex<double>* A, const int& lda, int* info) const;
1833  void POTRS(const char& UPLO, const int& n, const int& nrhs, const std::complex<double>* A, const int& lda, std::complex<double>* B, const int& ldb, int* info) const;
1834  void POTRI(const char& UPLO, const int& n, std::complex<double>* A, const int& lda, int* info) const;
1835  void POCON(const char& UPLO, const int& n, const std::complex<double>* A, const int& lda, const double& anorm, double* rcond, std::complex<double>* WORK, double* RWORK, int* info) const;
1836  void POSV(const char& UPLO, const int& n, const int& nrhs, std::complex<double>* A, const int& lda, std::complex<double>* B, const int& ldb, int* info) const;
1837  void POEQU(const int& n, const std::complex<double>* A, const int& lda, double* S, double* scond, double* amax, int* info) const;
1838  void PORFS(const char& UPLO, const int& n, const int& nrhs, std::complex<double>* A, const int& lda, const std::complex<double>* AF, const int& ldaf, const std::complex<double>* B, const int& ldb, std::complex<double>* X, const int& ldx, double* FERR, double* BERR, std::complex<double>* WORK, double* RWORK, int* info) const;
1839 
1840  void POSVX(const char& FACT, const char& UPLO, const int& n, const int& nrhs, std::complex<double>* A, const int& lda, std::complex<double>* AF, const int& ldaf, char* EQUED, double* S, std::complex<double>* B, const int& ldb, std::complex<double>* X, const int& ldx, double* rcond, double* FERR, double* BERR, std::complex<double>* WORK, double* RWORK, int* info) const;
1841 
1842  // General Linear System Routines
1843  void GELS(const char& TRANS, const int& m, const int& n, const int& nrhs, std::complex<double>* A, const int& lda, std::complex<double>* B, const int& ldb, std::complex<double>* WORK, const int& lwork, int* info) const;
1844  void GELSS(const int& m, const int& n, const int& nrhs, std::complex<double>* A, const int& lda, std::complex<double>* B, const int& ldb, double* S, const double& rcond, int* rank, std::complex<double>* WORK, const int& lwork, double* RWORK, int* info) const;
1845  void GEQRF(const int& m, const int& n, std::complex<double>* A, const int& lda, std::complex<double>* TAU, std::complex<double>* WORK, const int& lwork, int* info) const;
1846  void GEQR2(const int& m, const int& n, std::complex<double> A[], const int& lda, std::complex<double> TAU[], std::complex<double> WORK[], int* const info) const;
1847  void UNGQR(const int& m, const int& n, const int& k, std::complex<double>* A, const int& lda, const std::complex<double>* TAU, std::complex<double>* WORK, const int& lwork, int* info) const;
1848  void UNMQR(const char& SIDE, const char& TRANS, const int& m, const int& n, const int& k, std::complex<double>* A, const int& lda, const std::complex<double>* TAU, std::complex<double>* C, const int& ldc, std::complex<double>* WORK, const int& lwork, int* info) const;
1849  void UNM2R(const char& SIDE, const char& TRANS, const int& M, const int& N, const int& K, const std::complex<double> A[], const int& LDA, const std::complex<double> TAU[], std::complex<double> C[], const int& LDC, std::complex<double> WORK[], int* const INFO) const;
1850 
1851  void GETRF(const int& m, const int& n, std::complex<double>* A, const int& lda, int* IPIV, int* info) const;
1852  void GETRS(const char& TRANS, const int& n, const int& nrhs, const std::complex<double>* A, const int& lda, const int* IPIV, std::complex<double>* B, const int& ldb, int* info) const;
1853  void LASCL(const char& TYPE, const int& kl, const int& ku, const double& cfrom, const double& cto, const int& m, const int& n, std::complex<double>* A, const int& lda, int* info) const;
1854 
1855  void
1856  GEQP3 (const int& m,
1857  const int& n,
1858  std::complex<double>* A,
1859  const int& lda,
1860  int* jpvt,
1861  std::complex<double>* TAU,
1862  std::complex<double>* WORK,
1863  const int& lwork,
1864  double* RWORK,
1865  int* info) const;
1866 
1867  void LASWP (const int& N,
1868  std::complex<double> A[],
1869  const int& LDA,
1870  const int& K1,
1871  const int& K2,
1872  const int IPIV[],
1873  const int& INCX) const;
1874 
1875  void GBTRF(const int& m, const int& n, const int& kl, const int& ku, std::complex<double>* A, const int& lda, int* IPIV, int* info) const;
1876  void GBTRS(const char& TRANS, const int& n, const int& kl, const int& ku, const int& nrhs, const std::complex<double>* A, const int& lda, const int* IPIV, std::complex<double>* B, const int& ldb, int* info) const;
1877  void GTTRF(const int& n, std::complex<double>* dl, std::complex<double>* d, std::complex<double>* du, std::complex<double>* du2, int* IPIV, int* info) const;
1878  void GTTRS(const char& TRANS, const int& n, const int& nrhs, const std::complex<double>* dl, const std::complex<double>* d, const std::complex<double>* du, const std::complex<double>* du2, const int* IPIV, std::complex<double>* B, const int& ldb, int* info) const;
1879  void GETRI(const int& n, std::complex<double>* A, const int& lda, const int* IPIV, std::complex<double>* WORK, const int& lwork, int* info) const;
1880  void LATRS (const char& UPLO, const char& TRANS, const char& DIAG, const char& NORMIN, const int& N, std::complex<double>* A, const int& LDA, std::complex<double>* X, double* SCALE, double* CNORM, int* INFO) const;
1881  void GECON(const char& NORM, const int& n, const std::complex<double>* A, const int& lda, const double& anorm, double* rcond, std::complex<double>* WORK, double* RWORK, int* info) const;
1882  void GBCON(const char& NORM, const int& n, const int& kl, const int& ku, const std::complex<double>* A, const int& lda, int* IPIV, const double& anorm, double* rcond, std::complex<double>* WORK, double* RWORK, int* info) const;
1883  double LANGB(const char& NORM, const int& n, const int& kl, const int& ku, const std::complex<double>* A, const int& lda, double* WORK) const;
1884  void GESV(const int& n, const int& nrhs, std::complex<double>* A, const int& lda, int* IPIV, std::complex<double>* B, const int& ldb, int* info) const;
1885  void GEEQU(const int& m, const int& n, const std::complex<double>* A, const int& lda, double* R, double* C, double* rowcond, double* colcond, double* amax, int* info) const;
1886  void GERFS(const char& TRANS, const int& n, const int& nrhs, const std::complex<double>* A, const int& lda, const std::complex<double>* AF, const int& ldaf, const int* IPIV, const std::complex<double>* B, const int& ldb, std::complex<double>* X, const int& ldx, double* FERR, double* BERR, std::complex<double>* WORK, double* RWORK, int* info) const;
1887  void GBEQU(const int& m, const int& n, const int& kl, const int& ku, const std::complex<double>* A, const int& lda, double* R, double* C, double* rowcond, double* colcond, double* amax, int* info) const;
1888  void GBRFS(const char& TRANS, const int& n, const int& kl, const int& ku, const int& nrhs, const std::complex<double>* A, const int& lda, const std::complex<double>* AF, const int& ldaf, const int* IPIV, const std::complex<double>* B, const int& ldb, std::complex<double>* X, const int& ldx, double* FERR, double* BERR, std::complex<double>* WORK, double* RWORK, int* info) const;
1889 
1890  void GESVX(const char& FACT, const char& TRANS, const int& n, const int& nrhs, std::complex<double>* A, const int& lda, std::complex<double>* AF, const int& ldaf, int* IPIV, char* EQUED, double* R, double* C, std::complex<double>* B, const int& ldb, std::complex<double>* X, const int& ldx, double* rcond, double* FERR, double* BERR, std::complex<double>* WORK, double* RWORK, int* info) const;
1891 
1892  void GEHRD(const int& n, const int& ilo, const int& ihi, std::complex<double>* A, const int& lda, std::complex<double>* TAU, std::complex<double>* WORK, const int& lwork, int* info) const;
1893  void TRTRS(const char& UPLO, const char& TRANS, const char& DIAG, const int& n, const int& nrhs, const std::complex<double>* A, const int& lda, std::complex<double>* B, const int& ldb, int* info) const;
1894  void TRTRI(const char& UPLO, const char& DIAG, const int& n, const std::complex<double>* A, const int& lda, int* info) const;
1895 
1896  // Symmetric eigenvalue routines.
