/usr/include/linbox/matrix/matrixdomain/blas-matrix-domain.h is in liblinbox-dev 1.4.2-5build1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 | /* linbox/matrix/blas-matrix-domain.h
* Copyright (C) 2004 Pascal Giorgi, Clément Pernet
*
* Written by :
* Pascal Giorgi pascal.giorgi@ens-lyon.fr
* Clément Pernet clement.pernet@imag.fr
*
* originally placed as ../algorithms/blas-domain.h
*
* ========LICENCE========
* This file is part of the library LinBox.
*
* LinBox is free software: you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version.
*
* This library is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with this library; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
* ========LICENCE========
*/
/*! @file matrix/matrixdomain/blas-domain.h
* @ingroup matrixdomain
* @brief NO DOC
* @warning A <code>BlasMatrixDomain<Field></code> should be templated by a
* \link Givaro::Modular Modular\endlink field. In particular, this domain
* is not suitable for integers.
* @warning A \e Field does mean here a \e Field and not a general \f$\mathbf{Z}/m\mathbf{Z}\f$ \e ring. You'll be warned...
*/
#ifndef __LINBOX_blas_matrix_domain_H
#define __LINBOX_blas_matrix_domain_H
#include <linbox/linbox-config.h>
#include <iostream>
#include <vector>
#include <fflas-ffpack/ffpack/ffpack.h>
#include <fflas-ffpack/fflas/fflas.h>
#include "linbox/linbox-config.h"
#include "linbox/util/debug.h"
#include "linbox/matrix/dense-matrix.h"
#include "linbox/matrix/permutation-matrix.h"
#include "linbox/matrix/factorized-matrix.h"
namespace LinBox
{
/** @internal
* Class handling multiplication of a Matrix by an Operand with accumulation and scaling.
* Operand can be either a matrix or a vector.
*
* The only function: operator () is defined :
* - D = beta.C + alpha. A*B
* - C = beta.C + alpha. A*B
*/
template<class Operand1, class Operand2, class Operand3/*, class MatrixVectorType*/>
class BlasMatrixDomainMulAdd
#if 0
{
public:
typedef typename Operand1::Field Field;
Operand1 &operator() (//const Field &F,
Operand1 &D,
const typename Field::Element &beta, const Operand1 &C,
const typename Field::Element &alpha, const Operand2 &A, const Operand3 &B) const;
Operand1 &operator() (//const Field &F,
const typename Field::Element &beta, Operand1 &C,
const typename Field::Element &alpha, const Operand2 &A, const Operand3 &B) const;
#if 0 /* compiles without... */
// allowing disymetry of Operand2 and Operand3 (only if different type)
Operand1 &operator() (const Field &F,
Operand1 &D,
const typename Field::Element &beta, const Operand1 &C,
const typename Field::Element &alpha, const Operand3 &A, const Operand2 &B) const;
Operand1 &operator() (const Field &F,
const typename Field::Element &beta, Operand1 &C,
const typename Field::Element &alpha, const Operand3 &A, const Operand2 &B) const;
#endif
}
#endif
;
/*!@internal
* Adding two matrices
*/
template< class Field, class Operand1, class Operand2, class Operand3>
class BlasMatrixDomainAdd {
public:
Operand1 &operator() (const Field &F,
Operand1 &C, const Operand2 &A, const Operand3 &B) const;
};
/*!@internal
* Substracting two matrices
*/
template< class Field, class Operand1, class Operand2, class Operand3>
class BlasMatrixDomainSub {
public:
Operand1 &operator() (const Field &F,
Operand1 &C, const Operand2 &A, const Operand3 &B) const;
};
//! C -= A
template< class Field, class Operand1, class Operand2>
class BlasMatrixDomainSubin {
public:
Operand1 &operator() (const Field &F,
Operand1 &C, const Operand2 &A) const;
};
//! C += A
template< class Field, class Operand1, class Operand2>
class BlasMatrixDomainAddin {
public:
Operand1 &operator() (const Field &F,
Operand1 &C, const Operand2 &A) const;
};
/*!@internal
* Copying a matrix
*/
template< class Field, class Operand1, class Operand2>
class BlasMatrixDomainCopy {
public:
Operand1 &operator() (const Field &F,
Operand1 &B, const Operand2 &A) const;
};
/*!@internal
* multiplying two matrices.
