325 lines
11 KiB
Fortran
325 lines
11 KiB
Fortran
SUBROUTINE DLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA )
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*
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* -- LAPACK auxiliary routine (version 2.0) --
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* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
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* Courant Institute, Argonne National Lab, and Rice University
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* October 31, 1992
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*
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* .. Scalar Arguments ..
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CHARACTER DIRECT, PIVOT, SIDE
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INTEGER LDA, M, N
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION A( LDA, * ), C( * ), S( * )
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* ..
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*
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* Purpose
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* =======
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*
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* DLASR performs the transformation
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*
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* A := P*A, when SIDE = 'L' or 'l' ( Left-hand side )
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*
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* A := A*P', when SIDE = 'R' or 'r' ( Right-hand side )
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*
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* where A is an m by n real matrix and P is an orthogonal matrix,
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* consisting of a sequence of plane rotations determined by the
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* parameters PIVOT and DIRECT as follows ( z = m when SIDE = 'L' or 'l'
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* and z = n when SIDE = 'R' or 'r' ):
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*
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* When DIRECT = 'F' or 'f' ( Forward sequence ) then
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*
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* P = P( z - 1 )*...*P( 2 )*P( 1 ),
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*
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* and when DIRECT = 'B' or 'b' ( Backward sequence ) then
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*
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* P = P( 1 )*P( 2 )*...*P( z - 1 ),
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*
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* where P( k ) is a plane rotation matrix for the following planes:
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*
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* when PIVOT = 'V' or 'v' ( Variable pivot ),
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* the plane ( k, k + 1 )
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*
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* when PIVOT = 'T' or 't' ( Top pivot ),
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* the plane ( 1, k + 1 )
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*
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* when PIVOT = 'B' or 'b' ( Bottom pivot ),
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* the plane ( k, z )
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*
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* c( k ) and s( k ) must contain the cosine and sine that define the
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* matrix P( k ). The two by two plane rotation part of the matrix
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* P( k ), R( k ), is assumed to be of the form
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*
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* R( k ) = ( c( k ) s( k ) ).
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* ( -s( k ) c( k ) )
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*
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* This version vectorises across rows of the array A when SIDE = 'L'.
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*
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* Arguments
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* =========
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*
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* SIDE (input) CHARACTER*1
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* Specifies whether the plane rotation matrix P is applied to
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* A on the left or the right.
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* = 'L': Left, compute A := P*A
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* = 'R': Right, compute A:= A*P'
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*
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* DIRECT (input) CHARACTER*1
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* Specifies whether P is a forward or backward sequence of
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* plane rotations.
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* = 'F': Forward, P = P( z - 1 )*...*P( 2 )*P( 1 )
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* = 'B': Backward, P = P( 1 )*P( 2 )*...*P( z - 1 )
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*
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* PIVOT (input) CHARACTER*1
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* Specifies the plane for which P(k) is a plane rotation
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* matrix.
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* = 'V': Variable pivot, the plane (k,k+1)
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* = 'T': Top pivot, the plane (1,k+1)
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* = 'B': Bottom pivot, the plane (k,z)
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*
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* M (input) INTEGER
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* The number of rows of the matrix A. If m <= 1, an immediate
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* return is effected.
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*
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* N (input) INTEGER
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* The number of columns of the matrix A. If n <= 1, an
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* immediate return is effected.
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*
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* C, S (input) DOUBLE PRECISION arrays, dimension
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* (M-1) if SIDE = 'L'
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* (N-1) if SIDE = 'R'
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* c(k) and s(k) contain the cosine and sine that define the
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* matrix P(k). The two by two plane rotation part of the
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* matrix P(k), R(k), is assumed to be of the form
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* R( k ) = ( c( k ) s( k ) ).
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* ( -s( k ) c( k ) )
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*
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* A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
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* The m by n matrix A. On exit, A is overwritten by P*A if
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* SIDE = 'R' or by A*P' if SIDE = 'L'.
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*
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* LDA (input) INTEGER
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* The leading dimension of the array A. LDA >= max(1,M).