1897  void STEQR(const char& COMPZ, const int& n, double* D, double* E, std::complex<double>* Z, const int& ldz, double* WORK, int* info) const;
1898  void PTEQR(const char& COMPZ, const int& n, double* D, double* E, std::complex<double>* Z, const int& ldz, double* WORK, int* info) const;
1899  void HEEV(const char& JOBZ, const char& UPLO, const int& n, std::complex<double>* A, const int& lda, double* W, std::complex<double>* WORK, const int& lwork, double* RWORK, int* info) const;
1900  void HEGV(const int& itype, const char& JOBZ, const char& UPLO, const int& n, std::complex<double>* A, const int& lda, std::complex<double>* B, const int& ldb, double* W, std::complex<double>* WORK, const int& lwork, double* RWORK, int* info) const;
1901 
1902  // Non-hermitian eigenvalue routines.
1903  void HSEQR(const char& JOB, const char& COMPZ, const int& n, const int& ilo, const int& ihi, std::complex<double>* H, const int& ldh, std::complex<double>* W, std::complex<double>* Z, const int& ldz, std::complex<double>* WORK, const int& lwork, int* info) const;
1904  void GEES(const char& JOBVS, const char& SORT, int (*ptr2func)(std::complex<double>*), const int& n, std::complex<double>* A, const int& lda, int* sdim, std::complex<double>* W, std::complex<double>* VS, const int& ldvs, std::complex<double>* WORK, const int& lwork, double* RWORK, int* BWORK, int* info) const;
1905  void GEES(const char& JOBVS, const int& n, std::complex<double>* A, const int& lda, int* sdim, double* WR, double* WI, std::complex<double>* VS, const int& ldvs, std::complex<double>* WORK, const int& lwork, double* RWORK, int* BWORK, int* info) const;
1906 
1907  void GEEV(const char& JOBVL, const char& JOBVR, const int& n, std::complex<double>* A, const int& lda, std::complex<double>* W, std::complex<double>* VL, const int& ldvl, std::complex<double>* VR, const int& ldvr, std::complex<double>* WORK, const int& lwork, double* RWORK, int* info) const;
1908  void GEEV(const char& JOBVL, const char& JOBVR, const int& n, std::complex<double>* A, const int& lda, double* WR, double* WI, std::complex<double>* VL, const int& ldvl, std::complex<double>* VR, const int& ldvr, std::complex<double>* WORK, const int& lwork, double* RWORK, int* info) const;
1909 
1910  void GEEVX(const char& BALANC, const char& JOBVL, const char& JOBVR, const char& SENSE, const int& n, std::complex<double>* A, const int& lda, std::complex<double>* W, std::complex<double>* VL, const int& ldvl, std::complex<double>* VR, const int& ldvr, int* ilo, int* ihi, double* SCALE, double* abnrm, double* RCONDE, double* RCONDV, std::complex<double>* WORK, const int& lwork, double* RWORK, int* info) const;
1911  void GGEVX(const char& BALANC, const char& JOBVL, const char& JOBVR, const char& SENSE, const int& n, std::complex<double>* A, const int& lda, std::complex<double>* B, const int& ldb, std::complex<double>* ALPHA, std::complex<double>* BETA, std::complex<double>* VL, const int& ldvl, std::complex<double>* VR, const int& ldvr, int* ilo, int* ihi, double* lscale, double* rscale, double* abnrm, double* bbnrm, double* RCONDE, double* RCONDV, std::complex<double>* work, const int& lwork, double* RWORK, int* IWORK, int* BWORK, int* info) const;
1912  void GGEVX(const char& BALANC, const char& JOBVL, const char& JOBVR, const char& SENSE, const int& n, std::complex<double>* A, const int& lda, std::complex<double>* B, const int& ldb, double* ALPHAR, double* ALPHAI, std::complex<double>* BETA, std::complex<double>* VL, const int& ldvl, std::complex<double>* VR, const int& ldvr, int* ilo, int* ihi, double* lscale, double* rscale, double* abnrm, double* bbnrm, double* RCONDE, double* RCONDV, std::complex<double>* work, const int& lwork, double* RWORK, int* IWORK, int* BWORK, int* info) const;
1913  void GGEV(const char& JOBVL, const char& JOBVR, const int& n, std::complex<double> *A, const int& lda, std::complex<double> *B, const int& ldb, std::complex<double>* ALPHA, std::complex<double>* BETA, std::complex<double>* VL, const int& ldvl, std::complex<double>*VR, const int& ldvr, std::complex<double> *WORK, const int& lwork, double* RWORK, int* info) const;
1914 
1915  // SVD routine
1916  void GESVD(const char& JOBU, const char& JOBVT, const int& m, const int& n, std::complex<double>* A, const int& lda, double* S, std::complex<double>* U, const int& ldu, std::complex<double>* V, const int& ldv, std::complex<double>* WORK, const int& lwork, double* RWORK, int* info) const;
1917 
1918  // Triangular matrix routines.
1919  void TREVC(const char& SIDE, const char& HOWMNY, int* select, const int& n, const std::complex<double>* T, const int& ldt, std::complex<double>* VL, const int& ldvl, std::complex<double>* VR, const int& ldvr, const int& mm, int* m, std::complex<double>* WORK, double* RWORK, int* info) const;
1920  void TREVC(const char& SIDE, const int& n, const std::complex<double>* T, const int& ldt, std::complex<double>* VL, const int& ldvl, std::complex<double>* VR, const int& ldvr, const int& mm, int* m, std::complex<double>* WORK, double* RWORK, int* info) const;
1921 
1922  void TREXC(const char& COMPQ, const int& n, std::complex<double>* T, const int& ldt, std::complex<double>* Q, const int& ldq, int* ifst, int* ilst, std::complex<double>* WORK, int* info) const;
1923 
1924  // Rotation/reflection generators
1925  void LARTG( const std::complex<double> f, const std::complex<double> g, double* c, std::complex<double>* s, std::complex<double>* r ) const;
1926  void LARFG( const int& n, std::complex<double>* alpha, std::complex<double>* x, const int& incx, std::complex<double>* tau ) const;
1927 
1928  // Matrix balancing routines.
