Man page - tprfs(3)

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Manual

tprfs

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine ctprfs (character uplo, character trans, character diag, integern, integer nrhs, complex, dimension( * ) ap, 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 dtprfs (character uplo, character trans, character diag, integern, integer nrhs, double precision, dimension( * ) ap, double precision,dimension( ldb, * ) b, integer ldb, double precision, dimension( ldx, *) x, integer ldx, double precision, dimension( * ) ferr, doubleprecision, dimension( * ) berr, double precision, dimension( * ) work,integer, dimension( * ) iwork, integer info)
subroutine stprfs (character uplo, character trans, character diag, integern, integer nrhs, real, dimension( * ) ap, 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 ztprfs (character uplo, character trans, character diag, integern, integer nrhs, complex*16, dimension( * ) ap, complex*16, dimension(ldb, * ) b, integer ldb, complex*16, dimension( ldx, * ) x, integerldx, double precision, dimension( * ) ferr, double precision,dimension( * ) berr, complex*16, dimension( * ) work, double precision,dimension( * ) rwork, integer info)
Author

NAME

tprfs - tprfs: triangular iterative refinement

SYNOPSIS

Functions

subroutine ctprfs (uplo, trans, diag, n, nrhs, ap, b, ldb, x, ldx, ferr, berr, work, rwork, info)
CTPRFS
subroutine dtprfs (uplo, trans, diag, n, nrhs, ap, b, ldb, x, ldx, ferr, berr, work, iwork, info)
DTPRFS
subroutine stprfs (uplo, trans, diag, n, nrhs, ap, b, ldb, x, ldx, ferr, berr, work, iwork, info)
STPRFS
subroutine ztprfs (uplo, trans, diag, n, nrhs, ap, b, ldb, x, ldx, ferr, berr, work, rwork, info)
ZTPRFS

Detailed Description

Function Documentation

subroutine ctprfs (character uplo, character trans, character diag, integern, integer nrhs, complex, dimension( * ) ap, 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)

CTPRFS

Purpose:

CTPRFS provides error bounds and backward error estimates for the
solution to a system of linear equations with a triangular packed
coefficient matrix.

The solution matrix X must be computed by CTPTRS or some other
means before entering this routine. CTPRFS does not do iterative
refinement because doing so cannot improve the backward error.

Parameters

UPLO

UPLO is CHARACTER*1
= ’U’: A is upper triangular;
= ’L’: A is lower triangular.

TRANS

TRANS is CHARACTER*1
Specifies the form of the system of equations:
= ’N’: A * X = B (No transpose)
= ’T’: A**T * X = B (Transpose)
= ’C’: A**H * X = B (Conjugate transpose)

DIAG

DIAG is CHARACTER*1
= ’N’: A is non-unit triangular;
= ’U’: A is unit triangular.

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 triangular 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.
If DIAG = ’U’, the diagonal elements of A are not referenced
and are assumed to be 1.

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)
The 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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine dtprfs (character uplo, character trans, character diag, integern, integer nrhs, double precision, dimension( * ) ap, double precision,dimension( ldb, * ) b, integer ldb, double precision, dimension( ldx, *) x, integer ldx, double precision, dimension( * ) ferr, doubleprecision, dimension( * ) berr, double precision, dimension( * ) work,integer, dimension( * ) iwork, integer info)

DTPRFS

Purpose:

DTPRFS provides error bounds and backward error estimates for the
solution to a system of linear equations with a triangular packed
coefficient matrix.

The solution matrix X must be computed by DTPTRS or some other
means before entering this routine. DTPRFS does not do iterative
refinement because doing so cannot improve the backward error.

Parameters

UPLO

UPLO is CHARACTER*1
= ’U’: A is upper triangular;
= ’L’: A is lower triangular.

TRANS

TRANS is CHARACTER*1
Specifies the form of the system of equations:
= ’N’: A * X = B (No transpose)
= ’T’: A**T * X = B (Transpose)
= ’C’: A**H * X = B (Conjugate transpose = Transpose)

DIAG

DIAG is CHARACTER*1
= ’N’: A is non-unit triangular;
= ’U’: A is unit triangular.

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 triangular 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)*(2*n-j)/2) = A(i,j) for j<=i<=n.
If DIAG = ’U’, the diagonal elements of A are not referenced
and are assumed to be 1.

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)
The 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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine stprfs (character uplo, character trans, character diag, integern, integer nrhs, real, dimension( * ) ap, 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)

STPRFS

Purpose:

STPRFS provides error bounds and backward error estimates for the
solution to a system of linear equations with a triangular packed
coefficient matrix.

The solution matrix X must be computed by STPTRS or some other
means before entering this routine. STPRFS does not do iterative
refinement because doing so cannot improve the backward error.

Parameters

UPLO

UPLO is CHARACTER*1
= ’U’: A is upper triangular;
= ’L’: A is lower triangular.

TRANS

TRANS is CHARACTER*1
Specifies the form of the system of equations:
= ’N’: A * X = B (No transpose)
= ’T’: A**T * X = B (Transpose)
= ’C’: A**H * X = B (Conjugate transpose = Transpose)

DIAG

DIAG is CHARACTER*1
= ’N’: A is non-unit triangular;
= ’U’: A is unit triangular.

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 triangular 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)*(2*n-j)/2) = A(i,j) for j<=i<=n.
If DIAG = ’U’, the diagonal elements of A are not referenced
and are assumed to be 1.

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)
The 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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine ztprfs (character uplo, character trans, character diag, integern, integer nrhs, complex*16, dimension( * ) ap, complex*16, dimension(ldb, * ) b, integer ldb, complex*16, dimension( ldx, * ) x, integerldx, double precision, dimension( * ) ferr, double precision,dimension( * ) berr, complex*16, dimension( * ) work, double precision,dimension( * ) rwork, integer info)

ZTPRFS

Purpose:

ZTPRFS provides error bounds and backward error estimates for the
solution to a system of linear equations with a triangular packed
coefficient matrix.

The solution matrix X must be computed by ZTPTRS or some other
means before entering this routine. ZTPRFS does not do iterative
refinement because doing so cannot improve the backward error.

Parameters

UPLO

UPLO is CHARACTER*1
= ’U’: A is upper triangular;
= ’L’: A is lower triangular.

TRANS

TRANS is CHARACTER*1
Specifies the form of the system of equations:
= ’N’: A * X = B (No transpose)
= ’T’: A**T * X = B (Transpose)
= ’C’: A**H * X = B (Conjugate transpose)

DIAG

DIAG is CHARACTER*1
= ’N’: A is non-unit triangular;
= ’U’: A is unit triangular.

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 triangular 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.
If DIAG = ’U’, the diagonal elements of A are not referenced
and are assumed to be 1.

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)
The 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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Author

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