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SUBROUTINE DORMQL( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
$ WORK, LWORK, INFO )
*
* -- LAPACK routine (version 2.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* September 30, 1994
*
* .. Scalar Arguments ..
CHARACTER SIDE, TRANS
INTEGER INFO, K, LDA, LDC, LWORK, M, N
* ..
* .. Array Arguments ..
DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ),
$ WORK( LWORK )
* ..
*
* Purpose
* =======
*
* DORMQL overwrites the general real M-by-N matrix C with
*
* SIDE = 'L' SIDE = 'R'
* TRANS = 'N': Q * C C * Q
* TRANS = 'T': Q**T * C C * Q**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 DGEQLF. 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**T from the Left;
* = 'R': apply Q or Q**T from the Right.
*
* TRANS (input) CHARACTER*1
* = 'N': No transpose, apply Q;
* = 'T': Transpose, apply Q**T.
*
* 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,K)
* The i-th column must contain the vector which defines the
* elementary reflector H(i), for i = 1,2,...,k, as returned by
* DGEQLF in the last k columns 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.
* If SIDE = 'L', LDA >= max(1,M);
* if SIDE = 'R', LDA >= max(1,N).
*
* TAU (input) DOUBLE PRECISION array, dimension (K)
* TAU(i) must contain the scalar factor of the elementary
* reflector H(i), as returned by DGEQLF.
*
* 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**T*C or C*Q**T or C*Q.
*
* LDC (input) INTEGER
* The leading dimension of the array C. LDC >= max(1,M).
*
* WORK (workspace/output) DOUBLE PRECISION array, dimension (LWORK)
* On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*
* LWORK (input) INTEGER
* The dimension of the array WORK.
* If SIDE = 'L', LWORK >= max(1,N);
* if SIDE = 'R', LWORK >= max(1,M).
* For optimum performance LWORK >= N*NB if SIDE = 'L', and
* LWORK >= M*NB if SIDE = 'R', where NB is the optimal
* blocksize.
*
* INFO (output) INTEGER
* = 0: successful exit
* < 0: if INFO = -i, the i-th argument had an illegal value
*
* =====================================================================
*
* .. Parameters ..
INTEGER NBMAX, LDT
PARAMETER ( NBMAX = 64, LDT = NBMAX+1 )
* ..
* .. Local Scalars ..
LOGICAL LEFT, NOTRAN
INTEGER I, I1, I2, I3, IB, IINFO, IWS, LDWORK, MI, NB,
$ NBMIN, NI, NQ, NW
* ..
* .. Local Arrays ..
DOUBLE PRECISION T( LDT, NBMAX )
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER ILAENV
EXTERNAL LSAME, ILAENV
* ..
* .. External Subroutines ..
EXTERNAL DLARFB, DLARFT, DORM2L, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN
* ..
* .. Executable Statements ..
*
* Test the input arguments
*
INFO = 0
LEFT = LSAME( SIDE, 'L' )
NOTRAN = LSAME( TRANS, 'N' )
*
* NQ is the order of Q and NW is the minimum dimension of WORK
*
IF( LEFT ) THEN
NQ = M
NW = N
ELSE
NQ = N
NW = M
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, NQ ) ) THEN
INFO = -7
ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
INFO = -10
ELSE IF( LWORK.LT.MAX( 1, NW ) ) THEN
INFO = -12
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DORMQL', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) THEN
WORK( 1 ) = 1
RETURN
END IF
*
* Determine the block size. NB may be at most NBMAX, where NBMAX
* is used to define the local array T.
*
NB = MIN( NBMAX, ILAENV( 1, 'DORMQL', SIDE // TRANS, M, N, K,
$ -1 ) )
NBMIN = 2
LDWORK = NW
IF( NB.GT.1 .AND. NB.LT.K ) THEN
IWS = NW*NB
IF( LWORK.LT.IWS ) THEN
NB = LWORK / LDWORK
NBMIN = MAX( 2, ILAENV( 2, 'DORMQL', SIDE // TRANS, M, N, K,
$ -1 ) )
END IF
ELSE
IWS = NW
END IF
*
IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN
*
* Use unblocked code
*
CALL DORM2L( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK,
$ IINFO )
ELSE
*
* Use blocked code
*
IF( ( LEFT .AND. NOTRAN ) .OR.
$ ( .NOT.LEFT .AND. .NOT.NOTRAN ) ) THEN
I1 = 1
I2 = K
I3 = NB
ELSE
I1 = ( ( K-1 ) / NB )*NB + 1
I2 = 1
I3 = -NB
END IF
*
IF( LEFT ) THEN
NI = N
ELSE
MI = M
END IF
*
DO 10 I = I1, I2, I3
IB = MIN( NB, K-I+1 )
*
* Form the triangular factor of the block reflector
* H = H(i+ib-1) . . . H(i+1) H(i)
*
CALL DLARFT( 'Backward', 'Columnwise', NQ-K+I+IB-1, IB,
$ A( 1, I ), LDA, TAU( I ), T, LDT )
IF( LEFT ) THEN
*
* H or H' is applied to C(1:m-k+i+ib-1,1:n)
*
MI = M - K + I + IB - 1
ELSE
*
* H or H' is applied to C(1:m,1:n-k+i+ib-1)
*
NI = N - K + I + IB - 1
END IF
*
* Apply H or H'
*
CALL DLARFB( SIDE, TRANS, 'Backward', 'Columnwise', MI, NI,
$ IB, A( 1, I ), LDA, T, LDT, C, LDC, WORK,
$ LDWORK )
10 CONTINUE
END IF
WORK( 1 ) = IWS
RETURN
*
* End of DORMQL
*
END
SUBROUTINE DORM2L( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
$ WORK, INFO )
*
* -- LAPACK routine (version 2.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* February 29, 1992
*
* .. Scalar Arguments ..
CHARACTER SIDE, TRANS
INTEGER INFO, K, LDA, LDC, M, N
* ..
* .. Array Arguments ..
DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
* Purpose
* =======
*
* DORM2L 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 DGEQLF. 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,K)
* The i-th column must contain the vector which defines the
* elementary reflector H(i), for i = 1,2,...,k, as returned by
* DGEQLF in the last k columns 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.
* If SIDE = 'L', LDA >= max(1,M);
* if SIDE = 'R', LDA >= max(1,N).
*
* TAU (input) DOUBLE PRECISION array, dimension (K)
* TAU(i) must contain the scalar factor of the elementary
* reflector H(i), as returned by DGEQLF.
*
* 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, NQ ) ) THEN
INFO = -7
ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
INFO = -10
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DORM2L', -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
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( NQ-K+I, I )
A( NQ-K+I, I ) = ONE
CALL DLARF( SIDE, MI, NI, A( 1, I ), 1, TAU( I ), C, LDC,
$ WORK )
A( NQ-K+I, I ) = AII
10 CONTINUE
RETURN
*
* End of DORM2L
*
END
|