*/
template< class Field, class Operand1, class Operand2, class Operand3>
class BlasMatrixDomainMul {
public:
Operand1 &operator() (const Field &F,
Operand1 &C, const Operand2 &A, const Operand3 &B) const
{
return BlasMatrixDomainMulAdd<Operand1,Operand2,Operand3/*,Operand1::MatrixVectorType*/>()( F.zero, C, F.one, A, B );
}
};
/*! @internal
* Class handling in-place multiplication of a Matrix by an Operand.
* Operand can be either a matrix a permutation or a vector
*
* only function: operator () are defined :
* - A = A*B
* - B = A*B
* .
* @note In-place multiplications are proposed for the specialization
* with a matrix and a permutation.
* @warning Using mulin with two matrices is still defined but is
* non-sense
*/
// Operand 2 is always the type of the matrix which is not modified
// ( for example: BlasPermutation TriangularBlasMatrix )
template< class Field, class Operand1, class Operand2>
class BlasMatrixDomainMulin {
public:
// Defines a dummy mulin over generic matrices using a temporary
Operand1 &operator() (const Field &F,
Operand1 &A, const Operand2 &B) const
{
Operand1* tmp = new Operand1(A);
// Effective copy of A
*tmp = A;
BlasMatrixDomainMulAdd<Operand1,Operand1,Operand2/*,Operand1::MatrixVectorType()*/>()( F.zero, A, F.one, *tmp, B );
delete tmp;
return A;
}
Operand1 &operator() (const Field &F,
const Operand2 &A, Operand1 &B ) const
{
Operand1* tmp = new Operand1(B);
// Effective copy of B
*tmp = B;
BlasMatrixDomainMulAdd<Operand1,Operand1,Operand2/*,Operand1::MatrixVectorType()*/>()( F.zero, B, F.one, A, *tmp );
delete tmp;
return B;
}
};
namespace Protected {
template <class Field, class MatrixView>
class BlasMatrixDomainInv;
template <class Field, class MatrixView>
class BlasMatrixDomainDet;
template <class Field, class MatrixView>
class BlasMatrixDomainRank;
}
/*! @internal
* Class handling inversion of a Matrix.
*
* only function: operator () are defined :
* - Ainv = A^(-1)
*
* Returns nullity of matrix (0 iff inversion was ok)
*
* @warning Beware, if A is not const this allows an inplace computation
* and so A will be modified
*
*/
template< class Field, class Matrix1, class Matrix2>
class BlasMatrixDomainInv {
public:
int operator() (const Field &F, Matrix1 &Ainv, const Matrix2 &A) const ;
int operator() (const Field &F, Matrix1 &Ainv, Matrix2 &A) const ;
};
/*! @internal
* Class handling rank computation of a Matrix.
*
* only function: operator () are defined :
* - return the rank of A
*
* @warning Beware, if A is not const this allows an inplace computation
* and so A will be modified
*/
template< class Field, class Matrix>
class BlasMatrixDomainRank {
public:
unsigned int operator() (const Field &F, const Matrix& A) const;
unsigned int operator() (const Field &F, Matrix& A) const;
};
/*! @internal
* Class handling determinant computation of a Matrix.
*
* only function: operator () are defined :
* - return the determinant of A
*
* @warning Beware, if A is not const this allows an inplace computation
* and so A will be modified
*/
template< class Field, class Matrix>
class BlasMatrixDomainDet {
public:
typename Field::Element operator() (const Field &F, const Matrix& A) const;
typename Field::Element operator() (const Field &F, Matrix& A) const;
};
/*! @internal
* Class handling resolution of linear system of a Matrix.