1929 
1930  void GEBAL(const char& JOBZ, const int& n, std::complex<double>* A, const int& lda, int* ilo, int* ihi, double* scale, int* info) const;
1931 
1932  void GEBAK(const char& JOBZ, const char& SIDE, const int& n, const int& ilo, const int& ihi, const double* scale, const int& m, std::complex<double>* V, const int& ldv, int* info) const;
1933 
1934  // Random number generators
1935  std::complex<double> LARND( const int& idist, int* seed ) const;
1936  void LARNV( const int& idist, int* seed, const int& n, std::complex<double>* v ) const;
1937 
1938  // Machine characteristics
1939  int ILAENV( const int& ispec, const std::string& NAME, const std::string& OPTS, const int& N1 = -1, const int& N2 = -1, const int& N3 = -1, const int& N4 = -1 ) const;
1940 
1941  };
1942 
1943  // END INT, COMPLEX<DOUBLE> SPECIALIZATION DECLARATION //
1944 
1945 #endif // HAVE_TEUCHOS_COMPLEX
1946 
1947 #ifdef HAVE_TEUCHOSCORE_QUADMATH
1948 
1949  // BEGIN int, __float128 SPECIALIZATION DECLARATION //
1950 
1951  // mfh 18 Sep 2015: I had to write this specialization by hand,
1952  // since LAPACK does not provide it, so it is not complete.
1953  template<>
1954  class TEUCHOSNUMERICS_LIB_DLL_EXPORT LAPACK<int, __float128>
1955  {
1956  public:
1957  inline LAPACK(void) {}
1958  inline LAPACK(const LAPACK<int, __float128>& lapack) {}
1959  inline virtual ~LAPACK(void) {}
1960 
1961  void GEQRF(const int& m, const int& n, __float128* A, const int& lda, __float128* TAU, __float128* WORK, const int& lwork, int* info) const;
1962  void GEQR2(const int& m, const int& n, __float128 A[], const int& lda, __float128 TAU[], __float128 WORK[], int* const info) const;
1963  void GETRF(const int& m, const int& n, __float128* A, const int& lda, int* IPIV, int* info) const;
1964  void GETRS(const char& TRANS, const int& n, const int& nrhs, const __float128* A, const int& lda, const int* IPIV, __float128* B, const int& ldb, int* info) const;
1965  void GETRI(const int& n, __float128* A, const int& lda, const int* IPIV, __float128* WORK, const int& lwork, int* info) const;
1966  void LASWP (const int& N, __float128 A[], const int& LDA, const int& K1, const int& K2, const int IPIV[], const int& INCX) const;
1967 
1968  void ORM2R(const char& SIDE, const char& TRANS, const int& m, const int& n, const int& k, const __float128 A[], const int& lda, const __float128 TAU[], __float128 C[], const int& ldc, __float128 WORK[], int* const info) const;
1969  void ORGQR(const int& m, const int& n, const int& k, __float128* A, const int& lda, const __float128* TAU, __float128* WORK, const int& lwork, int* info) const;
1970  void UNGQR(const int& m, const int& n, const int& k, __float128* A, const int& lda, const __float128* TAU, __float128* WORK, const int& lwork, int* info) const;
1971 
1972  void LARFG( const int& n, __float128* alpha, __float128* x, const int& incx, __float128* tau ) const;
1973 
1974  __float128 LAPY2 (const __float128 x, const __float128 y) const;
1975  void LASCL (const char& TYPE, const int& kl, const int& ku, const __float128 cfrom, const __float128 cto, const int& m, const int& n, __float128* A, const int& lda, int* info) const;
1976 
1977  void GBTRF (const int& m, const int& n, const int& kl, const int& ku, __float128* A, const int& lda, int* IPIV, int* info) const;
1978  void GBTRS (const char& TRANS, const int& n, const int& kl, const int& ku, const int& nrhs, const __float128* A, const int& lda, const int* IPIV, __float128* B, const int& ldb, int* info) const;
1979  };
1980 
1981  // END int, __float128 SPECIALIZATION DECLARATION //
1982 
1983 #endif // HAVE_TEUCHOSCORE_QUADMATH
1984 
1985 #endif // DOXYGEN_SHOULD_SKIP_THIS
1986 
1987 } // namespace Teuchos
1988 
1989 #endif // _TEUCHOS_LAPACK_HPP_
Teuchos::LAPACK::MagnitudeType
Teuchos::ScalarTraits< ScalarType >::magnitudeType MagnitudeType
Definition: Teuchos_LAPACK.hpp:100
Teuchos::LAPACK::ORGQR
void ORGQR(const OrdinalType &m, const OrdinalType &n, const OrdinalType &k, ScalarType *A, const OrdinalType &lda, const ScalarType *TAU, ScalarType *WORK, const OrdinalType &lwork, OrdinalType *info) const
Compute explicit Q factor from QR factorization (GEQRF) (real case).
Definition: Teuchos_LAPACK.cpp:425
Teuchos::LAPACK::GEEQU
void GEEQU(const OrdinalType &m, const OrdinalType &n, const ScalarType *A, const OrdinalType &lda, ScalarType *R, ScalarType *C, ScalarType *rowcond, ScalarType *colcond, ScalarType *amax, OrdinalType *info) const
Computes row and column scalings intended to equilibrate an m by n matrix A and reduce its condition ...
Definition: Teuchos_LAPACK.cpp:280
Teuchos::LAPACK::GEQR2
void GEQR2(const OrdinalType &m, const OrdinalType &n, ScalarType A[], const OrdinalType &lda, ScalarType TAU[], ScalarType WORK[], OrdinalType *const info) const
BLAS 2 version of GEQRF, with known workspace size.
Definition: Teuchos_LAPACK.cpp:173
Teuchos::LAPACK::LARTG
void LARTG(const ScalarType &f, const ScalarType &g, MagnitudeType *c, ScalarType *s, ScalarType *r) const
Gnerates a plane rotation that zeros out the second component of the input vector.
Definition: Teuchos_LAPACK.cpp:460
Teuchos::LAPACK::GGEVX
void GGEVX(const char &BALANC, const char &JOBVL, const char &JOBVR, const char &SENSE, const OrdinalType &n, ScalarType *A, const OrdinalType &lda, ScalarType *B, const OrdinalType &ldb, MagnitudeType *ALPHAR, MagnitudeType *ALPHAI, ScalarType *BETA, ScalarType *VL, const OrdinalType &ldvl, ScalarType *VR, const OrdinalType &ldvr, OrdinalType *ilo, OrdinalType *ihi, MagnitudeType *lscale, MagnitudeType *rscale, MagnitudeType *abnrm, MagnitudeType *bbnrm, MagnitudeType *RCONDE, MagnitudeType *RCONDV, ScalarType *WORK, const OrdinalType &lwork, OrdinalType *IWORK, OrdinalType *BWORK, OrdinalType *info) const
Definition: Teuchos_LAPACK.cpp:376
Teuchos::ScalarTraits< ScalarType >::magnitudeType
ScalarType magnitudeType
Mandatory typedef for result of magnitude.
