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Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE DLASY2( LTRANL, LTRANR, ISGN, N1, N2, TL, LDTL, TR, 2: $ LDTR, B, LDB, SCALE, X, LDX, XNORM, INFO ) 3: * 4: * -- LAPACK auxiliary routine (version 3.2) -- 5: * -- LAPACK is a software package provided by Univ. of Tennessee, -- 6: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 7: * November 2006 8: * 9: * .. Scalar Arguments .. 10: LOGICAL LTRANL, LTRANR 11: INTEGER INFO, ISGN, LDB, LDTL, LDTR, LDX, N1, N2 12: DOUBLE PRECISION SCALE, XNORM 13: * .. 14: * .. Array Arguments .. 15: DOUBLE PRECISION B( LDB, * ), TL( LDTL, * ), TR( LDTR, * ), 16: $ X( LDX, * ) 17: * .. 18: * 19: * Purpose 20: * ======= 21: * 22: * DLASY2 solves for the N1 by N2 matrix X, 1 <= N1,N2 <= 2, in 23: * 24: * op(TL)*X + ISGN*X*op(TR) = SCALE*B, 25: * 26: * where TL is N1 by N1, TR is N2 by N2, B is N1 by N2, and ISGN = 1 or 27: * -1. op(T) = T or T', where T' denotes the transpose of T. 28: * 29: * Arguments 30: * ========= 31: * 32: * LTRANL (input) LOGICAL 33: * On entry, LTRANL specifies the op(TL): 34: * = .FALSE., op(TL) = TL, 35: * = .TRUE., op(TL) = TL'. 36: * 37: * LTRANR (input) LOGICAL 38: * On entry, LTRANR specifies the op(TR): 39: * = .FALSE., op(TR) = TR, 40: * = .TRUE., op(TR) = TR'. 41: * 42: * ISGN (input) INTEGER 43: * On entry, ISGN specifies the sign of the equation 44: * as described before. ISGN may only be 1 or -1. 45: * 46: * N1 (input) INTEGER 47: * On entry, N1 specifies the order of matrix TL. 48: * N1 may only be 0, 1 or 2. 49: * 50: * N2 (input) INTEGER 51: * On entry, N2 specifies the order of matrix TR. 52: * N2 may only be 0, 1 or 2. 53: * 54: * TL (input) DOUBLE PRECISION array, dimension (LDTL,2) 55: * On entry, TL contains an N1 by N1 matrix. 56: * 57: * LDTL (input) INTEGER 58: * The leading dimension of the matrix TL. LDTL >= max(1,N1). 59: * 60: * TR (input) DOUBLE PRECISION array, dimension (LDTR,2) 61: * On entry, TR contains an N2 by N2 matrix. 62: * 63: * LDTR (input) INTEGER 64: * The leading dimension of the matrix TR. LDTR >= max(1,N2). 65: * 66: * B (input) DOUBLE PRECISION array, dimension (LDB,2) 67: * On entry, the N1 by N2 matrix B contains the right-hand 68: * side of the equation. 