---
name: "dpprfs.f"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/dpprfs.f"
---

# dpprfs.f(3)

## NAME

SRC/dpprfs.f

## SYNOPSIS

### Functions/Subroutines

subroutine **dpprfs** (uplo, n, nrhs, ap, afp, b, ldb, x, ldx, ferr, berr, work, iwork, info)\
 **DPPRFS**

## Function/Subroutine Documentation

### subroutine dpprfs (character uplo, integer n, integer nrhs, double precision, dimension( \* ) ap, double precision, dimension( \* ) afp, double precision, dimension( ldb, \* ) b, integer ldb, double precision, dimension( ldx, \* ) x, integer ldx, double precision, dimension( \* ) ferr, double precision, dimension( \* ) berr, double precision, dimension( \* ) work, integer, dimension( \* ) iwork, integer info)

**DPPRFS**

**Purpose:**

```
!>
!> DPPRFS improves the computed solution to a system of linear
!> equations when the coefficient matrix is symmetric positive definite
!> and packed, and provides error bounds and backward error estimates
!> for the solution.
!>
```

**Parameters**

*UPLO*

```
!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangle of A is stored;
!>          = 'L':  Lower triangle of A is stored.
!>
```

*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 DOUBLE PRECISION array, dimension (N*(N+1)/2)
!>          The upper or lower triangle of the symmetric 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.
!>
```

*AFP*

```
!>          AFP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
!>          The triangular factor U or L from the Cholesky factorization
!>          A = U**T*U or A = L*L**T, as computed by DPPTRF/ZPPTRF,
!>          packed columnwise in a linear array in the same format as A
!>          (see AP).
!>
```

*B*

```
!>          B is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDX,NRHS)
!>          On entry, the solution matrix X, as computed by DPPTRS.
!>          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 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 DOUBLE PRECISION array, dimension (3*N)
!>
```

*IWORK*

```
!>          IWORK is INTEGER 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 **169** of file **dpprfs.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.