* with Operand as right or left and side
*
* only function: operator () are defined :
* - X = A^(-1).B
* - B = A^(-1).B
*/
template< class Field, class Operand1, class Matrix, class Operand2=Operand1>
class BlasMatrixDomainLeftSolve {
public:
Operand1 &operator() (const Field &F, Operand1 &X, const Matrix &A, const Operand2 &B) const;
Operand1 &operator() (const Field &F, const Matrix &A, Operand1 &B) const;
};
/*! @internal
* Class handling resolution of linear system of a Matrix.
* with Operand as right or left and side
*
* only function: operator () are defined :
* - X = B.A^(-1)
* - B = B.A^(-1)
*/
template< class Field, class Operand1, class Matrix, class Operand2=Operand1>
class BlasMatrixDomainRightSolve {
public:
Operand1 &operator() (const Field &F, Operand1 &X, const Matrix &A, const Operand2 &B) const;
Operand1 &operator() (const Field &F, const Matrix &A, Operand1 &B) const;
};
/*! @internal
* Class handling the minimal polynomial of a Matrix.
*/
template< class Field, class Polynomial, class Matrix>
class BlasMatrixDomainMinpoly {
public:
Polynomial& operator() (const Field &F, Polynomial& P, const Matrix& A) const;
};
/*! @internal
* Class handling the characteristic polynomial of a Matrix.
* \p ContPol is either:
*/
template< class Field, class ContPol, class Matrix>
class BlasMatrixDomainCharpoly {
public:
ContPol& operator() (const Field &F, ContPol& P, const Matrix& A) const;
};
template< class Field, class Matrix, class _Vrep>
class BlasMatrixDomainCharpoly<Field,BlasVector<Field,_Vrep>,Matrix> {
public:
BlasVector<Field,_Vrep>& operator() (const Field &F, BlasVector<Field,_Vrep>& P, const Matrix& A) const;
};
/**
* Interface for all functionnalities provided
* for BlasMatrix.
* @internal
* Done through specialization of all
* classes defined above.
*/
template <class Field_>
class BlasMatrixDomain {
public:
typedef Field_ Field;
typedef typename Field::Element Element;
typedef typename RawVector<Element >::Dense Rep;
typedef BlasMatrix<Field,Rep> OwnMatrix;
typedef BlasSubmatrix<OwnMatrix> Matrix;
typedef BlasSubmatrix<OwnMatrix> Submatrix;
protected:
const Field * _field;
public:
//! Constructor of BlasDomain.
/*
BlasMatrixDomain ()
BlasMatrixDomain (const Field& F )
void init(const Field& F )
BlasMatrixDomain (const BlasMatrixDomain<Field> & BMD)
const Field& field() const
T1& copy(T1& B, const T2& A) const
T1& add(T1& C, const T2& A, const T3& B) const
T1& sub(T1& C, const T2& A, const T3& B) const
T1& mul(T1& C, const T2& A, const T3& B) const
T1& mul(T1& C, const Elt& alpha, const T2& A, const T3& B) const
T1& axpy(T1& D, const T2& A, const T3& B, const T1& C) const
T1& maxpy(T1& D, const T2& A, const T3& B, const T1& C) const
T1& axmy(T1& D, const T2& A, const T3& B, const T1& C) const
T1& muladd(T1& D, const Elt& beta, const T1& C, const Elt& alpha, const T2& A, const T3& B) const
Matrix& inv( Matrix &B, Matrix &A) const
M1& inv( M1 &Ainv, const M2 &A, int& nullity) const // ?
Matrix& div( Matrix &C, const Matrix &A, const Matrix &B) const
T1& addin(T1& A, const T2& B) const
T1& subin(T1& A, const T2& B) const
T1& mulin_left(T1& A, const T2& B) const // A <- AB
T1& mulin_right(T1& A, const T2& B) const // A <- BA
T1& axpyin(T1& C, const T2& A, const T3& B) const
T1& maxpyin(T1& C, const T2& A, const T3& B) const
T1& axmyin(T1& C, const T2& A, const T3& B) const
const
T1& muladdin(const Elt& beta, T1& C, const Elt& alpha, const T2& A, const T3& B) const
Matrix& invin( Matrix &Ainv, Matrix &A) const //?
