trsv(3F)

NAME
     STRSV, DTRSV, CTRSV, ZTRSV - Solves a real or complex triangular
     system of equations

SYNOPSIS
     Real

        CALL STRSV (uplo, trans, diag, n, a, lda, x, incx)

     Double precision

        CALL DTRSV (uplo, trans, diag, n, a, lda, x, incx)

     Complex

        CALL CTRSV (uplo, trans, diag, n, a, lda, x, incx)

     Double complex

        CALL ZTRSV (uplo, trans, diag, n, a, lda, x, incx)

IMPLEMENTATION
     IRIX systems

DESCRIPTION
     STRSV and DTRSV solve a real triangular system of equations.

     CTRSV and ZTRSV solve a complex triangular system of equations.

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

          Equations      Operation
                               -1
          Ax=b           x <- A  x
           T                   -T
          A x=b          x <- A  x
           H                   -H
          A x=b          x <- A  x (CTRSV, ZTRSV only)

     where

     * b and x are n-element vectors

     * A is either a unit or nonunit n-by-n upper or lower triangular
       matrix
        -1
     * A   is the inverse of A
        T
     * A  is the transpose of A
        -T                    T
     * A   is the inverse of A
        H
     * A  is the conjugate transpose of A
        -H                    H
     * A   is the inverse of A

     On input, the right-hand side vector b is stored in 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:
                                          -1
               trans = 'N' or 'n':  x <- A  x

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

                                          -T
               trans = 'C' or 'c':  x <- A  x (STRSV, DTRSV), or
                     -H
               x <- A  x (CTRSV, ZTRSV)

     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.

     a         Array of dimension (lda,n).  (input)
               STRSV: Real array.
               DTRSV: Double precision array.
               CTRSV: Complex array.
               ZTRSV: Double complex array.

               Before entry with uplo = 'U' or 'u', the leading n-by-n
               upper triangular part of array a must contain the upper
               triangular matrix.  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 array a must contain the lower
               triangular matrix.  The strictly upper triangular part of a
               is not referenced.

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

     lda       Integer.  (input)
               Specifies the first dimension of a as declared in the
               calling program.  lda >= MAX(1,n).

     x         Array of dimension 1+(n-1) * |incx|.  (input and output)
               STRSV: Real array.
               DTRSV: Double precision array.
               CTRSV: Complex array.
               ZTRSV: Double complex array.

               On input, x contains the right-hand side vector b.  On
               output, x is overwritten with the solution 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)

SEE ALSO
     This man page is available only online.