sorghr.f.html
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SUBROUTINE <a name="SORGHR.1"></a><a href="sorghr.f.html#SORGHR.1">SORGHR</a>( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> -- LAPACK routine (version 3.1) --
</span><span class="comment">*</span><span class="comment"> Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment"> November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Scalar Arguments ..
</span> INTEGER IHI, ILO, INFO, LDA, LWORK, N
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> REAL A( LDA, * ), TAU( * ), WORK( * )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Purpose
</span><span class="comment">*</span><span class="comment"> =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> <a name="SORGHR.17"></a><a href="sorghr.f.html#SORGHR.1">SORGHR</a> generates a real orthogonal matrix Q which is defined as the
</span><span class="comment">*</span><span class="comment"> product of IHI-ILO elementary reflectors of order N, as returned by
</span><span class="comment">*</span><span class="comment"> <a name="SGEHRD.19"></a><a href="sgehrd.f.html#SGEHRD.1">SGEHRD</a>:
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Q = H(ilo) H(ilo+1) . . . H(ihi-1).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Arguments
</span><span class="comment">*</span><span class="comment"> =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> N (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The order of the matrix Q. N >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> ILO (input) INTEGER
</span><span class="comment">*</span><span class="comment"> IHI (input) INTEGER
</span><span class="comment">*</span><span class="comment"> ILO and IHI must have the same values as in the previous call
</span><span class="comment">*</span><span class="comment"> of <a name="SGEHRD.32"></a><a href="sgehrd.f.html#SGEHRD.1">SGEHRD</a>. Q is equal to the unit matrix except in the
</span><span class="comment">*</span><span class="comment"> submatrix Q(ilo+1:ihi,ilo+1:ihi).
</span><span class="comment">*</span><span class="comment"> 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> A (input/output) REAL array, dimension (LDA,N)
</span><span class="comment">*</span><span class="comment"> On entry, the vectors which define the elementary reflectors,
</span><span class="comment">*</span><span class="comment"> as returned by <a name="SGEHRD.38"></a><a href="sgehrd.f.html#SGEHRD.1">SGEHRD</a>.
</span><span class="comment">*</span><span class="comment"> On exit, the N-by-N orthogonal matrix Q.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDA (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array A. LDA >= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> TAU (input) REAL array, dimension (N-1)
</span><span class="comment">*</span><span class="comment"> TAU(i) must contain the scalar factor of the elementary
</span><span class="comment">*</span><span class="comment"> reflector H(i), as returned by <a name="SGEHRD.46"></a><a href="sgehrd.f.html#SGEHRD.1">SGEHRD</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> WORK (workspace/output) REAL array, dimension (MAX(1,LWORK))
</span><span class="comment">*</span><span class="comment"> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LWORK (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The dimension of the array WORK. LWORK >= IHI-ILO.
</span><span class="comment">*</span><span class="comment"> For optimum performance LWORK >= (IHI-ILO)*NB, where NB is
</span><span class="comment">*</span><span class="comment"> the optimal blocksize.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> If LWORK = -1, then a workspace query is assumed; the routine
</span><span class="comment">*</span><span class="comment"> only calculates the optimal size of the WORK array, returns
</span><span class="comment">*</span><span class="comment"> this value as the first entry of the WORK array, and no error
</span><span class="comment">*</span><span class="comment"> message related to LWORK is issued by <a name="XERBLA.59"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> INFO (output) INTEGER
</span><span class="comment">*</span><span class="comment"> = 0: successful exit
</span><span class="comment">*</span><span class="comment"> < 0: if INFO = -i, the i-th argument had an illegal value
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Parameters ..
</span> REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Scalars ..
</span> LOGICAL LQUERY
INTEGER I, IINFO, J, LWKOPT, NB, NH
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Subroutines ..
</span> EXTERNAL <a name="SORGQR.76"></a><a href="sorgqr.f.html#SORGQR.1">SORGQR</a>, <a name="XERBLA.76"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Functions ..
</span> INTEGER <a name="ILAENV.79"></a><a href="hfy-index.html#ILAENV">ILAENV</a>
EXTERNAL <a name="ILAENV.80"></a><a href="hfy-index.html#ILAENV">ILAENV</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Intrinsic Functions ..
</span> INTRINSIC MAX, MIN
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Test the input arguments
</span><span class="comment">*</span><span class="comment">
</span> 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
<span class="comment">*</span><span class="comment">
</span> IF( INFO.EQ.0 ) THEN
NB = <a name="ILAENV.105"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="SORGQR.105"></a><a href="sorgqr.f.html#SORGQR.1">SORGQR</a>'</span>, <span class="string">' '</span>, NH, NH, NH, -1 )
LWKOPT = MAX( 1, NH )*NB
WORK( 1 ) = LWKOPT
END IF
<span class="comment">*</span><span class="comment">
</span> IF( INFO.NE.0 ) THEN
CALL <a name="XERBLA.111"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="SORGHR.111"></a><a href="sorghr.f.html#SORGHR.1">SORGHR</a>'</span>, -INFO )
RETURN
ELSE IF( LQUERY ) THEN
RETURN
END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Quick return if possible
</span><span class="comment">*</span><span class="comment">
</span> IF( N.EQ.0 ) THEN
WORK( 1 ) = 1
RETURN
END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Shift the vectors which define the elementary reflectors one
</span><span class="comment">*</span><span class="comment"> column to the right, and set the first ilo and the last n-ihi
</span><span class="comment">*</span><span class="comment"> rows and columns to those of the unit matrix
</span><span class="comment">*</span><span class="comment">
</span> 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
<span class="comment">*</span><span class="comment">
</span> IF( NH.GT.0 ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Generate Q(ilo+1:ihi,ilo+1:ihi)
</span><span class="comment">*</span><span class="comment">
</span> CALL <a name="SORGQR.156"></a><a href="sorgqr.f.html#SORGQR.1">SORGQR</a>( NH, NH, NH, A( ILO+1, ILO+1 ), LDA, TAU( ILO ),
$ WORK, LWORK, IINFO )
END IF
WORK( 1 ) = LWKOPT
RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> End of <a name="SORGHR.162"></a><a href="sorghr.f.html#SORGHR.1">SORGHR</a>
</span><span class="comment">*</span><span class="comment">
</span> END
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