103 SUBROUTINE clarfg( N, ALPHA, X, INCX, TAU )
121 parameter( one = 1.0e+0, zero = 0.0e+0 )
125 REAL ALPHI, ALPHR, BETA, RSAFMN, SAFMIN, XNORM
128 REAL SCNRM2, SLAMCH, SLAPY3
130 EXTERNAL scnrm2, slamch, slapy3, cladiv
133 INTRINSIC abs, aimag, cmplx, real, sign
145 xnorm = scnrm2( n-1, x, incx )
146 alphr = real( alpha )
147 alphi = aimag( alpha )
149 IF( xnorm.EQ.zero .AND. alphi.EQ.zero )
THEN
158 beta = -sign( slapy3( alphr, alphi, xnorm ), alphr )
159 safmin = slamch(
'S' ) / slamch(
'E' )
160 rsafmn = one / safmin
163 IF( abs( beta ).LT.safmin )
THEN
169 CALL csscal( n-1, rsafmn, x, incx )
173 IF( (abs( beta ).LT.safmin) .AND. (knt .LT. 20) )
178 xnorm = scnrm2( n-1, x, incx )
179 alpha = cmplx( alphr, alphi )
180 beta = -sign( slapy3( alphr, alphi, xnorm ), alphr )
182 tau = cmplx( ( beta-alphr ) / beta, -alphi / beta )
183 alpha = cladiv( cmplx( one ), alpha-beta )
184 CALL cscal( n-1, alpha, x, incx )
subroutine clarfg(n, alpha, x, incx, tau)
CLARFG generates an elementary reflector (Householder matrix).