Matrix& invin(Matrix &A) const
M1& invin( M1 &Ainv, M2 &A, int& nullity) const
unsigned int rank(const Matrix &A) const
unsigned int rankin(Matrix &A) const
Element det(const Matrix &A) const
Element detin(Matrix &A) const
T& left_solve (T& X, const Matrix& A, const T& B) const
T& left_solve (const Matrix& A, T& B) const
T1& right_solve (T1& X, const Matrix& A, const T2& B) const
T& right_solve (const Matrix& A, T& B) const
Polynomial& minpoly( Polynomial& P, const Matrix& A ) const
Polynomial& charpoly( Polynomial& P, const Matrix& A ) const
std::list<Polynomial>& charpoly( std::list<Polynomial>& P, const Matrix& A ) const
bool isZero(const Matrix1 & A) const
bool areEqual(const Matrix1 & A, const Matrix2 & B) const
void setIdentity(Matrix & I) const
void setZero(Matrix & I) const
bool isIdentity(const Matrix1 & A) const
bool isIdentityGeneralized(const Matrix1 & A) const
Element& Magnitude(Element&r, const myBlasMatrix &A) const
inline std::ostream &write (std::ostream &os, const Matrix &A) const
inline std::ostream &write (std::ostream &os, const Matrix &A, bool maple_format) const
inline std::istream &read (std::istream &is, Matrix &A) const
*/
BlasMatrixDomain () {}
BlasMatrixDomain (const Field& F ) { init(F); }
void init(const Field& F )
{
_field = &F;
#if 0 // NO MORE USEFUL
#ifndef NDEBUG
if (!Givaro::probab_prime(F.characteristic())) {
std::cout << " *** WARNING *** " << std::endl;
std::cout << " You are using a BLAS Domain where your field is not prime " <<
F.characteristic() << std::endl;
}
#endif
#endif
}
//! Copy constructor
BlasMatrixDomain (const BlasMatrixDomain<Field> & BMD) :
_field(BMD._field)
{
#if 0 // NO MORE USEFUL
#ifndef NDEBUG
if (!Givaro::probab_prime(field().characteristic())) {
std::cout << " *** WARNING *** " << std::endl;
std::cout << " You are using a BLAS Domain where your field is not prime " << std::endl;
}
#endif
#endif
}
//! Field accessor
const Field& field() const { return *_field; }
/*
* Basics operation available matrix respecting BlasMatrix interface
*/
//! multiplication.
//! C = A*B
template <class Operand1, class Operand2, class Operand3>
Operand1& mul(Operand1& C, const Operand2& A, const Operand3& B) const
{
return BlasMatrixDomainMul<Field,Operand1,Operand2,Operand3>()(field(),C,A,B);
}
//! addition.
//! C = A+B
template <class Operand1, class Operand2, class Operand3>
Operand1& add(Operand1& C, const Operand2& A, const Operand3& B) const
{
return BlasMatrixDomainAdd<Field,Operand1,Operand2,Operand3>()(field(),C,A,B);
}
//! copy.
//! B = A
template <class Operand1, class Operand2>
Operand1& copy(Operand1& B, const Operand2& A) const
{
return BlasMatrixDomainCopy<Field,Operand1,Operand2>()(field(),B,A);
}
//! substraction
//! C = A-B
template <class Operand1, class Operand2, class Operand3>
Operand1& sub(Operand1& C, const Operand2& A, const Operand3& B) const
{
return BlasMatrixDomainSub<Field,Operand1,Operand2,Operand3>()(field(),C,A,B);
}
//! substraction (in place)
//! C -= B
template <class Operand1, class Operand3>
Operand1& subin(Operand1& C, const Operand3& B) const
{
return BlasMatrixDomainSubin<Field,Operand1,Operand3>()(field(),C,B);
}
//! addition (in place)
//! C += B
template <class Operand1, class Operand3>
Operand1& addin(Operand1& C, const Operand3& B) const
{
return BlasMatrixDomainAddin<Field,Operand1,Operand3>()(field(),C,B);
}
//! multiplication with scaling.
