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dtbsv examples
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Man Page Details
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 NAME
      DTBSV - solve one of the systems of equations   A*x = b, or
      A'*x = b,

 SYNOPSIS
      SUBROUTINE DTBSV ( UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX
                       )

          INTEGER      INCX, K, LDA, N

          CHARACTER*1  DIAG, TRANS, UPLO

          DOUBLE       PRECISION A( LDA, * ), X( * )

 PURPOSE
      DTBSV  solves one of the systems of equations

      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.

 PARAMETERS
      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 triangu-
             lar.

             DIAG = 'N' or 'n'   A is not assumed to be unit tri-
             angular.

             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 conven-
             tional 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 ele-
             ments of X. INCX must not be zero.  Unchanged on
             exit.

