Move LAPACK trunk into position.

1 files changed, 249 insertions, 0 deletions

diff --git a/SRC/dlasv2.f b/SRC/dlasv2.f
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+      SUBROUTINE DLASV2( F, G, H, SSMIN, SSMAX, SNR, CSR, SNL, CSL )
+*
+*  -- LAPACK auxiliary routine (version 3.1) --
+*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
+*     November 2006
+*
+*     .. Scalar Arguments ..
+      DOUBLE PRECISION   CSL, CSR, F, G, H, SNL, SNR, SSMAX, SSMIN
+*     ..
+*
+*  Purpose
+*  =======
+*
+*  DLASV2 computes the singular value decomposition of a 2-by-2
+*  triangular matrix
+*     [  F   G  ]
+*     [  0   H  ].
+*  On return, abs(SSMAX) is the larger singular value, abs(SSMIN) is the
+*  smaller singular value, and (CSL,SNL) and (CSR,SNR) are the left and
+*  right singular vectors for abs(SSMAX), giving the decomposition
+*
+*     [ CSL  SNL ] [  F   G  ] [ CSR -SNR ]  =  [ SSMAX   0   ]
+*     [-SNL  CSL ] [  0   H  ] [ SNR  CSR ]     [  0    SSMIN ].
+*
+*  Arguments
+*  =========
+*
+*  F       (input) DOUBLE PRECISION
+*          The (1,1) element of the 2-by-2 matrix.
+*
+*  G       (input) DOUBLE PRECISION
+*          The (1,2) element of the 2-by-2 matrix.
+*
+*  H       (input) DOUBLE PRECISION
+*          The (2,2) element of the 2-by-2 matrix.
+*
+*  SSMIN   (output) DOUBLE PRECISION
+*          abs(SSMIN) is the smaller singular value.
+*
+*  SSMAX   (output) DOUBLE PRECISION
+*          abs(SSMAX) is the larger singular value.
+*
+*  SNL     (output) DOUBLE PRECISION
+*  CSL     (output) DOUBLE PRECISION
+*          The vector (CSL, SNL) is a unit left singular vector for the
+*          singular value abs(SSMAX).
+*
+*  SNR     (output) DOUBLE PRECISION
+*  CSR     (output) DOUBLE PRECISION
+*          The vector (CSR, SNR) is a unit right singular vector for the
+*          singular value abs(SSMAX).
+*
+*  Further Details
+*  ===============
+*
+*  Any input parameter may be aliased with any output parameter.
+*
+*  Barring over/underflow and assuming a guard digit in subtraction, all
+*  output quantities are correct to within a few units in the last
+*  place (ulps).
+*
+*  In IEEE arithmetic, the code works correctly if one matrix element is
+*  infinite.
+*
+*  Overflow will not occur unless the largest singular value itself
+*  overflows or is within a few ulps of overflow. (On machines with
+*  partial overflow, like the Cray, overflow may occur if the largest
+*  singular value is within a factor of 2 of overflow.)
+*
+*  Underflow is harmless if underflow is gradual. Otherwise, results
+*  may correspond to a matrix modified by perturbations of size near
+*  the underflow threshold.
+*
+* =====================================================================
+*
+*     .. Parameters ..
+      DOUBLE PRECISION   ZERO
+      PARAMETER          ( ZERO = 0.0D0 )
+      DOUBLE PRECISION   HALF
+      PARAMETER          ( HALF = 0.5D0 )
+      DOUBLE PRECISION   ONE
+      PARAMETER          ( ONE = 1.0D0 )
+      DOUBLE PRECISION   TWO
+      PARAMETER          ( TWO = 2.0D0 )
+      DOUBLE PRECISION   FOUR
+      PARAMETER          ( FOUR = 4.0D0 )
+*     ..
+*     .. Local Scalars ..
+      LOGICAL            GASMAL, SWAP
+      INTEGER            PMAX
+      DOUBLE PRECISION   A, CLT, CRT, D, FA, FT, GA, GT, HA, HT, L, M,
+     $                   MM, R, S, SLT, SRT, T, TEMP, TSIGN, TT
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          ABS, SIGN, SQRT
+*     ..
+*     .. External Functions ..
+      DOUBLE PRECISION   DLAMCH
+      EXTERNAL           DLAMCH
+*     ..
+*     .. Executable Statements ..