Definition: Teuchos_ScalarTraitsDecl.hpp:93
Teuchos::LAPACK::SYTRD
void SYTRD(const char &UPLO, const OrdinalType &n, ScalarType *A, const OrdinalType &lda, ScalarType *D, ScalarType *E, ScalarType *TAU, ScalarType *WORK, const OrdinalType &lwork, OrdinalType *info) const
Reduces a real symmetric matrix A to tridiagonal form by orthogonal similarity transformations.
Definition: Teuchos_LAPACK.cpp:299
f
void f()
Definition: core/example/show_stack/cxx_main.cpp:55
Teuchos::LAPACK::ILAENV
OrdinalType ILAENV(const OrdinalType &ispec, const std::string &NAME, const std::string &OPTS, const OrdinalType &N1=-1, const OrdinalType &N2=-1, const OrdinalType &N3=-1, const OrdinalType &N4=-1) const
Chooses problem-dependent parameters for the local environment.
Definition: Teuchos_LAPACK.cpp:487
Teuchos::LAPACK::UNMQR
void UNMQR(const char &SIDE, const char &TRANS, const OrdinalType &m, const OrdinalType &n, const OrdinalType &k, ScalarType *A, const OrdinalType &lda, const ScalarType *TAU, ScalarType *C, const OrdinalType &ldc, ScalarType *WORK, const OrdinalType &lwork, OrdinalType *info) const
Apply Householder reflectors (complex case).
Definition: Teuchos_LAPACK.cpp:408
Teuchos::LAPACK::GGLSE
void GGLSE(const OrdinalType &m, const OrdinalType &n, const OrdinalType &p, ScalarType *A, const OrdinalType &lda, ScalarType *B, const OrdinalType &ldb, ScalarType *C, ScalarType *D, ScalarType *X, ScalarType *WORK, const OrdinalType &lwork, OrdinalType *info) const
Solves the linear equality-constrained least squares (LSE) problem where A is an m by n matrix...
Definition: Teuchos_LAPACK.cpp:166
Teuchos::LAPACK::TRTRI
void TRTRI(const char &UPLO, const char &DIAG, const OrdinalType &n, const ScalarType *A, const OrdinalType &lda, OrdinalType *info) const
Computes the inverse of an upper or lower triangular matrix A.
Definition: Teuchos_LAPACK.cpp:311
Teuchos::LAPACK::LARFG
void LARFG(const OrdinalType &n, ScalarType *alpha, ScalarType *x, const OrdinalType &incx, ScalarType *tau) const
Generates an elementary reflector of order n that zeros out the last n-1 components of the input vect...
Definition: Teuchos_LAPACK.cpp:464
Teuchos::LAPACK::GEBAK
void GEBAK(const char &JOBZ, const char &SIDE, const OrdinalType &n, const OrdinalType &ilo, const OrdinalType &ihi, const MagnitudeType *scale, const OrdinalType &m, ScalarType *V, const OrdinalType &ldv, OrdinalType *info) const
Forms the left or right eigenvectors of a general matrix that has been balanced by GEBAL by backward ...
Definition: Teuchos_LAPACK.cpp:471
Teuchos::LAPACK::POTRI
void POTRI(const char &UPLO, const OrdinalType &n, ScalarType *A, const OrdinalType &lda, OrdinalType *info) const
Computes the inverse of a real symmetric positive definite matrix A using the Cholesky factorization ...
Definition: Teuchos_LAPACK.cpp:130
Teuchos::LAPACK::GTTRS
void GTTRS(const char &TRANS, const OrdinalType &n, const OrdinalType &nrhs, const ScalarType *dl, const ScalarType *d, const ScalarType *du, const ScalarType *du2, const OrdinalType *IPIV, ScalarType *B, const OrdinalType &ldb, OrdinalType *info) const
Solves a system of linear equations A*X=B or A&#39;*X=B or A^H*X=B with a tridiagonal matrix A using the ...
Definition: Teuchos_LAPACK.cpp:230
Teuchos::ScalarTraits::squareroot
static T squareroot(T x)
Returns a number of magnitudeType that is the square root of this scalar type x.
Definition: Teuchos_ScalarTraitsDecl.hpp:154
Teuchos::LAPACK::SPEV
void SPEV(const char &JOBZ, const char &UPLO, const OrdinalType &n, ScalarType *AP, ScalarType *W, ScalarType *Z, const OrdinalType &ldz, ScalarType *WORK, OrdinalType *info) const
Computes the eigenvalues and, optionally, eigenvectors of a symmetric n by n matrix A in packed stora...
Definition: Teuchos_LAPACK.cpp:315
Teuchos::LAPACK::GTTRF
void GTTRF(const OrdinalType &n, ScalarType *dl, ScalarType *d, ScalarType *du, ScalarType *du2, OrdinalType *IPIV, OrdinalType *info) const
Computes an LU factorization of a n by n tridiagonal matrix A using partial pivoting with row interch...
Definition: Teuchos_LAPACK.cpp:226
Teuchos::LAPACK::ORM2R
void ORM2R(const char &SIDE, const char &TRANS, const OrdinalType &m, const OrdinalType &n, const OrdinalType &k, const ScalarType A[], const OrdinalType &lda, const ScalarType TAU[], ScalarType C[], const OrdinalType &ldc, ScalarType WORK[], OrdinalType *const info) const
BLAS 2 version of ORMQR; known workspace size.
Definition: Teuchos_LAPACK.cpp:404
Teuchos::LAPACK::TRTRS
void TRTRS(const char &UPLO, const char &TRANS, const char &DIAG, const OrdinalType &n, const OrdinalType &nrhs, const ScalarType *A, const OrdinalType &lda, ScalarType *B, const OrdinalType &ldb, OrdinalType *info) const
Solves a triangular linear system of the form A*X=B or A**T*X=B, where A is a triangular matrix...
Definition: Teuchos_LAPACK.cpp:307
Teuchos::LAPACK::POTRS
void POTRS(const char &UPLO, const OrdinalType &n, const OrdinalType &nrhs, const ScalarType *A, const OrdinalType &lda, ScalarType *B, const OrdinalType &ldb, OrdinalType *info) const
Solves a system of linear equations A*X=B, where A is a symmetric positive definite matrix factored b...
Definition: Teuchos_LAPACK.cpp:126
Teuchos::LAPACK::POSV
void POSV(const char &UPLO, const OrdinalType &n, const OrdinalType &nrhs, ScalarType *A, const OrdinalType &lda, ScalarType *B, const OrdinalType &ldb, OrdinalType *info) const
Computes the solution to a real system of linear equations A*X=B, where A is a symmetric positive def...
Definition: Teuchos_LAPACK.cpp:138
Teuchos_ConfigDefs.hpp
Teuchos header file which uses auto-configuration information to include necessary C++ headers...
