Purpose
To generate orthogonal symplectic matrices U or V, defined as products of symplectic reflectors and Givens rotators U = diag( HU(1),HU(1) ) GU(1) diag( FU(1),FU(1) ) diag( HU(2),HU(2) ) GU(2) diag( FU(2),FU(2) ) .... diag( HU(n),HU(n) ) GU(n) diag( FU(n),FU(n) ), V = diag( HV(1),HV(1) ) GV(1) diag( FV(1),FV(1) ) diag( HV(2),HV(2) ) GV(2) diag( FV(2),FV(2) ) .... diag( HV(n-1),HV(n-1) ) GV(n-1) diag( FV(n-1),FV(n-1) ), as returned by the SLICOT Library routines MB04TS or MB04TB. The matrices U and V are returned in terms of their first N/2 rows: [ U1 U2 ] [ V1 V2 ] U = [ ], V = [ ]. [ -U2 U1 ] [ -V2 V1 ]Specification
SUBROUTINE MB04WR( JOB, TRANS, N, ILO, Q1, LDQ1, Q2, LDQ2, CS, $ TAU, DWORK, LDWORK, INFO ) C .. Scalar Arguments .. CHARACTER JOB, TRANS INTEGER ILO, INFO, LDQ1, LDQ2, LDWORK, N C .. Array Arguments .. DOUBLE PRECISION CS(*), DWORK(*), Q1(LDQ1,*), Q2(LDQ2,*), TAU(*)Arguments
Input/Output Parameters
JOB CHARACTER*1 Specifies whether the matrix U or the matrix V is required: = 'U': generate U; = 'V': generate V. TRANS CHARACTER*1 If JOB = 'U' then TRANS must have the same value as the argument TRANA in the previous call of MB04TS or MB04TB. If JOB = 'V' then TRANS must have the same value as the argument TRANB in the previous call of MB04TS or MB04TB. N (input) INTEGER The order of the matrices Q1 and Q2. N >= 0. ILO (input) INTEGER ILO must have the same value as in the previous call of MB04TS or MB04TB. U and V are equal to the unit matrix except in the submatrices U([ilo:n n+ilo:2*n], [ilo:n n+ilo:2*n]) and V([ilo+1:n n+ilo+1:2*n], [ilo+1:n n+ilo+1:2*n]), respectively. 1 <= ILO <= N, if N > 0; ILO = 1, if N = 0. Q1 (input/output) DOUBLE PRECISION array, dimension (LDQ1,N) On entry, if JOB = 'U' and TRANS = 'N' then the leading N-by-N part of this array must contain in its i-th column the vector which defines the elementary reflector FU(i). If JOB = 'U' and TRANS = 'T' or TRANS = 'C' then the leading N-by-N part of this array must contain in its i-th row the vector which defines the elementary reflector FU(i). If JOB = 'V' and TRANS = 'N' then the leading N-by-N part of this array must contain in its i-th row the vector which defines the elementary reflector FV(i). If JOB = 'V' and TRANS = 'T' or TRANS = 'C' then the leading N-by-N part of this array must contain in its i-th column the vector which defines the elementary reflector FV(i). On exit, if JOB = 'U' and TRANS = 'N' then the leading N-by-N part of this array contains the matrix U1. If JOB = 'U' and TRANS = 'T' or TRANS = 'C' then the leading N-by-N part of this array contains the matrix U1**T. If JOB = 'V' and TRANS = 'N' then the leading N-by-N part of this array contains the matrix V1**T. If JOB = 'V' and TRANS = 'T' or TRANS = 'C' then the leading N-by-N part of this array contains the matrix V1. LDQ1 INTEGER The leading dimension of the array Q1. LDQ1 >= MAX(1,N). Q2 (input/output) DOUBLE PRECISION array, dimension (LDQ2,N) On entry, if JOB = 'U' then the leading N-by-N part of this array must contain in its i-th column the vector which defines the elementary reflector HU(i). If JOB = 'V' then the leading N-by-N part of this array must contain in its i-th row the vector which defines the elementary reflector HV(i). On exit, if JOB = 'U' then the leading N-by-N part of this array contains the matrix U2. If JOB = 'V' then the leading N-by-N part of this array contains the matrix V2**T. LDQ2 INTEGER The leading dimension of the array Q2. LDQ2 >= MAX(1,N). CS (input) DOUBLE PRECISION array, dimension (2N) On entry, if JOB = 'U' then the first 2N elements of this array must contain the cosines and sines of the symplectic Givens rotators GU(i). If JOB = 'V' then the first 2N-2 elements of this array must contain the cosines and sines of the symplectic Givens rotators GV(i). TAU (input) DOUBLE PRECISION array, dimension (N) On entry, if JOB = 'U' then the first N elements of this array must contain the scalar factors of the elementary reflectors FU(i). If JOB = 'V' then the first N-1 elements of this array must contain the scalar factors of the elementary reflectors FV(i).Workspace
DWORK DOUBLE PRECISION array, dimension (LDWORK) On exit, if INFO = 0, DWORK(1) returns the optimal value of LDWORK. On exit, if INFO = -12, DWORK(1) returns the minimum value of LDWORK. LDWORK INTEGER The length of the array DWORK. LDWORK >= MAX(1,2*(N-ILO+1)).Error Indicator
INFO INTEGER = 0: successful exit; < 0: if INFO = -i, the i-th argument had an illegal value.References
[1] Benner, P., Mehrmann, V., and Xu, H. A numerically stable, structure preserving method for computing the eigenvalues of real Hamiltonian or symplectic pencils. Numer. Math., Vol 78 (3), pp. 329-358, 1998. [2] Kressner, D. Block algorithms for orthogonal symplectic factorizations. BIT, 43 (4), pp. 775-790, 2003.Further Comments
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