# zptrfs.f - Man Page

SRC/zptrfs.f

## Synopsis

### Functions/Subroutines

subroutine **zptrfs** (uplo, n, nrhs, d, e, df, ef, b, ldb, x, ldx, ferr, berr, work, rwork, info)**ZPTRFS**

## Function/Subroutine Documentation

### subroutine zptrfs (character uplo, integer n, integer nrhs, double precision, dimension( * ) d, complex*16, dimension( * ) e, double precision, dimension( * ) df, complex*16, dimension( * ) ef, 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)

**ZPTRFS**

**Purpose:**

ZPTRFS 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 DOUBLE PRECISION array, dimension (N) The n real diagonal elements of the tridiagonal matrix A.

*E*E is COMPLEX*16 array, dimension (N-1) The (n-1) off-diagonal elements of the tridiagonal matrix A (see UPLO).

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

*EF*EF is COMPLEX*16 array, dimension (N-1) The (n-1) off-diagonal elements of the unit bidiagonal factor U or L from the factorization computed by ZPTTRF (see UPLO).

*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) On entry, the solution matrix X, as computed by ZPTTRS. 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 DOUBLE PRECISION 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 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 (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

**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.

Definition at line **181** of file **zptrfs.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK