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1 /*
2  Copyright (c) 2012 The Regents of the University of California,
3  through Lawrence Berkeley National Laboratory.
4 
5  Authors: Jack Poulson and Lin Lin
6 
7  This file is part of PEXSI. All rights reserved.
8 
9  Redistribution and use in source and binary forms, with or without
10  modification, are permitted provided that the following conditions are met:
11 
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15  this list of conditions and the following disclaimer in the documentation
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18  National Laboratory, U.S. Dept. of Energy nor the names of its contributors may
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42 */
46 #ifndef _PEXSI_BLAS_HPP_
47 #define _PEXSI_BLAS_HPP_
48 #include "pexsi/environment.hpp"
49 
50 namespace PEXSI {
51 
55 namespace blas {
56 
57  typedef int Int;
58  typedef std::complex<float> scomplex;
59  typedef std::complex<double> dcomplex;
60 
61 
62  // *********************************************************************
63  // Level 1 BLAS //
64  // *********************************************************************
65  void Axpy
66  ( Int n, float alpha, const float* x, Int incx, float* y, Int incy );
67  void Axpy
68  ( Int n, double alpha, const double* x, Int incx, double* y, Int incy );
69  void Axpy
70  ( Int n, scomplex alpha, const scomplex* x, Int incx, scomplex* y, Int incy );
71  void Axpy
72  ( Int n, dcomplex alpha, const dcomplex* x, Int incx, dcomplex* y, Int incy );
73  template<typename T>
74  void Axpy( Int n, T alpha, const T* x, Int incx, T* y, Int incy );
75 
76  void Copy( Int n, const int* x, Int incx, int* y, Int incy );
77  void Copy( Int n, const float* x, Int incx, float* y, Int incy );
78  void Copy( Int n, const double* x, Int incx, double* y, Int incy );
79  void Copy( Int n, const scomplex* x, Int incx, scomplex* y, Int incy );
80  void Copy( Int n, const dcomplex* x, Int incx, dcomplex* y, Int incy );
81  template<typename T>
82  void Copy( Int n, const T* x, Int incx, T* y, Int incy );
83 
84  float Dot( Int n, const float* x, Int incx, const float* y, Int incy );
85  double Dot( Int n, const double* x, Int incx, const double* y, Int incy );
86  scomplex Dot( Int n, const scomplex* x, Int incx, const scomplex* y, Int incy );
87  dcomplex Dot( Int n, const dcomplex* x, Int incx, const dcomplex* y, Int incy );
88  template<typename T>
89  T Dot( Int n, const T* x, Int incx, const T* y, Int incy );
90 
91  float Dotc
92  ( Int n, const float* x, Int incx, const float* y, Int incy );
93  double Dotc
94  ( Int n, const double* x, Int incx, const double* y, Int incy );
95  scomplex Dotc
96  ( Int n, const scomplex* x, Int incx, const scomplex* y, Int incy );
97  dcomplex Dotc
98  ( Int n, const dcomplex* x, Int incx, const dcomplex* y, Int incy );
99  template<typename T>
100  T Dotc( Int n, const T* x, Int incx, const T* y, Int incy );
101 
102  float Dotu
103  ( Int n, const float* x, Int incx, const float* y, Int incy );
104  double Dotu
105  ( Int n, const double* x, Int incx, const double* y, Int incy );
106  scomplex Dotu
107  ( Int n, const scomplex* x, Int incx, const scomplex* y, Int incy );
108  dcomplex Dotu
109  ( Int n, const dcomplex* x, Int incx, const dcomplex* y, Int incy );
110  template<typename T>
