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SUBROUTINE DOPMTR( SIDE, UPLO, TRANS, M, N, AP, 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, UPLO
INTEGER INFO, LDC, M, N
* ..
* .. Array Arguments ..
DOUBLE PRECISION AP( * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
* Purpose
* =======
*
* DOPMTR 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 of order nq, with nq = m if
* SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of
* nq-1 elementary reflectors, as returned by DSPTRD using packed
* storage:
*
* if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);
*
* if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).
*
* Arguments
* =========
*
* SIDE (input) CHARACTER*1
* = 'L': apply Q or Q**T from the Left;
* = 'R': apply Q or Q**T from the Right.
*
* UPLO (input) CHARACTER*1
* = 'U': Upper triangular packed storage used in previous
* call to DSPTRD;
* = 'L': Lower triangular packed storage used in previous
* call to DSPTRD.
*
* 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.
*
* AP (input) DOUBLE PRECISION array, dimension
* (M*(M+1)/2) if SIDE = 'L'
* (N*(N+1)/2) if SIDE = 'R'
* The vectors which define the elementary reflectors, as
* returned by DSPTRD. AP is modified by the routine but
* restored on exit.
*
* TAU (input) DOUBLE PRECISION array, dimension (M-1) if SIDE = 'L'
* or (N-1) if SIDE = 'R'
* TAU(i) must contain the scalar factor of the elementary
* reflector H(i), as returned by DSPTRD.
*
* 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) 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 FORWRD, LEFT, NOTRAN, UPPER
INTEGER I, I1, I2, I3, IC, II, 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' )
UPPER = LSAME( UPLO, 'U' )
*
* 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.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
INFO = -2
ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN
INFO = -3
ELSE IF( M.LT.0 ) THEN
INFO = -4
ELSE IF( N.LT.0 ) THEN
INFO = -5
ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
INFO = -9
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DOPMTR', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( M.EQ.0 .OR. N.EQ.0 )
$ RETURN
*
IF( UPPER ) THEN
*
* Q was determined by a call to DSPTRD with UPLO = 'U'
*
FORWRD = ( LEFT .AND. NOTRAN ) .OR.
$ ( .NOT.LEFT .AND. .NOT.NOTRAN )
*
IF( FORWRD ) THEN
I1 = 1
I2 = NQ - 1
I3 = 1
II = 2
ELSE
I1 = NQ - 1
I2 = 1
I3 = -1
II = NQ*( NQ+1 ) / 2 - 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:i,1:n)
*
MI = I
ELSE
*
* H(i) is applied to C(1:m,1:i)
*
NI = I
END IF
*
* Apply H(i)
*
AII = AP( II )
AP( II ) = ONE
CALL DLARF( SIDE, MI, NI, AP( II-I+1 ), 1, TAU( I ), C, LDC,
$ WORK )
AP( II ) = AII
*
IF( FORWRD ) THEN
II = II + I + 2
ELSE
II = II - I - 1
END IF
10 CONTINUE
ELSE
*
* Q was determined by a call to DSPTRD with UPLO = 'L'.
*
FORWRD = ( LEFT .AND. .NOT.NOTRAN ) .OR.
$ ( .NOT.LEFT .AND. NOTRAN )
*
IF( FORWRD ) THEN
I1 = 1
I2 = NQ - 1
I3 = 1
II = 2
ELSE
I1 = NQ - 1
I2 = 1
I3 = -1
II = NQ*( NQ+1 ) / 2 - 1
END IF
*
IF( LEFT ) THEN
NI = N
JC = 1
ELSE
MI = M
IC = 1
END IF
*
DO 20 I = I1, I2, I3
AII = AP( II )
AP( II ) = ONE
IF( LEFT ) THEN
*
* H(i) is applied to C(i+1:m,1:n)
*
MI = M - I
IC = I + 1
ELSE
*
* H(i) is applied to C(1:m,i+1:n)
*
NI = N - I
JC = I + 1
END IF
*
* Apply H(i)
*
CALL DLARF( SIDE, MI, NI, AP( II ), 1, TAU( I ),
$ C( IC, JC ), LDC, WORK )
AP( II ) = AII
*
IF( FORWRD ) THEN
II = II + NQ - I + 1
ELSE
II = II - NQ + I - 2
END IF
20 CONTINUE
END IF
RETURN
*
* End of DOPMTR
*
END
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