Note: before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.
The routine may be called by its
LAPACK
name dtrtri.
3 Description
F07TJF (DTRTRI) forms the inverse of a real triangular matrix A. 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
5 Parameters
1: UPLO – CHARACTER(1)Input
On entry: specifies whether A is upper or lower triangular.
UPLO='U'
A is upper triangular.
UPLO='L'
A is lower triangular.
Constraint:
UPLO='U' or 'L'.
2: DIAG – CHARACTER(1)Input
On entry: indicates whether A is a nonunit or unit triangular matrix.
DIAG='N'
A is a nonunit triangular matrix.
DIAG='U'
A is a unit triangular matrix; the diagonal elements are not referenced and are assumed to be 1.
Constraint:
DIAG='N' or 'U'.
3: N – INTEGERInput
On entry: n, the order of the matrix A.
Constraint:
N≥0.
4: A(LDA,*) – REAL (KIND=nag_wp) arrayInput/Output
Note: the second dimension of the array A
must be at least
max1,N.
On entry: the n by n triangular matrix A.
If UPLO='U', A is upper triangular and the elements of the array below the diagonal are not referenced.
If UPLO='L', A is lower triangular and the elements of the array above the diagonal are not referenced.
If DIAG='U', the diagonal elements of A are assumed to be 1, and are not referenced.
On exit: A is overwritten by A-1, using the same storage format as described above.
5: LDA – INTEGERInput
On entry: the first dimension of the array A as declared in the (sub)program from which F07TJF (DTRTRI) is called.
Constraint:
LDA≥max1,N.
6: INFO – INTEGEROutput
On exit: INFO=0 unless the routine detects an error (see Section 6).
6 Error Indicators and Warnings
Errors or warnings detected by the routine:
INFO<0
If INFO=-i, the ith parameter had an illegal value. An explanatory message is output, and execution of the program is terminated.
INFO>0
If INFO=i, ai,i is exactly zero; A is singular and its inverse cannot be computed.
7 Accuracy
The computed inverse X satisfies
XA-I≤cnεXA,
where cn is a modest linear function of n, and ε is the machine precision.
Note that a similar bound for AX-I cannot be guaranteed, although it is almost always satisfied.
The computed inverse satisfies the forward error bound