!>
!> ZLATRS3 solves one of the triangular systems
!>
!>    A * X = B * diag(scale),  A**T * X = B * diag(scale), or
!>    A**H * X = B * diag(scale)
!>
!> with scaling to prevent overflow.  Here A is an upper or lower
!> triangular matrix, A**T denotes the transpose of A, A**H denotes the
!> conjugate transpose of A. X and B are n-by-nrhs matrices and scale
!> is an nrhs-element vector of scaling factors. A scaling factor scale(j)
!> is usually less than or equal to 1, chosen such that X(:,j) is less
!> than the overflow threshold. If the matrix A is singular (A(j,j) = 0
!> for some j), then a non-trivial solution to A*X = 0 is returned. If
!> the system is so badly scaled that the solution cannot be represented
!> as (1/scale(k))*X(:,k), then x(:,k) = 0 and scale(k) is returned.
!>
!> This is a BLAS-3 version of LATRS for solving several right
!> hand sides simultaneously.
!>
!> 

UPLO

!>          UPLO is CHARACTER*1
!>          Specifies whether the matrix A is upper or lower triangular.
!>          = 'U':  Upper triangular
!>          = 'L':  Lower triangular
!> 

TRANS

!>          TRANS is CHARACTER*1
!>          Specifies the operation applied to A.
!>          = 'N':  Solve A * x = s*b  (No transpose)
!>          = 'T':  Solve A**T* x = s*b  (Transpose)
!>          = 'C':  Solve A**T* x = s*b  (Conjugate transpose)
!> 

DIAG

!>          DIAG is CHARACTER*1
!>          Specifies whether or not the matrix A is unit triangular.
!>          = 'N':  Non-unit triangular
!>          = 'U':  Unit triangular
!> 

NORMIN

!>          NORMIN is CHARACTER*1
!>          Specifies whether CNORM has been set or not.
!>          = 'Y':  CNORM contains the column norms on entry
!>          = 'N':  CNORM is not set on entry.  On exit, the norms will
!>                  be computed and stored in CNORM.
!> 

N

!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!> 

NRHS

!>          NRHS is INTEGER
!>          The number of columns of X.  NRHS >= 0.
!> 

A

!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          The triangular matrix A.  If UPLO = 'U', the leading n by n
!>          upper triangular part of the array A contains the upper
!>          triangular matrix, and the strictly lower triangular part of
!>          A is not referenced.  If UPLO = 'L', the leading n by n lower
!>          triangular part of the array A contains the lower triangular
!>          matrix, and the strictly upper triangular part of A is not
!>          referenced.  If DIAG = 'U', the diagonal elements of A are
!>          also not referenced and are assumed to be 1.
!> 

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max (1,N).
!> 

X

!>          X is COMPLEX*16 array, dimension (LDX,NRHS)
!>          On entry, the right hand side B of the triangular system.
!>          On exit, X is overwritten by the solution matrix X.
!> 

LDX

!>          LDX is INTEGER
!>          The leading dimension of the array X.  LDX >= max (1,N).
!> 

SCALE

!>          SCALE is DOUBLE PRECISION array, dimension (NRHS)
!>          The scaling factor s(k) is for the triangular system
!>          A * x(:,k) = s(k)*b(:,k)  or  A**T* x(:,k) = s(k)*b(:,k).
!>          If SCALE = 0, the matrix A is singular or badly scaled.
!>          If A(j,j) = 0 is encountered, a non-trivial vector x(:,k)
!>          that is an exact or approximate solution to A*x(:,k) = 0
!>          is returned. If the system so badly scaled that solution
!>          cannot be presented as x(:,k) * 1/s(k), then x(:,k) = 0
!>          is returned.
!> 

CNORM

!>          CNORM is DOUBLE PRECISION array, dimension (N)
!>
!>          If NORMIN = 'Y', CNORM is an input argument and CNORM(j)
!>          contains the norm of the off-diagonal part of the j-th column
!>          of A.  If TRANS = 'N', CNORM(j) must be greater than or equal
!>          to the infinity-norm, and if TRANS = 'T' or 'C', CNORM(j)
!>          must be greater than or equal to the 1-norm.
!>
!>          If NORMIN = 'N', CNORM is an output argument and CNORM(j)
!>          returns the 1-norm of the offdiagonal part of the j-th column
!>          of A.
!> 

WORK

!>          WORK is DOUBLE PRECISION array, dimension (LWORK).
!>          On exit, if INFO = 0, WORK(1) returns the optimal size of
!>          WORK.
!> 

LWORK

!>          LWORK is INTEGER
!>          The dimension of the array WORK.
!>
!>          If MIN(N,NRHS) = 0, LWORK >= 1, else
!>          LWORK >= MAX(1, 2*NBA * MAX(NBA, MIN(NRHS, 32)), where
!>          NBA = (N + NB - 1)/NB and NB is the optimal block size.
!>
!>          If LWORK = -1, then a workspace query is assumed; the routine
!>          only calculates the optimal dimensions of the WORK array, returns
!>          this value as the first entry of the WORK array, and no error
!>          message related to LWORK is issued by XERBLA.
!> 

INFO

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -k, the k-th argument had an illegal value
!> 

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.