NAG Library Routine Document
F07WKF (DTFTRI)
1 Purpose
F07WKF (DTFTRI) computes the inverse of a real triangular matrix, stored in Rectangular Full Packed (RFP) format.
The RFP storage format is described in
Section 3.3.3 in the F07 Chapter Introduction.
2 Specification
INTEGER |
N, INFO |
REAL (KIND=nag_wp) |
A(N*(N+1)/2) |
CHARACTER(1) |
TRANSR, UPLO, DIAG |
|
The routine may be called by its
LAPACK
name dtftri.
3 Description
F07WKF (DTFTRI) forms the inverse of a real triangular matrix , stored using RFP format. Note that the inverse of an upper (lower) triangular matrix is also upper (lower) triangular.
4 References
Du Croz J J and Higham N J (1992) Stability of methods for matrix inversion IMA J. Numer. Anal. 12 1–19
Gustavson F G, Waśniewski J, Dongarra J J and Langou J (2010) Rectangular full packed format for Cholesky's algorithm: factorization, solution, and inversion ACM Trans. Math. Software 37, 2
5 Parameters
- 1: TRANSR – CHARACTER(1)Input
On entry: specifies whether the RFP representation of
is normal or transposed.
- The matrix is stored in normal RFP format.
- The matrix is stored in transposed RFP format.
Constraint:
or .
- 2: UPLO – CHARACTER(1)Input
On entry: specifies whether
is upper or lower triangular.
- is upper triangular.
- is lower triangular.
Constraint:
or .
- 3: DIAG – CHARACTER(1)Input
On entry: indicates whether
is a nonunit or unit triangular matrix.
- is a nonunit triangular matrix.
- is a unit triangular matrix; the diagonal elements are not referenced and are assumed to be .
Constraint:
or .
- 4: N – INTEGERInput
On entry: , the order of the matrix .
Constraint:
.
- 5: A() – REAL (KIND=nag_wp) arrayInput/Output
On entry: the by triangular matrix , stored in RFP format.
On exit: is overwritten by , in the same storage format as .
- 6: INFO – INTEGEROutput
On exit:
unless the routine detects an error (see
Section 6).
6 Error Indicators and Warnings
Errors or warnings detected by the routine:
If , the th parameter had an illegal value. An explanatory message is output, and execution of the program is terminated.
If , is exactly zero; is singular and its inverse cannot be computed.
7 Accuracy
The computed inverse
satisfies
where
is a modest linear function of
, and
is the
machine precision.
Note that a similar bound for cannot be guaranteed, although it is almost always satisfied.
The computed inverse satisfies the forward error bound
See
Du Croz and Higham (1992).
The total number of floating point operations is approximately .
The complex analogue of this routine is
F07WXF (ZTFTRI).
9 Example
This example computes the inverse of the matrix
, where
and is stored using RFP format.
9.1 Program Text
Program Text (f07wkfe.f90)
9.2 Program Data
Program Data (f07wkfe.d)
9.3 Program Results
Program Results (f07wkfe.r)