111  T Dotu( Int n, const T* x, Int incx, const T* y, Int incy );
112 
113  float Nrm2( Int n, const float* x, Int incx );
114  double Nrm2( Int n, const double* x, Int incx );
115  float Nrm2( Int n, const scomplex* x, Int incx );
116  double Nrm2( Int n, const dcomplex* x, Int incx );
117  template<typename F> F Nrm2( Int n, const F* x, Int incx );
118 
119  void Scal( Int n, float alpha, float* x, Int incx );
120  void Scal( Int n, double alpha, double* x, Int incx );
121  void Scal( Int n, scomplex alpha, scomplex* x, Int incx );
122  void Scal( Int n, dcomplex alpha, dcomplex* x, Int incx );
123  template<typename F> void Scal( Int n, F alpha, F* x, Int incx );
124 
125  // *********************************************************************
126  // Level 2 BLAS
127  // *********************************************************************
128  void Gemv
129  ( char trans, Int m, Int n,
130  float alpha, const float* A, Int lda, const float* x, Int incx,
131  float beta, float* y, Int incy );
132  void Gemv
133  ( char trans, Int m, Int n,
134  double alpha, const double* A, Int lda, const double* x, Int incx,
135  double beta, double* y, Int incy );
136  void Gemv
137  ( char trans, Int m, Int n,
138  scomplex alpha, const scomplex* A, Int lda, const scomplex* x, Int incx,
139  scomplex beta, scomplex* y, Int incy );
140  void Gemv
141  ( char trans, Int m, Int n,
142  dcomplex alpha, const dcomplex* A, Int lda, const dcomplex* x, Int incx,
143  dcomplex beta, dcomplex* y, Int incy );
144  template<typename T>
145  void Gemv
146  ( char trans, Int m, Int n,
147  T alpha, const T* A, Int lda, const T* x, Int incx,
148  T beta, T* y, Int incy );
149 
150  void Ger
151  ( Int m, Int n,
152  float alpha, const float* x, Int incx, const float* y, Int incy,
153  float* A, Int lda );
154  void Ger
155  ( Int m, Int n,
156  double alpha, const double* x, Int incx, const double* y, Int incy,
157  double* A, Int lda );
158  void Ger
159  ( Int m, Int n,
160  scomplex alpha, const scomplex* x, Int incx, const scomplex* y, Int incy,
161  scomplex* A, Int lda );
162  void Ger
163  ( Int m, Int n,
164  dcomplex alpha, const dcomplex* x, Int incx, const dcomplex* y, Int incy,
165  dcomplex* A, Int lda );
166  template<typename T>
167  void Ger
168  ( char trans, Int m, Int n,
169  T alpha, const T* x, Int incx, const T* y, Int incy,
170  T beta, T* A, Int lda );
171 
172  void Gerc
173  ( Int m, Int n,
174  float alpha, const float* x, Int incx, const float* y, Int incy,
175  float* A, Int lda );
176  void Gerc
177  ( Int m, Int n,
178  double alpha, const double* x, Int incx, const double* y, Int incy,
179  double* A, Int lda );
180  void Gerc
181  ( Int m, Int n,
182  scomplex alpha, const scomplex* x, Int incx, const scomplex* y, Int incy,
183  scomplex* A, Int lda );
184  void Gerc
185  ( Int m, Int n,
186  dcomplex alpha, const dcomplex* x, Int incx, const dcomplex* y, Int incy,
187  dcomplex* A, Int lda );
188  template<typename T>
189  void Gerc
190  ( char trans, Int m, Int n,
191  T alpha, const T* x, Int incx, const T* y, Int incy,
192  T beta, T* A, Int lda );
193 
194  void Geru
195  ( Int m, Int n,
196  float alpha, const float* x, Int incx, const float* y, Int incy,
197  float* A, Int lda );
198  void Geru
199  ( Int m, Int n,
200  double alpha, const double* x, Int incx, const double* y, Int incy,
201  double* A, Int lda );
202  void Geru
