root / src / lapack / double / dlasd8.f @ 10
Historique | Voir | Annoter | Télécharger (8,6 ko)
| 1 |
SUBROUTINE DLASD8( ICOMPQ, K, D, Z, VF, VL, DIFL, DIFR, LDDIFR, |
|---|---|
| 2 |
$ DSIGMA, WORK, INFO ) |
| 3 |
* |
| 4 |
* -- LAPACK auxiliary routine (version 3.2.2) -- |
| 5 |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
| 6 |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
| 7 |
* June 2010 |
| 8 |
* |
| 9 |
* .. Scalar Arguments .. |
| 10 |
INTEGER ICOMPQ, INFO, K, LDDIFR |
| 11 |
* .. |
| 12 |
* .. Array Arguments .. |
| 13 |
DOUBLE PRECISION D( * ), DIFL( * ), DIFR( LDDIFR, * ), |
| 14 |
$ DSIGMA( * ), VF( * ), VL( * ), WORK( * ), |
| 15 |
$ Z( * ) |
| 16 |
* .. |
| 17 |
* |
| 18 |
* Purpose |
| 19 |
* ======= |
| 20 |
* |
| 21 |
* DLASD8 finds the square roots of the roots of the secular equation, |
| 22 |
* as defined by the values in DSIGMA and Z. It makes the appropriate |
| 23 |
* calls to DLASD4, and stores, for each element in D, the distance |
| 24 |
* to its two nearest poles (elements in DSIGMA). It also updates |
| 25 |
* the arrays VF and VL, the first and last components of all the |
| 26 |
* right singular vectors of the original bidiagonal matrix. |
| 27 |
* |
| 28 |
* DLASD8 is called from DLASD6. |
| 29 |
* |
| 30 |
* Arguments |
| 31 |
* ========= |
| 32 |
* |
| 33 |
* ICOMPQ (input) INTEGER |
| 34 |
* Specifies whether singular vectors are to be computed in |
| 35 |
* factored form in the calling routine: |
| 36 |
* = 0: Compute singular values only. |
| 37 |
* = 1: Compute singular vectors in factored form as well. |
| 38 |
* |
| 39 |
* K (input) INTEGER |
| 40 |
* The number of terms in the rational function to be solved |
| 41 |
* by DLASD4. K >= 1. |
| 42 |
* |
| 43 |
* D (output) DOUBLE PRECISION array, dimension ( K ) |
| 44 |
* On output, D contains the updated singular values. |
| 45 |
* |
| 46 |
* Z (input/output) DOUBLE PRECISION array, dimension ( K ) |
| 47 |
* On entry, the first K elements of this array contain the |
| 48 |
* components of the deflation-adjusted updating row vector. |
| 49 |
* On exit, Z is updated. |
| 50 |
* |
| 51 |
* VF (input/output) DOUBLE PRECISION array, dimension ( K ) |
| 52 |
* On entry, VF contains information passed through DBEDE8. |
| 53 |
* On exit, VF contains the first K components of the first |
| 54 |
* components of all right singular vectors of the bidiagonal |
| 55 |
* matrix. |
| 56 |
* |
| 57 |
* VL (input/output) DOUBLE PRECISION array, dimension ( K ) |
| 58 |
* On entry, VL contains information passed through DBEDE8. |
| 59 |
* On exit, VL contains the first K components of the last |
| 60 |
* components of all right singular vectors of the bidiagonal |
| 61 |
* matrix. |
| 62 |
* |
| 63 |
* DIFL (output) DOUBLE PRECISION array, dimension ( K ) |
| 64 |
* On exit, DIFL(I) = D(I) - DSIGMA(I). |
| 65 |
* |
| 66 |
* DIFR (output) DOUBLE PRECISION array, |
| 67 |
* dimension ( LDDIFR, 2 ) if ICOMPQ = 1 and |
| 68 |
* dimension ( K ) if ICOMPQ = 0. |
| 69 |
* On exit, DIFR(I,1) = D(I) - DSIGMA(I+1), DIFR(K,1) is not |
| 70 |
* defined and will not be referenced. |
| 71 |
* |
| 72 |
* If ICOMPQ = 1, DIFR(1:K,2) is an array containing the |
| 73 |
* normalizing factors for the right singular vector matrix. |
