 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ zstt22()

 subroutine zstt22 ( integer N, integer M, integer KBAND, double precision, dimension( * ) AD, double precision, dimension( * ) AE, double precision, dimension( * ) SD, double precision, dimension( * ) SE, complex*16, dimension( ldu, * ) U, integer LDU, complex*16, dimension( ldwork, * ) WORK, integer LDWORK, double precision, dimension( * ) RWORK, double precision, dimension( 2 ) RESULT )

ZSTT22

Purpose:
``` ZSTT22  checks a set of M eigenvalues and eigenvectors,

A U = U S

where A is Hermitian tridiagonal, the columns of U are unitary,
and S is diagonal (if KBAND=0) or Hermitian tridiagonal (if KBAND=1).
Two tests are performed:

RESULT(1) = | U* A U - S | / ( |A| m ulp )

RESULT(2) = | I - U*U | / ( m ulp )```
Parameters
 [in] N ``` N is INTEGER The size of the matrix. If it is zero, ZSTT22 does nothing. It must be at least zero.``` [in] M ``` M is INTEGER The number of eigenpairs to check. If it is zero, ZSTT22 does nothing. It must be at least zero.``` [in] KBAND ``` KBAND is INTEGER The bandwidth of the matrix S. It may only be zero or one. If zero, then S is diagonal, and SE is not referenced. If one, then S is Hermitian tri-diagonal.``` [in] AD ``` AD is DOUBLE PRECISION array, dimension (N) The diagonal of the original (unfactored) matrix A. A is assumed to be Hermitian tridiagonal.``` [in] AE ``` AE is DOUBLE PRECISION array, dimension (N) The off-diagonal of the original (unfactored) matrix A. A is assumed to be Hermitian tridiagonal. AE(1) is ignored, AE(2) is the (1,2) and (2,1) element, etc.``` [in] SD ``` SD is DOUBLE PRECISION array, dimension (N) The diagonal of the (Hermitian tri-) diagonal matrix S.``` [in] SE ``` SE is DOUBLE PRECISION array, dimension (N) The off-diagonal of the (Hermitian tri-) diagonal matrix S. Not referenced if KBSND=0. If KBAND=1, then AE(1) is ignored, SE(2) is the (1,2) and (2,1) element, etc.``` [in] U ``` U is DOUBLE PRECISION array, dimension (LDU, N) The unitary matrix in the decomposition.``` [in] LDU ``` LDU is INTEGER The leading dimension of U. LDU must be at least N.``` [out] WORK ` WORK is COMPLEX*16 array, dimension (LDWORK, M+1)` [in] LDWORK ``` LDWORK is INTEGER The leading dimension of WORK. LDWORK must be at least max(1,M).``` [out] RWORK ` RWORK is DOUBLE PRECISION array, dimension (N)` [out] RESULT ``` RESULT is DOUBLE PRECISION array, dimension (2) The values computed by the two tests described above. The values are currently limited to 1/ulp, to avoid overflow.```

Definition at line 143 of file zstt22.f.

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*
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
subroutine zgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZGEMM
Definition: zgemm.f:187
double precision function zlange(NORM, M, N, A, LDA, WORK)
ZLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: zlange.f:115
double precision function zlansy(NORM, UPLO, N, A, LDA, WORK)
ZLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: zlansy.f:123
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