tpsv(3F)

NAME
     STPSV, DTPSV, CTPSV, ZTPSV - Solves a real or complex triangular
     packed system of equations

SYNOPSIS
     Real

        CALL STPSV (uplo, trans, diag, n, ap, x, incx)

     Double precision

        CALL DTPSV (uplo, trans, diag, n, ap, x, incx)

     Complex

        CALL CTPSV (uplo, trans, diag, n, ap, x, incx)

     Double complex

        CALL ZTPSV (uplo, trans, diag, n, ap, x, incx)

DESCRIPTION
     These routines solve one of the following systems of equations, using
     the operation associated with each:

          Equations      Operation

          Ax=b           x <- A-1x

          ATx=b          x <- A-Tx

          AHx=b          x <- A-Hx (CTPSV, ZTPSV only)

     where

     * b and x are n-element vectors

     * A is either a unit or nonunit n-by-n upper or lower triangular band
       matrix with (k+1) diagonals

     * A-1 is the inverse of A

     * AT is the transpose of A

     * A-T is the inverse of AT


     * AH is the conjugate transpose of A

     * A-H is the inverse of AH


     On input, the right-hand side vector b is stored in the array argument
     x.  On output, the solution vector x overwrites b in the same array
     argument x.

     These routines have the following arguments:

     uplo      Character*1.  (input)
               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     Character*1.  (input)
               Specifies the operation to be performed, as follows:

               trans = 'N' or 'n':  x <- A-1x


               trans = 'T' or 't':  x <- A-Tx


               trans = 'C' or 'c':  x <- A-Tx (STPSV, DTPSV), or

               x <- A-Hx (CTPSV, ZTPSV)

     diag      Character*1.  (input)
               Specifies whether 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         Integer.  (input)
               Specifies the order of matrix A.  n >= 0.

     ap        Array of dimension (n(n+1))/2 .  (input)
               STPSV: Real array.
               DTPSV: Double precision array.
               CTPSV: Complex array.
               ZTPSV: Double complex array.

               Before entry with uplo = 'U' or 'u', array ap must contain
               the upper triangular matrix packed sequentially,
               column-by-column, so that ap(1) contains A(1,1), ap(2)
               contains A(1,2), ap(3) contains A(2,2), and so on.

               Before entry with uplo = 'L' or 'l', array ap must contain
               the lower triangular matrix packed sequentially,
               column-by-column, so that ap(1) contains A(1,1), ap(2)
               contains A(2,1), ap(3) contains A(3,1), and so on.

               When diag = 'U' or 'u', these routines assume that all
               elements of array a that represent diagonal elements of the
               matrix A are 1.  In this case, neither of these routines
               will reference any of the diagonal elements.

     x         Array of dimension 1+(n-1) * |incx|.  (input and output)
               STPSV: Real array.
               DTPSV: Double precision array.
               CTPSV: Complex array.
               ZTPSV: Double complex array.
               Contains the vector b, then the vector x.

     incx      Integer.  (input)
               Specifies the increment for the elements of x.  incx must
               not be 0.

NOTES
     Tests for singularity or near-singularity are not included in these
     routines.  You must perform such tests before calling either routine.

     These routines are Level 2 Basic Linear Algebra Subprograms (Level 2
     BLAS).

     When working backward (incx < 0), each routine starts at the end of
     the vector and moves backward, as follows:

          x(1-incx * (n-1)), x(1-incx * (n-2)), ..., x(1)