root / src / lapack / double / dlas2.f @ 1
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| 1 | 1 | equemene | SUBROUTINE DLAS2( F, G, H, SSMIN, SSMAX ) |
|---|---|---|---|
| 2 | 1 | equemene | * |
| 3 | 1 | equemene | * -- LAPACK auxiliary routine (version 3.2) -- |
| 4 | 1 | equemene | * -- LAPACK is a software package provided by Univ. of Tennessee, -- |
| 5 | 1 | equemene | * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
| 6 | 1 | equemene | * November 2006 |
| 7 | 1 | equemene | * |
| 8 | 1 | equemene | * .. Scalar Arguments .. |
| 9 | 1 | equemene | DOUBLE PRECISION F, G, H, SSMAX, SSMIN |
| 10 | 1 | equemene | * .. |
| 11 | 1 | equemene | * |
| 12 | 1 | equemene | * Purpose |
| 13 | 1 | equemene | * ======= |
| 14 | 1 | equemene | * |
| 15 | 1 | equemene | * DLAS2 computes the singular values of the 2-by-2 matrix |
| 16 | 1 | equemene | * [ F G ] |
| 17 | 1 | equemene | * [ 0 H ]. |
| 18 | 1 | equemene | * On return, SSMIN is the smaller singular value and SSMAX is the |
| 19 | 1 | equemene | * larger singular value. |
| 20 | 1 | equemene | * |
| 21 | 1 | equemene | * Arguments |
| 22 | 1 | equemene | * ========= |
| 23 | 1 | equemene | * |
| 24 | 1 | equemene | * F (input) DOUBLE PRECISION |
| 25 | 1 | equemene | * The (1,1) element of the 2-by-2 matrix. |
| 26 | 1 | equemene | * |
| 27 | 1 | equemene | * G (input) DOUBLE PRECISION |
| 28 | 1 | equemene | * The (1,2) element of the 2-by-2 matrix. |
| 29 | 1 | equemene | * |
| 30 | 1 | equemene | * H (input) DOUBLE PRECISION |
| 31 | 1 | equemene | * The (2,2) element of the 2-by-2 matrix. |
| 32 | 1 | equemene | * |
| 33 | 1 | equemene | * SSMIN (output) DOUBLE PRECISION |
| 34 | 1 | equemene | * The smaller singular value. |
| 35 | 1 | equemene | * |
| 36 | 1 | equemene | * SSMAX (output) DOUBLE PRECISION |
| 37 | 1 | equemene | * The larger singular value. |
| 38 | 1 | equemene | * |
| 39 | 1 | equemene | * Further Details |
| 40 | 1 | equemene | * =============== |
| 41 | 1 | equemene | * |
| 42 | 1 | equemene | * Barring over/underflow, all output quantities are correct to within |
| 43 | 1 | equemene | * a few units in the last place (ulps), even in the absence of a guard |
| 44 | 1 | equemene | * digit in addition/subtraction. |
| 45 | 1 | equemene | * |
| 46 | 1 | equemene | * In IEEE arithmetic, the code works correctly if one matrix element is |
| 47 | 1 | equemene | * infinite. |
| 48 | 1 | equemene | * |
| 49 | 1 | equemene | * Overflow will not occur unless the largest singular value itself |
| 50 | 1 | equemene | * overflows, or is within a few ulps of overflow. (On machines with |
| 51 | 1 | equemene | * partial overflow, like the Cray, overflow may occur if the largest |
| 52 | 1 | equemene | * singular value is within a factor of 2 of overflow.) |
| 53 | 1 | equemene | * |
| 54 | 1 | equemene | * Underflow is harmless if underflow is gradual. Otherwise, results |
| 55 | 1 | equemene | * may correspond to a matrix modified by perturbations of size near |
