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Test Your Knowledge in Computers #439
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A graphics processing unit (GPU) is a specialized electronic circuit designed to rapidly manipulate and alter memory to accelerate the creation of images in a frame buffer intended for output to a display device.
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# zpprfs.f(3) [centos man page]

```zpprfs.f(3)							      LAPACK							       zpprfs.f(3)

NAME
zpprfs.f -

SYNOPSIS
Functions/Subroutines
subroutine zpprfs (UPLO, N, NRHS, AP, AFP, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO)
ZPPRFS

Function/Subroutine Documentation
subroutine zpprfs (characterUPLO, integerN, integerNRHS, complex*16, dimension( * )AP, complex*16, dimension( * )AFP, complex*16, dimension(
ldb, * )B, integerLDB, complex*16, dimension( ldx, * )X, integerLDX, double precision, dimension( * )FERR, double precision, dimension( *
)BERR, complex*16, dimension( * )WORK, double precision, dimension( * )RWORK, integerINFO)
ZPPRFS

Purpose:

ZPPRFS improves the computed solution to a system of linear
equations when the coefficient matrix is Hermitian 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 COMPLEX*16 array, dimension (N*(N+1)/2)
The upper or lower triangle of the Hermitian 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 COMPLEX*16 array, dimension (N*(N+1)/2)
The triangular factor U or L from the Cholesky factorization
A = U**H*U or A = L*L**H, as computed by DPPTRF/ZPPTRF,
packed columnwise in a linear array in the same format as A
(see AP).

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 ZPPTRS.
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 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

Internal Parameters:

ITMAX is the maximum number of steps of iterative refinement.

Author:
Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:
November 2011

Definition at line 171 of file zpprfs.f.

Author
Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       zpprfs.f(3)```

## Check Out this Related Man Page

```cpprfs.f(3)							      LAPACK							       cpprfs.f(3)

NAME
cpprfs.f -

SYNOPSIS
Functions/Subroutines
subroutine cpprfs (UPLO, N, NRHS, AP, AFP, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO)
CPPRFS

Function/Subroutine Documentation
subroutine cpprfs (characterUPLO, integerN, integerNRHS, complex, dimension( * )AP, complex, dimension( * )AFP, complex, dimension( ldb, * )B,
integerLDB, complex, dimension( ldx, * )X, integerLDX, real, dimension( * )FERR, real, dimension( * )BERR, complex, dimension( * )WORK,
real, dimension( * )RWORK, integerINFO)
CPPRFS

Purpose:

CPPRFS improves the computed solution to a system of linear
equations when the coefficient matrix is Hermitian 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 COMPLEX array, dimension (N*(N+1)/2)
The upper or lower triangle of the Hermitian 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 COMPLEX array, dimension (N*(N+1)/2)
The triangular factor U or L from the Cholesky factorization
A = U**H*U or A = L*L**H, as computed by SPPTRF/CPPTRF,
packed columnwise in a linear array in the same format as A
(see AP).

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 CPPTRS.
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 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 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 (2*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

NAG Ltd.

Date:
November 2011

Definition at line 171 of file cpprfs.f.

Author
Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       cpprfs.f(3)```