LAPACK  3.9.1
LAPACK: Linear Algebra PACKage

◆ zlartg()

subroutine zlartg ( complex*16  F,
complex*16  G,
double precision  CS,
complex*16  SN,
complex*16  R 
)

ZLARTG generates a plane rotation with real cosine and complex sine.

Download ZLARTG + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 ZLARTG generates a plane rotation so that

    [  CS  SN  ]     [ F ]     [ R ]
    [  __      ]  .  [   ]  =  [   ]   where CS**2 + |SN|**2 = 1.
    [ -SN  CS  ]     [ G ]     [ 0 ]

 This is a faster version of the BLAS1 routine ZROTG, except for
 the following differences:
    F and G are unchanged on return.
    If G=0, then CS=1 and SN=0.
    If F=0, then CS=0 and SN is chosen so that R is real.
Parameters
[in]F
          F is COMPLEX*16
          The first component of vector to be rotated.
[in]G
          G is COMPLEX*16
          The second component of vector to be rotated.
[out]CS
          CS is DOUBLE PRECISION
          The cosine of the rotation.
[out]SN
          SN is COMPLEX*16
          The sine of the rotation.
[out]R
          R is COMPLEX*16
          The nonzero component of the rotated vector.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
  3-5-96 - Modified with a new algorithm by W. Kahan and J. Demmel

  This version has a few statements commented out for thread safety
  (machine parameters are computed on each entry). 10 feb 03, SJH.

Definition at line 102 of file zlartg.f.