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ONE, ZERO
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PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
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* ..
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* .. Local Scalars ..
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INTEGER I, INFO, J
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DOUBLE PRECISION CTEMP, STEMP, TEMP
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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* ..
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* .. External Subroutines ..
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EXTERNAL XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX
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* ..
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* .. Executable Statements ..
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*
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* Test the input parameters
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*
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INFO = 0
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IF( .NOT.( LSAME( SIDE, 'L' ) .OR. LSAME( SIDE, 'R' ) ) ) THEN
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INFO = 1
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ELSE IF( .NOT.( LSAME( PIVOT, 'V' ) .OR. LSAME( PIVOT,
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$ 'T' ) .OR. LSAME( PIVOT, 'B' ) ) ) THEN
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INFO = 2
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ELSE IF( .NOT.( LSAME( DIRECT, 'F' ) .OR. LSAME( DIRECT, 'B' ) ) )
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$ THEN
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INFO = 3
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ELSE IF( M.LT.0 ) THEN
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INFO = 4
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ELSE IF( N.LT.0 ) THEN
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INFO = 5
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ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
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INFO = 9
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'DLASR ', INFO )
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RETURN
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END IF
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*
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* Quick return if possible
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*
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IF( ( M.EQ.0 ) .OR. ( N.EQ.0 ) )
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$ RETURN
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IF( LSAME( SIDE, 'L' ) ) THEN
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*
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* Form P * A
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*
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IF( LSAME( PIVOT, 'V' ) ) THEN
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IF( LSAME( DIRECT, 'F' ) ) THEN
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DO 20 J = 1, M - 1
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CTEMP = C( J )
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STEMP = S( J )
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IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
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DO 10 I = 1, N
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TEMP = A( J+1, I )
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A( J+1, I ) = CTEMP*TEMP - STEMP*A( J, I )
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A( J, I ) = STEMP*TEMP + CTEMP*A( J, I )
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10 CONTINUE
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END IF
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20 CONTINUE
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ELSE IF( LSAME( DIRECT, 'B' ) ) THEN
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DO 40 J = M - 1, 1, -1
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CTEMP = C( J )
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STEMP = S( J )
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IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
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DO 30 I = 1, N
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TEMP = A( J+1, I )
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A( J+1, I ) = CTEMP*TEMP - STEMP*A( J, I )
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A( J, I ) = STEMP*TEMP + CTEMP*A( J, I )
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30 CONTINUE
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END IF
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40 CONTINUE
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END IF
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ELSE IF( LSAME( PIVOT, 'T' ) ) THEN
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IF( LSAME( DIRECT, 'F' ) ) THEN
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DO 60 J = 2, M
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CTEMP = C( J-1 )
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STEMP = S( J-1 )
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IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
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DO 50 I = 1, N
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TEMP = A( J, I )
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A( J, I ) = CTEMP*TEMP - STEMP*A( 1, I )
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A( 1, I ) = STEMP*TEMP + CTEMP*A( 1, I )
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50 CONTINUE
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END IF
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60 CONTINUE
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ELSE IF( LSAME( DIRECT, 'B' ) ) THEN
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DO 80 J = M, 2, -1
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CTEMP = C( J-1 )
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STEMP = S( J-1 )
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IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
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DO 70 I = 1, N
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TEMP = A( J, I )
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A( J, I ) = CTEMP*TEMP - STEMP*A( 1, I )
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A( 1, I ) = STEMP*TEMP + CTEMP*A( 1, I )
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70 CONTINUE
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END IF
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80 CONTINUE
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END IF
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ELSE IF( LSAME( PIVOT, 'B' ) ) THEN
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IF( LSAME( DIRECT, 'F' ) ) THEN
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DO 100 J = 1, M - 1
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CTEMP = C( J )
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STEMP = S( J )
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IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
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DO 90 I = 1, N
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TEMP = A( J, I )
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A( J, I ) = STEMP*A( M, I ) + CTEMP*TEMP
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A( M, I ) = CTEMP*A( M, I ) - STEMP*TEMP
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90 CONTINUE
