The routine may be called by the names f08fff, nagf_lapackeig_dorgtr or its LAPACK name dorgtr.
f08fff is intended to be used after a call to f08fef, which reduces a real symmetric matrix to symmetric tridiagonal form by an orthogonal similarity transformation: . f08fef represents the orthogonal matrix as a product of elementary reflectors.
This routine may be used to generate explicitly as a square matrix.
Golub G H and Van Loan C F (1996) Matrix Computations (3rd Edition) Johns Hopkins University Press, Baltimore
1: – Character(1)Input
On entry: this must be the same argument uplo as supplied to f08fef.
2: – IntegerInput
On entry: , the order of the matrix .
3: – Real (Kind=nag_wp) arrayInput/Output
Note: the second dimension of the array a
must be at least
On entry: details of the vectors which define the elementary reflectors, as returned by f08fef.
On exit: the orthogonal matrix .
4: – IntegerInput
On entry: the first dimension of the array a as declared in the (sub)program from which f08fff is called.
5: – Real (Kind=nag_wp) arrayInput
Note: the dimension of the array tau
must be at least
On entry: further details of the elementary reflectors, as returned by f08fef.
6: – Real (Kind=nag_wp) arrayWorkspace
On exit: if , contains the minimum value of lwork required for optimal performance.
7: – IntegerInput
On entry: the dimension of the array work as declared in the (sub)program from which f08fff is called.
If , a workspace query is assumed; the routine only calculates the optimal size of the work array, returns this value as the first entry of the work array, and no error message related to lwork is issued.
for optimal performance, , where is the optimal block size.
8: – IntegerOutput
On exit: unless the routine detects an error (see Section 6).
6Error Indicators and Warnings
If , argument had an illegal value. An explanatory message is output, and execution of the program is terminated.
The computed matrix differs from an exactly orthogonal matrix by a matrix such that
where is the machine precision.
8Parallelism and Performance
Background information to multithreading can be found in the Multithreading documentation.
f08fff is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
f08fff 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 total number of floating-point operations is approximately .