Teuchos::LAPACK::GBTRF
void GBTRF(const OrdinalType &m, const OrdinalType &n, const OrdinalType &kl, const OrdinalType &ku, ScalarType *A, const OrdinalType &lda, OrdinalType *IPIV, OrdinalType *info) const
Computes an LU factorization of a general banded m by n matrix A using partial pivoting with row inte...
Definition: Teuchos_LAPACK.cpp:218
Teuchos::LAPACK::LAPACK
LAPACK(void)
Default Constructor.
Definition: Teuchos_LAPACK.hpp:106
Teuchos::LAPACK::PTEQR
void PTEQR(const char &COMPZ, const OrdinalType &n, MagnitudeType *D, MagnitudeType *E, ScalarType *Z, const OrdinalType &ldz, MagnitudeType *WORK, OrdinalType *info) const
Computes the eigenvalues and, optionally, eigenvectors of a symmetric positive-definite tridiagonal n...
Definition: Teuchos_LAPACK.cpp:339
Teuchos::LAPACK::TREVC
void TREVC(const char &SIDE, const char &HOWMNY, OrdinalType *select, const OrdinalType &n, const ScalarType *T, const OrdinalType &ldt, ScalarType *VL, const OrdinalType &ldvl, ScalarType *VR, const OrdinalType &ldvr, const OrdinalType &mm, OrdinalType *m, ScalarType *WORK, OrdinalType *info) const
Definition: Teuchos_LAPACK.hpp:1309
Teuchos::LAPACK::PTTRF
void PTTRF(const OrdinalType &n, ScalarType *d, ScalarType *e, OrdinalType *info) const
Computes the L*D*L&#39; factorization of a Hermitian/symmetric positive definite tridiagonal matrix A...
Definition: Teuchos_LAPACK.cpp:114
Teuchos::LAPACK::STEQR
void STEQR(const char &COMPZ, const OrdinalType &n, MagnitudeType *D, MagnitudeType *E, ScalarType *Z, const OrdinalType &ldz, MagnitudeType *WORK, OrdinalType *info) const
Computes the eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal n by n matrix A usi...
Definition: Teuchos_LAPACK.cpp:335
Teuchos::ScalarTraits::sfmin
static magnitudeType sfmin()
Returns safe minimum (sfmin), such that 1/sfmin does not overflow.
Definition: Teuchos_ScalarTraitsDecl.hpp:114
Teuchos::ScalarTraits
This structure defines some basic traits for a scalar field type.
Definition: Teuchos_ScalarTraitsDecl.hpp:90
TEUCHOSNUMERICS_LIB_DLL_EXPORT
#define TEUCHOSNUMERICS_LIB_DLL_EXPORT
Definition: Teuchos_DLLExportMacro.h:39
Teuchos::LAPACK::LASWP
void LASWP(const OrdinalType &N, ScalarType A[], const OrdinalType &LDA, const OrdinalType &K1, const OrdinalType &K2, const OrdinalType IPIV[], const OrdinalType &INCX) const
Apply a series of row interchanges to the matrix A.
Definition: Teuchos_LAPACK.cpp:207
Teuchos::LAPACK::GETRF
void GETRF(const OrdinalType &m, const OrdinalType &n, ScalarType *A, const OrdinalType &lda, OrdinalType *IPIV, OrdinalType *info) const
Computes an LU factorization of a general m by n matrix A using partial pivoting with row interchange...
Definition: Teuchos_LAPACK.cpp:178
Teuchos::LAPACK::LANGB
ScalarTraits< ScalarType >::magnitudeType LANGB(const char &NORM, const OrdinalType &n, const OrdinalType &kl, const OrdinalType &ku, const ScalarType *A, const OrdinalType &lda, MagnitudeType *WORK) const
Returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of lar...
Definition: Teuchos_LAPACK.cpp:272
Teuchos::LAPACK::GGES
void GGES(const char &JOBVL, const char &JOBVR, const char &SORT, OrdinalType &(*ptr2func)(ScalarType *, ScalarType *, ScalarType *), const OrdinalType &n, ScalarType *A, const OrdinalType &lda, ScalarType *B, const OrdinalType &ldb, OrdinalType *sdim, MagnitudeType *ALPHAR, MagnitudeType *ALPHAI, MagnitudeType *BETA, ScalarType *VL, const OrdinalType &ldvl, ScalarType *VR, const OrdinalType &ldvr, ScalarType *WORK, const OrdinalType &lwork, OrdinalType *BWORK, OrdinalType *info) const
Definition: Teuchos_LAPACK.cpp:396
Teuchos::LAPACK::ORMHR
void ORMHR(const char &SIDE, const char &TRANS, const OrdinalType &m, const OrdinalType &n, const OrdinalType &ilo, const OrdinalType &ihi, const ScalarType *A, const OrdinalType &lda, const ScalarType *TAU, ScalarType *C, const OrdinalType &ldc, ScalarType *WORK, const OrdinalType &lwork, OrdinalType *info) const
Overwrites the general real m by n matrix C with the product of C and Q, which is a product of ihi-il...
Definition: Teuchos_LAPACK.cpp:437
Teuchos::LAPACK::LAPACK
LAPACK(const LAPACK< OrdinalType, ScalarType > &lapack)
Copy Constructor.
Definition: Teuchos_LAPACK.hpp:109
Teuchos::LAPACK::GEES
void GEES(const char &JOBVS, const char &SORT, OrdinalType &(*ptr2func)(ScalarType *, ScalarType *), const OrdinalType &n, ScalarType *A, const OrdinalType &lda, OrdinalType *sdim, ScalarType *WR, ScalarType *WI, ScalarType *VS, const OrdinalType &ldvs, ScalarType *WORK, const OrdinalType &lwork, OrdinalType *BWORK, OrdinalType *info) const
Definition: Teuchos_LAPACK.hpp:1192
Teuchos::LAPACK::GEBAL
void GEBAL(const char &JOBZ, const OrdinalType &n, ScalarType *A, const OrdinalType &lda, OrdinalType *ilo, OrdinalType *ihi, MagnitudeType *scale, OrdinalType *info) const
Balances a general matrix A, through similarity transformations to make the rows and columns as close...
Definition: Teuchos_LAPACK.cpp:467
Teuchos::LAPACK::PORFS
void PORFS(const char &UPLO, const OrdinalType &n, const OrdinalType &nrhs, const ScalarType *A, const OrdinalType &lda, const ScalarType *AF, const OrdinalType &ldaf, const ScalarType *B, const OrdinalType &ldb, ScalarType *X, const OrdinalType &ldx, ScalarType *FERR, ScalarType *BERR, ScalarType *WORK, OrdinalType *IWORK, OrdinalType *info) const
Improves the computed solution to a system of linear equations when the coefficient matrix is symmetr...
Definition: Teuchos_LAPACK.cpp:146
Teuchos::LAPACK::LARND
ScalarType LARND(const OrdinalType &idist, OrdinalType *seed) const
Returns a random number from a uniform or normal distribution.
Definition: Teuchos_LAPACK.hpp:1378
Teuchos::LAPACK::POTRF
void POTRF(const char &UPLO, const OrdinalType &n, ScalarType *A, const OrdinalType &lda, OrdinalType *info) const
Computes Cholesky factorization of a real symmetric positive definite matrix A.
