.TH DORGHR 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) " .SH NAME DORGHR - a real orthogonal matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by DGEHRD .SH SYNOPSIS .TP 19 SUBROUTINE DORGHR( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO ) .TP 19 .ti +4 INTEGER IHI, ILO, INFO, LDA, LWORK, N .TP 19 .ti +4 DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) .SH PURPOSE DORGHR generates a real orthogonal matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by DGEHRD: Q = H(ilo) H(ilo+1) . . . H(ihi-1). .br .SH ARGUMENTS .TP 8 N (input) INTEGER The order of the matrix Q. N >= 0. .TP 8 ILO (input) INTEGER IHI (input) INTEGER ILO and IHI must have the same values as in the previous call of DGEHRD. Q is equal to the unit matrix except in the submatrix Q(ilo+1:ihi,ilo+1:ihi). 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0. .TP 8 A (input/output) DOUBLE PRECISION array, dimension (LDA,N) On entry, the vectors which define the elementary reflectors, as returned by DGEHRD. On exit, the N-by-N orthogonal matrix Q. .TP 8 LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,N). .TP 8 TAU (input) DOUBLE PRECISION array, dimension (N-1) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by DGEHRD. .TP 8 WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. .TP 8 LWORK (input) INTEGER The dimension of the array WORK. LWORK >= IHI-ILO. For optimum performance LWORK >= (IHI-ILO)*NB, where NB is the optimal blocksize. If LWORK = -1, then 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 by XERBLA. .TP 8 INFO (output) INTEGER = 0: successful exit .br < 0: if INFO = -i, the i-th argument had an illegal value