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version 1.2, 2010/04/21 13:45:10 version 1.14, 2018/05/29 06:55:14
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   *> \brief \b DTBSV
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at
   *            http://www.netlib.org/lapack/explore-html/
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DTBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)
   *
   *       .. Scalar Arguments ..
   *       INTEGER INCX,K,LDA,N
   *       CHARACTER DIAG,TRANS,UPLO
   *       ..
   *       .. Array Arguments ..
   *       DOUBLE PRECISION A(LDA,*),X(*)
   *       ..
   *
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> DTBSV  solves one of the systems of equations
   *>
   *>    A*x = b,   or   A**T*x = b,
   *>
   *> where b and x are n element vectors and A is an n by n unit, or
   *> non-unit, upper or lower triangular band matrix, with ( k + 1 )
   *> diagonals.
   *>
   *> No test for singularity or near-singularity is included in this
   *> routine. Such tests must be performed before calling this routine.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] UPLO
   *> \verbatim
   *>          UPLO is CHARACTER*1
   *>           On entry, UPLO specifies whether the matrix is an upper or
   *>           lower triangular matrix as follows:
   *>
   *>              UPLO = 'U' or 'u'   A is an upper triangular matrix.
   *>
   *>              UPLO = 'L' or 'l'   A is a lower triangular matrix.
   *> \endverbatim
   *>
   *> \param[in] TRANS
   *> \verbatim
   *>          TRANS is CHARACTER*1
   *>           On entry, TRANS specifies the equations to be solved as
   *>           follows:
   *>
   *>              TRANS = 'N' or 'n'   A*x = b.
   *>
   *>              TRANS = 'T' or 't'   A**T*x = b.
   *>
   *>              TRANS = 'C' or 'c'   A**T*x = b.
   *> \endverbatim
   *>
   *> \param[in] DIAG
   *> \verbatim
   *>          DIAG is CHARACTER*1
   *>           On entry, DIAG specifies whether or not A is unit
   *>           triangular as follows:
   *>
   *>              DIAG = 'U' or 'u'   A is assumed to be unit triangular.
   *>
   *>              DIAG = 'N' or 'n'   A is not assumed to be unit
   *>                                  triangular.
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>           On entry, N specifies the order of the matrix A.
   *>           N must be at least zero.
   *> \endverbatim
   *>
   *> \param[in] K
   *> \verbatim
   *>          K is INTEGER
   *>           On entry with UPLO = 'U' or 'u', K specifies the number of
   *>           super-diagonals of the matrix A.
   *>           On entry with UPLO = 'L' or 'l', K specifies the number of
   *>           sub-diagonals of the matrix A.
   *>           K must satisfy  0 .le. K.
   *> \endverbatim
   *>
   *> \param[in] A
   *> \verbatim
   *>          A is DOUBLE PRECISION array, dimension ( LDA, N )
   *>           Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
   *>           by n part of the array A must contain the upper triangular
   *>           band part of the matrix of coefficients, supplied column by
   *>           column, with the leading diagonal of the matrix in row
   *>           ( k + 1 ) of the array, the first super-diagonal starting at
   *>           position 2 in row k, and so on. The top left k by k triangle
   *>           of the array A is not referenced.
   *>           The following program segment will transfer an upper
   *>           triangular band matrix from conventional full matrix storage
   *>           to band storage:
   *>
   *>                 DO 20, J = 1, N
   *>                    M = K + 1 - J
   *>                    DO 10, I = MAX( 1, J - K ), J
   *>                       A( M + I, J ) = matrix( I, J )
   *>              10    CONTINUE
   *>              20 CONTINUE
   *>
   *>           Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
   *>           by n part of the array A must contain the lower triangular
   *>           band part of the matrix of coefficients, supplied column by
   *>           column, with the leading diagonal of the matrix in row 1 of
   *>           the array, the first sub-diagonal starting at position 1 in
   *>           row 2, and so on. The bottom right k by k triangle of the
   *>           array A is not referenced.
   *>           The following program segment will transfer a lower
   *>           triangular band matrix from conventional full matrix storage
   *>           to band storage:
   *>
   *>                 DO 20, J = 1, N
   *>                    M = 1 - J
   *>                    DO 10, I = J, MIN( N, J + K )
   *>                       A( M + I, J ) = matrix( I, J )
   *>              10    CONTINUE
   *>              20 CONTINUE
   *>
   *>           Note that when DIAG = 'U' or 'u' the elements of the array A
   *>           corresponding to the diagonal elements of the matrix are not
   *>           referenced, but are assumed to be unity.
   *> \endverbatim
   *>
   *> \param[in] LDA
   *> \verbatim
   *>          LDA is INTEGER
   *>           On entry, LDA specifies the first dimension of A as declared
   *>           in the calling (sub) program. LDA must be at least
   *>           ( k + 1 ).
   *> \endverbatim
   *>
   *> \param[in,out] X
   *> \verbatim
   *>          X is DOUBLE PRECISION array, dimension at least
   *>           ( 1 + ( n - 1 )*abs( INCX ) ).
   *>           Before entry, the incremented array X must contain the n
   *>           element right-hand side vector b. On exit, X is overwritten
   *>           with the solution vector x.
   *> \endverbatim
   *>
   *> \param[in] INCX
   *> \verbatim
   *>          INCX is INTEGER
   *>           On entry, INCX specifies the increment for the elements of
   *>           X. INCX must not be zero.
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee
   *> \author Univ. of California Berkeley
   *> \author Univ. of Colorado Denver
   *> \author NAG Ltd.
   *
   *> \date December 2016
   *
   *> \ingroup double_blas_level2
   *
   *> \par Further Details:
   *  =====================
   *>
   *> \verbatim
   *>
   *>  Level 2 Blas routine.
   *>
   *>  -- Written on 22-October-1986.
   *>     Jack Dongarra, Argonne National Lab.
   *>     Jeremy Du Croz, Nag Central Office.
   *>     Sven Hammarling, Nag Central Office.
   *>     Richard Hanson, Sandia National Labs.
   *> \endverbatim
   *>
   *  =====================================================================
       SUBROUTINE DTBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)        SUBROUTINE DTBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)
   *
   *  -- Reference BLAS level2 routine (version 3.7.0) --
   *  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
   *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
   *     December 2016
   *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       INTEGER INCX,K,LDA,N        INTEGER INCX,K,LDA,N
       CHARACTER DIAG,TRANS,UPLO        CHARACTER DIAG,TRANS,UPLO
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       DOUBLE PRECISION A(LDA,*),X(*)        DOUBLE PRECISION A(LDA,*),X(*)
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  DTBSV  solves one of the systems of equations  
 *  
 *     A*x = b,   or   A'*x = b,  
 *  
 *  where b and x are n element vectors and A is an n by n unit, or  
 *  non-unit, upper or lower triangular band matrix, with ( k + 1 )  
 *  diagonals.  
 *  
 *  No test for singularity or near-singularity is included in this  
 *  routine. Such tests must be performed before calling this routine.  
 *  
 *  Arguments  
 *  ==========  
 *  
 *  UPLO   - CHARACTER*1.  
 *           On entry, UPLO specifies whether the matrix is an upper or  
 *           lower triangular matrix as follows:  
 *  
 *              UPLO = 'U' or 'u'   A is an upper triangular matrix.  
 *  
 *              UPLO = 'L' or 'l'   A is a lower triangular matrix.  
 *  
 *           Unchanged on exit.  
 *  
 *  TRANS  - CHARACTER*1.  
 *           On entry, TRANS specifies the equations to be solved as  
 *           follows:  
 *  
 *              TRANS = 'N' or 'n'   A*x = b.  
 *  
 *              TRANS = 'T' or 't'   A'*x = b.  
 *  
 *              TRANS = 'C' or 'c'   A'*x = b.  
 *  
 *           Unchanged on exit.  
 *  
 *  DIAG   - CHARACTER*1.  
 *           On entry, DIAG specifies whether or not A is unit  
 *           triangular as follows:  
 *  
 *              DIAG = 'U' or 'u'   A is assumed to be unit triangular.  
