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+ SUBROUTINE ZUNGHR( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
+*
+* -- LAPACK routine (version 3.1) --
+* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
+* November 2006
+*
+* .. Scalar Arguments ..
+ INTEGER IHI, ILO, INFO, LDA, LWORK, N
+* ..
+* .. Array Arguments ..
+ COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
+* ..
+*
+* Purpose
+* =======
+*
+* ZUNGHR generates a complex unitary matrix Q which is defined as the
+* product of IHI-ILO elementary reflectors of order N, as returned by
+* ZGEHRD:
+*
+* Q = H(ilo) H(ilo+1) . . . H(ihi-1).
+*
+* Arguments
+* =========
+*
+* N (input) INTEGER
+* The order of the matrix Q. N >= 0.
+*
+* ILO (input) INTEGER
+* IHI (input) INTEGER
+* ILO and IHI must have the same values as in the previous call
+* of ZGEHRD. 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.
+*
+* A (input/output) COMPLEX*16 array, dimension (LDA,N)
+* On entry, the vectors which define the elementary reflectors,
+* as returned by ZGEHRD.
+* On exit, the N-by-N unitary matrix Q.
+*
+* LDA (input) INTEGER
+* The leading dimension of the array A. LDA >= max(1,N).
+*
+* TAU (input) COMPLEX*16 array, dimension (N-1)
+* TAU(i) must contain the scalar factor of the elementary
+* reflector H(i), as returned by ZGEHRD.
+*
+* WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
+* On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
+*
+* 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.
+*
+* INFO (output) INTEGER
+* = 0: successful exit
+* < 0: if INFO = -i, the i-th argument had an illegal value
+*
+* =====================================================================
+*
+* .. Parameters ..
+ COMPLEX*16 ZERO, ONE
+ PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ),
+ $ ONE = ( 1.0D+0, 0.0D+0 ) )
+* ..
+* .. Local Scalars ..
+ LOGICAL LQUERY
+ INTEGER I, IINFO, J, LWKOPT, NB, NH
+* ..
+* .. External Subroutines ..
+ EXTERNAL XERBLA, ZUNGQR
+* ..
+* .. 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, 'ZUNGQR', ' ', NH, NH, NH, -1 )
+ LWKOPT = MAX( 1, NH )*NB
+ WORK( 1 ) = LWKOPT
+ END IF
+*
+ IF( INFO.NE.0 ) THEN
+ CALL XERBLA( 'ZUNGHR', -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 ZUNGQR( NH, NH, NH, A( ILO+1, ILO+1 ), LDA, TAU( ILO ),
+ $ WORK, LWORK, IINFO )
+ END IF
+ WORK( 1 ) = LWKOPT
+ RETURN
+*
+* End of ZUNGHR
+*
+ END