//! C = alpha.A*B
template <class Operand1, class Operand2, class Operand3>
Operand1& mul(Operand1& C, const Element& alpha, const Operand2& A, const Operand3& B) const
{
return muladdin(field().zero,C,alpha,A,B);
}
//! In place multiplication.
//! A = A*B
template <class Operand1, class Operand2>
Operand1& mulin_left(Operand1& A, const Operand2& B ) const
{
return BlasMatrixDomainMulin<Field,Operand1,Operand2>()(field(),A,B);
}
//! In place multiplication.
//! B = A*B
template <class Operand1, class Operand2>
Operand2& mulin_right(const Operand1& A, Operand2& B ) const
{
return BlasMatrixDomainMulin<Field,Operand2,Operand1>()(field(),A,B);
}
template <class Matrix1, class Matrix2>
inline Matrix1 &mulin (Matrix1 &A, const Matrix2 &B) const
{
return mulin_left (A, B);
}
//! axpy.
//! D = A*B + C
template <class Operand1, class Operand2, class Operand3>
Operand1& axpy(Operand1& D, const Operand2& A, const Operand3& B, const Operand1& C) const
{
return muladd(D,field().one,C,field().one,A,B);
}
//! axpyin.
//! C += A*B
template <class Operand1, class Operand2, class Operand3>
Operand1& axpyin(Operand1& C, const Operand2& A, const Operand3& B) const
{
return muladdin(field().one,C,field().one,A,B);
}
//! maxpy.
//! D = C - A*B
template <class Operand1, class Operand2, class Operand3>
Operand1& maxpy(Operand1& D, const Operand2& A, const Operand3& B, const Operand1& C)const
{
return muladd(D,field().one,C,field().mOne,A,B);
}
//! maxpyin.
//! C -= A*B
template <class Operand1, class Operand2, class Operand3>
Operand1& maxpyin(Operand1& C, const Operand2& A, const Operand3& B) const
{
return muladdin(field().one,C,field().mOne,A,B);
}
//! axmy.
//! D= A*B - C
template <class Operand1, class Operand2, class Operand3>
Operand1& axmy(Operand1& D, const Operand2& A, const Operand3& B, const Operand1& C) const
{
return muladd(D,field().mOne,C,field().one,A,B);
}
//! axmyin.
//! C = A*B - C
template <class Operand1, class Operand2, class Operand3>
Operand1& axmyin(Operand1& C, const Operand2& A, const Operand3& B) const
{
return muladdin(field().mOne,C,field().one,A,B);
}
//! general matrix-matrix multiplication and addition with scaling.
//! D= beta.C + alpha.A*B
template <class Operand1, class Operand2, class Operand3>
Operand1& muladd(Operand1& D, const Element& beta, const Operand1& C,
const Element& alpha, const Operand2& A, const Operand3& B) const
{
return BlasMatrixDomainMulAdd<Operand1,Operand2,Operand3/*,Operand1::MatrixVectorType()*/>()(D,beta,C,alpha,A,B);
}
//! muladdin.
//! C= beta.C + alpha.A*B.
template <class Operand1, class Operand2, class Operand3>
Operand1& muladdin(const Element& beta, Operand1& C,
const Element& alpha, const Operand2& A, const Operand3& B) const
{
return BlasMatrixDomainMulAdd<Operand1,Operand2,Operand3/*,Operand1::MatrixVectorType()*/>()(beta,C,alpha,A,B);
}
/*!