 *  
 *              DIAG = 'N' or 'n'   A is not assumed to be unit  
 *                                  triangular.  
 *  
 *           Unchanged on exit.  
 *  
 *  N      - INTEGER.  
 *           On entry, N specifies the order of the matrix A.  
 *           N must be at least zero.  
 *           Unchanged on exit.  
 *  
 *  K      - INTEGER.  
 *           On entry with UPLO = 'U' or 'u', K specifies the number of  
 *           super-diagonals of the matrix A.  
 *           On entry with UPLO = 'L' or 'l', K specifies the number of  
 *           sub-diagonals of the matrix A.  
 *           K must satisfy  0 .le. K.  
 *           Unchanged on exit.  
 *  
 *  A      - DOUBLE PRECISION array of DIMENSION ( LDA, n ).  
 *           Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )  
 *           by n part of the array A must contain the upper triangular  
 *           band part of the matrix of coefficients, supplied column by  
 *           column, with the leading diagonal of the matrix in row  
 *           ( k + 1 ) of the array, the first super-diagonal starting at  
 *           position 2 in row k, and so on. The top left k by k triangle  
 *           of the array A is not referenced.  
 *           The following program segment will transfer an upper  
 *           triangular band matrix from conventional full matrix storage  
 *           to band storage:  
 *  
 *                 DO 20, J = 1, N  
 *                    M = K + 1 - J  
 *                    DO 10, I = MAX( 1, J - K ), J  
 *                       A( M + I, J ) = matrix( I, J )  
 *              10    CONTINUE  
 *              20 CONTINUE  
 *  
 *           Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )  
 *           by n part of the array A must contain the lower triangular  
 *           band part of the matrix of coefficients, supplied column by  
 *           column, with the leading diagonal of the matrix in row 1 of  
 *           the array, the first sub-diagonal starting at position 1 in  
 *           row 2, and so on. The bottom right k by k triangle of the  
 *           array A is not referenced.  
 *           The following program segment will transfer a lower  
 *           triangular band matrix from conventional full matrix storage  
 *           to band storage:  
 *  
 *                 DO 20, J = 1, N  
 *                    M = 1 - J  
 *                    DO 10, I = J, MIN( N, J + K )  
 *                       A( M + I, J ) = matrix( I, J )  
 *              10    CONTINUE  
 *              20 CONTINUE  
 *  
 *           Note that when DIAG = 'U' or 'u' the elements of the array A  
 *           corresponding to the diagonal elements of the matrix are not  
 *           referenced, but are assumed to be unity.  
 *           Unchanged on exit.  
 *  
 *  LDA    - INTEGER.  
 *           On entry, LDA specifies the first dimension of A as declared  
 *           in the calling (sub) program. LDA must be at least  
 *           ( k + 1 ).  
 *           Unchanged on exit.  
 *  
 *  X      - DOUBLE PRECISION array of dimension at least  
 *           ( 1 + ( n - 1 )*abs( INCX ) ).  
 *           Before entry, the incremented array X must contain the n  
 *           element right-hand side vector b. On exit, X is overwritten  
 *           with the solution vector x.  
 *  
 *  INCX   - INTEGER.  
 *           On entry, INCX specifies the increment for the elements of  
 *           X. INCX must not be zero.  
 *           Unchanged on exit.  
 *  
 *  Further Details  
 *  ===============  
 *  
 *  Level 2 Blas routine.  
 *  
 *  -- Written on 22-October-1986.  
 *     Jack Dongarra, Argonne National Lab.  
 *     Jeremy Du Croz, Nag Central Office.  
 *     Sven Hammarling, Nag Central Office.  
 *     Richard Hanson, Sandia National Labs.  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
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           END IF            END IF
       ELSE        ELSE
 *  *
 *        Form  x := inv( A')*x.  *        Form  x := inv( A**T)*x.
 *  *
           IF (LSAME(UPLO,'U')) THEN            IF (LSAME(UPLO,'U')) THEN
               KPLUS1 = K + 1                KPLUS1 = K + 1
Removed from v.1.2  
changed lines
  Added in v.1.14

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