Definition: Teuchos_LAPACK.cpp:122
Teuchos::LAPACK::SYEV
void SYEV(const char &JOBZ, const char &UPLO, const OrdinalType &n, ScalarType *A, const OrdinalType &lda, ScalarType *W, ScalarType *WORK, const OrdinalType &lwork, OrdinalType *info) const
Computes all the eigenvalues and, optionally, eigenvectors of a symmetric n by n matrix A...
Definition: Teuchos_LAPACK.cpp:319
Teuchos::LAPACK::UNM2R
void UNM2R(const char &SIDE, const char &TRANS, const OrdinalType &M, const OrdinalType &N, const OrdinalType &K, const ScalarType A[], const OrdinalType &LDA, const ScalarType TAU[], ScalarType C[], const OrdinalType &LDC, ScalarType WORK[], OrdinalType *const INFO) const
BLAS 2 version of UNMQR; known workspace size.
Definition: Teuchos_LAPACK.cpp:416
Teuchos::LAPACK::TREXC
void TREXC(const char &COMPQ, const OrdinalType &n, ScalarType *T, const OrdinalType &ldt, ScalarType *Q, const OrdinalType &ldq, OrdinalType *ifst, OrdinalType *ilst, ScalarType *WORK, OrdinalType *info) const
Definition: Teuchos_LAPACK.cpp:452
Teuchos::LAPACK
The Templated LAPACK Wrapper Class.
Definition: Teuchos_LAPACK.hpp:96
TEUCHOS_MAX
#define TEUCHOS_MAX(x, y)
Definition: Teuchos_ConfigDefs.hpp:161
Teuchos::LAPACK::GGEV
void GGEV(const char &JOBVL, const char &JOBVR, const OrdinalType &n, ScalarType *A, const OrdinalType &lda, ScalarType *B, const OrdinalType &ldb, MagnitudeType *ALPHAR, MagnitudeType *ALPHAI, ScalarType *BETA, ScalarType *VL, const OrdinalType &ldvl, ScalarType *VR, const OrdinalType &ldvr, ScalarType *WORK, const OrdinalType &lwork, OrdinalType *info) const
Definition: Teuchos_LAPACK.cpp:384
Teuchos::LAPACK::SYGV
void SYGV(const OrdinalType &itype, const char &JOBZ, const char &UPLO, const OrdinalType &n, ScalarType *A, const OrdinalType &lda, ScalarType *B, const OrdinalType &ldb, ScalarType *W, ScalarType *WORK, const OrdinalType &lwork, OrdinalType *info) const
Computes all the eigenvalues and, optionally, eigenvectors of a symmetric n by n matrix pencil {A...
Definition: Teuchos_LAPACK.cpp:323
g
void g()
Definition: core/example/show_stack/cxx_main.cpp:47
Teuchos::LAPACK::PTTRS
void PTTRS(const OrdinalType &n, const OrdinalType &nrhs, const ScalarType *d, const ScalarType *e, ScalarType *B, const OrdinalType &ldb, OrdinalType *info) const
Solves a tridiagonal system A*X=B using the *D*L&#39; factorization of A computed by PTTRF.
Definition: Teuchos_LAPACK.cpp:118
Teuchos::LAPACK::LASCL
void LASCL(const char &TYPE, const OrdinalType &kl, const OrdinalType &ku, const MagnitudeType cfrom, const MagnitudeType cto, const OrdinalType &m, const OrdinalType &n, ScalarType *A, const OrdinalType &lda, OrdinalType *info) const
Multiplies the m by n matrix A by the real scalar cto/cfrom.
Definition: Teuchos_LAPACK.cpp:186
Teuchos::LAPACK::POSVX
void POSVX(const char &FACT, const char &UPLO, const OrdinalType &n, const OrdinalType &nrhs, ScalarType *A, const OrdinalType &lda, ScalarType *AF, const OrdinalType &ldaf, char *EQUED, ScalarType *S, ScalarType *B, const OrdinalType &ldb, ScalarType *X, const OrdinalType &ldx, ScalarType *rcond, ScalarType *FERR, ScalarType *BERR, ScalarType *WORK, OrdinalType *IWORK, OrdinalType *info) const
Uses the Cholesky factorization to compute the solution to a real system of linear equations A*X=B...
Definition: Teuchos_LAPACK.cpp:149
Teuchos::LAPACK::LAPY2
ScalarType LAPY2(const ScalarType &x, const ScalarType &y) const
Computes x^2 + y^2 safely, to avoid overflow.
Definition: Teuchos_LAPACK.cpp:500
Teuchos::LAPACK::TRSEN
void TRSEN(const char &JOB, const char &COMPQ, const OrdinalType *SELECT, const OrdinalType &n, ScalarType *T, const OrdinalType &ldt, ScalarType *Q, const OrdinalType &ldq, MagnitudeType *WR, MagnitudeType *WI, OrdinalType *M, ScalarType *S, MagnitudeType *SEP, ScalarType *WORK, const OrdinalType &lwork, OrdinalType *IWORK, const OrdinalType &liwork, OrdinalType *info) const
Definition: Teuchos_LAPACK.cpp:388
Teuchos::LAPACK::GEHRD
void GEHRD(const OrdinalType &n, const OrdinalType &ilo, const OrdinalType &ihi, ScalarType *A, const OrdinalType &lda, ScalarType *TAU, ScalarType *WORK, const OrdinalType &lwork, OrdinalType *info) const
Reduces a real general matrix A to upper Hessenberg form by orthogonal similarity transformations...
Definition: Teuchos_LAPACK.cpp:303
Teuchos::ScalarTraits::magnitude
static magnitudeType magnitude(T a)
Returns the magnitudeType of the scalar type a.
Definition: Teuchos_ScalarTraitsDecl.hpp:132
Teuchos::LAPACK::UNGQR
void UNGQR(const OrdinalType &m, const OrdinalType &n, const OrdinalType &k, ScalarType *A, const OrdinalType &lda, const ScalarType *TAU, ScalarType *WORK, const OrdinalType &lwork, OrdinalType *info) const
Compute explicit QR factor from QR factorization (GEQRF) (complex case).
Definition: Teuchos_LAPACK.cpp:429
Teuchos::LAPACK::GBCON
void GBCON(const char &NORM, const OrdinalType &n, const OrdinalType &kl, const OrdinalType &ku, const ScalarType *A, const OrdinalType &lda, OrdinalType *IPIV, const ScalarType &anorm, ScalarType *rcond, ScalarType *WORK, OrdinalType *IWORK, OrdinalType *info) const
Estimates the reciprocal of the condition number of a general banded real matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by GETRF.
Definition: Teuchos_LAPACK.cpp:268
Teuchos::LAPACK::GBTRS
void GBTRS(const char &TRANS, const OrdinalType &n, const OrdinalType &kl, const OrdinalType &ku, const OrdinalType &nrhs, const ScalarType *A, const OrdinalType &lda, const OrdinalType *IPIV, ScalarType *B, const OrdinalType &ldb, OrdinalType *info) const
Solves a system of linear equations A*X=B or A&#39;*X=B with a general banded n by n matrix A using the L...
