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