203  ( Int m, Int n,
204  scomplex alpha, const scomplex* x, Int incx, const scomplex* y, Int incy,
205  scomplex* A, Int lda );
206  void Geru
207  ( Int m, Int n,
208  dcomplex alpha, const dcomplex* x, Int incx, const dcomplex* y, Int incy,
209  dcomplex* A, Int lda );
210  template<typename T>
211  void Geru
212  ( char trans, Int m, Int n,
213  T alpha, const T* x, Int incx, const T* y, Int incy,
214  T beta, T* A, Int lda );
215 
216  void Hemv
217  ( char uplo, Int m,
218  float alpha, const float* A, Int lda, const float* x, Int incx,
219  float beta, float* y, Int incy );
220  void Hemv
221  ( char uplo, Int m,
222  double alpha, const double* A, Int lda, const double* x, Int incx,
223  double beta, double* y, Int incy );
224  void Hemv
225  ( char uplo, Int m,
226  scomplex alpha, const scomplex* A, Int lda, const scomplex* x, Int incx,
227  scomplex beta, scomplex* y, Int incy );
228  void Hemv
229  ( char uplo, Int m,
230  dcomplex alpha, const dcomplex* A, Int lda, const dcomplex* x, Int incx,
231  dcomplex beta, dcomplex* y, Int incy );
232  template<typename T>
233  void Hemv
234  ( char uplo, Int m,
235  T alpha, const T* A, Int lda, const T* x, Int incx,
236  T beta, T* y, Int incy );
237 
238  void Her
239  ( char uplo, Int m,
240  float alpha, const float* x, Int incx, float* A, Int lda );
241  void Her
242  ( char uplo, Int m,
243  double alpha, const double* x, Int incx, double* A, Int lda );
244  void Her
245  ( char uplo, Int m,
246  scomplex alpha, const scomplex* x, Int incx, scomplex* A, Int lda );
247  void Her
248  ( char uplo, Int m,
249  dcomplex alpha, const dcomplex* x, Int incx, dcomplex* A, Int lda );
250  template<typename T>
251  void Hemv( char uplo, Int m, T alpha, const T* x, Int incx, T* A, Int lda );
252 
253  void Her2
254  ( char uplo, Int m,
255  float alpha, const float* x, Int incx, const float* y, Int incy,
256  float* A, Int lda );
257  void Her2
258  ( char uplo, Int m,
259  double alpha, const double* x, Int incx, const double* y, Int incy,
260  double* A, Int lda );
261  void Her2
262  ( char uplo, Int m,
263  scomplex alpha, const scomplex* x, Int incx, const scomplex* y, Int incy,
264  scomplex* A, Int lda );
265  void Her2
266  ( char uplo, Int m,
267  dcomplex alpha, const dcomplex* x, Int incx, const dcomplex* y, Int incy,
268  dcomplex* A, Int lda );
269  template<typename T>
270  void Her2
271  ( char uplo, Int m,
272  T alpha, const T* x, Int incx, const T* y, Int incy,
273  T* A, Int lda );
274 
275  void Symv
276  ( char uplo, Int m,
277  float alpha, const float* A, Int lda, const float* x, Int incx,
278  float beta, float* y, Int incy );
279  void Symv
280  ( char uplo, Int m,
281  double alpha, const double* A, Int lda, const double* x, Int incx,
282  double beta, double* y, Int incy );
283  void Symv
284  ( char uplo, Int m,
285  scomplex alpha, const scomplex* A, Int lda, const scomplex* x, Int incx,
286  scomplex beta, scomplex* y, Int incy );
287  void Symv
288  ( char uplo, Int m,
289  dcomplex alpha, const dcomplex* A, Int lda, const dcomplex* x, Int incx,
290  dcomplex beta, dcomplex* y, Int incy );
291  template<typename T>
292  void Symv
293  ( char uplo, Int m,
294  T alpha, const T* A, Int lda, const T* x, Int incx,
295  T beta, T* y, Int incy );
296 
297  void Syr
298  ( char uplo, Int m,
299  float alpha, const float* x, Int incx, float* A, Int lda );
