strmv, dtrmv, ctrmv, ztrmv 

Marix-vector product for a triangular matrix

FORMAT

  {S,D,C,Z}TRMV (uplo, trans, diag, n, a, lda, x, incx)

Arguments

  uplo                character*1
                      On entry, specifies whether the matrix A is an upper-
                      or lower-triangular matrix:

                      If uplo = 'U' or 'u', A is an upper-triangular matrix.

                      If uplo = 'L' or
                      On exit, uplo is unchanged.

  trans               character*1
                      On entry, specifies the operation to be performed:

                      If trans = 'N' or 'n', the operation is y  =  alpha*Ax
                      + beta*y.

                      If trans = 'T' or 't', the operation is y  =
                      alpha*transp(A)*x + beta*y.

                      If trans = 'C' or 'c', the operation is y  =
                      alpha*conjug_transp(A)*x + beta*y.
                      On exit, trans is unchanged.
                       .IP "diag" 20 character*1
                      On entry, specifies whether the matrix A is unit-
                      triangular:

                      If diag = 'U' or 'u', A is a unit-triangular matrix.

                      If diag = 'N' or 'n', A is not a unit-triangular
                      matrix.
                      On exit, diag is unchanged.

  n                   integer*4
                      On entry, the order of the matrix A; n >= 0.
                      On exit, n is unchanged.

  a                   real*4 | real*8 | complex*8 | complex*16
                      On entry, a two-dimensional array with dimensions lda
                      by n.

  When uplo specifies the upper portion of the matrix, the leading n by n
  part of the array contains the upper-triangular part of the matrix, and the
  lower-triangular part of array A is not referenced.

  When uplo specifies the lower  portion of the matrix,  the leading n by n
  part of the array contains the lower-triangular part of the matrix, and the
  upper-triangular part of array A is not referenced.

  If diag is equal to 'U' or 'u', the diagonal elements of A are also not
  referenced, but are assumed to be unity.
  On exit, a is unchanged.

  lda                 integer*4
                      On entry, the first dimension of array A; lda >=
                      MAX(1,n).
                      On exit, lda is unchanged.

  x                   real*4 | real*8 | complex*8 | complex*16
                      On entry, a one-dimensional array X of length at least
                      (1+(n-1)*|incx|).  Array X contains the vector x.
                      On exit, x is overwritten with the transformed vector
                      x.

  incx                integer*4
                      On entry, the increment for the elements of X; incx
                      must not equal zero.
                      On exit, incx is unchanged.

Description

  The _TRMV subprograms compute a matrix-vector product for a triangular
  matrix or its transpose: x  =  Ax or  x  =  transp(A)*x .  In addition to
  these operations, the CTRMV and ZTRMV subprograms compute a matrix-vector
  product for conjugate transpose: x  =  conjug_transp(A)*x .

  x is a vector with n elements, and A is an n by n, unit or non-unit, upper-
  or lower-triangular matrix.

Example

  REAL*4 A(50,20), X(20)
  INCX = 1
  N = 20
  LDA = 50
  CALL STRMV('U','N','N',N,A,LDA,X,INCX)

  This FORTRAN code computes the product x  =  Ax where A is an upper-
  triangular matrix, of order 20, with a non-unit diagonal.