zgtsvx.f - Online Linux Manual PageSection : 3
Updated : Tue Nov 14 2017
Source : Version 3.8.0
Note : LAPACK
NAMEzgtsvx.f
SYNOPSIS
Functions/Subroutinessubroutine zgtsvx (FACT, TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF, DU2, IPIV, B, LDB, X, LDX, RCOND, FERR, BERR, WORK, RWORK, INFO)
ZGTSVX computes the solution to system of linear equations A * X = B for GT matrices
Function/Subroutine Documentation
subroutine zgtsvx (character FACT, character TRANS, integer N, integer NRHS, complex*16, dimension( * ) DL, complex*16, dimension( * ) D, complex*16, dimension( * ) DU, complex*16, dimension( * ) DLF, complex*16, dimension( * ) DF, complex*16, dimension( * ) DUF, complex*16, dimension( * ) DU2, integer, dimension( * ) IPIV, complex*16, dimension( ldb, * ) B, integer LDB, complex*16, dimension( ldx, * ) X, integer LDX, double precision RCOND, double precision, dimension( * ) FERR, double precision, dimension( * ) BERR, complex*16, dimension( * ) WORK, double precision, dimension( * ) RWORK, integer INFO) ZGTSVX computes the solution to system of linear equations A * X = B for GT matrices Purpose: ZGTSVX uses the LU factorization to compute the solution to a complex
system of linear equations A * X = B, A**T * X = B, or A**H * X = B,
where A is a tridiagonal matrix of order N and X and B are N-by-NRHS
matrices.
Error bounds on the solution and a condition estimate are also
provided.Description: The following steps are performed:
1. If FACT = 'N', the LU decomposition is used to factor the matrix A
as A = L * U, where L is a product of permutation and unit lower
bidiagonal matrices and U is upper triangular with nonzeros in
only the main diagonal and first two superdiagonals.
2. If some U(i,i)=0, so that U is exactly singular, 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.Parameters: FACT FACT is CHARACTER*1
Specifies whether or not the factored form of A has been
supplied on entry.
= 'F': DLF, DF, DUF, DU2, and IPIV contain the factored form
of A; DL, D, DU, DLF, DF, DUF, DU2 and IPIV will not
be modified.
= 'N': The matrix will be copied to DLF, DF, and DUF
and factored.
TRANS TRANS is 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)
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 matrix B. NRHS >= 0.
DL DL is COMPLEX*16 array, dimension (N-1)
The (n-1) subdiagonal elements of A.
D D is COMPLEX*16 array, dimension (N)
The n diagonal elements of A.
DU DU is COMPLEX*16 array, dimension (N-1)
The (n-1) superdiagonal elements of A.
DLF DLF is COMPLEX*16 array, dimension (N-1)
If FACT = 'F', then DLF is an input argument and on entry
contains the (n-1) multipliers that define the matrix L from
the LU factorization of A as computed by ZGTTRF.
If FACT = 'N', then DLF is an output argument and on exit
contains the (n-1) multipliers that define the matrix L from
the LU factorization of A.
DF DF is COMPLEX*16 array, dimension (N)
If FACT = 'F', then DF is an input argument and on entry
contains the n diagonal elements of the upper triangular
matrix U from the LU factorization of A.
If FACT = 'N', then DF is an output argument and on exit
contains the n diagonal elements of the upper triangular
matrix U from the LU factorization of A.
DUF DUF is COMPLEX*16 array, dimension (N-1)
If FACT = 'F', then DUF is an input argument and on entry
contains the (n-1) elements of the first superdiagonal of U.
If FACT = 'N', then DUF is an output argument and on exit
contains the (n-1) elements of the first superdiagonal of U.
DU2 DU2 is COMPLEX*16 array, dimension (N-2)
If FACT = 'F', then DU2 is an input argument and on entry
contains the (n-2) elements of the second superdiagonal of
U.
If FACT = 'N', then DU2 is an output argument and on exit
contains the (n-2) elements of the second superdiagonal of
U.
IPIV IPIV is INTEGER array, dimension (N)
If FACT = 'F', then IPIV is an input argument and on entry
contains the pivot indices from the LU factorization of A as
computed by ZGTTRF.
If FACT = 'N', then IPIV is an output argument and on exit
contains the pivot indices from the LU factorization of A;
row i of the matrix was interchanged with row IPIV(i).
IPIV(i) will always be either i or i+1; IPIV(i) = i indicates
a row interchange was not required.
B B is COMPLEX*16 array, dimension (LDB,NRHS)
The N-by-NRHS 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 N-by-NRHS solution matrix X.
LDX LDX is INTEGER
The leading dimension of the array X. LDX >= max(1,N).
RCOND RCOND is DOUBLE PRECISION
The estimate of 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 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 = -i, the i-th argument had an illegal value
> 0: if INFO = i, and i is
<= N: U(i,i) is exactly zero. The factorization
has not been completed unless i = N, but the
factor U is exactly singular, so the solution
and error bounds could not be 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.Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: December 2016 Definition at line 296 of file zgtsvx.f.
AuthorGenerated automatically by Doxygen for LAPACK from the source code. 0
Johanes Gumabo
Data Size : 27,491 byte
man-zgtsvx.3Build : 2024-12-29, 07:25 :
Visitor Screen : x
Visitor Counter ( page / site ) : 3 / 255,709
Visitor ID : :
Visitor IP : 3.145.54.210 :
Visitor Provider : AMAZON-02 :
Provider Position ( lat x lon ) : 39.962500 x -83.006100 : x
Provider Accuracy Radius ( km ) : 1000 :
Provider City : Columbus :
Provider Province : Ohio , : ,
Provider Country : United States :
Provider Continent : North America :
Visitor Recorder : Version :
Visitor Recorder : Library :
Online Linux Manual Page : Version : Online Linux Manual Page - Fedora.40 - march=x86-64 - mtune=generic - 24.12.29
Online Linux Manual Page : Library : lib_c - 24.10.03 - march=x86-64 - mtune=generic - Fedora.40
Online Linux Manual Page : Library : lib_m - 24.10.03 - march=x86-64 - mtune=generic - Fedora.40
Data Base : Version : Online Linux Manual Page Database - 24.04.13 - march=x86-64 - mtune=generic - fedora-38
Data Base : Library : lib_c - 23.02.07 - march=x86-64 - mtune=generic - fedora.36
Very long time ago, I have the best tutor, Wenzel Svojanovsky . If someone knows the email address of Wenzel Svojanovsky , please send an email to johanes_gumabo@yahoo.co.id .
If error, please print screen and send to johanes_gumabo@yahoo.co.id
Under development. Support me via PayPal.