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SUBROUTINE SLARZ( SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK )
* * -- LAPACK routine (version 3.3.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * -- April 2011 -- * * .. Scalar Arguments .. CHARACTER SIDE INTEGER INCV, L, LDC, M, N REAL TAU * .. * .. Array Arguments .. REAL C( LDC, * ), V( * ), WORK( * ) * .. * * Purpose * ======= * * SLARZ applies a real elementary reflector H to a real M-by-N * matrix C, from either the left or the right. H is represented in the * form * * H = I - tau * v * v**T * * where tau is a real scalar and v is a real vector. * * If tau = 0, then H is taken to be the unit matrix. * * * H is a product of k elementary reflectors as returned by STZRZF. * * Arguments * ========= * * SIDE (input) CHARACTER*1 * = 'L': form H * C * = 'R': form C * H * * M (input) INTEGER * The number of rows of the matrix C. * * N (input) INTEGER * The number of columns of the matrix C. * * L (input) INTEGER * The number of entries of the vector V containing * the meaningful part of the Householder vectors. * If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0. * * V (input) REAL array, dimension (1+(L-1)*abs(INCV)) * The vector v in the representation of H as returned by * STZRZF. V is not used if TAU = 0. * * INCV (input) INTEGER * The increment between elements of v. INCV <> 0. * * TAU (input) REAL * The value tau in the representation of H. * * C (input/output) REAL array, dimension (LDC,N) * On entry, the M-by-N matrix C. * On exit, C is overwritten by the matrix H * C if SIDE = 'L', * or C * H if SIDE = 'R'. * * LDC (input) INTEGER * The leading dimension of the array C. LDC >= max(1,M). * * WORK (workspace) REAL array, dimension * (N) if SIDE = 'L' * or (M) if SIDE = 'R' * * Further Details * =============== * * Based on contributions by * A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA * * ===================================================================== * * .. Parameters .. REAL ONE, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) * .. * .. External Subroutines .. EXTERNAL SAXPY, SCOPY, SGEMV, SGER * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. Executable Statements .. * IF( LSAME( SIDE, 'L' ) ) THEN * * Form H * C * IF( TAU.NE.ZERO ) THEN * * w( 1:n ) = C( 1, 1:n ) * CALL SCOPY( N, C, LDC, WORK, 1 ) * * w( 1:n ) = w( 1:n ) + C( m-l+1:m, 1:n )**T * v( 1:l ) * CALL SGEMV( 'Transpose', L, N, ONE, C( M-L+1, 1 ), LDC, V, $ INCV, ONE, WORK, 1 ) * * C( 1, 1:n ) = C( 1, 1:n ) - tau * w( 1:n ) * CALL SAXPY( N, -TAU, WORK, 1, C, LDC ) * * C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ... * tau * v( 1:l ) * w( 1:n )**T * CALL SGER( L, N, -TAU, V, INCV, WORK, 1, C( M-L+1, 1 ), $ LDC ) END IF * ELSE * * Form C * H * IF( TAU.NE.ZERO ) THEN * * w( 1:m ) = C( 1:m, 1 ) * CALL SCOPY( M, C, 1, WORK, 1 ) * * w( 1:m ) = w( 1:m ) + C( 1:m, n-l+1:n, 1:n ) * v( 1:l ) * CALL SGEMV( 'No transpose', M, L, ONE, C( 1, N-L+1 ), LDC, $ V, INCV, ONE, WORK, 1 ) * * C( 1:m, 1 ) = C( 1:m, 1 ) - tau * w( 1:m ) * CALL SAXPY( M, -TAU, WORK, 1, C, 1 ) * * C( 1:m, n-l+1:n ) = C( 1:m, n-l+1:n ) - ... * tau * w( 1:m ) * v( 1:l )**T * CALL SGER( M, L, -TAU, WORK, 1, V, INCV, C( 1, N-L+1 ), $ LDC ) * END IF * END IF * RETURN * * End of SLARZ * END |