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C DORGHR    SOURCE    BP208322  20/09/18    21:16:08     10718          *> \brief \b DORGHR**  =========== DOCUMENTATION ===========** Online html documentation available at*            http://www.netlib.org/lapack/explore-html/**> \htmlonly*> Download DORGHR + dependencies*> &lt;a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dorghr.f">*> [TGZ]&lt;/a>*> &lt;a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dorghr.f">*> [ZIP]&lt;/a>*> &lt;a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorghr.f">*> [TXT]&lt;/a>*> \endhtmlonly**  Definition:*  ===========**       SUBROUTINE DORGHR( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )**       .. Scalar Arguments ..*       INTEGER            IHI, ILO, INFO, LDA, LWORK, N*       ..*       .. Array Arguments ..*       REAL*8   A( LDA, * ), TAU( * ), WORK( * )*       ..***> \par Purpose:*  =============*>*> \verbatim*>*> 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).*> \endverbatim**  Arguments:*  ==========**> \param[in] N*> \verbatim*>          N is INTEGER*>          The order of the matrix Q. N >= 0.*> \endverbatim*>*> \param[in] ILO*> \verbatim*>          ILO is INTEGER*> \endverbatim*>*> \param[in] IHI*> \verbatim*>          IHI is 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 &lt;= ILO &lt;= IHI &lt;= N, if N > 0; ILO=1 and IHI=0, if N=0.*> \endverbatim*>*> \param[in,out] A*> \verbatim*>          A is REAL*8 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.*> \endverbatim*>*> \param[in] LDA*> \verbatim*>          LDA is INTEGER*>          The leading dimension of the array A. LDA >= max(1,N).*> \endverbatim*>*> \param[in] TAU*> \verbatim*>          TAU is REAL*8 array, dimension (N-1)*>          TAU(i) must contain the scalar factor of the elementary*>          reflector H(i), as returned by DGEHRD.*> \endverbatim*>*> \param[out] WORK*> \verbatim*>          WORK is REAL*8 array, dimension (MAX(1,LWORK))*>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.*> \endverbatim*>*> \param[in] LWORK*> \verbatim*>          LWORK is 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.*> \endverbatim*>*> \param[out] INFO*> \verbatim*>          INFO is INTEGER*>          = 0:  successful exit*>          &lt; 0:  if INFO = -i, the i-th argument had an illegal value*> \endverbatim**  Authors:*  ========**> \author Univ. of Tennessee*> \author Univ. of California Berkeley*> \author Univ. of Colorado Denver*> \author NAG Ltd.**> \date December 2016**> \ingroup doubleOTHERcomputational**  =====================================================================      SUBROUTINE DORGHR( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )**  -- LAPACK computational routine (version 3.7.0) --*  -- LAPACK is a software package provided by Univ. of Tennessee,    --*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--*     December 2016       IMPLICIT INTEGER(I-N)      IMPLICIT REAL*8(A-H,O-Z)**     .. Scalar Arguments ..      INTEGER            IHI, ILO, INFO, LDA, LWORK, N*     ..*     .. Array Arguments ..      REAL*8   A( LDA, * ), TAU( * ), WORK( * )*     ..**  =====================================================================**     .. Parameters ..      REAL*8   ZERO, ONE      PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )*     ..*     .. Local Scalars ..      LOGICAL            LQUERY      INTEGER            I, IINFO, J, LWKOPT, NB, NH*     ..*     .. External Subroutines ..*      EXTERNAL           DORGQR, XERBLA*     ..*     .. External Functions ..      INTEGER            ILAENV*      EXTERNAL           ILAENV*     ..*     .. Intrinsic Functions ..*      INTRINSIC          MAX, MIN*     ..*     .. Executable Statements ..**     Test the input arguments*      INFO = 0      NH = IHI - ILO      LQUERY = ( LWORK.EQ.-1 )      IF( N.LT.0 ) THEN         INFO = -1      ELSE IF( ILO.LT.1 .OR. ILO.GT.MAX( 1, N ) ) THEN         INFO = -2      ELSE IF( IHI.LT.MIN( ILO, N ) .OR. IHI.GT.N ) THEN         INFO = -3      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN         INFO = -5      ELSE IF( LWORK.LT.MAX( 1, NH ) .AND. .NOT.LQUERY ) THEN         INFO = -8      END IF*      IF( INFO.EQ.0 ) THEN         NB = ILAENV( 1, 'DORGQR', ' ', NH, NH, NH, -1 )         LWKOPT = MAX( 1, NH )*NB         WORK( 1 ) = LWKOPT      END IF*      IF( INFO.NE.0 ) THEN         CALL XERBLA( 'DORGHR', -INFO )         RETURN      ELSE IF( LQUERY ) THEN         RETURN      END IF**     Quick return if possible*      IF( N.EQ.0 ) THEN         WORK( 1 ) = 1         RETURN      END IF**     Shift the vectors which define the elementary reflectors one*     column to the right, and set the first ilo and the last n-ihi*     rows and columns to those of the unit matrix*      DO 40 J = IHI, ILO + 1, -1         DO 10 I = 1, J - 1            A( I, J ) = ZERO   10    CONTINUE         DO 20 I = J + 1, IHI            A( I, J ) = A( I, J-1 )   20    CONTINUE         DO 30 I = IHI + 1, N            A( I, J ) = ZERO   30    CONTINUE   40 CONTINUE      DO 60 J = 1, ILO         DO 50 I = 1, N            A( I, J ) = ZERO   50    CONTINUE         A( J, J ) = ONE   60 CONTINUE      DO 80 J = IHI + 1, N         DO 70 I = 1, N            A( I, J ) = ZERO   70    CONTINUE         A( J, J ) = ONE   80 CONTINUE*      IF( NH.GT.0 ) THEN**        Generate Q(ilo+1:ihi,ilo+1:ihi)*         CALL DORGQR( NH, NH, NH, A( ILO+1, ILO+1 ), LDA, TAU( ILO ),     \$                WORK, LWORK, IINFO )      END IF      WORK( 1 ) = LWKOPT      RETURN**     End of DORGHR*      END

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