| 74 |
* |
| 75 |
* LDDIFR (input) INTEGER |
| 76 |
* The leading dimension of DIFR, must be at least K. |
| 77 |
* |
| 78 |
* DSIGMA (input/output) DOUBLE PRECISION array, dimension ( K ) |
| 79 |
* On entry, the first K elements of this array contain the old |
| 80 |
* roots of the deflated updating problem. These are the poles |
| 81 |
* of the secular equation. |
| 82 |
* On exit, the elements of DSIGMA may be very slightly altered |
| 83 |
* in value. |
| 84 |
* |
| 85 |
* WORK (workspace) DOUBLE PRECISION array, dimension at least 3 * K |
| 86 |
* |
| 87 |
* INFO (output) INTEGER |
| 88 |
* = 0: successful exit. |
| 89 |
* < 0: if INFO = -i, the i-th argument had an illegal value. |
| 90 |
* > 0: if INFO = 1, a singular value did not converge |
| 91 |
* |
| 92 |
* Further Details |
| 93 |
* =============== |
| 94 |
* |
| 95 |
* Based on contributions by |
| 96 |
* Ming Gu and Huan Ren, Computer Science Division, University of |
| 97 |
* California at Berkeley, USA |
| 98 |
* |
| 99 |
* ===================================================================== |
| 100 |
* |
| 101 |
* .. Parameters .. |
| 102 |
DOUBLE PRECISION ONE |
| 103 |
PARAMETER ( ONE = 1.0D+0 ) |
| 104 |
* .. |
| 105 |
* .. Local Scalars .. |
| 106 |
INTEGER I, IWK1, IWK2, IWK2I, IWK3, IWK3I, J |
| 107 |
DOUBLE PRECISION DIFLJ, DIFRJ, DJ, DSIGJ, DSIGJP, RHO, TEMP |
| 108 |
* .. |
| 109 |
* .. External Subroutines .. |
| 110 |
EXTERNAL DCOPY, DLASCL, DLASD4, DLASET, XERBLA |
| 111 |
* .. |
| 112 |
* .. External Functions .. |
| 113 |
DOUBLE PRECISION DDOT, DLAMC3, DNRM2 |
| 114 |
EXTERNAL DDOT, DLAMC3, DNRM2 |
| 115 |
* .. |
| 116 |
* .. Intrinsic Functions .. |
| 117 |
INTRINSIC ABS, SIGN, SQRT |
| 118 |
* .. |
| 119 |
* .. Executable Statements .. |
| 120 |
* |
| 121 |
* Test the input parameters. |
| 122 |
* |
| 123 |
INFO = 0 |
| 124 |
* |
| 125 |
IF( ( ICOMPQ.LT.0 ) .OR. ( ICOMPQ.GT.1 ) ) THEN |
| 126 |
INFO = -1 |
| 127 |
ELSE IF( K.LT.1 ) THEN |
| 128 |
INFO = -2 |
| 129 |
ELSE IF( LDDIFR.LT.K ) THEN |
| 130 |
INFO = -9 |
| 131 |
END IF |
| 132 |
IF( INFO.NE.0 ) THEN |
| 133 |
CALL XERBLA( 'DLASD8', -INFO ) |
| 134 |
RETURN |
| 135 |
END IF |
| 136 |
* |
| 137 |
* Quick return if possible |
| 138 |
* |
| 139 |
IF( K.EQ.1 ) THEN |
| 140 |
D( 1 ) = ABS( Z( 1 ) ) |
| 141 |
DIFL( 1 ) = D( 1 ) |
| 142 |
IF( ICOMPQ.EQ.1 ) THEN |
| 143 |
DIFL( 2 ) = ONE |
| 144 |
DIFR( 1, 2 ) = ONE |
| 145 |
END IF |
| 146 |
RETURN |
| 147 |
END IF |
| 148 |
* |
| 149 |
* Modify values DSIGMA(i) to make sure all DSIGMA(i)-DSIGMA(j) can |
| 150 |
* be computed with high relative accuracy (barring over/underflow). |
| 151 |
* This is a problem on machines without a guard digit in |
| 152 |
* add/subtract (Cray XMP, Cray YMP, Cray C 90 and Cray 2). |
| 153 |
* The following code replaces DSIGMA(I) by 2*DSIGMA(I)-DSIGMA(I), |
| 154 |
* which on any of these machines zeros out the bottommost |
| 155 |
* bit of DSIGMA(I) if it is 1; this makes the subsequent |
| 156 |
* subtractions DSIGMA(I)-DSIGMA(J) unproblematic when cancellation |
| 157 |
* occurs. On binary machines with a guard digit (almost all |
| 158 |
* machines) it does not change DSIGMA(I) at all. On hexadecimal |
| 159 |