300  void Syr
301  ( char uplo, Int m,
302  double alpha, const double* x, Int incx, double* A, Int lda );
303  void Syr
304  ( char uplo, Int m,
305  scomplex alpha, const scomplex* x, Int incx, scomplex* A, Int lda );
306  void Syr
307  ( char uplo, Int m,
308  dcomplex alpha, const dcomplex* x, Int incx, dcomplex* A, Int lda );
309  template<typename T>
310  void Syr( char uplo, Int m, T alpha, const T* x, Int incx, T* A, Int lda );
311 
312  void Syr2
313  ( char uplo, Int m,
314  float alpha, const float* x, Int incx, const float* y, Int incy,
315  float* A, Int lda );
316  void Syr2
317  ( char uplo, Int m,
318  double alpha, const double* x, Int incx, const double* y, Int incy,
319  double* A, Int lda );
320  void Syr2
321  ( char uplo, Int m,
322  scomplex alpha, const scomplex* x, Int incx, const scomplex* y, Int incy,
323  scomplex* A, Int lda );
324  void Syr2
325  ( char uplo, Int m,
326  dcomplex alpha, const dcomplex* x, Int incx, const dcomplex* y, Int incy,
327  dcomplex* A, Int lda );
328  template<typename T>
329  void Syr2
330  ( char uplo, Int m,
331  T alpha, const T* x, Int incx, const T* y, Int incy,
332  T* A, Int lda );
333 
334  void Trmv
335  ( char uplo, char trans, char diag, Int m,
336  const float* A, Int lda, float* x, Int incx );
337  void Trmv
338  ( char uplo, char trans, char diag, Int m,
339  const double* A, Int lda, double* x, Int incx );
340  void Trmv
341  ( char uplo, char trans, char diag, Int m,
342  const scomplex* A, Int lda, scomplex* x, Int incx );
343  void Trmv
344  ( char uplo, char trans, char diag, Int m,
345  const dcomplex* A, Int lda, dcomplex* x, Int incx );
346  template<typename T>
347  void Trmv
348  ( char uplo, char trans, char diag, Int m,
349  const T* A, Int lda, T* x, Int incx );
350 
351  void Trsv
352  ( char uplo, char trans, char diag, Int m,
353  const float* A, Int lda, float* x, Int incx );
354  void Trsv
355  ( char uplo, char trans, char diag, Int m,
356  const double* A, Int lda, double* x, Int incx );
357  void Trsv
358  ( char uplo, char trans, char diag, Int m,
359  const scomplex* A, Int lda, scomplex* x, Int incx );
360  void Trsv
361  ( char uplo, char trans, char diag, Int m,
362  const dcomplex* A, Int lda, dcomplex* x, Int incx );
363  template<typename T>
364  void Trsv
365  ( char uplo, char trans, char diag, Int m,
366  const T* A, Int lda, T* x, Int incx );
367 
368  // *********************************************************************
369  // Level 3 BLAS
370  // *********************************************************************
371  void Gemm
372  ( char transA, char transB, Int m, Int n, Int k,
373  float alpha, const float* A, Int lda, const float* B, Int ldb,
374  float beta, float* C, Int ldc );
375  void Gemm
376  ( char transA, char transB, Int m, Int n, Int k,
377  double alpha, const double* A, Int lda, const double* B, Int ldb,
378  double beta, double* C, Int ldc );
379  void Gemm
380  ( char transA, char transB, Int m, Int n, Int k,
381  scomplex alpha, const scomplex* A, Int lda, const scomplex* B, Int ldb,
382  scomplex beta, scomplex* C, Int ldc );
383  void Gemm
384  ( char transA, char transB, Int m, Int n, Int k,
385  dcomplex alpha, const dcomplex* A, Int lda, const dcomplex* B, Int ldb,
386  dcomplex beta, dcomplex* C, Int ldc );
387  template<typename T>
388  void Gemm
389  ( char transA, char transB, Int m, Int n, Int k,
