--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/libcruft/lapack/ssterf.f	Sun Apr 27 22:34:17 2008 +0200
@@ -0,0 +1,364 @@
+      SUBROUTINE SSTERF( N, D, E, INFO )
+*
+*  -- LAPACK routine (version 3.1) --
+*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
+*     November 2006
+*
+*     .. Scalar Arguments ..
+      INTEGER            INFO, N
+*     ..
+*     .. Array Arguments ..
+      REAL               D( * ), E( * )
+*     ..
+*
+*  Purpose
+*  =======
+*
+*  SSTERF computes all eigenvalues of a symmetric tridiagonal matrix
+*  using the Pal-Walker-Kahan variant of the QL or QR algorithm.
+*
+*  Arguments
+*  =========
+*
+*  N       (input) INTEGER
+*          The order of the matrix.  N >= 0.
+*
+*  D       (input/output) REAL array, dimension (N)
+*          On entry, the n diagonal elements of the tridiagonal matrix.
+*          On exit, if INFO = 0, the eigenvalues in ascending order.
+*
+*  E       (input/output) REAL array, dimension (N-1)
+*          On entry, the (n-1) subdiagonal elements of the tridiagonal
+*          matrix.
+*          On exit, E has been destroyed.
+*
+*  INFO    (output) INTEGER
+*          = 0:  successful exit
+*          < 0:  if INFO = -i, the i-th argument had an illegal value
+*          > 0:  the algorithm failed to find all of the eigenvalues in
+*                a total of 30*N iterations; if INFO = i, then i
+*                elements of E have not converged to zero.
+*
+*  =====================================================================
+*
+*     .. Parameters ..
+      REAL               ZERO, ONE, TWO, THREE
+      PARAMETER          ( ZERO = 0.0E0, ONE = 1.0E0, TWO = 2.0E0,
+     $                   THREE = 3.0E0 )
+      INTEGER            MAXIT
+      PARAMETER          ( MAXIT = 30 )
+*     ..
+*     .. Local Scalars ..
+      INTEGER            I, ISCALE, JTOT, L, L1, LEND, LENDSV, LSV, M,
+     $                   NMAXIT
+      REAL               ALPHA, ANORM, BB, C, EPS, EPS2, GAMMA, OLDC,
+     $                   OLDGAM, P, R, RT1, RT2, RTE, S, SAFMAX, SAFMIN,
+     $                   SIGMA, SSFMAX, SSFMIN
+*     ..
+*     .. External Functions ..
+      REAL               SLAMCH, SLANST, SLAPY2
+      EXTERNAL           SLAMCH, SLANST, SLAPY2
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           SLAE2, SLASCL, SLASRT, XERBLA
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          ABS, SIGN, SQRT
+*     ..
+*     .. Executable Statements ..
+*
+*     Test the input parameters.
+*
+      INFO = 0
+*
+*     Quick return if possible
+*
+      IF( N.LT.0 ) THEN
+         INFO = -1
+         CALL XERBLA( 'SSTERF', -INFO )
+         RETURN
+      END IF
+      IF( N.LE.1 )
+     $   RETURN
+*
+*     Determine the unit roundoff for this environment.
+*
+      EPS = SLAMCH( 'E' )
+      EPS2 = EPS**2
+      SAFMIN = SLAMCH( 'S' )
+      SAFMAX = ONE / SAFMIN
+      SSFMAX = SQRT( SAFMAX ) / THREE
+      SSFMIN = SQRT( SAFMIN ) / EPS2
+*
+*     Compute the eigenvalues of the tridiagonal matrix.
+*
+      NMAXIT = N*MAXIT
+      SIGMA = ZERO
+      JTOT = 0
+*
+*     Determine where the matrix splits and choose QL or QR iteration
+*     for each block, according to whether top or bottom diagonal
+*     element is smaller.