* and decimal machines with a guard digit, it slightly |
| 160 |
* changes the bottommost bits of DSIGMA(I). It does not account |
| 161 |
* for hexadecimal or decimal machines without guard digits |
| 162 |
* (we know of none). We use a subroutine call to compute |
| 163 |
* 2*DLAMBDA(I) to prevent optimizing compilers from eliminating |
| 164 |
* this code. |
| 165 |
* |
| 166 |
DO 10 I = 1, K |
| 167 |
DSIGMA( I ) = DLAMC3( DSIGMA( I ), DSIGMA( I ) ) - DSIGMA( I ) |
| 168 |
10 CONTINUE |
| 169 |
* |
| 170 |
* Book keeping. |
| 171 |
* |
| 172 |
IWK1 = 1 |
| 173 |
IWK2 = IWK1 + K |
| 174 |
IWK3 = IWK2 + K |
| 175 |
IWK2I = IWK2 - 1 |
| 176 |
IWK3I = IWK3 - 1 |
| 177 |
* |
| 178 |
* Normalize Z. |
| 179 |
* |
| 180 |
RHO = DNRM2( K, Z, 1 ) |
| 181 |
CALL DLASCL( 'G', 0, 0, RHO, ONE, K, 1, Z, K, INFO ) |
| 182 |
RHO = RHO*RHO |
| 183 |
* |
| 184 |
* Initialize WORK(IWK3). |
| 185 |
* |
| 186 |
CALL DLASET( 'A', K, 1, ONE, ONE, WORK( IWK3 ), K ) |
| 187 |
* |
| 188 |
* Compute the updated singular values, the arrays DIFL, DIFR, |
| 189 |
* and the updated Z. |
| 190 |
* |
| 191 |
DO 40 J = 1, K |
| 192 |
CALL DLASD4( K, J, DSIGMA, Z, WORK( IWK1 ), RHO, D( J ), |
| 193 |
$ WORK( IWK2 ), INFO ) |
| 194 |
* |
| 195 |
* If the root finder fails, the computation is terminated. |
| 196 |
* |
| 197 |
IF( INFO.NE.0 ) THEN |
| 198 |
RETURN |
| 199 |
END IF |
| 200 |
WORK( IWK3I+J ) = WORK( IWK3I+J )*WORK( J )*WORK( IWK2I+J ) |
| 201 |
DIFL( J ) = -WORK( J ) |
| 202 |
DIFR( J, 1 ) = -WORK( J+1 ) |
| 203 |
DO 20 I = 1, J - 1 |
| 204 |
WORK( IWK3I+I ) = WORK( IWK3I+I )*WORK( I )* |
| 205 |
$ WORK( IWK2I+I ) / ( DSIGMA( I )- |
| 206 |
$ DSIGMA( J ) ) / ( DSIGMA( I )+ |
| 207 |
$ DSIGMA( J ) ) |
| 208 |
20 CONTINUE |
| 209 |
DO 30 I = J + 1, K |
| 210 |
WORK( IWK3I+I ) = WORK( IWK3I+I )*WORK( I )* |
| 211 |
$ WORK( IWK2I+I ) / ( DSIGMA( I )- |
| 212 |
$ DSIGMA( J ) ) / ( DSIGMA( I )+ |
| 213 |
$ DSIGMA( J ) ) |
| 214 |
30 CONTINUE |
| 215 |
40 CONTINUE |
| 216 |
* |
| 217 |
* Compute updated Z. |
| 218 |
* |
| 219 |
DO 50 I = 1, K |
| 220 |
Z( I ) = SIGN( SQRT( ABS( WORK( IWK3I+I ) ) ), Z( I ) ) |
| 221 |
50 CONTINUE |
| 222 |
* |
| 223 |
* Update VF and VL. |
| 224 |
* |
| 225 |
DO 80 J = 1, K |
| 226 |
DIFLJ = DIFL( J ) |
| 227 |
DJ = D( J ) |
| 228 |
DSIGJ = -DSIGMA( J ) |
| 229 |
IF( J.LT.K ) THEN |
| 230 |
DIFRJ = -DIFR( J, 1 ) |
| 231 |
DSIGJP = -DSIGMA( J+1 ) |
| 232 |
END IF |
| 233 |
WORK( J ) = -Z( J ) / DIFLJ / ( DSIGMA( J )+DJ ) |
| 234 |
DO 60 I = 1, J - 1 |
| 235 |
WORK( I ) = Z( I ) / ( DLAMC3( DSIGMA( I ), DSIGJ )-DIFLJ ) |
| 236 |
$ / ( DSIGMA( I )+DJ ) |
| 237 |
60 CONTINUE |
| 238 |
DO 70 I = J + 1, K |
| 239 |
WORK( I ) = Z( I ) / ( DLAMC3( DSIGMA( I ), DSIGJP )+DIFRJ ) |
| 240 |
$ / ( DSIGMA( I )+DJ ) |
| 241 |
70 CONTINUE |
| 242 |
TEMP = DNRM2( K, WORK, 1 ) |
| 243 |
WORK( IWK2I+J ) = DDOT( K, WORK, 1, VF, 1 ) / TEMP |
| 244 |
WORK( IWK3I+J ) = DDOT( K, WORK, 1, VL, 1 ) / TEMP |
| 245 |
IF( ICOMPQ.EQ.1 ) THEN |
| 246 |
DIFR( J, 2 ) = TEMP |
| 247 |
END IF |
| 248 |
80 CONTINUE |
| 249 |
* |
| 250 |
CALL DCOPY( K, WORK( IWK2 ), 1, VF, 1 ) |
| 251 |
CALL DCOPY( K, WORK( IWK3 ), 1, VL, 1 ) |
| 252 |
* |
| 253 |
RETURN |
| 254 |
* |
| 255 |
* End of DLASD8 |
| 256 |
* |
| 257 |
END |
| 258 |
|