Annotation of rpl/lapack/lapack/zlartg.f, revision 1.4
1.1 bertrand 1: SUBROUTINE ZLARTG( F, G, CS, SN, R )
2: *
3: * -- LAPACK auxiliary routine (version 3.2) --
4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6: * November 2006
7: *
8: * .. Scalar Arguments ..
9: DOUBLE PRECISION CS
10: COMPLEX*16 F, G, R, SN
11: * ..
12: *
13: * Purpose
14: * =======
15: *
16: * ZLARTG generates a plane rotation so that
17: *
18: * [ CS SN ] [ F ] [ R ]
19: * [ __ ] . [ ] = [ ] where CS**2 + |SN|**2 = 1.
20: * [ -SN CS ] [ G ] [ 0 ]
21: *
22: * This is a faster version of the BLAS1 routine ZROTG, except for
23: * the following differences:
24: * F and G are unchanged on return.
25: * If G=0, then CS=1 and SN=0.
26: * If F=0, then CS=0 and SN is chosen so that R is real.
27: *
28: * Arguments
29: * =========
30: *
31: * F (input) COMPLEX*16
32: * The first component of vector to be rotated.
33: *
34: * G (input) COMPLEX*16
35: * The second component of vector to be rotated.
36: *
37: * CS (output) DOUBLE PRECISION
38: * The cosine of the rotation.
39: *
40: * SN (output) COMPLEX*16
41: * The sine of the rotation.
42: *
43: * R (output) COMPLEX*16
44: * The nonzero component of the rotated vector.
45: *
46: * Further Details
47: * ======= =======
48: *
49: * 3-5-96 - Modified with a new algorithm by W. Kahan and J. Demmel
50: *
51: * This version has a few statements commented out for thread safety
52: * (machine parameters are computed on each entry). 10 feb 03, SJH.
53: *
54: * =====================================================================
55: *
56: * .. Parameters ..
57: DOUBLE PRECISION TWO, ONE, ZERO
58: PARAMETER ( TWO = 2.0D+0, ONE = 1.0D+0, ZERO = 0.0D+0 )
59: COMPLEX*16 CZERO
60: PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ) )
61: * ..
62: * .. Local Scalars ..
63: * LOGICAL FIRST
64: INTEGER COUNT, I
65: DOUBLE PRECISION D, DI, DR, EPS, F2, F2S, G2, G2S, SAFMIN,
66: $ SAFMN2, SAFMX2, SCALE
67: COMPLEX*16 FF, FS, GS
68: * ..
69: * .. External Functions ..
70: DOUBLE PRECISION DLAMCH, DLAPY2
71: EXTERNAL DLAMCH, DLAPY2
72: * ..
73: * .. Intrinsic Functions ..
74: INTRINSIC ABS, DBLE, DCMPLX, DCONJG, DIMAG, INT, LOG,
75: $ MAX, SQRT
76: * ..
77: * .. Statement Functions ..
78: DOUBLE PRECISION ABS1, ABSSQ
79: * ..
80: * .. Save statement ..
81: * SAVE FIRST, SAFMX2, SAFMIN, SAFMN2
82: * ..
83: * .. Data statements ..
84: * DATA FIRST / .TRUE. /
85: * ..
86: * .. Statement Function definitions ..
87: ABS1( FF ) = MAX( ABS( DBLE( FF ) ), ABS( DIMAG( FF ) ) )
88: ABSSQ( FF ) = DBLE( FF )**2 + DIMAG( FF )**2
89: * ..
90: * .. Executable Statements ..
91: *
92: * IF( FIRST ) THEN
93: SAFMIN = DLAMCH( 'S' )
94: EPS = DLAMCH( 'E' )
95: SAFMN2 = DLAMCH( 'B' )**INT( LOG( SAFMIN / EPS ) /
96: $ LOG( DLAMCH( 'B' ) ) / TWO )
97: SAFMX2 = ONE / SAFMN2
98: * FIRST = .FALSE.
