LAPACK  3.4.2
LAPACK: Linear Algebra PACKage
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ztprfs.f File Reference

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Function/Subroutine Documentation

subroutine ztprfs ( character  UPLO,
character  TRANS,
character  DIAG,
integer  N,
integer  NRHS,
complex*16, dimension( * )  AP,
complex*16, dimension( ldb, * )  B,
integer  LDB,
complex*16, dimension( ldx, * )  X,
integer  LDX,
double precision, dimension( * )  FERR,
double precision, dimension( * )  BERR,
complex*16, dimension( * )  WORK,
double precision, dimension( * )  RWORK,
integer  INFO 


Download ZTPRFS + dependencies [TGZ] [ZIP] [TXT]
 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 is CHARACTER*1
          = 'U':  A is upper triangular;
          = 'L':  A is lower triangular.
          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 is CHARACTER*1
          = 'N':  A is non-unit triangular;
          = 'U':  A is unit triangular.
          N is INTEGER
          The order of the matrix A.  N >= 0.
          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrices B and X.  NRHS >= 0.
          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 is COMPLEX*16 array, dimension (LDB,NRHS)
          The right hand side matrix B.
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).
          X is COMPLEX*16 array, dimension (LDX,NRHS)
          The solution matrix X.
          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).
          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 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 is COMPLEX*16 array, dimension (2*N)
          RWORK is DOUBLE PRECISION array, dimension (N)
          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.
November 2011

Definition at line 174 of file ztprfs.f.

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