DTRSV  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 matrix.


 No test for singularity or near-singularity is included in this


 routine. Such tests must be performed before calling this routine.

UPLO

          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.

TRANS

          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.

DIAG

          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.

N

          N is INTEGER


           On entry, N specifies the order of the matrix A.


           N must be at least zero.

A

          A is DOUBLE PRECISION array, dimension ( LDA, N )


           Before entry with  UPLO = 'U' or 'u', the leading n by n


           upper triangular part of the array A must contain the upper


           triangular matrix and the strictly lower triangular part of


           A is not referenced.


           Before entry with UPLO = 'L' or 'l', the leading n by n


           lower triangular part of the array A must contain the lower


           triangular matrix and the strictly upper triangular part of


           A is not referenced.


           Note that when  DIAG = 'U' or 'u', the diagonal elements of


           A are not referenced either, but are assumed to be unity.

LDA

          LDA is INTEGER


           On entry, LDA specifies the first dimension of A as declared


           in the calling (sub) program. LDA must be at least


           max( 1, n ).

X

          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.

INCX

          INCX is INTEGER


           On entry, INCX specifies the increment for the elements of


           X. INCX must not be zero.


  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.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

December 2016