99: * END IF
100: SCALE = MAX( ABS1( F ), ABS1( G ) )
101: FS = F
102: GS = G
103: COUNT = 0
104: IF( SCALE.GE.SAFMX2 ) THEN
105: 10 CONTINUE
106: COUNT = COUNT + 1
107: FS = FS*SAFMN2
108: GS = GS*SAFMN2
109: SCALE = SCALE*SAFMN2
110: IF( SCALE.GE.SAFMX2 )
111: $ GO TO 10
112: ELSE IF( SCALE.LE.SAFMN2 ) THEN
113: IF( G.EQ.CZERO ) THEN
114: CS = ONE
115: SN = CZERO
116: R = F
117: RETURN
118: END IF
119: 20 CONTINUE
120: COUNT = COUNT - 1
121: FS = FS*SAFMX2
122: GS = GS*SAFMX2
123: SCALE = SCALE*SAFMX2
124: IF( SCALE.LE.SAFMN2 )
125: $ GO TO 20
126: END IF
127: F2 = ABSSQ( FS )
128: G2 = ABSSQ( GS )
129: IF( F2.LE.MAX( G2, ONE )*SAFMIN ) THEN
130: *
131: * This is a rare case: F is very small.
132: *
133: IF( F.EQ.CZERO ) THEN
134: CS = ZERO
135: R = DLAPY2( DBLE( G ), DIMAG( G ) )
136: * Do complex/real division explicitly with two real divisions
137: D = DLAPY2( DBLE( GS ), DIMAG( GS ) )
138: SN = DCMPLX( DBLE( GS ) / D, -DIMAG( GS ) / D )
139: RETURN
140: END IF
141: F2S = DLAPY2( DBLE( FS ), DIMAG( FS ) )
142: * G2 and G2S are accurate
143: * G2 is at least SAFMIN, and G2S is at least SAFMN2
144: G2S = SQRT( G2 )
145: * Error in CS from underflow in F2S is at most
146: * UNFL / SAFMN2 .lt. sqrt(UNFL*EPS) .lt. EPS
147: * If MAX(G2,ONE)=G2, then F2 .lt. G2*SAFMIN,
148: * and so CS .lt. sqrt(SAFMIN)
149: * If MAX(G2,ONE)=ONE, then F2 .lt. SAFMIN
150: * and so CS .lt. sqrt(SAFMIN)/SAFMN2 = sqrt(EPS)
151: * Therefore, CS = F2S/G2S / sqrt( 1 + (F2S/G2S)**2 ) = F2S/G2S
152: CS = F2S / G2S
153: * Make sure abs(FF) = 1
154: * Do complex/real division explicitly with 2 real divisions
155: IF( ABS1( F ).GT.ONE ) THEN
156: D = DLAPY2( DBLE( F ), DIMAG( F ) )
157: FF = DCMPLX( DBLE( F ) / D, DIMAG( F ) / D )
158: ELSE
159: DR = SAFMX2*DBLE( F )
160: DI = SAFMX2*DIMAG( F )
161: D = DLAPY2( DR, DI )
162: FF = DCMPLX( DR / D, DI / D )
163: END IF
164: SN = FF*DCMPLX( DBLE( GS ) / G2S, -DIMAG( GS ) / G2S )
165: R = CS*F + SN*G
166: ELSE
167: *
168: * This is the most common case.
169: * Neither F2 nor F2/G2 are less than SAFMIN
170: * F2S cannot overflow, and it is accurate
171: *
172: F2S = SQRT( ONE+G2 / F2 )
173: * Do the F2S(real)*FS(complex) multiply with two real multiplies
174: R = DCMPLX( F2S*DBLE( FS ), F2S*DIMAG( FS ) )
175: CS = ONE / F2S
176: D = F2 + G2
177: * Do complex/real division explicitly with two real divisions
178: SN = DCMPLX( DBLE( R ) / D, DIMAG( R ) / D )
179: SN = SN*DCONJG( GS )
180: IF( COUNT.NE.0 ) THEN
181: IF( COUNT.GT.0 ) THEN
182: DO 30 I = 1, COUNT
183: R = R*SAFMX2
184: 30 CONTINUE
185: ELSE
186: DO 40 I = 1, -COUNT
187: R = R*SAFMN2
188: 40 CONTINUE
189: END IF
190: END IF
191: END IF
192: RETURN
193: *
194: * End of ZLARTG
195: *
196: END
CVSweb interface <joel.bertrand@systella.fr>
![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to zlartg.f CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [local] / rpl / lapack / lapack