390  T alpha, const T* A, Int lda, const T* B, Int ldb,
391  T beta, T* C, Int ldc );
392 
393  void Hemm
394  ( char side, char uplo, Int m, Int n,
395  float alpha, const float* A, Int lda, const float* B, Int ldb,
396  float beta, float* C, Int ldc );
397  void Hemm
398  ( char side, char uplo, Int m, Int n,
399  double alpha, const double* A, Int lda, const double* B, Int ldb,
400  double beta, double* C, Int ldc );
401  void Hemm
402  ( char side, char uplo, Int m, Int n,
403  scomplex alpha, const scomplex* A, Int lda, const scomplex* B, Int ldb,
404  scomplex beta, scomplex* C, Int ldc );
405  void Hemm
406  ( char side, char uplo, Int m, Int n,
407  dcomplex alpha, const dcomplex* A, Int lda, const dcomplex* B, Int ldb,
408  dcomplex beta, dcomplex* C, Int ldc );
409  template<typename T>
410  void Hemm
411  ( char side, char uplo, Int m, Int n,
412  T alpha, const T* A, Int lda, const T* B, Int ldb,
413  T beta, T* C, Int ldc );
414 
415  void Her2k
416  ( char uplo, char trans, Int n, Int k,
417  float alpha, const float* A, Int lda, const float* B, Int ldb,
418  float beta, float* C, Int ldc );
419  void Her2k
420  ( char uplo, char trans, Int n, Int k,
421  double alpha, const double* A, Int lda, const double* B, Int ldb,
422  double beta, double* C, Int ldc );
423  void Her2k
424  ( char uplo, char trans, Int n, Int k,
425  scomplex alpha, const scomplex* A, Int lda, const scomplex* B, Int ldb,
426  scomplex beta, scomplex* C, Int ldc );
427  void Her2k
428  ( char uplo, char trans, Int n, Int k,
429  dcomplex alpha, const dcomplex* A, Int lda, const dcomplex* B, Int ldb,
430  dcomplex beta, dcomplex* C, Int ldc );
431  template<typename T>
432  void Her2k
433  ( char uplo, char trans, Int n, Int k,
434  T alpha, const T* A, Int lda, const T* B, Int ldb,
435  T beta, T* C, Int ldc );
436 
437  void Herk
438  ( char uplo, char trans, Int n, Int k,
439  float alpha, const float* A, Int lda, float beta, float* C, Int ldc );
440  void Herk
441  ( char uplo, char trans, Int n, Int k,
442  double alpha, const double* A, Int lda, double beta, double* C, Int ldc );
443  void Herk
444  ( char uplo, char trans, Int n, Int k,
445  scomplex alpha, const scomplex* A, Int lda,
446  scomplex beta, scomplex* C, Int ldc );
447  void Herk
448  ( char uplo, char trans, Int n, Int k,
449  dcomplex alpha, const dcomplex* A, Int lda,
450  dcomplex beta, dcomplex* C, Int ldc );
451  template<typename T>
452  void Herk
453  ( char uplo, char trans, Int n, Int k,
454  T alpha, const T* A, Int lda,
455  T beta, T* C, Int ldc );
456 
457  void Symm
458  ( char side, char uplo, Int m, Int n,
459  float alpha, const float* A, Int lda, const float* B, Int ldb,
460  float beta, float* C, Int ldc );
461  void Symm
462  ( char side, char uplo, Int m, Int n,
463  double alpha, const double* A, Int lda, const double* B, Int ldb,
464  double beta, double* C, Int ldc );
465  void Symm
466  ( char side, char uplo, Int m, Int n,
467  scomplex alpha, const scomplex* A, Int lda, const scomplex* B, Int ldb,
468  scomplex beta, scomplex* C, Int ldc );
469  void Symm
470  ( char side, char uplo, Int m, Int n,
471  dcomplex alpha, const dcomplex* A, Int lda, const dcomplex* B, Int ldb,
472  dcomplex beta, dcomplex* C, Int ldc );
473  template<typename T>
474  void Symm
475  ( char side, char uplo, Int m, Int n,
476  T alpha, const T* A, Int lda, const T* B, Int ldb,
