stpsv, dtpsv, ctpsv, ztpsv 

Solve a system of linear equations with a triangular matrix in packed form

FORMAT

  {S,D,C,Z}TPSV (uplo, trans, diag, n, ap, 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 'l', A is a lower-triangular matrix.
                      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.

  ap                  real*4 | real*8 | complex*8 | complex*16
                      On entry, a one-dimensional array AP of length at least
                      n(n + 1)/2.

  If uplo specifies the upper triangular part of the matrix A, the array
  contains those elements of the matrix, packed sequentially, column by
  column, so that AP(1) contains a(11), AP(2) and AP(3) contain a(12) and
  a(22) respectively, and so on.

  If uplo specifies the lower triangular part to the matrix A, so that AP(1)
  contains a(11), AP(2) and AP(3) contain a(21) and a(31) respectively, and
  so on.

  If diag is equal to 'U' or 'u', the diagonal elements of A are not
  referenced, but are assumed to be unity.
  On exit, ap 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 _TPSV 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 CTPSV and ZTPSV subprograms solve the following system of
  equations: 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, supplied in packed form.

  The _TPSV 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(500), X(30)
  INCX = 1
  N = 30
  CALL DTPSV('L','T','N',N,AP,X,INCX)

  This FORTRAN code solves the system transp(A)*x = b where A is a lower-
  triangular matrix of order 30, with non-unit diagonal, stored in packed
  form.  The right hand side b is originally contained in the vector x.