1*> \brief \b ZSTT22
2*
3*  =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6*            http://www.netlib.org/lapack/explore-html/
7*
8*  Definition:
9*  ===========
10*
11*       SUBROUTINE ZSTT22( N, M, KBAND, AD, AE, SD, SE, U, LDU, WORK,
12*                          LDWORK, RWORK, RESULT )
13*
14*       .. Scalar Arguments ..
15*       INTEGER            KBAND, LDU, LDWORK, M, N
16*       ..
17*       .. Array Arguments ..
18*       DOUBLE PRECISION   AD( * ), AE( * ), RESULT( 2 ), RWORK( * ),
19*      $                   SD( * ), SE( * )
20*       COMPLEX*16         U( LDU, * ), WORK( LDWORK, * )
21*       ..
22*
23*
24*> \par Purpose:
25*  =============
26*>
27*> \verbatim
28*>
29*> ZSTT22  checks a set of M eigenvalues and eigenvectors,
30*>
31*>     A U = U S
32*>
33*> where A is Hermitian tridiagonal, the columns of U are unitary,
34*> and S is diagonal (if KBAND=0) or Hermitian tridiagonal (if KBAND=1).
35*> Two tests are performed:
36*>
37*>    RESULT(1) = | U* A U - S | / ( |A| m ulp )
38*>
39*>    RESULT(2) = | I - U*U | / ( m ulp )
40*> \endverbatim
41*
42*  Arguments:
43*  ==========
44*
45*> \param[in] N
46*> \verbatim
47*>          N is INTEGER
48*>          The size of the matrix.  If it is zero, ZSTT22 does nothing.
49*>          It must be at least zero.
50*> \endverbatim
51*>
52*> \param[in] M
53*> \verbatim
54*>          M is INTEGER
55*>          The number of eigenpairs to check.  If it is zero, ZSTT22
56*>          does nothing.  It must be at least zero.
57*> \endverbatim
58*>
59*> \param[in] KBAND
60*> \verbatim
61*>          KBAND is INTEGER
62*>          The bandwidth of the matrix S.  It may only be zero or one.
63*>          If zero, then S is diagonal, and SE is not referenced.  If
64*>          one, then S is Hermitian tri-diagonal.
65*> \endverbatim
66*>
67*> \param[in] AD
68*> \verbatim
69*>          AD is DOUBLE PRECISION array, dimension (N)
70*>          The diagonal of the original (unfactored) matrix A.  A is
71*>          assumed to be Hermitian tridiagonal.
72*> \endverbatim
73*>
74*> \param[in] AE
75*> \verbatim
76*>          AE is DOUBLE PRECISION array, dimension (N)
77*>          The off-diagonal of the original (unfactored) matrix A.  A
78*>          is assumed to be Hermitian tridiagonal.  AE(1) is ignored,
79*>          AE(2) is the (1,2) and (2,1) element, etc.
80*> \endverbatim
81*>
82*> \param[in] SD
83*> \verbatim
84*>          SD is DOUBLE PRECISION array, dimension (N)
85*>          The diagonal of the (Hermitian tri-) diagonal matrix S.
86*> \endverbatim
87*>
88*> \param[in] SE
89*> \verbatim
90*>          SE is DOUBLE PRECISION array, dimension (N)
91*>          The off-diagonal of the (Hermitian tri-) diagonal matrix S.
92*>          Not referenced if KBSND=0.  If KBAND=1, then AE(1) is
93*>          ignored, SE(2) is the (1,2) and (2,1) element, etc.
94*> \endverbatim
95*>
96*> \param[in] U
97*> \verbatim
98*>          U is DOUBLE PRECISION array, dimension (LDU, N)
99*>          The unitary matrix in the decomposition.
100*> \endverbatim
101*>
102*> \param[in] LDU
103*> \verbatim
104*>          LDU is INTEGER
105*>          The leading dimension of U.  LDU must be at least N.
106*> \endverbatim
107*>
108*> \param[out] WORK
109*> \verbatim
110*>          WORK is COMPLEX*16 array, dimension (LDWORK, M+1)
111*> \endverbatim
112*>
113*> \param[in] LDWORK
114*> \verbatim
115*>          LDWORK is INTEGER
116*>          The leading dimension of WORK.  LDWORK must be at least
117*>          max(1,M).
118*> \endverbatim
119*>
120*> \param[out] RWORK
121*> \verbatim
122*>          RWORK is DOUBLE PRECISION array, dimension (N)
123*> \endverbatim
124*>
125*> \param[out] RESULT
126*> \verbatim
127*>          RESULT is DOUBLE PRECISION array, dimension (2)
128*>          The values computed by the two tests described above.  The
129*>          values are currently limited to 1/ulp, to avoid overflow.
130*> \endverbatim
131*
132*  Authors:
133*  ========
134*
135*> \author Univ. of Tennessee
136*> \author Univ. of California Berkeley
137*> \author Univ. of Colorado Denver
138*> \author NAG Ltd.
