cgtt05.f3

!>
!> CGTT05 tests the error bounds from iterative refinement for the
!> computed solution to a system of equations A*X = B, where A is a
!> general tridiagonal matrix of order n and op(A) = A or A**T,
!> depending on TRANS.
!>
!> RESLTS(1) = test of the error bound
!>           = norm(X - XACT) / ( norm(X) * FERR )
!>
!> A large value is returned if this ratio is not less than one.
!>
!> RESLTS(2) = residual from the iterative refinement routine
!>           = the maximum of BERR / ( NZ*EPS + (*) ), where
!>             (*) = NZ*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i )
!>             and NZ = max. number of nonzeros in any row of A, plus 1
!> 

TRANS

!>          TRANS is CHARACTER*1
!>          Specifies the form of the system of equations.
!>          = 'N':  A * X = B     (No transpose)
!>          = 'T':  A**T * X = B  (Transpose)
!>          = 'C':  A**H * X = B  (Conjugate transpose = Transpose)
!> 

N

!>          N is INTEGER
!>          The number of rows of the matrices X and XACT.  N >= 0.
!> 

NRHS

!>          NRHS is INTEGER
!>          The number of columns of the matrices X and XACT.  NRHS >= 0.
!> 

DL

!>          DL is COMPLEX array, dimension (N-1)
!>          The (n-1) sub-diagonal elements of A.
!> 

D

!>          D is COMPLEX array, dimension (N)
!>          The diagonal elements of A.
!> 

DU

!>          DU is COMPLEX array, dimension (N-1)
!>          The (n-1) super-diagonal elements of A.
!> 

B

!>          B is COMPLEX array, dimension (LDB,NRHS)
!>          The right hand side vectors for the system of linear
!>          equations.
!> 

LDB

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

X

!>          X is COMPLEX array, dimension (LDX,NRHS)
!>          The computed solution vectors.  Each vector is stored as a
!>          column of the matrix X.
!> 

LDX

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

XACT

!>          XACT is COMPLEX array, dimension (LDX,NRHS)
!>          The exact solution vectors.  Each vector is stored as a
!>          column of the matrix XACT.
!> 

LDXACT

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

FERR

!>          FERR is REAL array, dimension (NRHS)
!>          The estimated forward error bounds for each solution vector
!>          X.  If XTRUE is the true solution, FERR bounds the magnitude
!>          of the largest entry in (X - XTRUE) divided by the magnitude
!>          of the largest entry in X.
!> 

BERR

!>          BERR is REAL array, dimension (NRHS)
!>          The componentwise relative backward error of each solution
!>          vector (i.e., the smallest relative change in any entry of A
!>          or B that makes X an exact solution).
!> 

RESLTS

!>          RESLTS is REAL array, dimension (2)
!>          The maximum over the NRHS solution vectors of the ratios:
!>          RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
!>          RESLTS(2) = BERR / ( NZ*EPS + (*) )
!> 

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