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Diffstat (limited to 'src/lib/lapack/dlasy2.f')
| -rw-r--r-- | src/lib/lapack/dlasy2.f | 381 |
1 files changed, 0 insertions, 381 deletions
diff --git a/src/lib/lapack/dlasy2.f b/src/lib/lapack/dlasy2.f deleted file mode 100644 index 3ff12070..00000000 --- a/src/lib/lapack/dlasy2.f +++ /dev/null @@ -1,381 +0,0 @@ - SUBROUTINE DLASY2( LTRANL, LTRANR, ISGN, N1, N2, TL, LDTL, TR, - $ LDTR, B, LDB, SCALE, X, LDX, XNORM, INFO ) -* -* -- LAPACK auxiliary routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 -* -* .. Scalar Arguments .. - LOGICAL LTRANL, LTRANR - INTEGER INFO, ISGN, LDB, LDTL, LDTR, LDX, N1, N2 - DOUBLE PRECISION SCALE, XNORM -* .. -* .. Array Arguments .. - DOUBLE PRECISION B( LDB, * ), TL( LDTL, * ), TR( LDTR, * ), - $ X( LDX, * ) -* .. -* -* Purpose -* ======= -* -* DLASY2 solves for the N1 by N2 matrix X, 1 <= N1,N2 <= 2, in -* -* op(TL)*X + ISGN*X*op(TR) = SCALE*B, -* -* where TL is N1 by N1, TR is N2 by N2, B is N1 by N2, and ISGN = 1 or -* -1. op(T) = T or T', where T' denotes the transpose of T. -* -* Arguments -* ========= -* -* LTRANL (input) LOGICAL -* On entry, LTRANL specifies the op(TL): -* = .FALSE., op(TL) = TL, -* = .TRUE., op(TL) = TL'. -* -* LTRANR (input) LOGICAL -* On entry, LTRANR specifies the op(TR): -* = .FALSE., op(TR) = TR, -* = .TRUE., op(TR) = TR'. -* -* ISGN (input) INTEGER -* On entry, ISGN specifies the sign of the equation -* as described before. ISGN may only be 1 or -1. -* -* N1 (input) INTEGER -* On entry, N1 specifies the order of matrix TL. -* N1 may only be 0, 1 or 2. -* -* N2 (input) INTEGER -* On entry, N2 specifies the order of matrix TR. -* N2 may only be 0, 1 or 2. -* -* TL (input) DOUBLE PRECISION array, dimension (LDTL,2) -* On entry, TL contains an N1 by N1 matrix. -* -* LDTL (input) INTEGER -* The leading dimension of the matrix TL. LDTL >= max(1,N1). -* -* TR (input) DOUBLE PRECISION array, dimension (LDTR,2) -* On entry, TR contains an N2 by N2 matrix. -* -* LDTR (input) INTEGER -* The leading dimension of the matrix TR. LDTR >= max(1,N2). -* -* B (input) DOUBLE PRECISION array, dimension (LDB,2) -* On entry, the N1 by N2 matrix B contains the right-hand -* side of the equation. -* -* LDB (input) INTEGER -* The leading dimension of the matrix B. LDB >= max(1,N1). -* -* SCALE (output) DOUBLE PRECISION -* On exit, SCALE contains the scale factor. SCALE is chosen -* less than or equal to 1 to prevent the solution overflowing. -* -* X (output) DOUBLE PRECISION array, dimension (LDX,2) -* On exit, X contains the N1 by N2 