+*
+      L1 = 1
+*
+   10 CONTINUE
+      IF( L1.GT.N )
+     $   GO TO 170
+      IF( L1.GT.1 )
+     $   E( L1-1 ) = ZERO
+      DO 20 M = L1, N - 1
+         IF( ABS( E( M ) ).LE.( SQRT( ABS( D( M ) ) )*
+     $       SQRT( ABS( D( M+1 ) ) ) )*EPS ) THEN
+            E( M ) = ZERO
+            GO TO 30
+         END IF
+   20 CONTINUE
+      M = N
+*
+   30 CONTINUE
+      L = L1
+      LSV = L
+      LEND = M
+      LENDSV = LEND
+      L1 = M + 1
+      IF( LEND.EQ.L )
+     $   GO TO 10
+*
+*     Scale submatrix in rows and columns L to LEND
+*
+      ANORM = SLANST( 'I', LEND-L+1, D( L ), E( L ) )
+      ISCALE = 0
+      IF( ANORM.GT.SSFMAX ) THEN
+         ISCALE = 1
+         CALL SLASCL( 'G', 0, 0, ANORM, SSFMAX, LEND-L+1, 1, D( L ), N,
+     $                INFO )
+         CALL SLASCL( 'G', 0, 0, ANORM, SSFMAX, LEND-L, 1, E( L ), N,
+     $                INFO )
+      ELSE IF( ANORM.LT.SSFMIN ) THEN
+         ISCALE = 2
+         CALL SLASCL( 'G', 0, 0, ANORM, SSFMIN, LEND-L+1, 1, D( L ), N,
+     $                INFO )
+         CALL SLASCL( 'G', 0, 0, ANORM, SSFMIN, LEND-L, 1, E( L ), N,
+     $                INFO )
+      END IF
+*
+      DO 40 I = L, LEND - 1
+         E( I ) = E( I )**2
+   40 CONTINUE
+*
+*     Choose between QL and QR iteration
+*
+      IF( ABS( D( LEND ) ).LT.ABS( D( L ) ) ) THEN
+         LEND = LSV
+         L = LENDSV
+      END IF
+*
+      IF( LEND.GE.L ) THEN
+*
+*        QL Iteration
+*
+*        Look for small subdiagonal element.
+*
+   50    CONTINUE
+         IF( L.NE.LEND ) THEN
+            DO 60 M = L, LEND - 1
+               IF( ABS( E( M ) ).LE.EPS2*ABS( D( M )*D( M+1 ) ) )
+     $            GO TO 70
+   60       CONTINUE
+         END IF
+         M = LEND
+*
+   70    CONTINUE
+         IF( M.LT.LEND )
+     $      E( M ) = ZERO
+         P = D( L )
+         IF( M.EQ.L )
+     $      GO TO 90
+*
+*        If remaining matrix is 2 by 2, use SLAE2 to compute its
+*        eigenvalues.
+*
+         IF( M.EQ.L+1 ) THEN
+            RTE = SQRT( E( L ) )
+            CALL SLAE2( D( L ), RTE, D( L+1 ), RT1, RT2 )
+            D( L ) = RT1
+            D( L+1 ) = RT2
+            E( L ) = ZERO
+            L = L + 2
+            IF( L.LE.LEND )
+     $         GO TO 50
+            GO TO 150
+         END IF
+*
+         IF( JTOT.EQ.NMAXIT )
+     $      GO TO 150
+         JTOT = JTOT + 1
+*
+*        Form shift.
+*
+         RTE = SQRT( E( L ) )
+         SIGMA = ( D( L+1 )-P ) / ( TWO*RTE )
+         R = SLAPY2( SIGMA, ONE )
+         SIGMA = P - ( RTE / ( SIGMA+SIGN( R, SIGMA ) ) )
+*
+         C = ONE
+         S = ZERO
+         GAMMA = D( M ) - SIGMA
+         P = GAMMA*GAMMA
+*
+*        Inner loop
+*
+         DO 80 I = M - 1, L, -1
+            BB = E( I )
+            R = P + BB
+            IF( I.NE.M-1 )
+     $         E( I+1 ) = S*R
+            OLDC = C
+            C = P / R
+            S = BB / R
+            OLDGAM = GAMMA
+            ALPHA = D( I )
+            GAMMA = C*( ALPHA-SIGMA ) - S*OLDGAM
+            D( I+1 ) = OLDGAM + ( ALPHA-GAMMA )
+            IF( C.NE.ZERO ) THEN
+               P = ( GAMMA*GAMMA ) / C
+            ELSE
+               P = OLDC*BB
+            END IF
+   80    CONTINUE
+*
+         E( L ) = S*P
+         D( L ) = SIGMA + GAMMA
+         GO TO 50
+*
+*        Eigenvalue found.