69: * 70: * LDB (input) INTEGER 71: * The leading dimension of the matrix B. LDB >= max(1,N1). 72: * 73: * SCALE (output) DOUBLE PRECISION 74: * On exit, SCALE contains the scale factor. SCALE is chosen 75: * less than or equal to 1 to prevent the solution overflowing. 76: * 77: * X (output) DOUBLE PRECISION array, dimension (LDX,2) 78: * On exit, X contains the N1 by N2 solution. 79: * 80: * LDX (input) INTEGER 81: * The leading dimension of the matrix X. LDX >= max(1,N1). 82: * 83: * XNORM (output) DOUBLE PRECISION 84: * On exit, XNORM is the infinity-norm of the solution. 85: * 86: * INFO (output) INTEGER 87: * On exit, INFO is set to 88: * 0: successful exit. 89: * 1: TL and TR have too close eigenvalues, so TL or 90: * TR is perturbed to get a nonsingular equation. 91: * NOTE: In the interests of speed, this routine does not 92: * check the inputs for errors. 93: * 94: * ===================================================================== 95: * 96: * .. Parameters .. 97: DOUBLE PRECISION ZERO, ONE 98: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) 99: DOUBLE PRECISION TWO, HALF, EIGHT 100: PARAMETER ( TWO = 2.0D+0, HALF = 0.5D+0, EIGHT = 8.0D+0 ) 101: * .. 102: * .. Local Scalars .. 103: LOGICAL BSWAP, XSWAP 104: INTEGER I, IP, IPIV, IPSV, J, JP, JPSV, K 105: DOUBLE PRECISION BET, EPS, GAM, L21, SGN, SMIN, SMLNUM, TAU1, 106: $ TEMP, U11, U12, U22, XMAX 107: * .. 108: * .. Local Arrays .. 109: LOGICAL BSWPIV( 4 ), XSWPIV( 4 ) 110: INTEGER JPIV( 4 ), LOCL21( 4 ), LOCU12( 4 ), 111: $ LOCU22( 4 ) 112: DOUBLE PRECISION BTMP( 4 ), T16( 4, 4 ), TMP( 4 ), X2( 2 ) 113: * .. 114: * .. External Functions .. 115: INTEGER IDAMAX 116: DOUBLE PRECISION DLAMCH 117: EXTERNAL IDAMAX, DLAMCH 118: * .. 119: * .. External Subroutines .. 120: EXTERNAL DCOPY, DSWAP 121: * .. 122: * .. Intrinsic Functions .. 123: INTRINSIC ABS, MAX 124: * .. 125: * .. Data statements .. 126: DATA LOCU12 / 3, 4, 1, 2 / , LOCL21 / 2, 1, 4, 3 / , 127: $ LOCU22 / 4, 3, 2, 1 / 128: DATA XSWPIV / .FALSE., .FALSE., .TRUE., .TRUE. / 129: DATA BSWPIV / .FALSE., .TRUE., .FALSE., .TRUE. / 130: * .. 131: * .. Executable Statements .. 