f07tj computes the inverse of a real triangular matrix.
- Type: System..::..StringOn entry: specifies whether is upper or lower triangular.
Constraint: or .
- is upper triangular.
- is lower triangular.
- Type: System..::..StringOn entry: indicates whether is a nonunit or unit triangular matrix.
Constraint: or .
- is a nonunit triangular matrix.
- is a unit triangular matrix; the diagonal elements are not referenced and are assumed to be .
- Type: System..::..Int32On entry: , the order of the matrix .Constraint: .
- Type: array<System..::..Double,2>[,](,)[,][,]An array of size [dim1, dim2]Note: dim1 must satisfy the constraint:Note: the second dimension of the array a must be at least .On entry: the by triangular matrix .
On exit: is overwritten by , using the same storage format as described above.
- If , is upper triangular and the elements of the array below the diagonal are not referenced.
- If , is lower triangular and the elements of the array above the diagonal are not referenced.
- If , the diagonal elements of are assumed to be , and are not referenced.
f07tj forms the inverse of a real triangular matrix . Note that the inverse of an upper (lower) triangular matrix is also upper (lower) triangular.
Du Croz J J and Higham N J (1992) Stability of methods for matrix inversion IMA J. Numer. Anal. 12 1–19
Some error messages may refer to parameters that are dropped from this interface (LDA) In these cases, an error in another parameter has usually caused an incorrect value to be inferred.
- If , argument had an illegal value. An explanatory message is output, and execution of the program is terminated.
Element of the diagonal is exactly zero. is singular its inverse cannot be computed.
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 method is (F07TWF not in this release).
This example computes the inverse of the matrix , where