* @name Solutions available for matrix respecting BlasMatrix interface
*/
//@{
//! Inversion
template <class Matrix1, class Matrix2>
Matrix1& inv( Matrix1 &Ainv, const Matrix2 &A) const
{
BlasMatrixDomainInv<Field,Matrix1,Matrix2>()(field(),Ainv,A);
return Ainv;
}
//! Inversion (in place)
template <class Matrix>
Matrix& invin( Matrix &Ainv, Matrix &A) const
{
BlasMatrixDomainInv<Field,Matrix,Matrix>()(field(),Ainv,A);
return Ainv;
}
//! Inversion (the matrix A is modified)
template <class Matrix>
Matrix& invin(Matrix &A) const
{
Matrix tmp(A);
//Matrix tmp(A.rowdim(), A.coldim());
//tmp = A;
//BlasMatrixDomainInv<Field,Matrix,Matrix>()(field(),A,tmp);
return inv(A, tmp);
}
/*! Division.
* C = A B^{-1} ==> C . B = A
*/
template <class Matrix>
Matrix& div( Matrix &C, const Matrix &A, const Matrix &B) const
{
return this->right_solve(C,B,A);
}
/** Matrix swap
* B <--> A. They must already have the same shape.
* @returns Reference to B
*/
inline Matrix &swap(Matrix &B, Matrix &A) const {
return B.swap(A);
}
//- Inversion w singular check
// template <class Matrix>
// Matrix& inv( Matrix &Ainv, const Matrix &A, int& nullity) const
// {
// nullity = BlasMatrixDomainInv<Field,Matrix,Matrix>()(field(),Ainv,A);
// return Ainv;
// }
//! Inversion w singular check
template <class Matrix1, class Matrix2>
Matrix1& inv( Matrix1 &Ainv, const Matrix2 &A, int& nullity) const
{
nullity = BlasMatrixDomainInv<Field,Matrix1,Matrix2>()(field(),Ainv,A);
return Ainv;
}
//! Inversion (the matrix A is modified) w singular check
template <class Matrix1, class Matrix2>
Matrix1& invin( Matrix1 &Ainv, Matrix2 &A, int& nullity) const
{
nullity = BlasMatrixDomainInv<Field,Matrix1,Matrix2>()(field(),Ainv,A);
return Ainv;
}
//! Rank
template <class Matrix>
unsigned int rank(const Matrix &A) const
{
return BlasMatrixDomainRank<Field,Matrix>()(field(),A);
}
//! in-place Rank (the matrix is modified)
template <class Matrix>
unsigned int rankin(Matrix &A) const
{
return BlasMatrixDomainRank<Field, Matrix>()(field(),A);
}
//! determinant
template <class Matrix>
Element det(const Matrix &A) const
{
return BlasMatrixDomainDet<Field, Matrix>()(field(),A);
}
//! in-place Determinant (the matrix is modified)
template <class Matrix>
Element detin(Matrix &A) const
{
return BlasMatrixDomainDet<Field, Matrix>()(field(),A);
}
//@}
/*!
* @name Solvers for Matrix (respecting BlasMatrix interface)
* with Operand as right or left hand side
*/
//@{
//! linear solve with matrix right hand side.
//! AX=B
template <class Operand, class Matrix>
Operand& left_solve (Operand& X, const Matrix& A, const Operand& B) const
{
return BlasMatrixDomainLeftSolve<Field,Operand,Matrix>()(field(),X,A,B);
}
//! linear solve with matrix right hand side, the result is stored in-place in B.
//! @pre A must be square
//! AX=B , (B<-X)
template <class Operand,class Matrix>
Operand& left_solve (const Matrix& A, Operand& B) const
{
return BlasMatrixDomainLeftSolve<Field,Operand,Matrix>()(field(),A,B);
}
//! linear solve with matrix right hand side.
//! XA=B
template <class Operand1, class Matrix, class Operand2>
Operand1& right_solve (Operand1& X, const Matrix& A, const Operand2& B) const
{
return BlasMatrixDomainRightSolve<Field,Operand1,Matrix,Operand2>()(field(),X,A,B);
}
//! linear solve with matrix right hand side, the result is stored in-place in B.
