lapack.hpp

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/*
         Copyright (c) 2012 The Regents of the University of California,
         through Lawrence Berkeley National Laboratory.  

   Authors: Jack Poulson and Lin Lin
         
   This file is part of PEXSI. All rights reserved.

         Redistribution and use in source and binary forms, with or without
         modification, are permitted provided that the following conditions are met:

         (1) Redistributions of source code must retain the above copyright notice, this
         list of conditions and the following disclaimer.
         (2) Redistributions in binary form must reproduce the above copyright notice,
         this list of conditions and the following disclaimer in the documentation
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         (3) Neither the name of the University of California, Lawrence Berkeley
         National Laboratory, U.S. Dept. of Energy nor the names of its contributors may
         be used to endorse or promote products derived from this software without
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*/
#ifndef _PEXSI_LAPACK_HPP_
#define _PEXSI_LAPACK_HPP_

#include "pexsi/environment.hpp"

namespace PEXSI {

namespace lapack {

        typedef  int                    Int; 
        typedef  std::complex<float>    scomplex;
        typedef  std::complex<double>   dcomplex;


        // *********************************************************************
        // Cholesky factorization
        // *********************************************************************

        void Potrf( char uplo, Int n, const float* A, Int lda );
        void Potrf( char uplo, Int n, const double* A, Int lda );
        void Potrf( char uplo, Int n, const scomplex* A, Int lda );
        void Potrf( char uplo, Int n, const dcomplex* A, Int lda );


        // *********************************************************************
        // LU factorization (with partial pivoting)
        // *********************************************************************

        void Getrf( Int m, Int n, float* A, Int lda, Int* p );
        void Getrf( Int m, Int n, double* A, Int lda, Int* p );
        void Getrf( Int m, Int n, scomplex* A, Int lda, Int* p );
        void Getrf( Int m, Int n, dcomplex* A, Int lda, Int* p );

        // *********************************************************************
        // For reducing well-conditioned Hermitian generalized-definite EVP's
        // to standard form.
        // *********************************************************************

        void Hegst
                ( Int itype, char uplo, 
                        Int n, float* A, Int lda, const float* B, Int ldb );
        void Hegst
                ( Int itype, char uplo,
                        Int n, double* A, Int lda, const double* B, Int ldb );
        void Hegst
                ( Int itype, char uplo,
                        Int n, scomplex* A, Int lda, const scomplex* B, Int ldb );
        void Hegst
                ( Int itype, char uplo,
                        Int n, dcomplex* A, Int lda, const dcomplex* B, Int ldb );

  // *********************************************************************
  // For solving the standard eigenvalue problem using the divide and
  // conquer algorithm
  // *********************************************************************

  void Syevd
    ( char jobz, char uplo, Int n, double* A, Int lda, double* eigs );

  // *********************************************************************
  // For solving the generalized eigenvalue problem using the divide and
  // conquer algorithm
  // *********************************************************************

  void Sygvd
    ( int itype, char jobz, char uplo, Int n, double* A, Int lda, 
      double* B, Int ldb, double* eigs );



        // *********************************************************************
        // For computing the inverse of a triangular matrix
        // *********************************************************************

        void Trtri
                ( char uplo, char diag, Int n, const float* A, Int lda );
        void Trtri
                ( char uplo, char diag, Int n, const double* A, Int lda );
        void Trtri
                ( char uplo, char diag, Int n, const scomplex* A, Int lda );
        void Trtri
                ( char uplo, char diag, Int n, const dcomplex* A, Int lda );


        // *********************************************************************
        // Compute the SVD of a general matrix using a divide and conquer algorithm
        // *********************************************************************

        void DivideAndConquerSVD
                ( Int m, Int n, float* A, Int lda, 
                        float* s, float* U, Int ldu, float* VTrans, Int ldvt );
        void DivideAndConquerSVD
                ( Int m, Int n, double* A, Int lda, 
                        double* s, double* U, Int ldu, double* VTrans, Int ldvt );
        void DivideAndConquerSVD
                ( Int m, Int n, scomplex* A, Int lda, 
                        float* s, scomplex* U, Int ldu, scomplex* VAdj, Int ldva );
        void DivideAndConquerSVD
                ( Int m, Int n, dcomplex* A, Int lda, 
                        double* s, dcomplex* U, Int ldu, dcomplex* VAdj, Int ldva );