477  T beta, T* C, Int ldc );
478 
479  void Syr2k
480  ( char uplo, char trans, Int n, Int k,
481  float alpha, const float* A, Int lda, const float* B, Int ldb,
482  float beta, float* C, Int ldc );
483  void Syr2k
484  ( char uplo, char trans, Int n, Int k,
485  double alpha, const double* A, Int lda, const double* B, Int ldb,
486  double beta, double* C, Int ldc );
487  void Syr2k
488  ( char uplo, char trans, Int n, Int k,
489  scomplex alpha, const scomplex* A, Int lda, const scomplex* B, Int ldb,
490  scomplex beta, scomplex* C, Int ldc );
491  void Syr2k
492  ( char uplo, char trans, Int n, Int k,
493  dcomplex alpha, const dcomplex* A, Int lda, const dcomplex* B, Int ldb,
494  dcomplex beta, dcomplex* C, Int ldc );
495  template<typename T>
496  void Syr2k
497  ( char uplo, char trans, Int n, Int k,
498  T alpha, const T* A, Int lda, const T* B, Int ldb,
499  T beta, T* C, Int ldc );
500 
501  void Syrk
502  ( char uplo, char trans, Int n, Int k,
503  float alpha, const float* A, Int lda,
504  float beta, float* C, Int ldc );
505  void Syrk
506  ( char uplo, char trans, Int n, Int k,
507  double alpha, const double* A, Int lda,
508  double beta, double* C, Int ldc );
509  void Syrk
510  ( char uplo, char trans, Int n, Int k,
511  scomplex alpha, const scomplex* A, Int lda,
512  scomplex beta, scomplex* C, Int ldc );
513  void Syrk
514  ( char uplo, char trans, Int n, Int k,
515  dcomplex alpha, const dcomplex* A, Int lda,
516  dcomplex beta, dcomplex* C, Int ldc );
517  template<typename T>
518  void Syrk
519  ( char uplo, char trans, Int n, Int k,
520  T alpha, const T* A, Int lda,
521  T beta, T* C, Int ldc );
522 
523  void Trmm
524  ( char side, char uplo, char trans, char unit, Int m, Int n,
525  float alpha, const float* A, Int lda, float* B, Int ldb );
526  void Trmm
527  ( char side, char uplo, char trans, char unit, Int m, Int n,
528  double alpha, const double* A, Int lda, double* B, Int ldb );
529  void Trmm
530  ( char side, char uplo, char trans, char unit, Int m, Int n,
531  scomplex alpha, const scomplex* A, Int lda, scomplex* B, Int ldb );
532  void Trmm
533  ( char side, char uplo, char trans, char unit, Int m, Int n,
534  dcomplex alpha, const dcomplex* A, Int lda, dcomplex* B, Int ldb );
535  template<typename T>
536  void Trmm
537  ( char side, char uplo, char trans, char unit, Int m, Int n,
538  T alpha, const T* A, Int lda, T* B, Int ldb );
539 
540  void Trsm
541  ( char side, char uplo, char trans, char unit, Int m, Int n,
542  float alpha, const float* A, Int lda, float* B, Int ldb );
543  void Trsm
544  ( char side, char uplo, char trans, char unit, Int m, Int n,
545  double alpha, const double* A, Int lda, double* B, Int ldb );
546  void Trsm
547  ( char side, char uplo, char trans, char unit, Int m, Int n,
548  scomplex alpha, const scomplex* A, Int lda, scomplex* B, Int ldb );
549  void Trsm
550  ( char side, char uplo, char trans, char unit, Int m, Int n,
551  dcomplex alpha, const dcomplex* A, Int lda, dcomplex* B, Int ldb );
552  template<typename T>
553  void Trsm
554  ( char side, char uplo, char trans, char unit, Int m, Int n,
555  T alpha, const T* A, Int lda, T* B, Int ldb );
556 
557 } // namespace blas
558 } // namespace PEXSI
559 
560 #endif //_PEXSI_BLAS_HPP_
environment.hpp
Environmental variables.
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