# cptrfs.f man page

cptrfs.f

## Synopsis

### Functions/Subroutines

subroutine **cptrfs** (UPLO, **N**, **NRHS**, D, E, DF, EF, B, **LDB**, X, LDX, FERR, BERR, WORK, RWORK, INFO)**CPTRFS**

## Function/Subroutine Documentation

### subroutine cptrfs (character UPLO, integer N, integer NRHS, real, dimension( * ) D, complex, dimension( * ) E, real, dimension( * ) DF, complex, dimension( * ) EF, complex, dimension( ldb, * ) B, integer LDB, complex, dimension( ldx, * ) X, integer LDX, real, dimension( * ) FERR, real, dimension( * ) BERR, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer INFO)

**CPTRFS**

**Purpose:**

CPTRFS improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution.

**Parameters:**-
*UPLO*UPLO is CHARACTER*1 Specifies whether the superdiagonal or the subdiagonal of the tridiagonal matrix A is stored and the form of the factorization: = 'U': E is the superdiagonal of A, and A = U**H*D*U; = 'L': E is the subdiagonal of A, and A = L*D*L**H. (The two forms are equivalent if A is real.)

*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 matrix B. NRHS >= 0.

*D*D is REAL array, dimension (N) The n real diagonal elements of the tridiagonal matrix A.

*E*E is COMPLEX array, dimension (N-1) The (n-1) off-diagonal elements of the tridiagonal matrix A (see UPLO).

*DF*DF is REAL array, dimension (N) The n diagonal elements of the diagonal matrix D from the factorization computed by CPTTRF.

*EF*EF is COMPLEX array, dimension (N-1) The (n-1) off-diagonal elements of the unit bidiagonal factor U or L from the factorization computed by CPTTRF (see UPLO).

*B*B is COMPLEX 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 array, dimension (LDX,NRHS) On entry, the solution matrix X, as computed by CPTTRS. On exit, the improved solution matrix X.

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

*FERR*FERR is REAL array, dimension (NRHS) The 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).

*BERR*BERR is REAL 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 array, dimension (N)

*RWORK*RWORK is REAL array, dimension (N)

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

**Internal Parameters:**

ITMAX is the maximum number of steps of iterative refinement.

**Author:**-
Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**December 2016

Definition at line 185 of file cptrfs.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page cptrfs(3) is an alias of cptrfs.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK