stbsv

STBSV(1)                         BLAS routine                         STBSV(1)



NAME
       STBSV - solves one of the systems of equations   A*x = b, or A'*x = b,

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

           INTEGER                                        INCX,K,LDA,N

           CHARACTER                                      DIAG,TRANS,UPLO

           REAL                                           A(LDA,*),X(*)

PURPOSE
       STBSV  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.


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      - REAL             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      - REAL             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.




BLAS routine                     November 2008                        STBSV(1)