LAPACK 3.3.1
Linear Algebra PACKage

dorghr.f

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00001       SUBROUTINE DORGHR( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
00002 *
00003 *  -- LAPACK routine (version 3.2) --
00004 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00005 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00006 *     November 2006
00007 *
00008 *     .. Scalar Arguments ..
00009       INTEGER            IHI, ILO, INFO, LDA, LWORK, N
00010 *     ..
00011 *     .. Array Arguments ..
00012       DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
00013 *     ..
00014 *
00015 *  Purpose
00016 *  =======
00017 *
00018 *  DORGHR generates a real orthogonal matrix Q which is defined as the
00019 *  product of IHI-ILO elementary reflectors of order N, as returned by
00020 *  DGEHRD:
00021 *
00022 *  Q = H(ilo) H(ilo+1) . . . H(ihi-1).
00023 *
00024 *  Arguments
00025 *  =========
00026 *
00027 *  N       (input) INTEGER
00028 *          The order of the matrix Q. N >= 0.
00029 *
00030 *  ILO     (input) INTEGER
00031 *  IHI     (input) INTEGER
00032 *          ILO and IHI must have the same values as in the previous call
00033 *          of DGEHRD. Q is equal to the unit matrix except in the
00034 *          submatrix Q(ilo+1:ihi,ilo+1:ihi).
00035 *          1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
00036 *
00037 *  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
00038 *          On entry, the vectors which define the elementary reflectors,
00039 *          as returned by DGEHRD.
00040 *          On exit, the N-by-N orthogonal matrix Q.
00041 *
00042 *  LDA     (input) INTEGER
00043 *          The leading dimension of the array A. LDA >= max(1,N).
00044 *
00045 *  TAU     (input) DOUBLE PRECISION array, dimension (N-1)
00046 *          TAU(i) must contain the scalar factor of the elementary
00047 *          reflector H(i), as returned by DGEHRD.
00048 *
00049 *  WORK    (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
00050 *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
00051 *
00052 *  LWORK   (input) INTEGER
00053 *          The dimension of the array WORK. LWORK >= IHI-ILO.
00054 *          For optimum performance LWORK >= (IHI-ILO)*NB, where NB is
00055 *          the optimal blocksize.
00056 *
00057 *          If LWORK = -1, then a workspace query is assumed; the routine
00058 *          only calculates the optimal size of the WORK array, returns
00059 *          this value as the first entry of the WORK array, and no error
00060 *          message related to LWORK is issued by XERBLA.
00061 *
00062 *  INFO    (output) INTEGER
00063 *          = 0:  successful exit
00064 *          < 0:  if INFO = -i, the i-th argument had an illegal value
00065 *
00066 *  =====================================================================
00067 *
00068 *     .. Parameters ..
00069       DOUBLE PRECISION   ZERO, ONE
00070       PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
00071 *     ..
00072 *     .. Local Scalars ..
00073       LOGICAL            LQUERY
00074       INTEGER            I, IINFO, J, LWKOPT, NB, NH
00075 *     ..
00076 *     .. External Subroutines ..
00077       EXTERNAL           DORGQR, XERBLA
00078 *     ..
00079 *     .. External Functions ..
00080       INTEGER            ILAENV
00081       EXTERNAL           ILAENV
00082 *     ..
00083 *     .. Intrinsic Functions ..
00084       INTRINSIC          MAX, MIN
00085 *     ..
00086 *     .. Executable Statements ..
00087 *
00088 *     Test the input arguments
00089 *
00090       INFO = 0
00091       NH = IHI - ILO
00092       LQUERY = ( LWORK.EQ.-1 )
00093       IF( N.LT.0 ) THEN
00094          INFO = -1
00095       ELSE IF( ILO.LT.1 .OR. ILO.GT.MAX( 1, N ) ) THEN
00096          INFO = -2
00097       ELSE IF( IHI.LT.MIN( ILO, N ) .OR. IHI.GT.N ) THEN
00098          INFO = -3
00099       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
00100          INFO = -5
00101       ELSE IF( LWORK.LT.MAX( 1, NH ) .AND. .NOT.LQUERY ) THEN
00102          INFO = -8
00103       END IF
00104 *
00105       IF( INFO.EQ.0 ) THEN
00106          NB = ILAENV( 1, 'DORGQR', ' ', NH, NH, NH, -1 )
00107          LWKOPT = MAX( 1, NH )*NB
00108          WORK( 1 ) = LWKOPT
00109       END IF
00110 *
00111       IF( INFO.NE.0 ) THEN
00112          CALL XERBLA( 'DORGHR', -INFO )
00113          RETURN
00114       ELSE IF( LQUERY ) THEN
00115          RETURN
00116       END IF
00117 *
00118 *     Quick return if possible
00119 *
00120       IF( N.EQ.0 ) THEN
00121          WORK( 1 ) = 1
00122          RETURN
00123       END IF
00124 *
00125 *     Shift the vectors which define the elementary reflectors one
00126 *     column to the right, and set the first ilo and the last n-ihi
00127 *     rows and columns to those of the unit matrix
00128 *
00129       DO 40 J = IHI, ILO + 1, -1
00130          DO 10 I = 1, J - 1
00131             A( I, J ) = ZERO
00132    10    CONTINUE
00133          DO 20 I = J + 1, IHI
00134             A( I, J ) = A( I, J-1 )
00135    20    CONTINUE
00136          DO 30 I = IHI + 1, N
00137             A( I, J ) = ZERO
00138    30    CONTINUE
00139    40 CONTINUE
00140       DO 60 J = 1, ILO
00141          DO 50 I = 1, N
00142             A( I, J ) = ZERO
00143    50    CONTINUE
00144          A( J, J ) = ONE
00145    60 CONTINUE
00146       DO 80 J = IHI + 1, N
00147          DO 70 I = 1, N
00148             A( I, J ) = ZERO
00149    70    CONTINUE
00150          A( J, J ) = ONE
00151    80 CONTINUE
00152 *
00153       IF( NH.GT.0 ) THEN
00154 *
00155 *        Generate Q(ilo+1:ihi,ilo+1:ihi)
00156 *
00157          CALL DORGQR( NH, NH, NH, A( ILO+1, ILO+1 ), LDA, TAU( ILO ),
00158      $                WORK, LWORK, IINFO )
00159       END IF
00160       WORK( 1 ) = LWKOPT
00161       RETURN
00162 *
00163 *     End of DORGHR
00164 *
00165       END
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