table of contents
| gtrfs(3) | Library Functions Manual | gtrfs(3) |
NAME¶
gtrfs - gtrfs: iterative refinement
SYNOPSIS¶
Functions¶
subroutine CGTRFS (trans, n, nrhs, dl, d, du, dlf, df, duf,
du2, ipiv, b, ldb, x, ldx, ferr, berr, work, rwork, info)
CGTRFS subroutine DGTRFS (trans, n, nrhs, dl, d, du, dlf, df,
duf, du2, ipiv, b, ldb, x, ldx, ferr, berr, work, iwork, info)
DGTRFS subroutine SGTRFS (trans, n, nrhs, dl, d, du, dlf, df,
duf, du2, ipiv, b, ldb, x, ldx, ferr, berr, work, iwork, info)
SGTRFS subroutine ZGTRFS (trans, n, nrhs, dl, d, du, dlf, df,
duf, du2, ipiv, b, ldb, x, ldx, ferr, berr, work, rwork, info)
ZGTRFS
Detailed Description¶
Function Documentation¶
subroutine CGTRFS (character trans, integer n, integer nrhs, complex, dimension( * ) dl, complex, dimension( * ) d, complex, dimension( * ) du, complex, dimension( * ) dlf, complex, dimension( * ) df, complex, dimension( * ) duf, complex, dimension( * ) du2, 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)¶
CGTRFS
Purpose:
!> !> CGTRFS improves the computed solution to a system of linear !> equations when the coefficient matrix is tridiagonal, and provides !> error bounds and backward error estimates for the solution. !>
Parameters
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) !>
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 matrix B. NRHS >= 0. !>
DL
!> DL is COMPLEX array, dimension (N-1) !> The (n-1) subdiagonal elements of A. !>
D
!> D is COMPLEX array, dimension (N) !> The diagonal elements of A. !>
DU
!> DU is COMPLEX array, dimension (N-1) !> The (n-1) superdiagonal elements of A. !>
DLF
!> DLF is COMPLEX array, dimension (N-1) !> The (n-1) multipliers that define the matrix L from the !> LU factorization of A as computed by CGTTRF. !>
DF
!> DF is COMPLEX array, dimension (N) !> The n diagonal elements of the upper triangular matrix U from !> the LU factorization of A. !>
DUF
!> DUF is COMPLEX array, dimension (N-1) !> The (n-1) elements of the first superdiagonal of U. !>
DU2
!> DU2 is COMPLEX array, dimension (N-2) !> The (n-2) elements of the second superdiagonal of U. !>
IPIV
!> IPIV is INTEGER array, dimension (N) !> The pivot indices; for 1 <= i <= n, row i of the matrix was !> interchanged with row IPIV(i). IPIV(i) will always be either !> i or i+1; IPIV(i) = i indicates a row interchange was not !> required. !>
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 CGTTRS. !> 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.
Definition at line 207 of file cgtrfs.f.
subroutine DGTRFS (character trans, integer n, integer nrhs, double precision, dimension( * ) dl, double precision, dimension( * ) d, double precision, dimension( * ) du, double precision, dimension( * ) dlf, double precision, dimension( * ) df, double precision, dimension( * ) duf, double precision, dimension( * ) du2, 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)¶
DGTRFS
Purpose:
!> !> DGTRFS improves the computed solution to a system of linear !> equations when the coefficient matrix is tridiagonal, and provides !> error bounds and backward error estimates for the solution. !>
Parameters
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) !>
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 matrix B. NRHS >= 0. !>
DL
!> DL is DOUBLE PRECISION array, dimension (N-1) !> The (n-1) subdiagonal elements of A. !>
D
!> D is DOUBLE PRECISION array, dimension (N) !> The diagonal elements of A. !>
DU
!> DU is DOUBLE PRECISION array, dimension (N-1) !> The (n-1) superdiagonal elements of A. !>
DLF
!> DLF is DOUBLE PRECISION array, dimension (N-1) !> The (n-1) multipliers that define the matrix L from the !> LU factorization of A as computed by DGTTRF. !>
DF
!> DF is DOUBLE PRECISION array, dimension (N) !> The n diagonal elements of the upper triangular matrix U from !> the LU factorization of A. !>
DUF
!> DUF is DOUBLE PRECISION array, dimension (N-1) !> The (n-1) elements of the first superdiagonal of U. !>
DU2
!> DU2 is DOUBLE PRECISION array, dimension (N-2) !> The (n-2) elements of the second superdiagonal of U. !>
IPIV
!> IPIV is INTEGER array, dimension (N) !> The pivot indices; for 1 <= i <= n, row i of the matrix was !> interchanged with row IPIV(i). IPIV(i) will always be either !> i or i+1; IPIV(i) = i indicates a row interchange was not !> required. !>
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 DGTTRS. !> 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 206 of file dgtrfs.f.
