TRSNA estimates reciprocal condition numbers for specified eigenvalues.
Purpose:
TRSNA estimates reciprocal condition numbers for specified eigenvalues and/or right eigenvectors of a real upper quasi-triangular matrix T (or of any matrix Q*T*Q**T with Q orthogonal). T must be in Schur canonical form (as returned by SHSEQR), that is, block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each 2-by-2 diagonal block has its diagonal elements equal and its off-diagonal elements of opposite sign.
- Parameters:
JOB – [in]
JOB is CHARACTER*1
Specifies whether condition numbers are required for eigenvalues (S) or eigenvectors (SEP):
= ‘E’: for eigenvalues only (S);
= ‘V’: for eigenvectors only (SEP);
= ‘B’: for both eigenvalues and eigenvectors (S and SEP).HOWMNY – [in]
HOWMNY is CHARACTER*1
= ‘A’: compute condition numbers for all eigenpairs;
= ‘S’: compute condition numbers for selected eigenpairs specified by the array SELECT.SELECT – [in]
SELECT is LOGICAL array, dimension (N)
If HOWMNY = ‘S’, SELECT specifies the eigenpairs for which condition numbers are required. To select condition numbers for the eigenpair corresponding to a real eigenvalue w(j), SELECT(j) must be set to .TRUE.. To select condition numbers corresponding to a complex conjugate pair of eigenvalues w(j) and w(j+1), either SELECT(j) or SELECT(j+1) or both, must be set to .TRUE..
If HOWMNY = ‘A’, SELECT is not referenced.N – [in]
N is INTEGER
The order of the matrix T. N >= 0.
T – [in]
T is REAL array, dimension (LDT,N)
The upper quasi-triangular matrix T, in Schur canonical form.
LDT – [in]
LDT is INTEGER
The leading dimension of the array T. LDT >= fla_max(1,N).
VL – [in]
VL is REAL array, dimension (LDVL,M)
If JOB = ‘E’ or ‘B’, VL must contain left eigenvectors of T (or of any Q*T*Q**T with Q orthogonal), corresponding to the eigenpairs specified by HOWMNY and SELECT. The eigenvectors must be stored in consecutive columns of VL, as returned by SHSEIN or STREVC.
If JOB = ‘V’, VL is not referenced.LDVL – [in]
LDVL is INTEGER
The leading dimension of the array VL. LDVL >= 1; and if JOB = ‘E’ or ‘B’, LDVL >= N.
VR – [in]
VR is REAL array, dimension (LDVR,M)
If JOB = ‘E’ or ‘B’, VR must contain right eigenvectors of T (or of any Q*T*Q**T with Q orthogonal), corresponding to the eigenpairs specified by HOWMNY and SELECT. The eigenvectors must be stored in consecutive columns of VR, as returned by SHSEIN or STREVC.
If JOB = ‘V’, VR is not referenced.LDVR – [in]
LDVR is INTEGER
The leading dimension of the array VR.
LDVR >= 1; and if JOB = ‘E’ or ‘B’, LDVR >= N.S – [out]
S is REAL array, dimension (MM)
If JOB = ‘E’ or ‘B’, the reciprocal condition numbers of the selected eigenvalues, stored in consecutive elements of the array. For a complex conjugate pair of eigenvalues two consecutive elements of S are set to the same value. Thus S(j), SEP(j), and the j-th columns of VL and VR all correspond to the same eigenpair (but not in general the j-th eigenpair, unless all eigenpairs are selected).
If JOB = ‘V’, S is not referenced.SEP – [out]
SEP is REAL array, dimension (MM)
If JOB = ‘V’ or ‘B’, the estimated reciprocal condition numbers of the selected eigenvectors, stored in consecutive elements of the array. For a complex eigenvector two consecutive elements of SEP are set to the same value. If the eigenvalues cannot be reordered to compute SEP(j), SEP(j) is set to 0; this can only occur when the true value would be very small anyway.
If JOB = ‘E’, SEP is not referenced.MM – [in]
MM is INTEGER
The number of elements in the arrays S (if JOB = ‘E’ or ‘B’) and/or SEP (if JOB = ‘V’ or ‘B’). MM >= M.
M – [out]
M is INTEGER
The number of elements of the arrays S and/or SEP actually used to store the estimated condition numbers. If HOWMNY = ‘A’, M is set to N.
WORK – [out]
WORK is REAL array, dimension (LDWORK,N+6)
If JOB = ‘E’, WORK is not referenced.
LDWORK – [in]
LDWORK is INTEGER
The leading dimension of the array WORK. LDWORK >= 1; and if JOB = ‘V’ or ‘B’, LDWORK >= N.
IWORK – [out]
IWORK is INTEGER array, dimension (2*(N-1))
If JOB = ‘E’, IWORK is not referenced.
INFO – [out]
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value