10-17-2017
Quote:
Originally Posted by
pedot
... .. at least on what did you sort first in term of overall plan until getting such beautiful output..
Thanks for the "beautiful output" - it has been defined by you, hasn't it? Not sure I understand that quote - are you asking for the heuristics applied?
First it is mandatory to look at the input data and the desired output to find out what needs to be eliminated, what propagated and mayhap transformed or converted. Seeing previous attempts (with part successes or failures) always helps. That's why I frequently comment
Quote:
Please become accustomed to provide decent context info of your problem.
It is always helpful to carefully and detailedly phrase a request, and to support it with system info like OS and shell, related environment (variables, options), preferred tools, adequate (representative) sample input and desired output data and the logics connecting the two including your own attempts at a solution, and, if existent, system (error) messages verbatim, to avoid ambiguities and keep people from guessing.
With above, the basis for a solution is established. Now, build a prototype to see if the logics is close to what is requested, then tweak the solution before finally polishing it... the former gets the logics right, the latter adds e.g. error handling or ergonomy / user friendlyness.
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LEARN ABOUT REDHAT
cptrfs
CPTRFS(l) ) CPTRFS(l)
NAME
CPTRFS - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and
tridiagonal, and provides error bounds and backward error estimates for the solution
SYNOPSIS
SUBROUTINE CPTRFS( UPLO, N, NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO )
CHARACTER UPLO
INTEGER INFO, LDB, LDX, N, NRHS
REAL BERR( * ), D( * ), DF( * ), FERR( * ), RWORK( * )
COMPLEX B( LDB, * ), E( * ), EF( * ), WORK( * ), X( LDX, * )
PURPOSE
CPTRFS improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and tridi-
agonal, and provides error bounds and backward error estimates for the solution.
ARGUMENTS
UPLO (input) CHARACTER*1
Specifies whether the superdiagonal or the subdiagonal of the tridiagonal matrix A is stored and the form of the factorization:
= 'U': E is the superdiagonal of A, and A = U**H*D*U;
= 'L': E is the subdiagonal of A, and A = L*D*L**H. (The two forms are equivalent if A is real.)
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 matrix B. NRHS >= 0.
D (input) REAL array, dimension (N)
The n real diagonal elements of the tridiagonal matrix A.
E (input) COMPLEX array, dimension (N-1)
The (n-1) off-diagonal elements of the tridiagonal matrix A (see UPLO).
DF (input) REAL array, dimension (N)
The n diagonal elements of the diagonal matrix D from the factorization computed by CPTTRF.
EF (input) COMPLEX array, dimension (N-1)
The (n-1) off-diagonal elements of the unit bidiagonal factor U or L from the factorization computed by CPTTRF (see UPLO).
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 CPTTRS. 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 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).
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 solution).
WORK (workspace) COMPLEX array, dimension (N)
RWORK (workspace) REAL array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
PARAMETERS
ITMAX is the maximum number of steps of iterative refinement.
LAPACK version 3.0 15 June 2000 CPTRFS(l)