139*
140*> \ingroup complex16_eig
141*
142*  =====================================================================
143      SUBROUTINE ZSTT22( N, M, KBAND, AD, AE, SD, SE, U, LDU, WORK,
144     $                   LDWORK, RWORK, RESULT )
145*
146*  -- LAPACK test routine --
147*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
148*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
149*
150*     .. Scalar Arguments ..
151      INTEGER            KBAND, LDU, LDWORK, M, N
152*     ..
153*     .. Array Arguments ..
154      DOUBLE PRECISION   AD( * ), AE( * ), RESULT( 2 ), RWORK( * ),
155     $                   SD( * ), SE( * )
156      COMPLEX*16         U( LDU, * ), WORK( LDWORK, * )
157*     ..
158*
159*  =====================================================================
160*
161*     .. Parameters ..
162      DOUBLE PRECISION   ZERO, ONE
163      PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )
164      COMPLEX*16         CZERO, CONE
165      PARAMETER          ( CZERO = ( 0.0D+0, 0.0D+0 ),
166     $                   CONE = ( 1.0D+0, 0.0D+0 ) )
167*     ..
168*     .. Local Scalars ..
169      INTEGER            I, J, K
170      DOUBLE PRECISION   ANORM, ULP, UNFL, WNORM
171      COMPLEX*16         AUKJ
172*     ..
173*     .. External Functions ..
174      DOUBLE PRECISION   DLAMCH, ZLANGE, ZLANSY
175      EXTERNAL           DLAMCH, ZLANGE, ZLANSY
176*     ..
177*     .. External Subroutines ..
178      EXTERNAL           ZGEMM
179*     ..
180*     .. Intrinsic Functions ..
181      INTRINSIC          ABS, DBLE, MAX, MIN
182*     ..
183*     .. Executable Statements ..
184*
185      RESULT( 1 ) = ZERO
186      RESULT( 2 ) = ZERO
187      IF( N.LE.0 .OR. M.LE.0 )
188     $   RETURN
189*
190      UNFL = DLAMCH( 'Safe minimum' )
191      ULP = DLAMCH( 'Epsilon' )
192*
193*     Do Test 1
194*
195*     Compute the 1-norm of A.
196*
197      IF( N.GT.1 ) THEN
198         ANORM = ABS( AD( 1 ) ) + ABS( AE( 1 ) )
199         DO 10 J = 2, N - 1
200            ANORM = MAX( ANORM, ABS( AD( J ) )+ABS( AE( J ) )+
201     $              ABS( AE( J-1 ) ) )
202   10    CONTINUE
203         ANORM = MAX( ANORM, ABS( AD( N ) )+ABS( AE( N-1 ) ) )
204      ELSE
205         ANORM = ABS( AD( 1 ) )
206      END IF
207      ANORM = MAX( ANORM, UNFL )
208*
209*     Norm of U*AU - S
210*
211      DO 40 I = 1, M
212         DO 30 J = 1, M
213            WORK( I, J ) = CZERO
214            DO 20 K = 1, N
215               AUKJ = AD( K )*U( K, J )
216               IF( K.NE.N )
217     $            AUKJ = AUKJ + AE( K )*U( K+1, J )
218               IF( K.NE.1 )
219     $            AUKJ = AUKJ + AE( K-1 )*U( K-1, J )
220               WORK( I, J ) = WORK( I, J ) + U( K, I )*AUKJ
221   20       CONTINUE
222   30    CONTINUE
223         WORK( I, I ) = WORK( I, I ) - SD( I )
224         IF( KBAND.EQ.1 ) THEN
225            IF( I.NE.1 )
226     $         WORK( I, I-1 ) = WORK( I, I-1 ) - SE( I-1 )
227            IF( I.NE.N )
228     $         WORK( I, I+1 ) = WORK( I, I+1 ) - SE( I )
229         END IF
230   40 CONTINUE
231*
232      WNORM = ZLANSY( '1', 'L', M, WORK, M, RWORK )
233*
234      IF( ANORM.GT.WNORM ) THEN
235         RESULT( 1 ) = ( WNORM / ANORM ) / ( M*ULP )
236      ELSE
237         IF( ANORM.LT.ONE ) THEN
238            RESULT( 1 ) = ( MIN( WNORM, M*ANORM ) / ANORM ) / ( M*ULP )
239         ELSE
240            RESULT( 1 ) = MIN( WNORM / ANORM, DBLE( M ) ) / ( M*ULP )
241         END IF
242      END IF
243*
244*     Do Test 2
245*
246*     Compute  U*U - I
247*
248      CALL ZGEMM( 'T', 'N', M, M, N, CONE, U, LDU, U, LDU, CZERO, WORK,
249     $            M )
250*
251      DO 50 J = 1, M
252         WORK( J, J ) = WORK( J, J ) - ONE
253   50 CONTINUE
254*
255      RESULT( 2 ) = MIN( DBLE( M ), ZLANGE( '1', M, M, WORK, M,
256     $              RWORK ) ) / ( M*ULP )
257*
258      RETURN
259*
260*     End of ZSTT22
261*
262      END
263