Definition: Teuchos_LAPACK.cpp:222
Teuchos::LAPACK::GEQRF
void GEQRF(const OrdinalType &m, const OrdinalType &n, ScalarType *A, const OrdinalType &lda, ScalarType *TAU, ScalarType *WORK, const OrdinalType &lwork, OrdinalType *info) const
Computes a QR factorization of a general m by n matrix A.
Definition: Teuchos_LAPACK.cpp:170
Teuchos::LAPACK::GESVD
void GESVD(const char &JOBU, const char &JOBVT, const OrdinalType &m, const OrdinalType &n, ScalarType *A, const OrdinalType &lda, MagnitudeType *S, ScalarType *U, const OrdinalType &ldu, ScalarType *V, const OrdinalType &ldv, ScalarType *WORK, const OrdinalType &lwork, MagnitudeType *RWORK, OrdinalType *info) const
Computes the singular values (and optionally, vectors) of a real matrix A.
Definition: Teuchos_LAPACK.cpp:368
Teuchos::LAPACK::GESV
void GESV(const OrdinalType &n, const OrdinalType &nrhs, ScalarType *A, const OrdinalType &lda, OrdinalType *IPIV, ScalarType *B, const OrdinalType &ldb, OrdinalType *info) const
Computes the solution to a real system of linear equations A*X=B, where A is factored through GETRF a...
Definition: Teuchos_LAPACK.cpp:276
Teuchos::LAPACK::~LAPACK
virtual ~LAPACK(void)
Destructor.
Definition: Teuchos_LAPACK.hpp:112
Teuchos::LAPACK::GEEV
void GEEV(const char &JOBVL, const char &JOBVR, const OrdinalType &n, ScalarType *A, const OrdinalType &lda, MagnitudeType *WR, MagnitudeType *WI, ScalarType *VL, const OrdinalType &ldvl, ScalarType *VR, const OrdinalType &ldvr, ScalarType *WORK, const OrdinalType &lwork, MagnitudeType *RWORK, OrdinalType *info) const
Computes for an n by n real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors.
Definition: Teuchos_LAPACK.cpp:359
Teuchos::LAPACK::GETRS
void GETRS(const char &TRANS, const OrdinalType &n, const OrdinalType &nrhs, const ScalarType *A, const OrdinalType &lda, const OrdinalType *IPIV, ScalarType *B, const OrdinalType &ldb, OrdinalType *info) const
Solves a system of linear equations A*X=B or A&#39;*X=B with a general n by n matrix A using the LU facto...
Definition: Teuchos_LAPACK.cpp:182
Teuchos::LAPACK::GEEVX
void GEEVX(const char &BALANC, const char &JOBVL, const char &JOBVR, const char &SENSE, const OrdinalType &n, ScalarType *A, const OrdinalType &lda, ScalarType *WR, ScalarType *WI, ScalarType *VL, const OrdinalType &ldvl, ScalarType *VR, const OrdinalType &ldvr, OrdinalType *ilo, OrdinalType *ihi, MagnitudeType *SCALE, MagnitudeType *abnrm, MagnitudeType *RCONDE, MagnitudeType *RCONDV, ScalarType *WORK, const OrdinalType &lwork, OrdinalType *IWORK, OrdinalType *info) const
Definition: Teuchos_LAPACK.cpp:372
Teuchos::LAPACK::GESVX
void GESVX(const char &FACT, const char &TRANS, const OrdinalType &n, const OrdinalType &nrhs, ScalarType *A, const OrdinalType &lda, ScalarType *AF, const OrdinalType &ldaf, OrdinalType *IPIV, char *EQUED, ScalarType *R, ScalarType *C, ScalarType *B, const OrdinalType &ldb, ScalarType *X, const OrdinalType &ldx, ScalarType *rcond, ScalarType *FERR, ScalarType *BERR, ScalarType *WORK, OrdinalType *IWORK, OrdinalType *info) const
Uses the LU factorization to compute the solution to a real system of linear equations A*X=B...
Definition: Teuchos_LAPACK.cpp:295
Teuchos_ScalarTraits.hpp
Defines basic traits for the scalar field type.
Teuchos::ScalarTraits::zero
static T zero()
Returns representation of zero for this scalar type.
Definition: Teuchos_ScalarTraitsDecl.hpp:134
Teuchos::LAPACK::GETRI
void GETRI(const OrdinalType &n, ScalarType *A, const OrdinalType &lda, const OrdinalType *IPIV, ScalarType *WORK, const OrdinalType &lwork, OrdinalType *info) const
Computes the inverse of a matrix A using the LU factorization computed by GETRF.
Definition: Teuchos_LAPACK.cpp:234
Teuchos::LAPACK::GELS
void GELS(const char &TRANS, const OrdinalType &m, const OrdinalType &n, const OrdinalType &nrhs, ScalarType *A, const OrdinalType &lda, ScalarType *B, const OrdinalType &ldb, ScalarType *WORK, const OrdinalType &lwork, OrdinalType *info) const
Solves an over/underdetermined real m by n linear system A using QR or LQ factorization of A...
Definition: Teuchos_LAPACK.cpp:153
Teuchos::LAPACK::GELSS
void GELSS(const OrdinalType &m, const OrdinalType &n, const OrdinalType &nrhs, ScalarType *A, const OrdinalType &lda, ScalarType *B, const OrdinalType &ldb, MagnitudeType *S, const MagnitudeType rcond, OrdinalType *rank, ScalarType *WORK, const OrdinalType &lwork, MagnitudeType *RWORK, OrdinalType *info) const
Use the SVD to solve a possibly rank-deficient linear least-squares problem.
Definition: Teuchos_LAPACK.hpp:682
Teuchos::LAPACK::HEEV
void HEEV(const char &JOBZ, const char &UPLO, const OrdinalType &n, ScalarType *A, const OrdinalType &lda, MagnitudeType *W, ScalarType *WORK, const OrdinalType &lwork, MagnitudeType *RWORK, OrdinalType *info) const
Computes all the eigenvalues and, optionally, eigenvectors of a Hermitian n by n matrix A...
Definition: Teuchos_LAPACK.cpp:327
Teuchos::LAPACK::LARNV
void LARNV(const OrdinalType &idist, OrdinalType *seed, const OrdinalType &n, ScalarType *v) const
Returns a vector of random numbers from a chosen distribution.
