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SUBROUTINE BDLAAPP( ISIDE, M, N, NB, A, LDA, NITRAF, ITRAF,
$ DTRAF, WORK )
IMPLICIT NONE
*
* .. Scalar Arguments ..
INTEGER ISIDE, LDA, M, N, NB, NITRAF
* ..
* .. Array Arguments ..
INTEGER ITRAF( * )
DOUBLE PRECISION A( LDA, * ), DTRAF( * ), WORK( * )
*
*
* Purpose
* =======
*
* BDLAAPP computes
*
* B = Q**T * A or B = A * Q,
*
* where A is an M-by-N matrix and Q is an orthogonal matrix represented
* by the parameters in the arrays ITRAF and DTRAF as described in
* BDTREXC.
*
* This is an auxiliary routine called by BDTRSEN.
*
* Arguments
* =========
*
* ISIDE (input) INTEGER
* Specifies whether Q multiplies A from the left or right as
* follows:
* = 0: compute B = Q**T * A;
* = 1: compute B = A * Q.
*
* M (input) INTEGER
* The number of rows of A.
*
* N (input) INTEGER
* The number of columns of A.
*
* NB (input) INTEGER
* If ISIDE = 0, the Q is applied block column-wise to the rows
* of A and NB specifies the maximal width of the block columns.
* If ISIDE = 1, this variable is not referenced.
*
* A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
* On entry, the matrix A.
* On exit, A is overwritten by B.
*
* LDA (input) INTEGER
* The leading dimension of the array A. LDA >= max(1,N).
*
* NITRAF (input) INTEGER
* Length of the array ITRAF. NITRAF >= 0.
*
* ITRAF (input) INTEGER array, length NITRAF
* List of parameters for representing the transformation
* matrix Q, see BDTREXC.
*
* DTRAF (output) DOUBLE PRECISION array, length k, where
* List of parameters for representing the transformation
* matrix Q, see BDTREXC.
*
* WORK (workspace) DOUBLE PRECISION array, dimension (N)
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
* ..
* .. Local Scalars ..
INTEGER I, IT, J, NNB, PD
DOUBLE PRECISION TAU
* ..
* .. External Subroutines ..
EXTERNAL DLARFX, DROT
* .. Intrinsic Functions ..
INTRINSIC MIN
* ..
* .. Executable Statements ..
*
* Quick return if possible.
*
IF( M.LE.0 .OR. N.LE.0 )
$ RETURN
*
IF( ISIDE.EQ.0 ) THEN
*
* Apply Q from left.
*
DO 20 J = 1, N, NB
PD = 1
NNB = MIN( NB, N - J + 1 )
DO 10 I = 1, NITRAF
IT = ITRAF(I)
IF( IT.LE.M ) THEN
*
* Apply Givens rotation.
*
CALL DROT( NNB, A(IT,J), LDA, A(IT+1,J), LDA,
$ DTRAF(PD), DTRAF(PD+1) )
PD = PD + 2
ELSE IF( IT.LE.2*M ) THEN
*
* Apply Householder reflector of first kind.
*
TAU = DTRAF(PD)
DTRAF(PD) = ONE
CALL DLARFX( 'Left', 3, NNB, DTRAF(PD), TAU,
$ A(IT-M,J), LDA, WORK )
DTRAF(PD) = TAU
PD = PD + 3
ELSE
*
* Apply Householder reflector of second kind.
*
TAU = DTRAF(PD+2)
DTRAF(PD+2) = ONE
CALL DLARFX( 'Left', 3, NNB, DTRAF(PD), TAU,
$ A(IT-2*M,J), LDA, WORK )
DTRAF(PD+2) = TAU
PD = PD + 3
END IF
10 CONTINUE
20 CONTINUE
ELSE
PD = 1
DO 30 I = 1, NITRAF
IT = ITRAF(I)
IF( IT.LE.N ) THEN
*
* Apply Givens rotation.
*
CALL DROT( M, A(1,IT), 1, A(1,IT+1), 1, DTRAF(PD),
$ DTRAF(PD+1) )
PD = PD + 2
ELSE IF( IT.LE.2*N ) THEN
*
* Apply Householder reflector of first kind.
*
TAU = DTRAF(PD)
DTRAF(PD) = ONE
CALL DLARFX( 'Right', M, 3, DTRAF(PD), TAU, A(1,IT-N),
$ LDA, WORK )
DTRAF(PD) = TAU
PD = PD + 3
ELSE
*
* Apply Householder reflector of second kind.
*
TAU = DTRAF(PD+2)
DTRAF(PD+2) = ONE
CALL DLARFX( 'Right', M, 3, DTRAF(PD), TAU, A(1,IT-2*N),
$ LDA, WORK )
DTRAF(PD+2) = TAU
PD = PD + 3
END IF
30 CONTINUE
END IF
*
RETURN
*
* End of BDLAAPP
*
END
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