subroutine SGTRFS (character trans, integer n, integer nrhs, real, dimension( * ) dl, real, dimension( * ) d, real, dimension( * ) du, real, dimension( * ) dlf, real, dimension( * ) df, real, dimension( * ) duf, real, dimension( * ) du2, 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)¶
SGTRFS
Purpose:
!> !> SGTRFS improves the computed solution to a system of linear !> equations when the coefficient matrix is tridiagonal, and provides !> error bounds and backward error estimates for the solution. !>
Parameters
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) !>
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 matrix B. NRHS >= 0. !>
DL
!> DL is REAL array, dimension (N-1) !> The (n-1) subdiagonal elements of A. !>
D
!> D is REAL array, dimension (N) !> The diagonal elements of A. !>
DU
!> DU is REAL array, dimension (N-1) !> The (n-1) superdiagonal elements of A. !>
DLF
!> DLF is REAL array, dimension (N-1) !> The (n-1) multipliers that define the matrix L from the !> LU factorization of A as computed by SGTTRF. !>
DF
!> DF is REAL array, dimension (N) !> The n diagonal elements of the upper triangular matrix U from !> the LU factorization of A. !>
DUF
!> DUF is REAL array, dimension (N-1) !> The (n-1) elements of the first superdiagonal of U. !>
DU2
!> DU2 is REAL array, dimension (N-2) !> The (n-2) elements of the second superdiagonal of U. !>
IPIV
!> IPIV is INTEGER array, dimension (N) !> The pivot indices; for 1 <= i <= n, row i of the matrix was !> interchanged with row IPIV(i). IPIV(i) will always be either !> i or i+1; IPIV(i) = i indicates a row interchange was not !> required. !>
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 SGTTRS. !> 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.
Definition at line 206 of file sgtrfs.f.
subroutine ZGTRFS (character trans, integer n, integer nrhs, complex*16, dimension( * ) dl, complex*16, dimension( * ) d, complex*16, dimension( * ) du, complex*16, dimension( * ) dlf, complex*16, dimension( * ) df, complex*16, dimension( * ) duf, complex*16, dimension( * ) du2, 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)¶
ZGTRFS
Purpose:
!> !> ZGTRFS improves the computed solution to a system of linear !> equations when the coefficient matrix is tridiagonal, and provides !> error bounds and backward error estimates for the solution. !>
Parameters
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) !>
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 matrix B. NRHS >= 0. !>
DL
!> DL is COMPLEX*16 array, dimension (N-1) !> The (n-1) subdiagonal elements of A. !>
D
!> D is COMPLEX*16 array, dimension (N) !> The diagonal elements of A. !>
DU
!> DU is COMPLEX*16 array, dimension (N-1) !> The (n-1) superdiagonal elements of A. !>
DLF
!> DLF is COMPLEX*16 array, dimension (N-1) !> The (n-1) multipliers that define the matrix L from the !> LU factorization of A as computed by ZGTTRF. !>
DF
!> DF is COMPLEX*16 array, dimension (N) !> The n diagonal elements of the upper triangular matrix U from !> the LU factorization of A. !>
DUF
!> DUF is COMPLEX*16 array, dimension (N-1) !> The (n-1) elements of the first superdiagonal of U. !>
DU2
!> DU2 is COMPLEX*16 array, dimension (N-2) !> The (n-2) elements of the second superdiagonal of U. !>
IPIV
!> IPIV is INTEGER array, dimension (N) !> The pivot indices; for 1 <= i <= n, row i of the matrix was !> interchanged with row IPIV(i). IPIV(i) will always be either !> i or i+1; IPIV(i) = i indicates a row interchange was not !> required. !>
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 ZGTTRS. !> 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.
Definition at line 207 of file zgtrfs.f.
Author¶
Generated automatically by Doxygen for LAPACK from the source code.
| Version 3.12.0 | LAPACK |