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SUBROUTINE <a name="SSTERF.1"></a><a href="ssterf.f.html#SSTERF.1">SSTERF</a>( N, D, E, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> -- LAPACK routine (version 3.1) --
</span><span class="comment">*</span><span class="comment"> Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment"> November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Scalar Arguments ..
</span> INTEGER INFO, N
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> REAL D( * ), E( * )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Purpose
</span><span class="comment">*</span><span class="comment"> =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> <a name="SSTERF.17"></a><a href="ssterf.f.html#SSTERF.1">SSTERF</a> computes all eigenvalues of a symmetric tridiagonal matrix
</span><span class="comment">*</span><span class="comment"> using the Pal-Walker-Kahan variant of the QL or QR algorithm.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Arguments
</span><span class="comment">*</span><span class="comment"> =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> N (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The order of the matrix. N >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> D (input/output) REAL array, dimension (N)
</span><span class="comment">*</span><span class="comment"> On entry, the n diagonal elements of the tridiagonal matrix.
</span><span class="comment">*</span><span class="comment"> On exit, if INFO = 0, the eigenvalues in ascending order.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> E (input/output) REAL array, dimension (N-1)
</span><span class="comment">*</span><span class="comment"> On entry, the (n-1) subdiagonal elements of the tridiagonal
</span><span class="comment">*</span><span class="comment"> matrix.
</span><span class="comment">*</span><span class="comment"> On exit, E has been destroyed.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> INFO (output) INTEGER
</span><span class="comment">*</span><span class="comment"> = 0: successful exit
</span><span class="comment">*</span><span class="comment"> < 0: if INFO = -i, the i-th argument had an illegal value
</span><span class="comment">*</span><span class="comment"> > 0: the algorithm failed to find all of the eigenvalues in
</span><span class="comment">*</span><span class="comment"> a total of 30*N iterations; if INFO = i, then i
</span><span class="comment">*</span><span class="comment"> elements of E have not converged to zero.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Parameters ..
</span> REAL ZERO, ONE, TWO, THREE
PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0, TWO = 2.0E0,
$ THREE = 3.0E0 )
INTEGER MAXIT
PARAMETER ( MAXIT = 30 )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Scalars ..
</span> 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
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Functions ..
</span> REAL <a name="SLAMCH.59"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>, <a name="SLANST.59"></a><a href="slanst.f.html#SLANST.1">SLANST</a>, <a name="SLAPY2.59"></a><a href="slapy2.f.html#SLAPY2.1">SLAPY2</a>
EXTERNAL <a name="SLAMCH.60"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>, <a name="SLANST.60"></a><a href="slanst.f.html#SLANST.1">SLANST</a>, <a name="SLAPY2.60"></a><a href="slapy2.f.html#SLAPY2.1">SLAPY2</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Subroutines ..
</span> EXTERNAL <a name="SLAE2.63"></a><a href="slae2.f.html#SLAE2.1">SLAE2</a>, <a name="SLASCL.63"></a><a href="slascl.f.html#SLASCL.1">SLASCL</a>, <a name="SLASRT.63"></a><a href="slasrt.f.html#SLASRT.1">SLASRT</a>, <a name="XERBLA.63"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Intrinsic Functions ..
</span> INTRINSIC ABS, SIGN, SQRT
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Test the input parameters.
</span><span class="comment">*</span><span class="comment">
</span> INFO = 0
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Quick return if possible
</span><span class="comment">*</span><span class="comment">
</span> IF( N.LT.0 ) THEN
INFO = -1
CALL <a name="XERBLA.78"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="SSTERF.78"></a><a href="ssterf.f.html#SSTERF.1">SSTERF</a>'</span>, -INFO )
RETURN
END IF
IF( N.LE.1 )
$ RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Determine the unit roundoff for this environment.
</span><span class="comment">*</span><span class="comment">
</span> EPS = <a name="SLAMCH.86"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>( <span class="string">'E'</span> )
EPS2 = EPS**2
SAFMIN = <a name="SLAMCH.88"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>( <span class="string">'S'</span> )
SAFMAX = ONE / SAFMIN
SSFMAX = SQRT( SAFMAX ) / THREE
SSFMIN = SQRT( SAFMIN ) / EPS2
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Compute the eigenvalues of the tridiagonal matrix.
</span><span class="comment">*</span><span class="comment">
</span> NMAXIT = N*MAXIT
SIGMA = ZERO
JTOT = 0
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Determine where the matrix splits and choose QL or QR iteration
</span><span class="comment">*</span><span class="comment"> for each block, according to whether top or bottom diagonal
</span><span class="comment">*</span><span class="comment"> element is smaller.
</span><span class="comment">*</span><span class="comment">
</span> L1 = 1
<span class="comment">*</span><span class="comment">
</span> 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
<span class="comment">*</span><span class="comment">
</span> 30 CONTINUE
L = L1
LSV = L
LEND = M
LENDSV = LEND
L1 = M + 1
IF( LEND.EQ.L )
$ GO TO 10
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Scale submatrix in rows and columns L to LEND
</span><span class="comment">*</span><span class="comment">
</span> ANORM = <a name="SLANST.130"></a><a href="slanst.f.html#SLANST.1">SLANST</a>( <span class="string">'I'</span>, LEND-L+1, D( L ), E( L ) )
ISCALE = 0
IF( ANORM.GT.SSFMAX ) THEN
ISCALE = 1
CALL <a name="SLASCL.134"></a><a href="slascl.f.html#SLASCL.1">SLASCL</a>( <span class="string">'G'</span>, 0, 0, ANORM, SSFMAX, LEND-L+1, 1, D( L ), N,
$ INFO )
CALL <a name="SLASCL.136"></a><a href="slascl.f.html#SLASCL.1">SLASCL</a>( <span class="string">'G'</span>, 0, 0, ANORM, SSFMAX, LEND-L, 1, E( L ), N,
$ INFO )
ELSE IF( ANORM.LT.SSFMIN ) THEN
ISCALE = 2
CALL <a name="SLASCL.140"></a><a href="slascl.f.html#SLASCL.1">SLASCL</a>( <span class="string">'G'</span>, 0, 0, ANORM, SSFMIN, LEND-L+1, 1, D( L ), N,
$ INFO )
CALL <a name="SLASCL.142"></a><a href="slascl.f.html#SLASCL.1">SLASCL</a>( <span class="string">'G'</span>, 0, 0, ANORM, SSFMIN, LEND-L, 1, E( L ), N,
$ INFO )
END IF
<span class="comment">*</span><span class="comment">
</span> DO 40 I = L, LEND - 1
E( I ) = E( I )**2
40 CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Choose between QL and QR iteration
</span><span class="comment">*</span><span class="comment">
</span> IF( ABS( D( LEND ) ).LT.ABS( D( L ) ) ) THEN
LEND = LSV
L = LENDSV
END IF
<span class="comment">*</span><span class="comment">
</span> IF( LEND.GE.L ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> QL Iteration
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Look for small subdiagonal element.
</span><span class="comment">*</span><span class="comment">
</span> 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
<span class="comment">*</span><span class="comment">
</span> 70 CONTINUE
IF( M.LT.LEND )
$ E( M ) = ZERO
P = D( L )
IF( M.EQ.L )
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