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 https://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 number of rows of the matrix .
2: – IntegerInput
On entry: , the number of columns of the matrix .
3: – IntegerInput
On entry: , the number of right-hand sides, i.e., the number of columns of the matrices and .
4: – Real (Kind=nag_wp) arrayInput/Output
Note: the second dimension of the array a
must be at least
On entry: the matrix .
On exit: a has been overwritten by details of its complete orthogonal factorization.
5: – IntegerInput
On entry: the first dimension of the array a as declared in the (sub)program from which f08baf is called.
6: – Real (Kind=nag_wp) arrayInput/Output
Note: the second dimension of the array b
must be at least
On entry: the right-hand side matrix .
On exit: the solution matrix .
7: – IntegerInput
On entry: the first dimension of the array b as declared in the (sub)program from which f08baf is called.
8: – Integer arrayInput/Output
Note: the dimension of the array jpvt
must be at least
On entry: if , the th column of is permuted to the front of , otherwise column is a free column.
On exit: if , the th column of was the th column of .
9: – Real (Kind=nag_wp)Input
On entry: used to determine the effective rank of , which is defined as the order of the largest leading triangular sub-matrix in the factorization of , whose estimated condition number is .
if the condition number of a is not known then (where is machine precision, see x02ajf) is a good choice. Negative values or values less than machine precision should be avoided since this will cause a to have an effective that could be larger than its actual rank, leading to meaningless results.
10: – IntegerOutput
On exit: the effective rank of , i.e., the order of the sub-matrix . This is the same as the order of the sub-matrix in the complete orthogonal factorization of .
11: – Real (Kind=nag_wp) arrayWorkspace
On exit: if , contains the minimum value of lwork required for optimal performance.
12: – IntegerInput
On entry: the dimension of the array work as declared in the (sub)program from which f08baf 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 and is the optimal block size.
13: – 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.
Background information to multithreading can be found in the Multithreading documentation.
f08baf is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
f08baf 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.