132: * 133: * Do not check the input parameters for errors 134: * 135: INFO = 0 136: * 137: * Quick return if possible 138: * 139: IF( N1.EQ.0 .OR. N2.EQ.0 ) 140: $ RETURN 141: * 142: * Set constants to control overflow 143: * 144: EPS = DLAMCH( 'P' ) 145: SMLNUM = DLAMCH( 'S' ) / EPS 146: SGN = ISGN 147: * 148: K = N1 + N1 + N2 - 2 149: GO TO ( 10, 20, 30, 50 )K 150: * 151: * 1 by 1: TL11*X + SGN*X*TR11 = B11 152: * 153: 10 CONTINUE 154: TAU1 = TL( 1, 1 ) + SGN*TR( 1, 1 ) 155: BET = ABS( TAU1 ) 156: IF( BET.LE.SMLNUM ) THEN 157: TAU1 = SMLNUM 158: BET = SMLNUM 159: INFO = 1 160: END IF 161: * 162: SCALE = ONE 163: GAM = ABS( B( 1, 1 ) ) 164: IF( SMLNUM*GAM.GT.BET ) 165: $ SCALE = ONE / GAM 166: * 167: X( 1, 1 ) = ( B( 1, 1 )*SCALE ) / TAU1 168: XNORM = ABS( X( 1, 1 ) ) 169: RETURN 170: * 171: * 1 by 2: 172: * TL11*[X11 X12] + ISGN*[X11 X12]*op[TR11 TR12] = [B11 B12] 173: * [TR21 TR22] 174: * 175: 20 CONTINUE 176: * 177: SMIN = MAX( EPS*MAX( ABS( TL( 1, 1 ) ), ABS( TR( 1, 1 ) ), 178: $ ABS( TR( 1, 2 ) ), ABS( TR( 2, 1 ) ), ABS( TR( 2, 2 ) ) ), 179: $ SMLNUM ) 180: TMP( 1 ) = TL( 1, 1 ) + SGN*TR( 1, 1 ) 181: TMP( 4 ) = TL( 1, 1 ) + SGN*TR( 2, 2 ) 182: IF( LTRANR ) THEN 183: TMP( 2 ) = SGN*TR( 2, 1 ) 184: TMP( 3 ) = SGN*TR( 1, 2 ) 185: ELSE 186: TMP( 2 ) = SGN*TR( 1, 2 ) 187: TMP( 3 ) = SGN*TR( 2, 1 ) 188: END IF 189: BTMP( 1 ) = B( 1, 1 ) 190: BTMP( 2 ) = B( 1, 2 ) 191: GO TO 40 192: * 193: * 2 by 1: 194: * op[TL11 TL12]*[X11] + ISGN* [X11]*TR11 = [B11] 195: * [TL21 TL22] [X21] [X21] [B21] 196: * 197: 30 CONTINUE 198: SMIN = MAX( EPS*MAX( ABS( TR( 1, 1 ) ), ABS( TL( 1, 1 ) ), 199: $ ABS( TL( 1, 2 ) ), ABS( TL( 2, 1 ) ), ABS( TL( 2, 2 ) ) ), 200: $ SMLNUM ) 201: TMP( 1 ) = TL( 1, 1 ) + SGN*TR( 1, 1 ) 202: TMP( 4 ) = TL( 2, 2 ) + SGN*TR( 1, 1 ) 203: IF( LTRANL ) THEN 204: TMP( 2 ) = TL( 1, 2 ) 205: TMP( 3 ) = TL( 2, 1 ) 206: ELSE 207: TMP( 2 ) = TL( 2, 1 ) 208: TMP( 3 ) = TL( 1, 2 ) 209: END IF 210: BTMP( 1 ) = B( 1, 1 ) 211: BTMP( 2 ) = B( 2, 1 ) 212: 40 CONTINUE 213: * 214: * Solve 2 by 2 system using complete pivoting. 215: * Set pivots less than SMIN to SMIN. 216: * 217: IPIV = IDAMAX( 4, TMP, 1 ) 218: U11 = TMP( IPIV ) 219: IF( ABS( U11 ).LE.SMIN ) THEN 220: INFO = 1 221: U11 = SMIN 222: END IF 223: U12 = TMP( LOCU12( IPIV ) ) 224: L21 = TMP( LOCL21( IPIV ) ) / U11 225: U22 = TMP( LOCU22( IPIV ) ) - U12*L21 226: XSWAP = XSWPIV( IPIV ) 227: BSWAP = BSWPIV( IPIV ) 228: IF( ABS( U22 ).LE.SMIN ) THEN 229: INFO = 1 230: U22 = SMIN 231: END IF 232: IF( BSWAP ) THEN 233: TEMP = BTMP( 2 ) 234: BTMP( 2 ) = BTMP( 1 ) - L21*TEMP 235: BTMP( 1 ) = TEMP 236: ELSE 237: BTMP( 2 ) = BTMP( 2 ) - L21*BTMP( 1 ) 238: END IF 239: SCALE = ONE 240: IF( ( TWO*SMLNUM )*ABS( BTMP( 2 ) ).GT.ABS( U22 ) .OR. 241: $ ( TWO*SMLNUM )*ABS( BTMP( 1 ) ).GT.ABS( U11 ) ) THEN 242: SCALE = HALF / MAX( ABS( BTMP( 1 ) ), ABS( BTMP( 2 ) ) ) 243: BTMP( 1 ) = BTMP( 1 )*SCALE 244: BTMP( 2 ) = BTMP( 2 )*SCALE 245: END IF 246: X2( 2 ) = BTMP( 2 ) / U22 247: X2( 1 ) = BTMP( 1 ) / U11 - ( U12 / U11 )*X2( 2 ) 248: IF( XSWAP ) THEN 249: TEMP = X2( 2 ) 250: X2( 2 ) = X2( 1 ) 251: X2( 1 ) = TEMP 252: END IF 253: X( 1, 1 ) = X2( 1 ) 254: IF( N1.EQ.1 ) THEN 255: X( 1, 2 ) = X2( 2 ) 256: XNORM = ABS( X( 1, 1 ) ) + ABS( X( 1, 2 ) ) 257: ELSE 258: X( 2, 1 ) = X2( 2 ) 259: XNORM = MAX( ABS( X( 1, 1 ) ), ABS( X( 2, 1 ) ) ) 260: END IF 261: RETURN 262: * 263: * 2 by 2: 264: * op[TL11 TL12]*[X11 X12] +ISGN* [X11 X12]*op[TR11 TR12] = [B11 B12] 265: * [TL21 TL22] [X21 X22] [X21 X22] [TR21 TR22] [B21 B22] 266: * 267: * Solve equivalent 4 by 4 system using complete pivoting. 268: * Set pivots less than SMIN to SMIN. 269: * 270: 50 CONTINUE 271: SMIN = MAX( ABS( TR( 1, 1 ) ), ABS( TR( 1, 2 ) ), 272: $ ABS( TR( 2, 1 ) ), ABS( TR( 2, 2 ) ) ) 273: SMIN = MAX( SMIN, ABS( TL( 1, 1 ) ), ABS( TL( 1, 2 ) ), 274: $ ABS( TL( 2, 1 ) ), ABS( TL( 2, 2 ) ) ) 275: SMIN = MAX( EPS*SMIN, SMLNUM ) 276: BTMP( 1 ) = ZERO 277: CALL DCOPY( 16, BTMP, 0, T16, 1 ) 278: T16( 1, 1 ) = TL( 1, 1 ) + SGN*TR( 1, 1 ) 279: T16( 2, 2 ) = TL( 2, 2 ) + SGN*TR( 1, 1 ) 280: T16( 3, 3 ) = TL( 1, 1 ) + SGN*TR( 2, 2 ) 281: T16( 4, 4 ) = TL( 2, 2 ) + SGN*TR( 2, 2 ) 282: IF( LTRANL ) THEN 283: T16( 1, 2 ) = TL( 2, 1 ) 284: T16( 2, 1 ) = TL( 1, 2 ) 285: T16( 3, 4 ) = TL( 2, 1 ) 286: T16( 4, 3 ) = TL( 1, 2 ) 287: ELSE 288: T16( 1, 2 ) = TL( 1, 2 ) 289: T16( 2, 1 ) = TL( 2, 1 ) 290: T16( 3, 4 ) = TL( 1, 2 ) 291: T16( 4, 3 ) = TL( 2, 1 ) 292: END IF 293: IF( LTRANR ) THEN 294: T16( 1, 3 ) = SGN*TR( 1, 2 ) 295: T16( 2, 4 ) = SGN*TR( 1, 2 ) 296: T16( 3, 1 ) = SGN*TR( 2, 1 ) 297: T16( 4, 2 ) = SGN*TR( 2, 1 ) 298: ELSE 299: T16( 1, 3 ) = SGN*TR( 2, 1 ) 300: T16( 2, 4 ) = SGN*TR( 2, 1 ) 301: T16( 3, 1 ) = SGN*TR( 1, 2 ) 302: T16( 4, 2 ) = SGN*TR( 1, 