Computes the QL factorization of a general m-by-n matrix.
The routine forms the
QLfactorization of a general
A(see Orthogonal Factorizations). No pivoting is performed.
The routine does not form the matrix
Qis represented as a product of min(
n) elementary reflectors. Routines are provided to work with
Qin this representation.
- The number of rows in the matrixINTEGER.A().m≥0
- The number of columns inINTEGER.A().n≥0
- REALforsgeqlfDOUBLE PRECISIONfordgeqlfCOMPLEXforcgeqlfDOUBLE COMPLEXforzgeqlf.Arrays:Arraya(contains the matrixlda,*)A.The second dimension ofamust be at least max(1,n).workis a workspace array, its dimensionmax(1,.lwork)
- The leading dimension ofINTEGER.a; at least max(1,m).
- The size of theINTEGER.workarray; at least max(1,n).If, then a workspace query is assumed; the routine only calculates the optimal size of thelwork= -1workarray, returns this value as the first entry of theworkarray, and no error message related tolworkis issued by xerbla.SeeApplication Notesfor the suggested value oflwork.
- Overwritten on exit by the factorization data as follows:if, the lower triangle of the subarraym≥na(m-n+1:m, 1:n) contains then-by-nlower triangular matrixL; if