# dlib C++ Library - pbtrf.h

    // Copyright (C) 2010  Davis E. King (davis@dlib.net)
    // License: Boost Software License   See LICENSE.txt for the full license.
    #ifndef DLIB_LAPACk_BDC_Hh_
    #define DLIB_LAPACk_BDC_Hh_

    #include "fortran_id.h"
    #include "../matrix.h"
    namespace dlib
    {
        namespace lapack
        {
            namespace binding
            {
                extern "C"
                {
                    void DLIB_FORTRAN_ID(dpbtrf) (const char *uplo, const integer *n, const integer *kd,
                                                  double *ab, const integer *ldab, integer *info);

                    void DLIB_FORTRAN_ID(spbtrf) (const char *uplo, const integer *n, const integer *kd,
                                                  float *ab, const integer *ldab, integer *info);

                }

                inline integer pbtrf (const char uplo, const integer n, const integer kd,
                                      double* ab, const integer ldab)
                {
                    integer info = 0;
                    DLIB_FORTRAN_ID(dpbtrf)(&uplo, &n, &kd, ab, &ldab, &info);
                    return info;
                }

                inline integer pbtrf (const char uplo, const integer n, const integer kd,
                                      float* ab, const integer ldab)
                {
                    integer info = 0;
                    DLIB_FORTRAN_ID(spbtrf)(&uplo, &n, &kd, ab, &ldab, &info);
                    return info;
                }
            }

        // ------------------------------------------------------------------------------------
    /*  DPBTRF(l)		LAPACK routine (version	1.1)		    DPBTRF(l)

    NAME
      DPBTRF - compute the Cholesky	factorization of a real	symmetric positive
      definite band	matrix A

    SYNOPSIS

      SUBROUTINE DPBTRF( UPLO, N, KD, AB, LDAB, INFO )

          CHARACTER	     UPLO

          INTEGER	     INFO, KD, LDAB, N

          DOUBLE	     PRECISION AB( LDAB, * )

    PURPOSE
      DPBTRF computes the Cholesky factorization of	a real symmetric positive
      definite band	matrix A.

      The factorization has	the form
         A = U**T *	U,  if UPLO = 'U', or
         A = L  * L**T,  if	UPLO = 'L',
      where	U is an	upper triangular matrix	and L is lower triangular.

    ARGUMENTS

      UPLO	  (input) CHARACTER*1
    	  = 'U':  Upper	triangle of A is stored;
    	  = 'L':  Lower	triangle of A is stored.

      N	  (input) INTEGER
    	  The order of the matrix A.  N	>= 0.

      KD	  (input) INTEGER
    	  The number of	superdiagonals of the matrix A if UPLO = 'U', or the
    	  number of subdiagonals if UPLO = 'L'.	 KD >= 0.

      AB	  (input/output) DOUBLE	PRECISION array, dimension (LDAB,N)
    	  On entry, the	upper or lower triangle	of the symmetric band matrix
    	  A, stored in the first KD+1 rows of the array.  The j-th column of
    	  A is stored in the j-th column of the	array AB as follows: if	UPLO
    	  = 'U', AB(kd+1+i-j,j)	= A(i,j) for max(1,j-kd)<=i<=j;	if UPLO	=
    	  'L', AB(1+i-j,j)    =	A(i,j) for j<=i<=min(n,j+kd).

    	  On exit, if INFO = 0,	the triangular factor U	or L from the Chole-
    	  sky factorization A =	U**T*U or A = L*L**T of	the band matrix	A, in
    	  the same storage format as A.

      LDAB	  (input) INTEGER
    	  The leading dimension	of the array AB.  LDAB >= KD+1.

      INFO	  (output) INTEGER
    	  = 0:	successful exit
    	  < 0:	if INFO	= -i, the i-th argument	had an illegal value
    	  > 0:	if INFO	= i, the leading minor of order	i is not positive
    	  definite, and	the factorization could	not be completed.

    FURTHER	DETAILS
      The band storage scheme is illustrated by the	following example, when	N =
      6, KD	= 2, and UPLO =	'U':

      On entry:			  On exit:

          *	   *   a13  a24	 a35  a46      *    *	u13  u24  u35  u46
          *	  a12  a23  a34	 a45  a56      *   u12	u23  u34  u45  u56
         a11  a22  a33  a44	 a55  a66     u11  u22	u33  u44  u55  u66

      Similarly, if	UPLO = 'L' the format of A is as follows:

      On entry:			  On exit:

         a11  a22  a33  a44	 a55  a66     l11  l22	l33  l44  l55  l66
         a21  a32  a43  a54	 a65   *      l21  l32	l43  l54  l65	*
         a31  a42  a53  a64	  *    *      l31  l42	l53  l64   *	*

      Array	elements marked	* are not used by the routine.

      Contributed by
      Peter	Mayes and Giuseppe Radicati, IBM ECSEC,	Rome, March 23,	1989 */

        // ------------------------------------------------------------------------------------

            template <
                typename T,
                long NR1, long NC1,
                typename MM
                >
            int pbtrf (
                char uplo, matrix<T,NR1,NC1,MM,column_major_layout>& ab
            )
            {
                const long ldab = ab.nr();
                const long n = ab.nc();
                const long kd = ldab - 1; // assume fully packed

                int info = binding::pbtrf(uplo, n, kd, &ab(0,0), ldab);

                return info;
            }

        // ------------------------------------------------------------------------------------

            template <
                typename T,
                long NR1, long NC1,
                typename MM
                >
            int pbtrf (
                char uplo, matrix<T,NR1,NC1,MM,row_major_layout>& ab
            )
            {
                const long ldab = ab.nr();
                const long n = ab.nc();
                const long kd = ldab - 1; // assume fully packed

                matrix<T,NC1,NR1,MM,row_major_layout> abt = trans(ab);

                int info = binding::pbtrf(uplo, n, kd, &abt(0,0), ldab);

                ab = trans(abt);

                return info;
            }

        // ------------------------------------------------------------------------------------

        }

    }

    // ----------------------------------------------------------------------------------------

    #endif // DLIB_LAPACk_BDC_Hh_