SUBROUTINE DORML2( 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
* =======
*
* DORML2 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(k) . . . H(2) H(1)
*
* as returned by DGELQF. 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
* DGELQF in the first 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 DGELQF.
*
* 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, IC, JC, 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( 'DORML2', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 )
$ RETURN
*
IF( ( LEFT .AND. NOTRAN ) .OR. ( .NOT.LEFT .AND. .NOT.NOTRAN ) )
$ THEN
I1 = 1
I2 = K
I3 = 1
ELSE
I1 = K
I2 = 1
I3 = -1
END IF
*
IF( LEFT ) THEN
NI = N
JC = 1
ELSE
MI = M
IC = 1
END IF
*
DO 10 I = I1, I2, I3
IF( LEFT ) THEN
*
* H(i) is applied to C(i:m,1:n)
*
MI = M - I + 1
IC = I
ELSE
*
* H(i) is applied to C(1:m,i:n)
*
NI = N - I + 1
JC = I
END IF
*
* Apply H(i)
*
AII = A( I, I )
A( I, I ) = ONE
CALL DLARF( SIDE, MI, NI, A( I, I ), LDA, TAU( I ),
$ C( IC, JC ), LDC, WORK )
A( I, I ) = AII
10 CONTINUE
RETURN
*
* End of DORML2
*
END