solution. -* -* LDX (input) INTEGER -* The leading dimension of the matrix X. LDX >= max(1,N1). -* -* XNORM (output) DOUBLE PRECISION -* On exit, XNORM is the infinity-norm of the solution. -* -* INFO (output) INTEGER -* On exit, INFO is set to -* 0: successful exit. -* 1: TL and TR have too close eigenvalues, so TL or -* TR is perturbed to get a nonsingular equation. -* NOTE: In the interests of speed, this routine does not -* check the inputs for errors. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO, ONE - PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) - DOUBLE PRECISION TWO, HALF, EIGHT - PARAMETER ( TWO = 2.0D+0, HALF = 0.5D+0, EIGHT = 8.0D+0 ) -* .. -* .. Local Scalars .. - LOGICAL BSWAP, XSWAP - INTEGER I, IP, IPIV, IPSV, J, JP, JPSV, K - DOUBLE PRECISION BET, EPS, GAM, L21, SGN, SMIN, SMLNUM, TAU1, - $ TEMP, U11, U12, U22, XMAX -* .. -* .. Local Arrays .. - LOGICAL BSWPIV( 4 ), XSWPIV( 4 ) - INTEGER JPIV( 4 ), LOCL21( 4 ), LOCU12( 4 ), - $ LOCU22( 4 ) - DOUBLE PRECISION BTMP( 4 ), T16( 4, 4 ), TMP( 4 ), X2( 2 ) -* .. -* .. External Functions .. - INTEGER IDAMAX - DOUBLE PRECISION DLAMCH - EXTERNAL IDAMAX, DLAMCH -* .. -* .. External Subroutines .. - EXTERNAL DCOPY, DSWAP -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, MAX -* .. -* .. Data statements .. - DATA LOCU12 / 3, 4, 1, 2 / , LOCL21 / 2, 1, 4, 3 / , - $ LOCU22 / 4, 3, 2, 1 / - DATA XSWPIV / .FALSE., .FALSE., .TRUE., .TRUE. / - DATA BSWPIV / .FALSE., .TRUE., .FALSE., .TRUE. / -* .. -* .. Executable Statements .. -* -* Do not check the input parameters for errors -* - INFO = 0 -* -* Quick return if possible -* - IF( N1.EQ.0 .OR. N2.EQ.0 ) - $ RETURN -* -* Set constants to control overflow -* - EPS = DLAMCH( 'P' ) - SMLNUM = DLAMCH( 'S' ) / EPS - SGN = ISGN -* - K = N1 + N1 + N2 - 2 - GO TO ( 10, 20, 30, 50 )K -* -* 1 by 1: TL11*X + SGN*X*TR11 = B11 -* - 10 CONTINUE - TAU1 = TL( 1, 1 ) + SGN*TR( 1, 1 ) - BET = ABS( TAU1 ) - IF( BET.LE.SMLNUM ) THEN - TAU1 = SMLNUM - BET = SMLNUM - INFO = 1 - END IF -* - SCALE = ONE - GAM = ABS( B( 1, 1 ) ) - IF( SMLNUM*GAM.GT.BET ) - $ SCALE = ONE / GAM -* - X( 1, 1 ) = ( B( 1, 1 )*SCALE ) / TAU1 - XNORM = ABS( X( 1, 1 ) ) - RETURN -* -* 1 by 2: -* TL11*[X11 X12] + ISGN*[X11 X12]*op[TR11 TR12] = [B11 B12] -* [TR21 TR22] -* - 20 CONTINUE -* - SMIN = MAX( EPS*MAX( ABS( TL( 1, 1 ) ), ABS( TR( 1, 1 ) ), - $ ABS( TR( 1, 2 ) ), ABS( TR( 2, 1 ) ), ABS( TR( 2, 2 ) ) ), - $ SMLNUM ) - TMP( 1 ) = TL( 1, 1 ) + SGN*TR( 1, 1 ) - TMP( 4 ) = TL( 1, 1 ) + SGN*TR( 2, 2 ) - IF( LTRANR ) THEN - TMP( 2 ) = SGN*TR( 2, 1 ) - TMP( 3 ) = SGN*TR( 1, 2 ) - ELSE - TMP( 2 ) = SGN*TR( 1, 2 ) - TMP( 3 ) = SGN*TR( 2, 1 ) - END IF - BTMP( 1 ) = B( 1, 1 ) - BTMP( 2 ) = B( 1, 2 ) - GO TO 40 -* -* 2 by 1: -* op[TL11 TL12]*[X11] + ISGN* [X11]*TR11 = [B11] -* [TL21 TL22] [X21] [X21] [B21] -* - 30 CONTINUE - SMIN = MAX( EPS*MAX( ABS( TR( 1, 1 ) ), ABS( TL( 1, 1 ) ), - $ ABS( TL( 1, 2 ) ), ABS( TL( 2, 1 ) ), ABS( TL( 2, 2 ) ) ), - $ SMLNUM ) - TMP( 1 ) = TL( 1, 1 ) + SGN*TR( 1, 1 ) - TMP( 4 ) = TL( 2, 2 ) + SGN*TR( 1, 1 ) - IF( LTRANL ) THEN - TMP( 2 ) = TL( 1, 2 ) - TMP( 3 ) = TL( 2, 1 ) - ELSE - TMP( 2 ) = TL( 2, 1 ) - TMP( 3 ) = TL( 1, 2 ) - END IF - BTMP( 1 ) = B( 1, 1 ) - BTMP( 2 ) = B( 2, 1 ) - 40 CONTINUE -* -* Solve 2 by 2 system using complete pivoting. -* Set pivots less than SMIN to SMIN. -* - IPIV = IDAMAX( 4, TMP, 1 ) - U11 = TMP( IPIV ) - IF( ABS( U11 ).LE.SMIN ) THEN - INFO = 1 - U11 = SMIN - END IF - U12 = TMP( LOCU12( IPIV ) ) - L21 = TMP( LOCL21( IPIV ) ) / U11 - U22 = TMP( LOCU22( IPIV ) ) - U12*L21 - XSWAP = XSWPIV( IPIV ) - BSWAP = BSWPIV( IPIV ) - IF( ABS( U22 ).LE.SMIN ) THEN - INFO = 1 - U22 = SMIN - END IF - IF( BSWAP ) THEN - TEMP = BTMP( 2 ) - BTMP( 2 ) = BTMP( 1 ) - L21*TEMP - BTMP( 1 ) = TEMP - ELSE - BTMP( 2 ) = BTMP( 2 ) - L21*BTMP( 1 ) - END IF - SCALE = ONE - IF( ( TWO*SMLNUM )*ABS( BTMP( 2 ) ).GT.ABS( U22 ) .OR. - $ ( TWO*SMLNUM )*ABS( BTMP( 1 ) ).GT.ABS( U11 ) ) THEN - SCALE = HALF / MAX( ABS( BTMP( 1 ) ), ABS( BTMP( 2 ) ) ) - BTMP( 1 ) = BTMP( 1 )*SCALE - BTMP( 2 ) = BTMP( 2 )*SCALE - END IF - X2( 2 ) = BTMP( 2 ) / U22 - X2( 1 ) = BTMP( 1 ) / U11 - ( U12 / U11 )*X2( 2 ) - IF( XSWAP ) THEN - TEMP = X2( 2 ) - X2( 2 ) = X2( 1 ) - X2( 1 ) = TEMP - END IF - X( 1, 1 ) = X2( 1 ) - IF( N1.EQ.1 ) THEN - X( 1, 2 ) = X2( 2 ) - XNORM = ABS( X( 1, 1 ) ) + ABS( X( 1, 2 ) ) - ELSE - X( 2, 1 ) = X2( 2 ) - XNORM = MAX( ABS( X( 1, 1 ) ), ABS( X( 2, 1 ) ) ) - END IF - RETURN -* -* 2 by 2: -* op[TL11 TL12]*[X11 X12] +ISGN* [X11 X12]*op[TR11 TR12] = [B11 B12] -* [TL21 TL22] [X21 X22] [X21 X22] [TR21 TR22] [B21 B22] -* -* Solve equivalent 4 by 4 system using complete pivoting. -* Set pivots less than SMIN to SMIN. -* - 50 CONTINUE - SMIN = MAX( ABS( TR( 1, 1 ) ), ABS( TR( 1, 2 ) ), - $ ABS( TR( 2, 1 ) ), ABS( TR( 2, 2 ) ) ) - SMIN = MAX( SMIN, ABS( TL( 1, 1 ) ), ABS( TL( 1, 2 ) ), - $ ABS( TL( 2, 1 ) ), ABS( TL( 2, 2 ) ) ) - SMIN = MAX( EPS*SMIN, SMLNUM ) - BTMP( 1 ) = ZERO - CALL DCOPY( 16, BTMP, 0, T16, 1 ) - T16( 1, 1 ) = TL( 1, 1 ) + SGN*TR( 1, 1 ) - T16( 2, 2 ) = TL( 2, 2 ) + SGN*TR( 1, 1 ) - T16( 3, 3 ) = TL( 1, 1 ) + SGN*TR( 2, 2 ) - T16( 4, 4 ) = TL( 2, 