gerfs - gerfs: iterative refinement

Generated automatically by Doxygen for LAPACK from the source code. Version 3.12.0 Sun Jul 20 2025 01:40:05 gerfs(3)

subroutinecgerfs(charactertrans,integern,integernrhs,complex,dimension(lda,*)a,integerlda,complex,dimension(ldaf,*)af,integerldaf,integer,dimension(*)ipiv,complex,dimension(ldb,*)b,integerldb,complex,dimension(ldx,*)x,integerldx,real,dimension(*)ferr,real,dimension(*)berr,complex,dimension(*)work,real,dimension(*)rwork,integerinfo)CGERFSPurpose: CGERFS improves the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution. ParametersTRANS 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 matrices B and X. NRHS >= 0. A A is COMPLEX array, dimension (LDA,N) The original N-by-N matrix A. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). AF AF is COMPLEX array, dimension (LDAF,N) The factors L and U from the factorization A = P*L*U as computed by CGETRF. LDAF LDAF is INTEGER The leading dimension of the array AF. LDAF >= max(1,N). IPIV IPIV is INTEGER array, dimension (N) The pivot indices from CGETRF; for 1<=i<=N, row i of the matrix was interchanged with row IPIV(i). 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 CGETRS. 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 InternalParameters: ITMAX is the maximum number of steps of iterative refinement. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. subroutinedgerfs(charactertrans,integern,integernrhs,doubleprecision,dimension(lda,*)a,integerlda,doubleprecision,dimension(ldaf,*)af,integerldaf,integer,dimension(*)ipiv,doubleprecision,dimension(ldb,*)b,integerldb,doubleprecision,dimension(ldx,*)x,integerldx,doubleprecision,dimension(*)ferr,doubleprecision,dimension(*)berr,doubleprecision,dimension(*)work,integer,dimension(*)iwork,integerinfo)DGERFSPurpose: DGERFS improves the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution. ParametersTRANS 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 matrices B and X. NRHS >= 0. A A is DOUBLE PRECISION array, dimension (LDA,N) The original N-by-N matrix A. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). AF AF is DOUBLE PRECISION array, dimension (LDAF,N) The factors L and U from the factorization A = P*L*U as computed by DGETRF. LDAF LDAF is INTEGER The leading dimension of the array AF. LDAF >= max(1,N). IPIV IPIV is INTEGER array, dimension (N) The pivot indices from DGETRF; for 1<=i<=N, row i of the matrix was interchanged with row IPIV(i). 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 DGETRS. 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 InternalParameters: ITMAX is the maximum number of steps of iterative refinement. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. subroutinesgerfs(charactertrans,integern,integernrhs,real,dimension(lda,*)a,integerlda,real,dimension(ldaf,*)af,integerldaf,integer,dimension(*)ipiv,real,dimension(ldb,*)b,integerldb,real,dimension(ldx,*)x,integerldx,real,dimension(*)ferr,real,dimension(*)berr,real,dimension(*)work,integer,dimension(*)iwork,integerinfo)SGERFSPurpose: SGERFS improves the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution. ParametersTRANS 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 matrices B and X. NRHS >= 0. A A is REAL array, dimension (LDA,N) The original N-by-N matrix A. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). AF AF is REAL array, dimension (LDAF,N) The factors L and U from the factorization A = P*L*U as computed by SGETRF. LDAF LDAF is INTEGER The leading dimension of the array AF. LDAF >= max(1,N). IPIV IPIV is INTEGER array, dimension (N) The pivot indices from SGETRF; for 1<=i<=N, row i of the matrix was interchanged with row IPIV(i). 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 SGETRS. 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 InternalParameters: ITMAX is the maximum number of steps of iterative refinement. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. subroutinezgerfs(charactertrans,integern,integernrhs,complex*16,dimension(lda,*)a,integerlda,complex*16,dimension(ldaf,*)af,integerldaf,integer,dimension(*)ipiv,complex*16,dimension(ldb,*)b,integerldb,complex*16,dimension(ldx,*)x,integerldx,doubleprecision,dimension(*)ferr,doubleprecision,dimension(*)berr,complex*16,dimension(*)work,doubleprecision,dimension(*)rwork,integerinfo)ZGERFSPurpose: ZGERFS improves the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution. ParametersTRANS 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 matrices B and X. NRHS >= 0. A A is COMPLEX*16 array, dimension (LDA,N) The original N-by-N matrix A. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). AF AF is COMPLEX*16 array, dimension (LDAF,N) The factors L and U from the factorization A = P*L*U as computed by ZGETRF. LDAF LDAF is INTEGER The leading dimension of the array AF. LDAF >= max(1,N). IPIV IPIV is INTEGER array, dimension (N) The pivot indices from ZGETRF; for 1<=i<=N, row i of the matrix was interchanged with row IPIV(i). 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 ZGETRS. 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 InternalParameters: ITMAX is the maximum number of steps of iterative refinement. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.

gerfs - gerfs: iterative refinement

Functions subroutine cgerfs (trans, n, nrhs, a, lda, af, ldaf, ipiv, b, ldb, x, ldx, ferr, berr, work, rwork, info) CGERFS subroutine dgerfs (trans, n, nrhs, a, lda, af, ldaf, ipiv, b, ldb, x, ldx, ferr, berr, work, iwork, info) DGERFS subroutine sgerfs (trans, n, nrhs, a, lda, af, ldaf, ipiv, b, ldb, x, ldx, ferr, berr, work, iwork, info) SGERFS subroutine zgerfs (trans, n, nrhs, a, lda, af, ldaf, ipiv, b, ldb, x, ldx, ferr, berr, work, rwork, info) ZGERFS