+*
+   90    CONTINUE
+         D( L ) = P
+*
+         L = L + 1
+         IF( L.LE.LEND )
+     $      GO TO 50
+         GO TO 150
+*
+      ELSE
+*
+*        QR Iteration
+*
+*        Look for small superdiagonal element.
+*
+  100    CONTINUE
+         DO 110 M = L, LEND + 1, -1
+            IF( ABS( E( M-1 ) ).LE.EPS2*ABS( D( M )*D( M-1 ) ) )
+     $         GO TO 120
+  110    CONTINUE
+         M = LEND
+*
+  120    CONTINUE
+         IF( M.GT.LEND )
+     $      E( M-1 ) = ZERO
+         P = D( L )
+         IF( M.EQ.L )
+     $      GO TO 140
+*
+*        If remaining matrix is 2 by 2, use SLAE2 to compute its
+*        eigenvalues.
+*
+         IF( M.EQ.L-1 ) THEN
+            RTE = SQRT( E( L-1 ) )
+            CALL SLAE2( D( L ), RTE, D( L-1 ), RT1, RT2 )
+            D( L ) = RT1
+            D( L-1 ) = RT2
+            E( L-1 ) = ZERO
+            L = L - 2
+            IF( L.GE.LEND )
+     $         GO TO 100
+            GO TO 150
+         END IF
+*
+         IF( JTOT.EQ.NMAXIT )
+     $      GO TO 150
+         JTOT = JTOT + 1
+*
+*        Form shift.
+*
+         RTE = SQRT( E( L-1 ) )
+         SIGMA = ( D( L-1 )-P ) / ( TWO*RTE )
+         R = SLAPY2( SIGMA, ONE )
+         SIGMA = P - ( RTE / ( SIGMA+SIGN( R, SIGMA ) ) )
+*
+         C = ONE
+         S = ZERO
+         GAMMA = D( M ) - SIGMA
+         P = GAMMA*GAMMA
+*
+*        Inner loop
+*
+         DO 130 I = M, L - 1
+            BB = E( I )
+            R = P + BB
+            IF( I.NE.M )
+     $         E( I-1 ) = S*R
+            OLDC = C
+            C = P / R
+            S = BB / R
+            OLDGAM = GAMMA
+            ALPHA = D( I+1 )
+            GAMMA = C*( ALPHA-SIGMA ) - S*OLDGAM
+            D( I ) = OLDGAM + ( ALPHA-GAMMA )
+            IF( C.NE.ZERO ) THEN
+               P = ( GAMMA*GAMMA ) / C
+            ELSE
+               P = OLDC*BB
+            END IF
+  130    CONTINUE
+*
+         E( L-1 ) = S*P
+         D( L ) = SIGMA + GAMMA
+         GO TO 100
+*
+*        Eigenvalue found.
+*
+  140    CONTINUE
+         D( L ) = P
+*
+         L = L - 1
+         IF( L.GE.LEND )
+     $      GO TO 100
+         GO TO 150
+*
+      END IF
+*
+*     Undo scaling if necessary
+*
+  150 CONTINUE
+      IF( ISCALE.EQ.1 )
+     $   CALL SLASCL( 'G', 0, 0, SSFMAX, ANORM, LENDSV-LSV+1, 1,
+     $                D( LSV ), N, INFO )
+      IF( ISCALE.EQ.2 )
+     $   CALL SLASCL( 'G', 0, 0, SSFMIN, ANORM, LENDSV-LSV+1, 1,
+     $                D( LSV ), N, INFO )
+*
+*     Check for no convergence to an eigenvalue after a total
+*     of N*MAXIT iterations.
+*
+      IF( JTOT.LT.NMAXIT )
+     $   GO TO 10
+      DO 160 I = 1, N - 1
+         IF( E( I ).NE.ZERO )
+     $      INFO = INFO + 1
+  160 CONTINUE
+      GO TO 180
+*
+*     Sort eigenvalues in increasing order.
+*
+  170 CONTINUE
+      CALL SLASRT( 'I', N, D, INFO )
+*
+  180 CONTINUE
+      RETURN
+*
+*     End of SSTERF
+*
+      END