2 ) + SGN*TR( 2, 2 ) - IF( LTRANL ) THEN - T16( 1, 2 ) = TL( 2, 1 ) - T16( 2, 1 ) = TL( 1, 2 ) - T16( 3, 4 ) = TL( 2, 1 ) - T16( 4, 3 ) = TL( 1, 2 ) - ELSE - T16( 1, 2 ) = TL( 1, 2 ) - T16( 2, 1 ) = TL( 2, 1 ) - T16( 3, 4 ) = TL( 1, 2 ) - T16( 4, 3 ) = TL( 2, 1 ) - END IF - IF( LTRANR ) THEN - T16( 1, 3 ) = SGN*TR( 1, 2 ) - T16( 2, 4 ) = SGN*TR( 1, 2 ) - T16( 3, 1 ) = SGN*TR( 2, 1 ) - T16( 4, 2 ) = SGN*TR( 2, 1 ) - ELSE - T16( 1, 3 ) = SGN*TR( 2, 1 ) - T16( 2, 4 ) = SGN*TR( 2, 1 ) - T16( 3, 1 ) = SGN*TR( 1, 2 ) - T16( 4, 2 ) = SGN*TR( 1, 2 ) - END IF - BTMP( 1 ) = B( 1, 1 ) - BTMP( 2 ) = B( 2, 1 ) - BTMP( 3 ) = B( 1, 2 ) - BTMP( 4 ) = B( 2, 2 ) -* -* Perform elimination -* - DO 100 I = 1, 3 - XMAX = ZERO - DO 70 IP = I, 4 - DO 60 JP = I, 4 - IF( ABS( T16( IP, JP ) ).GE.XMAX ) THEN - XMAX = ABS( T16( IP, JP ) ) - IPSV = IP - JPSV = JP - END IF - 60 CONTINUE - 70 CONTINUE - IF( IPSV.NE.I ) THEN - CALL DSWAP( 4, T16( IPSV, 1 ), 4, T16( I, 1 ), 4 ) - TEMP = BTMP( I ) - BTMP( I ) = BTMP( IPSV ) - BTMP( IPSV ) = TEMP - END IF - IF( JPSV.NE.I ) - $ CALL DSWAP( 4, T16( 1, JPSV ), 1, T16( 1, I ), 1 ) - JPIV( I ) = JPSV - IF( ABS( T16( I, I ) ).LT.SMIN ) THEN - INFO = 1 - T16( I, I ) = SMIN - END IF - DO 90 J = I + 1, 4 - T16( J, I ) = T16( J, I ) / T16( I, I ) - BTMP( J ) = BTMP( J ) - T16( J, I )*BTMP( I ) - DO 80 K = I + 1, 4 - T16( J, K ) = T16( J, K ) - T16( J, I )*T16( I, K ) - 80 CONTINUE - 90 CONTINUE - 100 CONTINUE - IF( ABS( T16( 4, 4 ) ).LT.SMIN ) - $ T16( 4, 4 ) = SMIN - SCALE = ONE - IF( ( EIGHT*SMLNUM )*ABS( BTMP( 1 ) ).GT.ABS( T16( 1, 1 ) ) .OR. - $ ( EIGHT*SMLNUM )*ABS( BTMP( 2 ) ).GT.ABS( T16( 2, 2 ) ) .OR. - $ ( EIGHT*SMLNUM )*ABS( BTMP( 3 ) ).GT.ABS( T16( 3, 3 ) ) .OR. - $ ( EIGHT*SMLNUM )*ABS( BTMP( 4 ) ).GT.ABS( T16( 4, 4 ) ) ) THEN - SCALE = ( ONE / EIGHT ) / MAX( ABS( BTMP( 1 ) ), - $ ABS( BTMP( 2 ) ), ABS( BTMP( 3 ) ), ABS( BTMP( 4 ) ) ) - BTMP( 1 ) = BTMP( 1 )*SCALE - BTMP( 2 ) = BTMP( 2 )*SCALE - BTMP( 3 ) = BTMP( 3 )*SCALE - BTMP( 4 ) = BTMP( 4 )*SCALE - END IF - DO 120 I = 1, 4 - K = 5 - I - TEMP = ONE / T16( K, K ) - TMP( K ) = BTMP( K )*TEMP - DO 110 J = K + 1, 4 - TMP( K ) = TMP( K ) - ( TEMP*T16( K, J ) )*TMP( J ) - 110 CONTINUE - 120 CONTINUE - DO 130 I = 1, 3 - IF( JPIV( 4-I ).NE.4-I ) THEN - TEMP = TMP( 4-I ) - TMP( 4-I ) = TMP( JPIV( 4-I ) ) - TMP( JPIV( 4-I ) ) = TEMP - END IF - 130 CONTINUE - X( 1, 1 ) = TMP( 1 ) - X( 2, 1 ) = TMP( 2 ) - X( 1, 2 ) = TMP( 3 ) - X( 2, 2 ) = TMP( 4 ) - XNORM = MAX( ABS( TMP( 1 ) )+ABS( TMP( 3 ) ), - $ ABS( TMP( 2 ) )+ABS( TMP( 4 ) ) ) - RETURN -* -* End of DLASY2 -* - END |