Man page - hprfs(3)

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Manual

hprfs

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine chprfs (character uplo, integer n, integer nrhs, complex,dimension( * ) ap, complex, dimension( * ) afp, integer, dimension( * )ipiv, 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 csprfs (character uplo, integer n, integer nrhs, complex,dimension( * ) ap, complex, dimension( * ) afp, integer, dimension( * )ipiv, 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 dsprfs (character uplo, integer n, integer nrhs, doubleprecision, dimension( * ) ap, double precision, dimension( * ) afp,integer, dimension( * ) ipiv, 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 ssprfs (character uplo, integer n, integer nrhs, real,dimension( * ) ap, real, dimension( * ) afp, integer, dimension( * )ipiv, 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 zhprfs (character uplo, integer n, integer nrhs, complex*16,dimension( * ) ap, complex*16, dimension( * ) afp, integer, dimension(* ) ipiv, 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)
subroutine zsprfs (character uplo, integer n, integer nrhs, complex*16,dimension( * ) ap, complex*16, dimension( * ) afp, integer, dimension(* ) ipiv, 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

hprfs - {hp,sp}rfs: iterative refinement

SYNOPSIS

Functions

subroutine chprfs (uplo, n, nrhs, ap, afp, ipiv, b, ldb, x, ldx, ferr, berr, work, rwork, info)
CHPRFS
subroutine csprfs (uplo, n, nrhs, ap, afp, ipiv, b, ldb, x, ldx, ferr, berr, work, rwork, info)
CSPRFS
subroutine dsprfs (uplo, n, nrhs, ap, afp, ipiv, b, ldb, x, ldx, ferr, berr, work, iwork, info)
DSPRFS
subroutine ssprfs (uplo, n, nrhs, ap, afp, ipiv, b, ldb, x, ldx, ferr, berr, work, iwork, info)
SSPRFS
subroutine zhprfs (uplo, n, nrhs, ap, afp, ipiv, b, ldb, x, ldx, ferr, berr, work, rwork, info)
ZHPRFS
subroutine zsprfs (uplo, n, nrhs, ap, afp, ipiv, b, ldb, x, ldx, ferr, berr, work, rwork, info)
ZSPRFS

Detailed Description

Function Documentation

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

CHPRFS

Purpose:

CHPRFS improves the computed solution to a system of linear
equations when the coefficient matrix is Hermitian indefinite
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)*(2*n-j)/2) = A(i,j) for j<=i<=n.

AFP

AFP is COMPLEX array, dimension (N*(N+1)/2)
The factored form of the matrix A. AFP contains the block
diagonal matrix D and the multipliers used to obtain the
factor U or L from the factorization A = U*D*U**H or
A = L*D*L**H as computed by CHPTRF, stored as a packed
triangular matrix.

IPIV

IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by CHPTRF.

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 CHPTRS.
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 csprfs (character uplo, integer n, integer nrhs, complex,dimension( * ) ap, complex, dimension( * ) afp, integer, dimension( * )ipiv, 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)

CSPRFS

Purpose:

CSPRFS improves the computed solution to a system of linear
equations when the coefficient matrix is symmetric indefinite
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 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)*(2*n-j)/2) = A(i,j) for j<=i<=n.

AFP

AFP is COMPLEX array, dimension (N*(N+1)/2)
The factored form of the matrix A. AFP contains the block
diagonal matrix D and the multipliers used to obtain the
factor U or L from the factorization A = U*D*U**T or
A = L*D*L**T as computed by CSPTRF, stored as a packed
triangular matrix.

IPIV

IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by CSPTRF.

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 CSPTRS.
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 dsprfs (character uplo, integer n, integer nrhs, doubleprecision, dimension( * ) ap, double precision, dimension( * ) afp,integer, dimension( * ) ipiv, 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)

DSPRFS

Purpose:

DSPRFS improves the computed solution to a system of linear
equations when the coefficient matrix is symmetric indefinite
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)*(2*n-j)/2) = A(i,j) for j<=i<=n.

AFP

AFP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
The factored form of the matrix A. AFP contains the block
diagonal matrix D and the multipliers used to obtain the
factor U or L from the factorization A = U*D*U**T or
A = L*D*L**T as computed by DSPTRF, stored as a packed
triangular matrix.

IPIV

IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by DSPTRF.

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 DSPTRS.
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 ssprfs (character uplo, integer n, integer nrhs, real,dimension( * ) ap, real, dimension( * ) afp, integer, dimension( * )ipiv, 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)

SSPRFS

Purpose:

SSPRFS improves the computed solution to a system of linear
equations when the coefficient matrix is symmetric indefinite
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)*(2*n-j)/2) = A(i,j) for j<=i<=n.

AFP

AFP is REAL array, dimension (N*(N+1)/2)
The factored form of the matrix A. AFP contains the block
diagonal matrix D and the multipliers used to obtain the
factor U or L from the factorization A = U*D*U**T or
A = L*D*L**T as computed by SSPTRF, stored as a packed
triangular matrix.

IPIV

IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by SSPTRF.

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 SSPTRS.
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 zhprfs (character uplo, integer n, integer nrhs, complex*16,dimension( * ) ap, complex*16, dimension( * ) afp, integer, dimension(* ) ipiv, 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)

ZHPRFS

Purpose:

ZHPRFS improves the computed solution to a system of linear
equations when the coefficient matrix is Hermitian indefinite
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)*(2*n-j)/2) = A(i,j) for j<=i<=n.

AFP

AFP is COMPLEX*16 array, dimension (N*(N+1)/2)
The factored form of the matrix A. AFP contains the block
diagonal matrix D and the multipliers used to obtain the
factor U or L from the factorization A = U*D*U**H or
A = L*D*L**H as computed by ZHPTRF, stored as a packed
triangular matrix.

IPIV

IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by ZHPTRF.

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 ZHPTRS.
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.

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

ZSPRFS

Purpose:

ZSPRFS improves the computed solution to a system of linear
equations when the coefficient matrix is symmetric indefinite
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 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)*(2*n-j)/2) = A(i,j) for j<=i<=n.

AFP

AFP is COMPLEX*16 array, dimension (N*(N+1)/2)
The factored form of the matrix A. AFP contains the block
diagonal matrix D and the multipliers used to obtain the
factor U or L from the factorization A = U*D*U**T or
A = L*D*L**T as computed by ZSPTRF, stored as a packed
triangular matrix.

IPIV

IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by ZSPTRF.

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 ZSPTRS.
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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