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ZTRRFS(l)) ZTRRFS(l)NAMEZTRRFS - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrixSYNOPSISSUBROUTINE ZTRRFS( UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO ) CHARACTER DIAG, TRANS, UPLO INTEGER INFO, LDA, LDB, LDX, N, NRHS DOUBLE PRECISION BERR( * ), FERR( * ), RWORK( * ) COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * ), X( LDX, * )PURPOSEZTRRFS provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix. The solution matrix X must be com- puted by ZTRTRS or some other means before entering this routine. ZTRRFS does not do iterative refinement because doing so cannot improve the backward error.ARGUMENTSUPLO (input) CHARACTER*1 = 'U': A is upper triangular; = 'L': A is lower triangular. TRANS (input) 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 (input) CHARACTER*1 = 'N': A is non-unit triangular; = 'U': A is unit triangular. N (input) INTEGER The order of the matrix A. N >= 0. NRHS (input) INTEGER The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0. A (input) COMPLEX*16 array, dimension (LDA,N) The triangular matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of the array A contains the upper triangular matrix, and the strictly lower trian- gular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower trian- gular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If DIAG = 'U', the diagonal ele- ments of A are also not referenced and are assumed to be 1. LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,N). B (input) COMPLEX*16 array, dimension (LDB,NRHS) The right hand side matrix B. LDB (input) INTEGER The leading dimension of the array B. LDB >= max(1,N). X (input) COMPLEX*16 array, dimension (LDX,NRHS) The solution matrix X. LDX (input) INTEGER The leading dimension of the array X. LDX >= max(1,N). FERR (output) 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 esti- mate is as reliable as the estimate for RCOND, and is almost always a slight over- estimate of the true error. BERR (output) 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 solu- tion). WORK (workspace) COMPLEX*16 array, dimension (2*N) RWORK (workspace) DOUBLE PRECISION array, dimension (N) INFO (output) INTEGER = 0: successful exit < 0: if INFO =, the i-th argument had an illegal value-iLAPACK version 3.015 June 2000 ZTRRFS(l)

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