# zpprfs.f(3) [centos man page]

zpprfs.f(3) LAPACK zpprfs.f(3)NAME

zpprfs.f-SYNOPSIS

Functions/Subroutines subroutine zpprfs (UPLO, N, NRHS, AP, AFP, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO) ZPPRFSFunction/Subroutine Documentation subroutine zpprfs (characterUPLO, integerN, integerNRHS, complex*16, dimension( * )AP, complex*16, dimension( * )AFP, complex*16, dimension( ldb, * )B, integerLDB, complex*16, dimension( ldx, * )X, integerLDX, double precision, dimension( * )FERR, double precision, dimension( * )BERR, complex*16, dimension( * )WORK, double precision, dimension( * )RWORK, integerINFO) ZPPRFS Purpose: ZPPRFS 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. Parameters: UPLO UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. 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. AP AP is COMPLEX*16 array, dimension (N*(N+1)/2) The upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear 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 AFP is COMPLEX*16 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 DPPTRF/ZPPTRF, packed columnwise in a linear array in the same format as A (see AP). 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 ZPPTRS. 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 =, 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. Date: November 2011 Definition at line 171 of file zpprfs.f.-iAuthorGenerated automatically by Doxygen for LAPACK from the source code.Version 3.4.2Tue Sep 25 2012 zpprfs.f(3)

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zhprfs.f(3) LAPACK zhprfs.f(3)NAME

zhprfs.f-SYNOPSIS

Functions/Subroutines subroutine zhprfs (UPLO, N, NRHS, AP, AFP, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO) ZHPRFSFunction/Subroutine Documentation subroutine zhprfs (characterUPLO, integerN, integerNRHS, complex*16, dimension( * )AP, complex*16, dimension( * )AFP, integer, dimension( * )IPIV, complex*16, dimension( ldb, * )B, integerLDB, complex*16, dimension( ldx, * )X, integerLDX, double precision, dimension( * )FERR, double precision, dimension( * )BERR, complex*16, dimension( * )WORK, double precision, dimension( * )RWORK, integerINFO) ZHPRFS Purpose: ZHPRFS improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite and packed, and provides error bounds and backward error estimates for the solution. Parameters: UPLO UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. 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. AP AP is COMPLEX*16 array, dimension (N*(N+1)/2) The upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear 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)*(2*n-j)/2) = A(i,j) for j<=i<=n. AFP AFP is COMPLEX*16 array, dimension (N*(N+1)/2) The factored form of the matrix A. AFP contains the block diagonal matrix D and the multipliers used to obtain the factor U or L from the factorization A = U*D*U**H or A = L*D*L**H as computed by ZHPTRF, stored as a packed triangular matrix. IPIV IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by ZHPTRF. 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 ZHPTRS. 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 =, 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. Date: November 2011 Definition at line 180 of file zhprfs.f.-iAuthorGenerated automatically by Doxygen for LAPACK from the source code.Version 3.4.2Tue Sep 25 2012 zhprfs.f(3)