//! @pre A must be square
//! XA=B , (B<-X)
template <class Operand, class Matrix>
Operand& right_solve (const Matrix& A, Operand& B) const
{
return BlasMatrixDomainRightSolve<Field,Operand,Matrix>()(field(),A,B);
}
//! minimal polynomial computation.
template <class Polynomial, class Matrix>
Polynomial& minpoly( Polynomial& P, const Matrix& A ) const
{
return BlasMatrixDomainMinpoly<Field, Polynomial, Matrix>()(field(),P,A);
}
//! characteristic polynomial computation.
template <class Polynomial, class Matrix >
Polynomial& charpoly( Polynomial& P, const Matrix& A ) const
{
typedef typename Polynomial::Rep PolyRep ;
commentator().start ("Givaro::Modular Dense Charpoly ", "MDCharpoly");
std::list<PolyRep> P_list;
P_list.clear();
BlasMatrixDomainCharpoly<Field, std::list<PolyRep>, Matrix >()(field(),P_list,A);
PolyRep tmp(A.rowdim()+1);
PolyRep Pt ;
typename std::list<PolyRep>::iterator it = P_list.begin();
Pt = *(it++);
while( it!=P_list.end() ){
// Waiting for an implementation of a domain of polynomials
mulpoly( tmp, Pt, *it);
Pt = tmp;
// delete &(*it);
++it;
}
commentator().stop ("done", NULL, "MDCharpoly");
P=Pt;
return P;
}
//! characteristic polynomial computation.
template <class Polynomial, class Matrix >
std::list<Polynomial>& charpoly( std::list<Polynomial>& P, const Matrix& A ) const
{
return BlasMatrixDomainCharpoly<Field, std::list<Polynomial>, Matrix >()(field(),P,A);
}
//private:
//! @todo Temporary: waiting for an implementation of a domain of polynomial
template<class Polynomial>
Polynomial &
mulpoly(Polynomial &res, const Polynomial & P1, const Polynomial & P2) const
{
size_t i,j;
res.resize(P1.size()+P2.size()-1);
for (i=0;i<res.size();i++)
field().assign(res[i],field().zero);
for ( i=0;i<P1.size();i++)
for ( j=0;j<P2.size();j++)
field().axpyin(res[i+j],P1[i],P2[j]);
return res;
}
//@}
template<class Matrix1, class Matrix2>
bool areEqual(const Matrix1 & A, const Matrix2 & B) const
{
if ( (A.rowdim() != B.rowdim()) || (A.coldim() != B.coldim()) )
return false ;
Element a, b; field().init(a); field().init(b);
for (size_t i = 0 ; i < A.rowdim() ; ++i)
for (size_t j = 0 ; j < A.coldim() ; ++j)
if (!field().areEqual(A.getEntry(a,i,j),B.getEntry(b,i,j))) //!@bug use refs
return false ;
return true ;
}
template<class Matrix>
void setIdentity(Matrix & I) const
{
for (size_t i = 0 ; i< I.rowdim() ; ++i)
for (size_t j = 0 ; j < I.coldim() ; ++j) {
if (i == j)
I.setEntry(i,j,field().one);
else
I.setEntry(i,j,field().zero);
}
}
//!@bug use fflas-ffpack
template<class Matrix>
void setZero(Matrix & I) const
{
// use Iterator
for (size_t i = 0 ; i< I.rowdim() ; ++i)
for (size_t j = 0 ; j < I.coldim() ; ++j) {
I.setEntry(i,j,field().zero);
}
}
template<class Matrix1>
bool isZero(const Matrix1 & A) const
{
for (size_t i = 0 ; i < A.rowdim() ; ++i)
for (size_t j = 0 ; j < A.coldim() ; ++j)
if (!field().isZero(A.getEntry(i,j))) //!@bug use refs
return false ;
return true ;
}
template<class Matrix1>
bool isIdentity(const Matrix1 & A) const
{
if (A.rowdim() != A.coldim())
return false ;
for (size_t i = 0 ; i < A.rowdim() ; ++i)
