Provided by: libblas-doc_1.2.20110419-2ubuntu1_all #### NAME

```       ZTRSV  -  solve one of the systems of equations   A*x = b, or A'*x = b, or conjg( A' )*x =
b,

```

#### SYNOPSIS

```       SUBROUTINE ZTRSV ( UPLO, TRANS, DIAG, N, A, LDA, X, INCX )

INTEGER      INCX, LDA, N

CHARACTER*1  DIAG, TRANS, UPLO

COMPLEX*16   A( LDA, * ), X( * )

```

#### PURPOSE

```       ZTRSV  solves one of the systems of equations

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

No  test  for singularity or near-singularity is included in this routine. Such tests must
be performed before calling this routine.

```

#### PARAMETERS

```       UPLO   - CHARACTER*1.
On entry, UPLO 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.

Unchanged on exit.

TRANS  - CHARACTER*1.
On entry, TRANS specifies the equations to be solved as follows:

TRANS = 'N' or 'n'   A*x = b.

TRANS = 'T' or 't'   A'*x = b.

TRANS = 'C' or 'c'   conjg( A' )*x = b.

Unchanged on exit.

DIAG   - CHARACTER*1.
On entry, DIAG specifies whether or not 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.

Unchanged on exit.

N      - INTEGER.
On  entry,  N  specifies  the  order  of  the  matrix  A.  N must be at least zero.
Unchanged on exit.

A      - COMPLEX*16       array of DIMENSION ( LDA, n ).
Before entry with  UPLO = 'U' or 'u', the leading n by n upper triangular  part  of
the  array  A  must  contain  the  upper  triangular  matrix and 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  the  array A must contain the lower
triangular matrix and the strictly upper triangular part of A  is  not  referenced.
Note  that  when   DIAG = 'U' or 'u', the diagonal elements of A are not referenced
either, but are assumed to be unity.  Unchanged on exit.

LDA    - INTEGER.
On entry, LDA specifies the first dimension of A as declared in the  calling  (sub)
program. LDA must be at least max( 1, n ).  Unchanged on exit.

X      - COMPLEX*16       array of dimension at least
(  1 + ( n - 1 )*abs( INCX ) ).  Before entry, the incremented array X must contain
the n element right-hand side vector b. On exit, X is overwritten with the solution
vector x.

INCX   - INTEGER.
On  entry,  INCX  specifies  the  increment for the elements of X. INCX must not be
zero.  Unchanged on exit.

Level 2 Blas routine.

-- Written on 22-October-1986.  Jack Dongarra, Argonne  National  Lab.   Jeremy  Du
Croz,  Nag  Central  Office.  Sven Hammarling, Nag Central Office.  Richard Hanson,
Sandia National Labs.
```