Definition: Teuchos_LAPACK.cpp:479
Teuchos::LAPACK::TGSEN
void TGSEN(const OrdinalType &ijob, const OrdinalType &wantq, const OrdinalType &wantz, const OrdinalType *SELECT, const OrdinalType &n, ScalarType *A, const OrdinalType &lda, ScalarType *B, const OrdinalType &ldb, MagnitudeType *ALPHAR, MagnitudeType *ALPHAI, MagnitudeType *BETA, ScalarType *Q, const OrdinalType &ldq, ScalarType *Z, const OrdinalType &ldz, OrdinalType *M, MagnitudeType *PL, MagnitudeType *PR, MagnitudeType *DIF, ScalarType *WORK, const OrdinalType &lwork, OrdinalType *IWORK, const OrdinalType &liwork, OrdinalType *info) const
Definition: Teuchos_LAPACK.cpp:392
Teuchos::LAPACK::ORMQR
void ORMQR(const char &SIDE, const char &TRANS, const OrdinalType &m, const OrdinalType &n, const OrdinalType &k, ScalarType *A, const OrdinalType &lda, const ScalarType *TAU, ScalarType *C, const OrdinalType &ldc, ScalarType *WORK, const OrdinalType &lwork, OrdinalType *info) const
Definition: Teuchos_LAPACK.cpp:400
Teuchos::LAPACK::POCON
void POCON(const char &UPLO, const OrdinalType &n, const ScalarType *A, const OrdinalType &lda, const ScalarType &anorm, ScalarType *rcond, ScalarType *WORK, OrdinalType *IWORK, OrdinalType *info) const
Estimates the reciprocal of the condition number (1-norm) of a real symmetric positive definite matri...
Definition: Teuchos_LAPACK.cpp:134
Teuchos::LAPACK::GERFS
void GERFS(const char &TRANS, const OrdinalType &n, const OrdinalType &nrhs, const ScalarType *A, const OrdinalType &lda, const ScalarType *AF, const OrdinalType &ldaf, const OrdinalType *IPIV, const ScalarType *B, const OrdinalType &ldb, ScalarType *X, const OrdinalType &ldx, ScalarType *FERR, ScalarType *BERR, ScalarType *WORK, OrdinalType *IWORK, OrdinalType *info) const
Improves the computed solution to a system of linear equations and provides error bounds and backward...
Definition: Teuchos_LAPACK.cpp:284
Teuchos::LAPACK::GEQP3
void GEQP3(const OrdinalType &m, const OrdinalType &n, ScalarType *A, const OrdinalType &lda, OrdinalType *jpvt, ScalarType *TAU, ScalarType *WORK, const OrdinalType &lwork, MagnitudeType *RWORK, OrdinalType *info) const
Computes a QR factorization with column pivoting of a matrix A: A*P = Q*R using Level 3 BLAS...
Definition: Teuchos_LAPACK.cpp:191
Teuchos::LAPACK::LAMCH
ScalarType LAMCH(const char &CMACH) const
Determines machine parameters for floating point characteristics.
Definition: Teuchos_LAPACK.cpp:483
Teuchos::LAPACK::HEGV
void HEGV(const OrdinalType &itype, const char &JOBZ, const char &UPLO, const OrdinalType &n, ScalarType *A, const OrdinalType &lda, ScalarType *B, const OrdinalType &ldb, MagnitudeType *W, ScalarType *WORK, const OrdinalType &lwork, MagnitudeType *RWORK, OrdinalType *info) const
Computes all the eigenvalues and, optionally, eigenvectors of a generalized Hermitian-definite n by n...
Definition: Teuchos_LAPACK.cpp:331
Teuchos::LAPACK::ORGHR
void ORGHR(const OrdinalType &n, const OrdinalType &ilo, const OrdinalType &ihi, ScalarType *A, const OrdinalType &lda, const ScalarType *TAU, ScalarType *WORK, const OrdinalType &lwork, OrdinalType *info) const
Generates a real orthogonal matrix Q which is the product of ihi-ilo elementary reflectors of order n...
Definition: Teuchos_LAPACK.cpp:433
TEUCHOS_MIN
#define TEUCHOS_MIN(x, y)
Definition: Teuchos_ConfigDefs.hpp:162
Teuchos::LAPACK::GECON
void GECON(const char &NORM, const OrdinalType &n, const ScalarType *A, const OrdinalType &lda, const ScalarType &anorm, ScalarType *rcond, ScalarType *WORK, OrdinalType *IWORK, OrdinalType *info) const
Estimates the reciprocal of the condition number of a general real matrix A, in either the 1-norm or ...
Definition: Teuchos_LAPACK.cpp:264
Teuchos::LAPACK::LATRS
void LATRS(const char &UPLO, const char &TRANS, const char &DIAG, const char &NORMIN, const OrdinalType &N, ScalarType *A, const OrdinalType &LDA, ScalarType *X, MagnitudeType *SCALE, MagnitudeType *CNORM, OrdinalType *INFO) const
Robustly solve a possibly singular triangular linear system.
Definition: Teuchos_LAPACK.cpp:238
Teuchos::LAPACK::TGEVC
void TGEVC(const char &SIDE, const char &HOWMNY, const OrdinalType *SELECT, const OrdinalType &n, ScalarType *S, const OrdinalType &lds, ScalarType *P, const OrdinalType &ldp, ScalarType *VL, const OrdinalType &ldvl, ScalarType *VR, const OrdinalType &ldvr, const OrdinalType &mm, OrdinalType *M, ScalarType *WORK, OrdinalType *info) const
Definition: Teuchos_LAPACK.cpp:456
Teuchos::ScalarTraits::one
static T one()
Returns representation of one for this scalar type.
Definition: Teuchos_ScalarTraitsDecl.hpp:136
Teuchos::LAPACK::HSEQR
void HSEQR(const char &JOB, const char &COMPZ, const OrdinalType &n, const OrdinalType &ilo, const OrdinalType &ihi, ScalarType *H, const OrdinalType &ldh, ScalarType *WR, ScalarType *WI, ScalarType *Z, const OrdinalType &ldz, ScalarType *WORK, const OrdinalType &lwork, OrdinalType *info) const
Computes the eigenvalues of a real upper Hessenberg matrix H and, optionally, the matrices T and Z fr...
Definition: Teuchos_LAPACK.cpp:343
Teuchos::LAPACK::GBRFS
void GBRFS(const char &TRANS, const OrdinalType &n, const OrdinalType &kl, const OrdinalType &ku, const OrdinalType &nrhs, const ScalarType *A, const OrdinalType &lda, const ScalarType *AF, const OrdinalType &ldaf, const OrdinalType *IPIV, const ScalarType *B, const OrdinalType &ldb, ScalarType *X, const OrdinalType &ldx, ScalarType *FERR, ScalarType *BERR, ScalarType *WORK, OrdinalType *IWORK, OrdinalType *info) const
Improves the computed solution to a banded system of linear equations and provides error bounds and b...
Definition: Teuchos_LAPACK.cpp:292
Teuchos::LAPACK::POEQU
void POEQU(const OrdinalType &n, const ScalarType *A, const OrdinalType &lda, MagnitudeType *S, MagnitudeType *scond, MagnitudeType *amax, OrdinalType *info) const
Computes row and column scalings intended to equilibrate a symmetric positive definite matrix A and r...
Definition: Teuchos_LAPACK.cpp:142
Teuchos::LAPACK::GBEQU
void GBEQU(const OrdinalType &m, const OrdinalType &n, const OrdinalType &kl, const OrdinalType &ku, const ScalarType *A, const OrdinalType &lda, MagnitudeType *R, MagnitudeType *C, MagnitudeType *rowcond, MagnitudeType *colcond, MagnitudeType *amax, OrdinalType *info) const
Computes row and column scalings intended to equilibrate an m by n banded matrix A and reduce its con...
Definition: Teuchos_LAPACK.cpp:288
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