NAG Library Routine Document
computes the solution to a real system of linear equations
symmetric positive definite tridiagonal matrix, and
|Integer, Intent (In)||:: ||n, nrhs, ldb|
|Integer, Intent (Out)||:: ||info|
|Real (Kind=nag_wp), Intent (Inout)||:: ||d(*), e(*), b(ldb,*)|C Header Interface
f07jaf_ (const Integer *n, const Integer *nrhs, double d, double e, double b, const Integer *ldb, Integer *info)|
The routine may be called by its
f07jaf (dptsv) factors as . The factored form of is then used to solve the system of equations.
Anderson E, Bai Z, Bischof C, Blackford S, Demmel J, Dongarra J J, Du Croz J J, Greenbaum A, Hammarling S, McKenney A and Sorensen D (1999) LAPACK Users' Guide
(3rd Edition) SIAM, Philadelphia http://www.netlib.org/lapack/lug
Golub G H and Van Loan C F (1996) Matrix Computations (3rd Edition) Johns Hopkins University Press, Baltimore
- 1: – IntegerInput
On entry: , the order of the matrix .
- 2: – IntegerInput
On entry: , the number of right-hand sides, i.e., the number of columns of the matrix .
- 3: – Real (Kind=nag_wp) arrayInput/Output
the dimension of the array d
must be at least
On entry: the diagonal elements of the tridiagonal matrix .
On exit: the diagonal elements of the diagonal matrix from the factorization .
- 4: – Real (Kind=nag_wp) arrayInput/Output
the dimension of the array e
must be at least
On entry: the subdiagonal elements of the tridiagonal matrix .
subdiagonal elements of the unit bidiagonal factor
can also be regarded as the superdiagonal of the unit bidiagonal factor
- 5: – Real (Kind=nag_wp) arrayInput/Output
the second dimension of the array b
must be at least
On entry: the by right-hand side matrix .
On exit: if , the by solution matrix .
- 6: – IntegerInput
: the first dimension of the array b
as declared in the (sub)program from which f07jaf (dptsv)
- 7: – IntegerOutput
unless the routine detects an error (see Section 6
Error Indicators and Warnings
If , argument had an illegal value. An explanatory message is output, and execution of the program is terminated.
The leading minor of order is not positive definite,
and the solution has not been computed.
The factorization has not been completed unless .
The computed solution for a single right-hand side,
, satisfies an equation of the form
is the machine precision
. An approximate error bound for the computed solution is given by
, the condition number of
with respect to the solution of the linear equations. See Section 4.4 of Anderson et al. (1999)
for further details.
is a comprehensive LAPACK driver that returns forward and backward error bounds and an estimate of the condition number. Alternatively, f04bgf
and returns a forward error bound and condition estimate. f04bgf
calls f07jaf (dptsv)
to solve the equations.
Parallelism and Performance
f07jaf (dptsv) makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.
Please consult the X06 Chapter Introduction
for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the Users' Note
for your implementation for any additional implementation-specific information.
The number of floating-point operations required for the factorization of is proportional to , and the number of floating-point operations required for the solution of the equations is proportional to , where is the number of right-hand sides.
The complex analogue of this routine is f07jnf (zptsv)
This example solves the equations
is the symmetric positive definite tridiagonal matrix
Details of the factorization of are also output.
Program Text (f07jafe.f90)
Program Data (f07jafe.d)
Program Results (f07jafe.r)