Man page - pprfs(3)

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Manual

pprfs

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine cpprfs (character uplo, integer n, integer nrhs, complex,dimension( * ) ap, complex, dimension( * ) afp, 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)
subroutine dpprfs (character uplo, integer n, integer nrhs, doubleprecision, 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)
subroutine spprfs (character uplo, integer n, integer nrhs, real,dimension( * ) ap, real, dimension( * ) afp, real, dimension( ldb, * )b, integer ldb, real, dimension( ldx, * ) x, integer ldx, real,dimension( * ) ferr, real, dimension( * ) berr, real, dimension( * )work, integer, dimension( * ) iwork, integer info)
subroutine zpprfs (character uplo, integer n, integer nrhs, complex*16,dimension( * ) ap, complex*16, dimension( * ) afp, 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)
Author

NAME

pprfs - pprfs: iterative refinement

SYNOPSIS

Functions

subroutine cpprfs (uplo, n, nrhs, ap, afp, b, ldb, x, ldx, ferr, berr, work, rwork, info)
CPPRFS
subroutine dpprfs (uplo, n, nrhs, ap, afp, b, ldb, x, ldx, ferr, berr, work, iwork, info)
DPPRFS
subroutine spprfs (uplo, n, nrhs, ap, afp, b, ldb, x, ldx, ferr, berr, work, iwork, info)
SPPRFS
subroutine zpprfs (uplo, n, nrhs, ap, afp, b, ldb, x, ldx, ferr, berr, work, rwork, info)
ZPPRFS

Detailed Description

Function Documentation

subroutine cpprfs (character uplo, integer n, integer nrhs, complex,dimension( * ) ap, complex, dimension( * ) afp, 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)

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
= ā€™Uā€™: Upper triangle of A is stored;
= ā€™Lā€™: 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 = ā€™Uā€™, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = ā€™Lā€™, 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

Univ. of Colorado Denver

NAG Ltd.

subroutine dpprfs (character uplo, integer n, integer nrhs, doubleprecision, 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
= ā€™Uā€™: Upper triangle of A is stored;
= ā€™Lā€™: 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 = ā€™Uā€™, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = ā€™Lā€™, 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.

subroutine spprfs (character uplo, integer n, integer nrhs, real,dimension( * ) ap, real, dimension( * ) afp, real, dimension( ldb, * )b, integer ldb, real, dimension( ldx, * ) x, integer ldx, real,dimension( * ) ferr, real, dimension( * ) berr, real, dimension( * )work, integer, dimension( * ) iwork, integer info)

SPPRFS

Purpose:

SPPRFS 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
= ā€™Uā€™: Upper triangle of A is stored;
= ā€™Lā€™: 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 REAL 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 = ā€™Uā€™, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = ā€™Lā€™, AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.

AFP

AFP is REAL 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 SPPTRF/CPPTRF,
packed columnwise in a linear array in the same format as A
(see AP).

B

B is REAL 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 REAL array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by SPPTRS.
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 REAL 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.

subroutine zpprfs (character uplo, integer n, integer nrhs, complex*16,dimension( * ) ap, complex*16, dimension( * ) afp, 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)

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
= ā€™Uā€™: Upper triangle of A is stored;
= ā€™Lā€™: 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 = ā€™Uā€™, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = ā€™Lā€™, 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

Univ. of Colorado Denver

NAG Ltd.

Author

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