| 56 | 1 | equemene | * the underflow threshold. |
| 57 | 1 | equemene | * |
| 58 | 1 | equemene | * ==================================================================== |
| 59 | 1 | equemene | * |
| 60 | 1 | equemene | * .. Parameters .. |
| 61 | 1 | equemene | DOUBLE PRECISION ZERO |
| 62 | 1 | equemene | PARAMETER ( ZERO = 0.0D0 ) |
| 63 | 1 | equemene | DOUBLE PRECISION ONE |
| 64 | 1 | equemene | PARAMETER ( ONE = 1.0D0 ) |
| 65 | 1 | equemene | DOUBLE PRECISION TWO |
| 66 | 1 | equemene | PARAMETER ( TWO = 2.0D0 ) |
| 67 | 1 | equemene | * .. |
| 68 | 1 | equemene | * .. Local Scalars .. |
| 69 | 1 | equemene | DOUBLE PRECISION AS, AT, AU, C, FA, FHMN, FHMX, GA, HA |
| 70 | 1 | equemene | * .. |
| 71 | 1 | equemene | * .. Intrinsic Functions .. |
| 72 | 1 | equemene | INTRINSIC ABS, MAX, MIN, SQRT |
| 73 | 1 | equemene | * .. |
| 74 | 1 | equemene | * .. Executable Statements .. |
| 75 | 1 | equemene | * |
| 76 | 1 | equemene | FA = ABS( F ) |
| 77 | 1 | equemene | GA = ABS( G ) |
| 78 | 1 | equemene | HA = ABS( H ) |
| 79 | 1 | equemene | FHMN = MIN( FA, HA ) |
| 80 | 1 | equemene | FHMX = MAX( FA, HA ) |
| 81 | 1 | equemene | IF( FHMN.EQ.ZERO ) THEN |
| 82 | 1 | equemene | SSMIN = ZERO |
| 83 | 1 | equemene | IF( FHMX.EQ.ZERO ) THEN |
| 84 | 1 | equemene | SSMAX = GA |
| 85 | 1 | equemene | ELSE |
| 86 | 1 | equemene | SSMAX = MAX( FHMX, GA )*SQRT( ONE+ |
| 87 | 1 | equemene | $ ( MIN( FHMX, GA ) / MAX( FHMX, GA ) )**2 ) |
| 88 | 1 | equemene | END IF |
| 89 | 1 | equemene | ELSE |
| 90 | 1 | equemene | IF( GA.LT.FHMX ) THEN |
| 91 | 1 | equemene | AS = ONE + FHMN / FHMX |
| 92 | 1 | equemene | AT = ( FHMX-FHMN ) / FHMX |
| 93 | 1 | equemene | AU = ( GA / FHMX )**2 |
| 94 | 1 | equemene | C = TWO / ( SQRT( AS*AS+AU )+SQRT( AT*AT+AU ) ) |
| 95 | 1 | equemene | SSMIN = FHMN*C |
| 96 | 1 | equemene | SSMAX = FHMX / C |
| 97 | 1 | equemene | ELSE |
| 98 | 1 | equemene | AU = FHMX / GA |
| 99 | 1 | equemene | IF( AU.EQ.ZERO ) THEN |
| 100 | 1 | equemene | * |
| 101 | 1 | equemene | * Avoid possible harmful underflow if exponent range |
| 102 | 1 | equemene | * asymmetric (true SSMIN may not underflow even if |
| 103 | 1 | equemene | * AU underflows) |
| 104 | 1 | equemene | * |
| 105 | 1 | equemene | SSMIN = ( FHMN*FHMX ) / GA |
| 106 | 1 | equemene | SSMAX = GA |
| 107 | 1 | equemene | ELSE |
| 108 | 1 | equemene | AS = ONE + FHMN / FHMX |
| 109 | 1 | equemene | AT = ( FHMX-FHMN ) / FHMX |
| 110 | 1 | equemene | C = ONE / ( SQRT( ONE+( AS*AU )**2 )+ |
| 111 | 1 | equemene | $ SQRT( ONE+( AT*AU )**2 ) ) |
| 112 | 1 | equemene | SSMIN = ( FHMN*C )*AU |
| 113 | 1 | equemene | SSMIN = SSMIN + SSMIN |
| 114 | 1 | equemene | SSMAX = GA / ( C+C ) |
| 115 | 1 | equemene | END IF |
| 116 | 1 | equemene | END IF |
| 117 | 1 | equemene | END IF |
| 118 | 1 | equemene | RETURN |
| 119 | 1 | equemene | * |
| 120 | 1 | equemene | * End of DLAS2 |
| 121 | 1 | equemene | * |
| 122 | 1 | equemene | END |