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DOPGTR(l)) DOPGTR(l)NAMEDOPGTR - generate a real orthogonal matrix Q which is defined as the product of n-1 ele- mentary reflectors H(i) of order n, as returned by DSPTRD using packed storageSYNOPSISSUBROUTINE DOPGTR( UPLO, N, AP, TAU, Q, LDQ, WORK, INFO ) CHARACTER UPLO INTEGER INFO, LDQ, N DOUBLE PRECISION AP( * ), Q( LDQ, * ), TAU( * ), WORK( * )PURPOSEDOPGTR generates a real orthogonal matrix Q which is defined as the product of n-1 elemen- tary reflectors H(i) of order n, as returned by DSPTRD using packed storage: if UPLO = 'U', Q = H(n-1) . . . H(2) H(1), if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).ARGUMENTSUPLO (input) CHARACTER*1 = 'U': Upper triangular packed storage used in previous call to DSPTRD; = 'L': Lower triangular packed storage used in previous call to DSPTRD. N (input) INTEGER The order of the matrix Q. N >= 0. AP (input) DOUBLE PRECISION array, dimension (N*(N+1)/2) The vectors which define the elementary reflectors, as returned by DSPTRD. TAU (input) DOUBLE PRECISION array, dimension (N-1) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by DSPTRD. Q (output) DOUBLE PRECISION array, dimension (LDQ,N) The N-by-N orthogonal matrix Q. LDQ (input) INTEGER The leading dimension of the array Q. LDQ >= max(1,N). WORK (workspace) DOUBLE PRECISION array, dimension (N-1) INFO (output) INTEGER = 0: successful exit < 0: if INFO =, the i-th argument had an illegal value-iLAPACK version 3.015 June 2000 DOPGTR(l)

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