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LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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| subroutine sptsvx | ( | character | fact, |
| integer | n, | ||
| integer | nrhs, | ||
| real, dimension( * ) | d, | ||
| real, dimension( * ) | e, | ||
| real, dimension( * ) | df, | ||
| real, dimension( * ) | ef, | ||
| real, dimension( ldb, * ) | b, | ||
| integer | ldb, | ||
| real, dimension( ldx, * ) | x, | ||
| integer | ldx, | ||
| real | rcond, | ||
| real, dimension( * ) | ferr, | ||
| real, dimension( * ) | berr, | ||
| real, dimension( * ) | work, | ||
| integer | info | ||
| ) |
SPTSVX computes the solution to system of linear equations A * X = B for PT matrices
Download SPTSVX + dependencies [TGZ] [ZIP] [TXT]
SPTSVX uses the factorization A = L*D*L**T to compute the solution to a real system of linear equations A*X = B, where A is an N-by-N symmetric positive definite tridiagonal matrix and X and B are N-by-NRHS 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**T, where L
is a unit lower bidiagonal matrix and D is diagonal. The
factorization can also be regarded as having the form
A = U**T*D*U.
2. If the leading principal minor of order i is not positive,
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. | [in] | FACT | FACT is CHARACTER*1
Specifies whether or not the factored form of A has been
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. |
| [in] | N | N is INTEGER
The order of the matrix A. N >= 0. |
| [in] | NRHS | NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices B and X. NRHS >= 0. |
| [in] | D | D is REAL array, dimension (N)
The n diagonal elements of the tridiagonal matrix A. |
| [in] | E | E is REAL array, dimension (N-1)
The (n-1) subdiagonal elements of the tridiagonal matrix A. |
| [in,out] | DF | DF is REAL 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**T 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**T factorization of A. |
| [in,out] | EF | EF is REAL array, dimension (N-1)
If FACT = 'F', then EF is an input argument and on entry
contains the (n-1) subdiagonal elements of the unit
bidiagonal factor L from the L*D*L**T factorization of A.
If FACT = 'N', then EF is an output argument and on exit
contains the (n-1) subdiagonal elements of the unit
bidiagonal factor L from the L*D*L**T factorization of A. |
| [in] | B | B is REAL array, dimension (LDB,NRHS)
The N-by-NRHS right hand side matrix B. |
| [in] | LDB | LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N). |
| [out] | X | X is REAL array, dimension (LDX,NRHS)
If INFO = 0 of INFO = N+1, the N-by-NRHS solution matrix X. |
| [in] | LDX | LDX is INTEGER
The leading dimension of the array X. LDX >= max(1,N). |
| [out] | RCOND | RCOND is REAL
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. |
| [out] | FERR | FERR is 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). |
| [out] | BERR | BERR is 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). |
| [out] | WORK | WORK is REAL array, dimension (2*N) |
| [out] | 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: the leading principal minor of order i of A
is not positive, 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. |
Definition at line 226 of file sptsvx.f.
1.9.7