trmv(3F)

NAME
     dtrmv, strmv, ztrmv, ctrmv, dtrsv, strsv, ztrsv, ctrsv - BLAS Level Two
     Matrix-Vector Product and Solution of system of equations.


FORTRAN 77 SYNOPSIS
     subroutine dtrmv( uplo, trans, diag, n, a, lda, x, incx )
     subroutine dtrsv( uplo, trans, diag, n, a, lda, x, incx )
           character*1        uplo, trans, diag
           integer            n, lda, incx
           double precision   a( lda,*), x(*)

     subroutine strmv( uplo, trans, diag, n, a, lda, x, incx )
     subroutine strsv( uplo, trans, diag, n, a, lda, x, incx )
           character*1        uplo, trans, diag
           integer            n, lda, incx
           real               a( lda,*), x(*)

     subroutine ztrmv( uplo, trans, diag, n, a, lda, x, incx )
     subroutine ztrsv( uplo, trans, diag, n, a, lda, x, incx )
           character*1        uplo, trans, diag
           integer            n, lda, incx
           double complex     a( lda,*), x(*)

     subroutine ctrmv( uplo, trans, diag, n, a, lda, x, incx )
     subroutine ctrsv( uplo, trans, diag, n, a, lda, x, incx )
           character*1        uplo, trans, diag
           integer            n, lda, incx
           complex            a( lda,*), x(*)



C SYNOPSIS
     void dtrmv( uplo, trans, diag, n, a, lda, x, incx )
     void dtrsv( uplo, trans, diag, n, a, lda, x, incx )
           MatrixTriangle        uplo;
           MatrixTranspose       trans;
           MatrixUnitTriangular  diag;
           Integer               n, lda, incx;
           double                (*a)[lda*n], (*x)[ n ];

     void strmv( uplo, trans, diag, n, a, lda, x, incx )
     void strsv( uplo, trans, diag, n, a, lda, x, incx )
           MatrixTriangle        uplo;
           MatrixTranspose       trans;
           MatrixUnitTriangular  diag;
           Integer               n, lda, incx;
           float                 (*a)[lda*n], (*x)[ n ];

     void ztrmv( uplo, trans, diag, n, a, lda, x, incx )
     void ztrsv( uplo, trans, diag, n, a, lda, x, incx )
           MatrixTriangle        uplo;
           MatrixTranspose       trans;
           MatrixUnitTriangular  diag;
           Integer               n, lda, incx;
           Zomplex               (*a)[lda*n], (*x)[ n ];

     void ctrmv( uplo, trans, diag, n, a, lda, x, incx )
     void ctrsv( uplo, trans, diag, n, a, lda, x, incx )
           MatrixTriangle        uplo;
           MatrixTranspose       trans;
           MatrixUnitTriangular  diag;
           Integer               n, lda, incx;

           Complex               (*a)[lda*n], (*x)[ n ];



DESCRIPTION
     dtrmv, strmv, ztrmv and ctrmv perform one of the matrix-vector operations

           x := A*x,   or   x := A'*x,   or   x := conjg( A' )*x,

     where x is an n element vector and  A is an n by n unit, or non-unit,
     upper or lower triangular matrix.

     dtrsv, strsv, ztrsv and ctrsv solve one of the systems of equations

           A*x = b,   or   A'*x = b,   or   conjg( 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 matrix.  No test for singularity or near-
     singularity is included in these routines. Such tests must be performed
     before calling these routines.


PARAMETERS
     uplo    On entry, uplo specifies whether the matrix is an upper or lower
             triangular matrix as follows:

                  FORTRAN
                  uplo = 'U' or 'u'        A is an upper triangular matrix.
                  uplo = 'L' or 'l'        A is a lower triangular matrix.

                  C
                  uplo = UpperTriangle     A is an upper triangular matrix.
                  uplo = LowerTriangle     A is a lower triangular matrix.

             Unchanged on exit.

     trans   On entry, trans specifies the operation to be

                  FORTRAN
                  trans = 'N' or 'n'       x := A*x /  A*x = b.
                 trans = 'T' or 't'        x := A'*x / A'*x = b.
                  trans = 'C' or 'c'       x := conjg( A' )*x  /
                                                conjg( A' )*x = b.

                  C
                  trans = NoTranspose           x := A*x /  A*x = b.
                  trans = Transpose             x := A'*x / A'*x = b.
                  trans = ConjugateTranspose    x := conjg( A' )*x  /
                                                conjg( A' )*x = b.

             For real value matrices, trans='C' and trans='T' has the same
             meaning.

             Unchanged on exit.

     diag    On entry, diag specifies whether or not A is unit triangular as
             follows:

                  FORTRAN
                  diag = 'U' or 'u'   A is assumed to be unit triangular.
                  diag = 'N' or 'n'   A is not assumed to be unit triangular.

                  C
                  diag = UnitTriangular    A is assumed to be unit
                                           triangular.
                  diag = NotUnitTriangular A is not assumed to be unit
                                           triangular.

             Unchanged on exit.

     n       On entry, n specifies the order of the matrix A. n must be at
             least zero.
             Unchanged on exit.

     a       An array containing the matrix A.

             FORTRAN
             Array of dimension (lda, n).

             C
             A pointer to an array of size lda*n.
             See note below about array storage convention for C.

             Before entry with uplo = 'U' or 'u' or , the elements of the
             array a corresponding to the leading n by n upper triangular part
             of the matrix A must contain the upper triangular matrix and the
             elements corresponding to the strictly lower triangular part of A
             are not referenced.

             Before entry with uplo = 'L' or 'l' or , the elements
             corresponding to the leading n by n lower triangular elements of
             the matrix A  must contain the lower triangular matrix and the
             corresponding strictly upper triangular part of the matrix A is
             not referenced.

             Note that when diag = 'U' or 'u' or , the elements of a
             corresponding to the diagonal elements of the matrix A are not
             referenced either, but are assumed to be unity.

             Unchanged on exit.

     lda     On entry, lda specifies the first dimension of A as declared in
             the calling (sub) program.  lda must be at least max( 1, n ).
             Unchanged on exit.

     x       Array of size at least ( 1 + ( n - 1 )*abs( incx ) ). Before
             entry, the incremented array x must contain the vector x. On
             exit, x is overwritten with the transformed/solution vector x.

     incx    On entry, incx specifies the increment for the elements of x.
             incx must not be zero.
             Unchanged on exit.

       The matrices  are assumed  to be stored in a  one dimensional C array
       in an analogous fashion as a Fortran array (column major). Therefore,
       the element  A(i+1,j)  of matrix A  is stored  immediately  after the
       element  A(i,j), while  A(i,j+1) is lda  elements apart from  A(i,j).
       The element A(i,j) of the matrix can be accessed directly by reference
       to  a[ (j-1)*lda + (i-1) ].


AUTHORS
          Jack Dongarra, Argonne National Laboratory.
          Iain Duff, AERE Harwell.
          Jeremy Du Croz, Numerical Algorithms Group Ltd.
          Sven Hammarling, Numerical Algorithms Group Ltd.