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CPPRFS(l)) CPPRFS(l)NAMECPPRFS - improve the computed solution to a system of linear equations when the coeffi- cient matrix is Hermitian positive definite and packed, and provides error bounds and backward error estimates for the solutionSYNOPSISSUBROUTINE CPPRFS( UPLO, N, NRHS, AP, AFP, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO ) CHARACTER UPLO INTEGER INFO, LDB, LDX, N, NRHS REAL BERR( * ), FERR( * ), RWORK( * ) COMPLEX AFP( * ), AP( * ), B( LDB, * ), WORK( * ), X( LDX, * )PURPOSECPPRFS improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and packed, and provides error bounds and backward error estimates for the solution.ARGUMENTSUPLO (input) CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. 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. AP (input) COMPLEX array, dimension (N*(N+1)/2) The upper or lower triangle of the Hermitian matrix A, packed columnwise in a lin- ear 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. AFP (input) COMPLEX array, dimension (N*(N+1)/2) The triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, as computed by SPPTRF/CPPTRF, packed columnwise in a linear array in the same format as A (see AP). B (input) COMPLEX 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/output) COMPLEX array, dimension (LDX,NRHS) On entry, the solution matrix X, as computed by CPPTRS. On exit, the improved solution matrix X. LDX (input) INTEGER The leading dimension of the array X. LDX >= max(1,N). FERR (output) 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 esti- mate is as reliable as the estimate for RCOND, and is almost always a slight over- estimate of the true error. BERR (output) 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 solu- tion). WORK (workspace) COMPLEX array, dimension (2*N) RWORK (workspace) REAL array, dimension (N) INFO (output) INTEGER = 0: successful exit < 0: if INFO =, the i-th argument had an illegal value-iPARAMETERSITMAX is the maximum number of steps of iterative refinement.LAPACK version 3.015 June 2000 CPPRFS(l)

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