103 *
104 * -- LAPACK auxiliary routine --
105 * -- LAPACK is a software package provided by Univ. of Tennessee, --
106 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
107 *
108 * .. Scalar Arguments ..
109  DOUBLE PRECISION CS
110  COMPLEX*16 F, G, R, SN
111 * ..
112 *
113 * =====================================================================
114 *
115 * .. Parameters ..
116  DOUBLE PRECISION TWO, ONE, ZERO
117  parameter( two = 2.0d+0, one = 1.0d+0, zero = 0.0d+0 )
118  COMPLEX*16 CZERO
119  parameter( czero = ( 0.0d+0, 0.0d+0 ) )
120 * ..
121 * .. Local Scalars ..
122 * LOGICAL FIRST
123  INTEGER COUNT, I
124  DOUBLE PRECISION D, DI, DR, EPS, F2, F2S, G2, G2S, SAFMIN,
125  $ SAFMN2, SAFMX2, SCALE
126  COMPLEX*16 FF, FS, GS
127 * ..
128 * .. External Functions ..
129  DOUBLE PRECISION DLAMCH, DLAPY2
130  LOGICAL DISNAN
131  EXTERNAL dlamch, dlapy2, disnan
132 * ..
133 * .. Intrinsic Functions ..
134  INTRINSIC abs, dble, dcmplx, dconjg, dimag, int, log,
135  $ max, sqrt
136 * ..
137 * .. Statement Functions ..
138  DOUBLE PRECISION ABS1, ABSSQ
139 * ..
140 * .. Statement Function definitions ..
141  abs1( ff ) = max( abs( dble( ff ) ), abs( dimag( ff ) ) )
142  abssq( ff ) = dble( ff )**2 + dimag( ff )**2
143 * ..
144 * .. Executable Statements ..
145 *
146  safmin = dlamch( 'S' )
147  eps = dlamch( 'E' )
148  safmn2 = dlamch( 'B' )**int( log( safmin / eps ) /
149  $ log( dlamch( 'B' ) ) / two )
150  safmx2 = one / safmn2
151  scale = max( abs1( f ), abs1( g ) )
152  fs = f
153  gs = g
154  count = 0
155  IF( scale.GE.safmx2 ) THEN
156  10 CONTINUE
157  count = count + 1
158  fs = fs*safmn2
159  gs = gs*safmn2
160  scale = scale*safmn2
161  IF( scale.GE.safmx2 .AND. count .LT. 20 )
162  $ GO TO 10
163  ELSE IF( scale.LE.safmn2 ) THEN
164  IF( g.EQ.czero.OR.disnan( abs( g ) ) ) THEN
165  cs = one
166  sn = czero
167  r = f
168  RETURN
169  END IF
170  20 CONTINUE
171  count = count - 1
172  fs = fs*safmx2
173  gs = gs*safmx2
174  scale = scale*safmx2
175  IF( scale.LE.safmn2 )
176  $ GO TO 20
177  END IF
178  f2 = abssq( fs )
179  g2 = abssq( gs )
180  IF( f2.LE.max( g2, one )*safmin ) THEN
181 *
182 * This is a rare case: F is very small.
183 *
184  IF( f.EQ.czero ) THEN
185  cs = zero
186  r = dlapy2( dble( g ), dimag( g ) )
187 * Do complex/real division explicitly with two real divisions
188  d = dlapy2( dble( gs ), dimag( gs ) )
189  sn = dcmplx( dble( gs ) / d, -dimag( gs ) / d )
190  RETURN
191  END IF
192  f2s = dlapy2( dble( fs ), dimag( fs ) )
193 * G2 and G2S are accurate
194 * G2 is at least SAFMIN, and G2S is at least SAFMN2
195  g2s = sqrt( g2 )
196 * Error in CS from underflow in F2S is at most
197 * UNFL / SAFMN2 .lt. sqrt(UNFL*EPS) .lt. EPS
198 * If MAX(G2,ONE)=G2, then F2 .lt. G2*SAFMIN,
199 * and so CS .lt. sqrt(SAFMIN)
200 * If MAX(G2,ONE)=ONE, then F2 .lt. SAFMIN
201 * and so CS .lt. sqrt(SAFMIN)/SAFMN2 = sqrt(EPS)
202 * Therefore, CS = F2S/G2S / sqrt( 1 + (F2S/G2S)**2 ) = F2S/G2S
203  cs = f2s / g2s
204 * Make sure abs(FF) = 1
205 * Do complex/real division explicitly with 2 real divisions
206  IF( abs1( f ).GT.one ) THEN
207  d = dlapy2( dble( f ), dimag( f ) )
208  ff = dcmplx( dble( f ) / d, dimag( f ) / d )
209  ELSE
210  dr = safmx2*dble( f )
211  di = safmx2*dimag( f )
212  d = dlapy2( dr, di )
213  ff = dcmplx( dr / d, di / d )
214  END IF
215  sn = ff*dcmplx( dble( gs ) / g2s, -dimag( gs ) / g2s )
216  r = cs*f + sn*g
217  ELSE
218 *
219 * This is the most common case.
220 * Neither F2 nor F2/G2 are less than SAFMIN
221 * F2S cannot overflow, and it is accurate
222 *
223  f2s = sqrt( one+g2 / f2 )
224 * Do the F2S(real)*FS(complex) multiply with two real multiplies
225  r = dcmplx( f2s*dble( fs ), f2s*dimag( fs ) )
226  cs = one / f2s
227  d = f2 + g2
228 * Do complex/real division explicitly with two real divisions
229  sn = dcmplx( dble( r ) / d, dimag( r ) / d )
230  sn = sn*dconjg( gs )
231  IF( count.NE.0 ) THEN
232  IF( count.GT.0 ) THEN
233  DO 30 i = 1, count
234  r = r*safmx2
235  30 CONTINUE
236  ELSE
237  DO 40 i = 1, -count
238  r = r*safmn2
239  40 CONTINUE
240  END IF
241  END IF
242  END IF
243  RETURN
244 *
245 * End of ZLARTG
246 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
logical function disnan(DIN)
DISNAN tests input for NaN.
Definition: disnan.f:59
double precision function dlapy2(X, Y)
DLAPY2 returns sqrt(x2+y2).
Definition: dlapy2.f:63
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