if (!field().isOne(A.getEntry(i,i)))
return false;
for (size_t i = 0 ; i < A.rowdim() ; ++i)
for (size_t j = 0 ; j < i ; ++j)
if (!field().isZero(A.getEntry(i,j))) //!@bug use refs
return false ;
for (size_t i = 0 ; i < A.rowdim() ; ++i)
for (size_t j = i+1 ; j < A.coldim() ; ++j)
if (!field().isZero(A.getEntry(i,j))) //!@bug use refs
return false ;
return true ;
}
template<class Matrix1>
bool isIdentityGeneralized(const Matrix1 & A) const
{
size_t mn = std::min(A.rowdim(),A.coldim());
for (size_t i = 0 ; i < mn ; ++i)
if (!field().isOne(A.getEntry(i,i)))
return false;
for (size_t i = 0 ; i < A.rowdim() ; ++i)
for (size_t j = 0 ; j < std::min(i,mn) ; ++j)
if (!field().isZero(A.getEntry(i,j))) //!@bug use refs
return false ;
for (size_t i = 0 ; i < A.rowdim() ; ++i)
for (size_t j = i+1 ; j < A.coldim() ; ++j)
if (!field().isZero(A.getEntry(i,j))) //!@bug use refs
return false ;
return true ;
}
// if there is some comparison on the elements, max abs of elements.
// whenever a max exists
template<class myBlasMatrix>
Element& Magnitude(Element&r, const myBlasMatrix &A) const
{
r = 0;
for (size_t i = 0 ; i < A.rowdim(); ++i)
for (size_t j = 0 ; j < A.coldim(); ++j) {
Element z = A.getEntry(i,j);
if (z < 0) z = -z ;
if (r < z )
r = z;
}
return r;
}
#if 0
template<class myBlasMatrix>
Integer & Magnitude(Integer &r, const myBlasMatrix1 &A)
{
r = 0;
Integer z;
for (size_t i = 0 ; i < A.rowdim(); ++i)
for (size_t j = 0 ; j < A.coldim(); ++j) {
z = Integer::abs((Integer)A.refEntry(i,j));
if (r > z)
r = z;
}
return r;
}
// all entries in A are smaller than a long
template<class myBlasMatrix>
size_t & Magnitude(size_t &r, const myBlasMatrix1 &A)
{
r = 0;
for (size_t i = 0 ; i < A.rowdim(); ++i)
for (size_t j = 0 ; j < A.coldim(); ++j) {
if (r > (size_t)std::abs(A.refEntry(i,j)))
r = z;
}
return r;
}
template<class myBlasMatrix>
double & Magnitude(double &r, const myBlasMatrix1 &A)
{
r = 0;
for (size_t i = 0 ; i < A.rowdim(); ++i)
for (size_t j = 0 ; j < A.coldim(); ++j) {
if (r > (double)std::abs(A.refEntry(i,j)))
r = z;
}
return r;
}
#endif
public:
/** Print matrix.
* @param os Output stream to which matrix is written.
* @param A Matrix.
* @returns reference to os.
*/
template <class Matrix>
inline std::ostream &write (std::ostream &os, const Matrix &A) const
{
return A.write (os);
}
template <class Matrix>
inline std::ostream &write (std::ostream &os, const Matrix &A, bool maple_format) const
{
return A.write (os, field(), maple_format);
}
/** Read matrix
* @param is Input stream from which matrix is read.
* @param A Matrix.
* @returns reference to is.
*/
template <class Matrix>
inline std::istream &read (std::istream &is, Matrix &A) const
{
return A.read (is, field());
}
}; /* end of class BlasMatrixDomain */
} /* end of namespace LinBox */
#include "linbox/matrix/matrixdomain/blas-matrix-domain.inl"
#endif /* __LINBOX_blas_matrix_domain_H */
// Local Variables:
// mode: C++
// tab-width: 8
// indent-tabs-mode: nil
// c-basic-offset: 8
// End:
// vim:sts=8:sw=8:ts=8:noet:sr:cino=>s,f0,{0,g0,(0,\:0,t0,+0,=s
|