ztprfs.f3

!>
!> ZTPRFS provides error bounds and backward error estimates for the
!> solution to a system of linear equations with a triangular packed
!> coefficient matrix.
!>
!> The solution matrix X must be computed by ZTPTRS or some other
!> means before entering this routine.  ZTPRFS does not do iterative
!> refinement because doing so cannot improve the backward error.
!> 

UPLO

!>          UPLO is CHARACTER*1
!>          = 'U':  A is upper triangular;
!>          = 'L':  A is lower triangular.
!> 

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)
!> 

DIAG

!>          DIAG is CHARACTER*1
!>          = 'N':  A is non-unit triangular;
!>          = 'U':  A is unit triangular.
!> 

N

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

NRHS

!>          NRHS is INTEGER
!>          The number of right hand sides, i.e., the number of columns
!>          of the matrices B and X.  NRHS >= 0.
!> 

AP

!>          AP is COMPLEX*16 array, dimension (N*(N+1)/2)
!>          The upper or lower triangular matrix A, packed columnwise in
!>          a linear array.  The j-th column of A is stored in the array
!>          AP as follows:
!>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
!>          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
!>          If DIAG = 'U', the diagonal elements of A are not referenced
!>          and are assumed to be 1.
!> 

B

!>          B is COMPLEX*16 array, dimension (LDB,NRHS)
!>          The right hand side matrix B.
!> 

LDB

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

X

!>          X is COMPLEX*16 array, dimension (LDX,NRHS)
!>          The solution matrix X.
!> 

LDX

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

FERR

!>          FERR is DOUBLE PRECISION array, dimension (NRHS)
!>          The estimated forward error bound for each solution vector
!>          X(j) (the j-th column of the solution matrix X).
!>          If XTRUE is the true solution corresponding to X(j), FERR(j)
!>          is an estimated upper bound for the magnitude of the largest
!>          element in (X(j) - XTRUE) divided by the magnitude of the
!>          largest element in X(j).  The estimate is as reliable as
!>          the estimate for RCOND, and is almost always a slight
!>          overestimate of the true error.
!> 

BERR

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

WORK

!>          WORK is COMPLEX*16 array, dimension (2*N)
!> 

RWORK

!>          RWORK is DOUBLE PRECISION array, dimension (N)
!> 

INFO

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

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.