Include dependency graph for zgst07.c:
Functions | |
| int | zgst07 (trans_t trans, int n, int nrhs, SuperMatrix *A, doublecomplex *b, int ldb, doublecomplex *x, int ldx, doublecomplex *xact, int ldxact, double *ferr, double *berr, double *reslts) |
Detailed Description
ZGST07 tests the error bounds from iterative refinement for the computed solution to a system of equations op(A)*X = B
Function Documentation
◆ zgst07()
| int zgst07 | ( | trans_t | trans, |
| int | n, | ||
| int | nrhs, | ||
| SuperMatrix * | A, | ||
| doublecomplex * | b, | ||
| int | ldb, | ||
| doublecomplex * | x, | ||
| int | ldx, | ||
| doublecomplex * | xact, | ||
| int | ldxact, | ||
| double * | ferr, | ||
| double * | berr, | ||
| double * | reslts | ||
| ) |
ZGST07 tests the error bounds from iterative refinement for the computed solution to a system of equations op(A)*X = B, where A is a general n by n matrix and op(A) = A or A**T, depending on TRANS.
RESLTS(1) = test of the error bound = norm(X - XACT) / ( norm(X) * FERR ) A large value is returned if this ratio is not less than one.
RESLTS(2) = residual from the iterative refinement routine = the maximum of BERR / ( (n+1)*EPS + (*) ), where (*) = (n+1)*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i )
- Parameters
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[in] trans Specifies the form of the system of equations. = NOTRANS: A *x = b = TRANS : A'*x = b, where A' is the transpose of A = CONJ : A'*x = b, where A' is the transpose of A [in] n The number of rows of the matrices X and XACT. N >= 0. [in] nrhs The number of columns of the matrices X and XACT. NRHS >= 0. [in] A The original n by n matrix A, dimension(A->nrow, A->ncol). [in] b The right hand side vectors for the system of linear equations, dimension(LDB,NRHS). [in] ldb The leading dimension of the array B. LDB >= max(1,N). [in] x The computed solution vectors, dimension(LDX,NRHS). Each vector is stored as a column of the matrix X. [in] ldx The leading dimension of the array X. LDX >= max(1,N). [in] xact The exact solution vectors, dimension(LDX,NRHS). Each vector is stored as a column of the matrix XACT. [in] ldxact The leading dimension of the array XACT. LDXACT >= max(1,N). [in] ferr The estimated forward error bounds for each solution vector X, dimension(NRHS). If XTRUE is the true solution, FERR bounds the magnitude of the largest entry in (X - XTRUE) divided by the magnitude of the largest entry in X. [in] berr The componentwise relative backward error of each solution vector (i.e., the smallest relative change in any entry of A or B that makes X an exact solution), dimension(NRHS). [out] reslts The maximum over the NRHS solution vectors of the ratios, dimension(2): RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR ) RESLTS(2) = BERR / ( (n+1)*EPS + (*) )
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