2 ) 303: END IF 304: BTMP( 1 ) = B( 1, 1 ) 305: BTMP( 2 ) = B( 2, 1 ) 306: BTMP( 3 ) = B( 1, 2 ) 307: BTMP( 4 ) = B( 2, 2 ) 308: * 309: * Perform elimination 310: * 311: DO 100 I = 1, 3 312: XMAX = ZERO 313: DO 70 IP = I, 4 314: DO 60 JP = I, 4 315: IF( ABS( T16( IP, JP ) ).GE.XMAX ) THEN 316: XMAX = ABS( T16( IP, JP ) ) 317: IPSV = IP 318: JPSV = JP 319: END IF 320: 60 CONTINUE 321: 70 CONTINUE 322: IF( IPSV.NE.I ) THEN 323: CALL DSWAP( 4, T16( IPSV, 1 ), 4, T16( I, 1 ), 4 ) 324: TEMP = BTMP( I ) 325: BTMP( I ) = BTMP( IPSV ) 326: BTMP( IPSV ) = TEMP 327: END IF 328: IF( JPSV.NE.I ) 329: $ CALL DSWAP( 4, T16( 1, JPSV ), 1, T16( 1, I ), 1 ) 330: JPIV( I ) = JPSV 331: IF( ABS( T16( I, I ) ).LT.SMIN ) THEN 332: INFO = 1 333: T16( I, I ) = SMIN 334: END IF 335: DO 90 J = I + 1, 4 336: T16( J, I ) = T16( J, I ) / T16( I, I ) 337: BTMP( J ) = BTMP( J ) - T16( J, I )*BTMP( I ) 338: DO 80 K = I + 1, 4 339: T16( J, K ) = T16( J, K ) - T16( J, I )*T16( I, K ) 340: 80 CONTINUE 341: 90 CONTINUE 342: 100 CONTINUE 343: IF( ABS( T16( 4, 4 ) ).LT.SMIN ) 344: $ T16( 4, 4 ) = SMIN 345: SCALE = ONE 346: IF( ( EIGHT*SMLNUM )*ABS( BTMP( 1 ) ).GT.ABS( T16( 1, 1 ) ) .OR. 347: $ ( EIGHT*SMLNUM )*ABS( BTMP( 2 ) ).GT.ABS( T16( 2, 2 ) ) .OR. 348: $ ( EIGHT*SMLNUM )*ABS( BTMP( 3 ) ).GT.ABS( T16( 3, 3 ) ) .OR. 349: $ ( EIGHT*SMLNUM )*ABS( BTMP( 4 ) ).GT.ABS( T16( 4, 4 ) ) ) THEN 350: SCALE = ( ONE / EIGHT ) / MAX( ABS( BTMP( 1 ) ), 351: $ ABS( BTMP( 2 ) ), ABS( BTMP( 3 ) ), ABS( BTMP( 4 ) ) ) 352: BTMP( 1 ) = BTMP( 1 )*SCALE 353: BTMP( 2 ) = BTMP( 2 )*SCALE 354: BTMP( 3 ) = BTMP( 3 )*SCALE 355: BTMP( 4 ) = BTMP( 4 )*SCALE 356: END IF 357: DO 120 I = 1, 4 358: K = 5 - I 359: TEMP = ONE / T16( K, K ) 360: TMP( K ) = BTMP( K )*TEMP 361: DO 110 J = K + 1, 4 362: TMP( K ) = TMP( K ) - ( TEMP*T16( K, J ) )*TMP( J ) 363: 110 CONTINUE 364: 120 CONTINUE 365: DO 130 I = 1, 3 366: IF( JPIV( 4-I ).NE.4-I ) THEN 367: TEMP = TMP( 4-I ) 368: TMP( 4-I ) = TMP( JPIV( 4-I ) ) 369: TMP( JPIV( 4-I ) ) = TEMP 370: END IF 371: 130 CONTINUE 372: X( 1, 1 ) = TMP( 1 ) 373: X( 2, 1 ) = TMP( 2 ) 374: X( 1, 2 ) = TMP( 3 ) 375: X( 2, 2 ) = TMP( 4 ) 376: XNORM = MAX( ABS( TMP( 1 ) )+ABS( TMP( 3 ) ), 377: $ ABS( TMP( 2 ) )+ABS( TMP( 4 ) ) ) 378: RETURN 379: * 380: * End of DLASY2 381: * 382: END