+*
+      FT = F
+      FA = ABS( FT )
+      HT = H
+      HA = ABS( H )
+*
+*     PMAX points to the maximum absolute element of matrix
+*       PMAX = 1 if F largest in absolute values
+*       PMAX = 2 if G largest in absolute values
+*       PMAX = 3 if H largest in absolute values
+*
+      PMAX = 1
+      SWAP = ( HA.GT.FA )
+      IF( SWAP ) THEN
+         PMAX = 3
+         TEMP = FT
+         FT = HT
+         HT = TEMP
+         TEMP = FA
+         FA = HA
+         HA = TEMP
+*
+*        Now FA .ge. HA
+*
+      END IF
+      GT = G
+      GA = ABS( GT )
+      IF( GA.EQ.ZERO ) THEN
+*
+*        Diagonal matrix
+*
+         SSMIN = HA
+         SSMAX = FA
+         CLT = ONE
+         CRT = ONE
+         SLT = ZERO
+         SRT = ZERO
+      ELSE
+         GASMAL = .TRUE.
+         IF( GA.GT.FA ) THEN
+            PMAX = 2
+            IF( ( FA / GA ).LT.DLAMCH( 'EPS' ) ) THEN
+*
+*              Case of very large GA
+*
+               GASMAL = .FALSE.
+               SSMAX = GA
+               IF( HA.GT.ONE ) THEN
+                  SSMIN = FA / ( GA / HA )
+               ELSE
+                  SSMIN = ( FA / GA )*HA
+               END IF
+               CLT = ONE
+               SLT = HT / GT
+               SRT = ONE
+               CRT = FT / GT
+            END IF
+         END IF
+         IF( GASMAL ) THEN
+*
+*           Normal case
+*
+            D = FA - HA
+            IF( D.EQ.FA ) THEN
+*
+*              Copes with infinite F or H
+*
+               L = ONE
+            ELSE
+               L = D / FA
+            END IF
+*
+*           Note that 0 .le. L .le. 1
+*
+            M = GT / FT
+*
+*           Note that abs(M) .le. 1/macheps
+*
+            T = TWO - L
+*
+*           Note that T .ge. 1
+*
+            MM = M*M
+            TT = T*T
+            S = SQRT( TT+MM )
+*
+*           Note that 1 .le. S .le. 1 + 1/macheps
+*
+            IF( L.EQ.ZERO ) THEN
+               R = ABS( M )
+            ELSE
+               R = SQRT( L*L+MM )
+            END IF
+*
+*           Note that 0 .le. R .le. 1 + 1/macheps
+*
+            A = HALF*( S+R )
+*
+*           Note that 1 .le. A .le. 1 + abs(M)
+*
+            SSMIN = HA / A
+            SSMAX = FA*A
+            IF( MM.EQ.ZERO ) THEN
+*
+*              Note that M is very tiny
+*
+               IF( L.EQ.ZERO ) THEN
+                  T = SIGN( TWO, FT )*SIGN( ONE, GT )
+               ELSE
+                  T = GT / SIGN( D, FT ) + M / T
+               END IF
+            ELSE
+               T = ( M / ( S+T )+M / ( R+L ) )*( ONE+A )
+            END IF
+            L = SQRT( T*T+FOUR )
+            CRT = TWO / L
+            SRT = T / L
+            CLT = ( CRT+SRT*M ) / A
+            SLT = ( HT / FT )*SRT / A
+         END IF
+      END IF
+      IF( SWAP ) THEN
+         CSL = SRT
+         SNL = CRT
+         CSR = SLT
+         SNR = CLT
+      ELSE
+         CSL = CLT
+         SNL = SLT
+         CSR = CRT
+         SNR = SRT
+      END IF
+*
+*     Correct signs of SSMAX and SSMIN
+*
+      IF( PMAX.EQ.1 )
+     $   TSIGN = SIGN( ONE, CSR )*SIGN( ONE, CSL )*SIGN( ONE, F )
+      IF( PMAX.EQ.2 )
+     $   TSIGN = SIGN( ONE, SNR )*SIGN( ONE, CSL )*SIGN( ONE, G )
+      IF( PMAX.EQ.3 )
+     $   TSIGN = SIGN( ONE, SNR )*SIGN( ONE, SNL )*SIGN( ONE, H )
+      SSMAX = SIGN( SSMAX, TSIGN )
+      SSMIN = SIGN( SSMIN, TSIGN*SIGN( ONE, F )*SIGN( ONE, H ) )
+      RETURN
+*
+*     End of DLASV2
+*
+      END