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SUBROUTINE DLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA ) |
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* |
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* -- LAPACK auxiliary routine (version 3.2) -- |
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* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
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* November 2006 |
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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 applies a sequence of plane rotations to a real matrix A, |
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* from either the left or the right. |
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* |
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* When SIDE = 'L', the transformation takes the form |
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* |
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* A := P*A |
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* |
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* and when SIDE = 'R', the transformation takes the form |
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* |
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* A := A*P**T |
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* |
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* where P is an orthogonal matrix consisting of a sequence of z plane |
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* rotations, with z = M when SIDE = 'L' and z = N when SIDE = 'R', |
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* and P**T is the transpose of P. |
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* |
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* When DIRECT = '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' (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 defined by the 2-by-2 rotation |
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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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* When PIVOT = 'V' (Variable pivot), the rotation is performed |
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* for the plane (k,k+1), i.e., P(k) has the form |
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* |
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* P(k) = ( 1 ) |
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* ( ... ) |
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* ( 1 ) |
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* ( c(k) s(k) ) |
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* ( -s(k) c(k) ) |
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* ( 1 ) |
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* ( ... ) |
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* ( 1 ) |
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* |
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* where R(k) appears as a rank-2 modification to the identity matrix in |
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* rows and columns k and k+1. |
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* |
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* When PIVOT = 'T' (Top pivot), the rotation is performed for the |
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* plane (1,k+1), so P(k) has the form |
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* |
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* P(k) = ( c(k) s(k) ) |
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* ( 1 ) |
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* ( ... ) |
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* ( 1 ) |
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* ( -s(k) c(k) ) |
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* ( 1 ) |
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* ( ... ) |
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* ( 1 ) |
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* |
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* where R(k) appears in rows and columns 1 and k+1. |
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* |
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* Similarly, when PIVOT = 'B' (Bottom pivot), the rotation is |
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* performed for the plane (k,z), giving P(k) the form |
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* |
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* P(k) = ( 1 ) |
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* ( ... ) |
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* ( 1 ) |
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* ( c(k) s(k) ) |
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* ( 1 ) |
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* ( ... ) |
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* ( 1 ) |
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* ( -s(k) c(k) ) |
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* |
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* where R(k) appears in rows and columns k and z. The rotations are |
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* performed without ever forming P(k) explicitly. |
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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**T |
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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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* 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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* 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 (input) DOUBLE PRECISION array, dimension |
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* (M-1) if SIDE = 'L' |
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* (N-1) if SIDE = 'R' |
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* The cosines c(k) of the plane rotations. |
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* |
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* S (input) DOUBLE PRECISION array, dimension |
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* (M-1) if SIDE = 'L' |
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* (N-1) if SIDE = 'R' |
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* The sines s(k) of the plane rotations. The 2-by-2 plane |
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* rotation part of the matrix P(k), R(k), has 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**T 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 |