strsv, dtrsv, ctrsv, ztrsv 

Solver of a system of linear equations with a triangular matrix

FORMAT

  {S,D,C,Z}TRSV (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 system to be solved:

                      If trans = 'N' or 'n', the system is Ax = b.

                      If trans = 'T' or 't', the system is transp(A)*x = b.

                      If trans = 'C' or 'c', the system is conjug_transp(A)*x
                      = b.
                      On exit, trans is unchanged.

  diag                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 b.
                      On exit, x is overwritten with the solution 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 _TRSV subprograms solve one of the following systems of linear
  equations for x:  Ax = b  or  transp(A)*x = b .  In addition to these
  operations, the CTRSV and ZTRSV subprograms solve the following systems of
  linear equation:  conjug_transp(A)*x = b .

  b and x are vectors with n elements and A is an n by n, unit or non-unit,
  upper- or lower-triangular matrix.

  The _TRSV routines do not perform checks for singularity or near
  singularity of the triangular matrix.  The requirements for such a test
  depend on the application.  If necessary, perform the test in your
  application program before calling this routine.

Example

  REAL*8 A(100,40), X(40)
  INCX = 1
  N = 40
  LDA = 100
  CALL DTRSV('L','N','U',N,A,LDA,X,INCX)

  This FORTRAN code solves the system Ax=b where A is a lower-triangular
  matrix of order 40, with a unit diagonal.  The right hand side b is
  originally stored in the vector x.