        //
        // Compute the SVD of a general matrix using the QR algorithm
        //

        void QRSVD
                ( Int m, Int n, float* A, Int lda, 
                        float* s, float* U, Int ldu, float* VTrans, Int ldvt );
        void QRSVD
                ( Int m, Int n, double* A, Int lda, 
                        double* s, double* U, Int ldu, double* VTrans, Int ldvt );
        void QRSVD
                ( Int m, Int n, scomplex* A, Int lda, 
                        float* s, scomplex* U, Int ldu, scomplex* VAdj, Int ldva );
        void QRSVD
                ( Int m, Int n, dcomplex* A, Int lda, 
                        double* s, dcomplex* U, Int ldu, dcomplex* VAdj, Int ldva );


        // *********************************************************************
        // Compute the singular values of a general matrix using the QR algorithm
        // *********************************************************************

        void SingularValues( Int m, Int n, float* A, Int lda, float* s );
        void SingularValues( Int m, Int n, double* A, Int lda, double* s );
        void SingularValues( Int m, Int n, scomplex* A, Int lda, float* s );
        void SingularValues( Int m, Int n, dcomplex* A, Int lda, double* s );

        // *********************************************************************
        // Compute the SVD of a bidiagonal matrix using the QR algorithm
        // *********************************************************************

        void BidiagQRAlg
                ( char uplo, Int n, Int numColsVTrans, Int numRowsU,
                        float* d, float* e, float* VTrans, Int ldVTrans, float* U, Int ldU );
        void BidiagQRAlg
                ( char uplo, Int n, Int numColsVTrans, Int numRowsU, 
                        double* d, double* e, double* VTrans, Int ldVTrans, double* U, Int ldU );
        void BidiagQRAlg
                ( char uplo, Int n, Int numColsVAdj, Int numRowsU,
                        float* d, float* e, scomplex* VAdj, Int ldVAdj, scomplex* U, Int ldU );
        void BidiagQRAlg
                ( char uplo, Int n, Int numColsVAdj, Int numRowsU, 
                        double* d, double* e, dcomplex* VAdj, Int ldVAdj, dcomplex* U, Int ldU );

        // *********************************************************************
        // Compute the linear least square problem using SVD
        // *********************************************************************
        void SVDLeastSquare( Int m, Int n, Int nrhs, float * A, Int lda,
                        float * B, Int ldb, float * S, float rcond,
                        Int* rank );
        void SVDLeastSquare( Int m, Int n, Int nrhs, double * A, Int lda,
                        double * B, Int ldb, double * S, double rcond,
                        Int* rank );
        void SVDLeastSquare( Int m, Int n, Int nrhs, scomplex * A, Int lda,
                        scomplex * B, Int ldb, float * S, float rcond,
                        Int* rank );
        void SVDLeastSquare( Int m, Int n, Int nrhs, dcomplex * A, Int lda,
                        dcomplex * B, Int ldb, double * S, double rcond,
                        Int* rank );

        // *********************************************************************
        // Copy
        // *********************************************************************

        void Lacpy( char uplo, Int m, Int n, const double* A, Int lda,
                        double* B, Int ldb      );

        void Lacpy( char uplo, Int m, Int n, const dcomplex* A, Int lda,
                        dcomplex* B, Int ldb    );

        // *********************************************************************
        // Inverting a factorized matrix: Getri
        // *********************************************************************


        void Getri ( Int n, double* A, Int lda, const Int* ipiv );

        void Getri ( Int n, dcomplex* A, Int lda, const Int* ipiv );






        double Lange ( char norm, Int m, Int n, float * A, Int lda, float* work);
        double Lange ( char norm, Int m, Int n, double * A, Int lda, double* work);
        double Lange ( char norm, Int m, Int n, scomplex * A, Int lda, scomplex* work);
        double Lange ( char norm, Int m, Int n, dcomplex * A, Int lda, dcomplex* work);

} // namespace lapack
} // namespace PEXSI

#endif //_PEXSI_LAPACK_HPP_