
NAMEzptsvx.f SYNOPSISFunctions/Subroutinessubroutine zptsvx (FACT, N, NRHS, D, E, DF, EF, B, LDB, X, LDX, RCOND, FERR, BERR, WORK, RWORK, INFO) Function/Subroutine Documentationsubroutine zptsvx (characterFACT, integerN, integerNRHS, double precision, dimension( * )D, complex*16, dimension( * )E, double precision, dimension( * )DF, complex*16, dimension( * )EF, complex*16, dimension( ldb, * )B, integerLDB, complex*16, dimension( ldx, * )X, integerLDX, double precisionRCOND, double precision, dimension( * )FERR, double precision, dimension( * )BERR, complex*16, dimension( * )WORK, double precision, dimension( * )RWORK, integerINFO)ZPTSVX computes the solution to system of linear equations A * X = B for PT matrices Purpose:ZPTSVX uses the factorization A = L*D*L**H to compute the solution to a complex system of linear equations A*X = B, where A is an NbyN Hermitian positive definite tridiagonal matrix and X and B are NbyNRHS matrices. Error bounds on the solution and a condition estimate are also provided. The following steps are performed: 1. If FACT = 'N', the matrix A is factored as A = L*D*L**H, where L is a unit lower bidiagonal matrix and D is diagonal. The factorization can also be regarded as having the form A = U**H*D*U. 2. If the leading ibyi principal minor is not positive definite, then the routine returns with INFO = i. Otherwise, the factored form of A is used to estimate the condition number of the matrix A. If the reciprocal of the condition number is less than machine precision, INFO = N+1 is returned as a warning, but the routine still goes on to solve for X and compute error bounds as described below. 3. The system of equations is solved for X using the factored form of A. 4. Iterative refinement is applied to improve the computed solution matrix and calculate error bounds and backward error estimates for it. FACT
Author:
FACT is CHARACTER*1 Specifies whether or not the factored form of the matrix A is supplied on entry. = 'F': On entry, DF and EF contain the factored form of A. D, E, DF, and EF will not be modified. = 'N': The matrix A will be copied to DF and EF and factored.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.D D is DOUBLE PRECISION array, dimension (N) The n diagonal elements of the tridiagonal matrix A.E E is COMPLEX*16 array, dimension (N1) The (n1) subdiagonal elements of the tridiagonal matrix A.DF DF is DOUBLE PRECISION array, dimension (N) If FACT = 'F', then DF is an input argument and on entry contains the n diagonal elements of the diagonal matrix D from the L*D*L**H factorization of A. If FACT = 'N', then DF is an output argument and on exit contains the n diagonal elements of the diagonal matrix D from the L*D*L**H factorization of A.EF EF is COMPLEX*16 array, dimension (N1) If FACT = 'F', then EF is an input argument and on entry contains the (n1) subdiagonal elements of the unit bidiagonal factor L from the L*D*L**H factorization of A. If FACT = 'N', then EF is an output argument and on exit contains the (n1) subdiagonal elements of the unit bidiagonal factor L from the L*D*L**H factorization of A.B B is COMPLEX*16 array, dimension (LDB,NRHS) The NbyNRHS 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) If INFO = 0 or INFO = N+1, the NbyNRHS solution matrix X.LDX LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N).RCOND RCOND is DOUBLE PRECISION The reciprocal condition number of the matrix A. If RCOND is less than the machine precision (in particular, if RCOND = 0), the matrix is singular to working precision. This condition is indicated by a return code of INFO > 0.FERR FERR is DOUBLE PRECISION array, dimension (NRHS) The forward error bound for each solution vector X(j) (the jth 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 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 (N)RWORK RWORK is DOUBLE PRECISION array, dimension (N)INFO INFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith argument had an illegal value > 0: if INFO = i, and i is <= N: the leading minor of order i of A is not positive definite, so the factorization could not be completed, and the solution has not been computed. RCOND = 0 is returned. = N+1: U is nonsingular, but RCOND is less than machine precision, meaning that the matrix is singular to working precision. Nevertheless, the solution and error bounds are computed because there are a number of situations where the computed solution can be more accurate than the value of RCOND would suggest. Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
September 2012
Definition at line 234 of file zptsvx.f.
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