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+ SUBROUTINE DORMR2( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
+ $ WORK, INFO )
+*
+* -- LAPACK routine (version 3.1) --
+* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
+* November 2006
+*
+* .. Scalar Arguments ..
+ CHARACTER SIDE, TRANS
+ INTEGER INFO, K, LDA, LDC, M, N
+* ..
+* .. Array Arguments ..
+ DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
+* ..
+*
+* Purpose
+* =======
+*
+* DORMR2 overwrites the general real m by n matrix C with
+*
+* Q * C if SIDE = 'L' and TRANS = 'N', or
+*
+* Q'* C if SIDE = 'L' and TRANS = 'T', or
+*
+* C * Q if SIDE = 'R' and TRANS = 'N', or
+*
+* C * Q' if SIDE = 'R' and TRANS = 'T',
+*
+* where Q is a real orthogonal matrix defined as the product of k
+* elementary reflectors
+*
+* Q = H(1) H(2) . . . H(k)
+*
+* as returned by DGERQF. Q is of order m if SIDE = 'L' and of order n
+* if SIDE = 'R'.
+*
+* Arguments
+* =========
+*
+* SIDE (input) CHARACTER*1
+* = 'L': apply Q or Q' from the Left
+* = 'R': apply Q or Q' from the Right
+*
+* TRANS (input) CHARACTER*1
+* = 'N': apply Q (No transpose)
+* = 'T': apply Q' (Transpose)
+*
+* M (input) INTEGER
+* The number of rows of the matrix C. M >= 0.
+*
+* N (input) INTEGER
+* The number of columns of the matrix C. N >= 0.
+*
+* K (input) INTEGER
+* The number of elementary reflectors whose product defines
+* the matrix Q.
+* If SIDE = 'L', M >= K >= 0;
+* if SIDE = 'R', N >= K >= 0.
+*
+* A (input) DOUBLE PRECISION array, dimension
+* (LDA,M) if SIDE = 'L',
+* (LDA,N) if SIDE = 'R'
+* The i-th row must contain the vector which defines the
+* elementary reflector H(i), for i = 1,2,...,k, as returned by
+* DGERQF in the last k rows of its array argument A.
+* A is modified by the routine but restored on exit.
+*
+* LDA (input) INTEGER
+* The leading dimension of the array A. LDA >= max(1,K).
+*
+* TAU (input) DOUBLE PRECISION array, dimension (K)
+* TAU(i) must contain the scalar factor of the elementary
+* reflector H(i), as returned by DGERQF.
+*
+* C (input/output) DOUBLE PRECISION array, dimension (LDC,N)
+* On entry, the m by n matrix C.
+* On exit, C is overwritten by Q*C or Q'*C or C*Q' or C*Q.
+*
+* LDC (input) INTEGER
+* The leading dimension of the array C. LDC >= max(1,M).
+*
+* WORK (workspace) DOUBLE PRECISION array, dimension
+* (N) if SIDE = 'L',
+* (M) if SIDE = 'R'
+*
+* INFO (output) INTEGER
+* = 0: successful exit
+* < 0: if INFO = -i, the i-th argument had an illegal value
+*
+* =====================================================================
+*
+* .. Parameters ..
+ DOUBLE PRECISION ONE
+ PARAMETER ( ONE = 1.0D+0 )
+* ..
+* .. Local Scalars ..
+ LOGICAL LEFT, NOTRAN
+ INTEGER I, I1, I2, I3, MI, NI, NQ
+ DOUBLE PRECISION AII
+* ..
+* .. External Functions ..
+ LOGICAL LSAME
+ EXTERNAL LSAME
+* ..
+* .. External Subroutines ..
+ EXTERNAL DLARF, XERBLA
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC MAX
+* ..
+* .. Executable Statements ..
+*
+* Test the input arguments
+*
+ INFO = 0
+ LEFT = LSAME( SIDE, 'L' )
+ NOTRAN = LSAME( TRANS, 'N' )
+*
+* NQ is the order of Q
+*
+ IF( LEFT ) THEN
+ NQ = M
+ ELSE
+ NQ = N
+ END IF
+ IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
+ INFO = -1
+ ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN
+ INFO = -2
+ ELSE IF( M.LT.0 ) THEN
+ INFO = -3
+ ELSE IF( N.LT.0 ) THEN
+ INFO = -4
+ ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN
+ INFO = -5
+ ELSE IF( LDA.LT.MAX( 1, K ) ) THEN
+ INFO = -7
+ ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
+ INFO = -10
+ END IF
+ IF( INFO.NE.0 ) THEN
+ CALL XERBLA( 'DORMR2', -INFO )
+ RETURN
+ END IF
+*
+* Quick return if possible
+*
+ IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 )
+ $ RETURN
+*
+ IF( ( LEFT .AND. .NOT.NOTRAN ) .OR. ( .NOT.LEFT .AND. NOTRAN ) )
+ $ THEN
+ I1 = 1
+ I2 = K
+ I3 = 1
+ ELSE
+ I1 = K
+ I2 = 1
+ I3 = -1
+ END IF
+*
+ IF( LEFT ) THEN
+ NI = N
+ ELSE
+ MI = M
+ END IF
+*
+ DO 10 I = I1, I2, I3
+ IF( LEFT ) THEN
+*
+* H(i) is applied to C(1:m-k+i,1:n)
+*
+ MI = M - K + I
+ ELSE
+*
+* H(i) is applied to C(1:m,1:n-k+i)
+*
+ NI = N - K + I
+ END IF
+*
+* Apply H(i)
+*
+ AII = A( I, NQ-K+I )
+ A( I, NQ-K+I ) = ONE
+ CALL DLARF( SIDE, MI, NI, A( I, 1 ), LDA, TAU( I ), C, LDC,
+ $ WORK )
+ A( I, NQ-K+I ) = AII
+ 10 CONTINUE
+ RETURN
+*
+* End of DORMR2
+*
+ END