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END IF
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100 CONTINUE
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ELSE IF( LSAME( DIRECT, 'B' ) ) THEN
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DO 120 J = M - 1, 1, -1
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CTEMP = C( J )
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STEMP = S( J )
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IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
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DO 110 I = 1, N
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TEMP = A( J, I )
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A( J, I ) = STEMP*A( M, I ) + CTEMP*TEMP
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A( M, I ) = CTEMP*A( M, I ) - STEMP*TEMP
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110 CONTINUE
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END IF
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120 CONTINUE
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END IF
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END IF
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ELSE IF( LSAME( SIDE, 'R' ) ) THEN
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*
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* Form A * P'
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*
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IF( LSAME( PIVOT, 'V' ) ) THEN
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IF( LSAME( DIRECT, 'F' ) ) THEN
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DO 140 J = 1, N - 1
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CTEMP = C( J )
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STEMP = S( J )
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IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
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DO 130 I = 1, M
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TEMP = A( I, J+1 )
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A( I, J+1 ) = CTEMP*TEMP - STEMP*A( I, J )
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A( I, J ) = STEMP*TEMP + CTEMP*A( I, J )
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130 CONTINUE
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END IF
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140 CONTINUE
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ELSE IF( LSAME( DIRECT, 'B' ) ) THEN
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DO 160 J = N - 1, 1, -1
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CTEMP = C( J )
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STEMP = S( J )
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IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
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DO 150 I = 1, M
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TEMP = A( I, J+1 )
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A( I, J+1 ) = CTEMP*TEMP - STEMP*A( I, J )
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A( I, J ) = STEMP*TEMP + CTEMP*A( I, J )
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150 CONTINUE
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END IF
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160 CONTINUE
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END IF
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ELSE IF( LSAME( PIVOT, 'T' ) ) THEN
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IF( LSAME( DIRECT, 'F' ) ) THEN
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DO 180 J = 2, N
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CTEMP = C( J-1 )
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STEMP = S( J-1 )
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IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
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DO 170 I = 1, M
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TEMP = A( I, J )
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A( I, J ) = CTEMP*TEMP - STEMP*A( I, 1 )
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A( I, 1 ) = STEMP*TEMP + CTEMP*A( I, 1 )
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170 CONTINUE
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END IF
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180 CONTINUE
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ELSE IF( LSAME( DIRECT, 'B' ) ) THEN
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DO 200 J = N, 2, -1
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CTEMP = C( J-1 )
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STEMP = S( J-1 )
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IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
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DO 190 I = 1, M
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TEMP = A( I, J )
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A( I, J ) = CTEMP*TEMP - STEMP*A( I, 1 )
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A( I, 1 ) = STEMP*TEMP + CTEMP*A( I, 1 )
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190 CONTINUE
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END IF
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200 CONTINUE
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END IF
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ELSE IF( LSAME( PIVOT, 'B' ) ) THEN
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IF( LSAME( DIRECT, 'F' ) ) THEN
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DO 220 J = 1, N - 1
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CTEMP = C( J )
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STEMP = S( J )
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IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
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DO 210 I = 1, M
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TEMP = A( I, J )
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A( I, J ) = STEMP*A( I, N ) + CTEMP*TEMP
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A( I, N ) = CTEMP*A( I, N ) - STEMP*TEMP
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210 CONTINUE
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END IF
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220 CONTINUE
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ELSE IF( LSAME( DIRECT, 'B' ) ) THEN
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DO 240 J = N - 1, 1, -1
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CTEMP = C( J )
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STEMP = S( J )
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IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
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DO 230 I = 1, M
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TEMP = A( I, J )
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A( I, J ) = STEMP*A( I, N ) + CTEMP*TEMP
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A( I, N ) = CTEMP*A( I, N ) - STEMP*TEMP
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230 CONTINUE
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END IF
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240 CONTINUE
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END IF
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END IF
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END IF
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*
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RETURN
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*
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* End of DLASR
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*
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END
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