Reorders the Schur factorization of a matrix and (optionally) computes the reciprocal condition numbers and invariant subspace for the selected cluster of eigenvalues.
p?trsenreorders the real Schur factorization of a real matrix
T, so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper quasi-triangular matrix
T, and the leading columns of
Qform an orthonormal basis of the corresponding right invariant subspace. The reordering is performed by
routinecomputes the reciprocal condition numbers of the cluster of eigenvalues and/or the invariant subspace.
Tmust be in Schur form (as returned by
p?lahqr), that is, block upper triangular with 1-by-1 and 2-by-2 diagonal blocks.
Intel's compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.
Notice revision #20110804
This notice covers the following instruction sets: SSE2, SSE4.2, AVX2, AVX-512.
- (global )CHARACTER*1Specifies whether condition numbers are required for the cluster of eigenvalues (s) or the invariant subspace (sep):= 'N': no condition numbers are required;= 'E': only the condition number for the cluster of eigenvalues is computed (s);= 'V': only the condition number for the invariant subspace is computed (sep);= 'B': condition numbers for both the cluster and the invariant subspace are computed (sandsep).
- (global )CHARACTER*1= 'V': update the matrixqof Schur vectors;= 'N': do not updateq.
- (global )LOGICALarray of sizenselectspecifies the eigenvalues in the selected cluster. To select a real eigenvaluew(j),select(must be set toj).TRUE.. To select a complex conjugate pair of eigenvaluesw(j) andw(j+1), corresponding to a 2-by-2 diagonal block, eitherselect(orj)select(or both must be set toj+1)