LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ zstt21()

 subroutine zstt21 ( integer n, 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( * ) work, double precision, dimension( * ) rwork, double precision, dimension( 2 ) result )

ZSTT21

Purpose:
ZSTT21  checks a decomposition of the form

A = U S U**H

where **H means conjugate transpose, A is real symmetric tridiagonal,
U is unitary, and S is real and diagonal (if KBAND=0) or symmetric
tridiagonal (if KBAND=1).  Two tests are performed:

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

RESULT(2) = | I - U U**H | / ( n ulp )
Parameters
 [in] N N is INTEGER The size of the matrix. If it is zero, ZSTT21 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 symmetric tri-diagonal. [in] AD AD is DOUBLE PRECISION array, dimension (N) The diagonal of the original (unfactored) matrix A. A is assumed to be real symmetric tridiagonal. [in] AE AE is DOUBLE PRECISION array, dimension (N-1) The off-diagonal of the original (unfactored) matrix A. A is assumed to be symmetric tridiagonal. AE(1) is the (1,2) and (2,1) element, AE(2) is the (2,3) and (3,2) element, etc. [in] SD SD is DOUBLE PRECISION array, dimension (N) The diagonal of the real (symmetric tri-) diagonal matrix S. [in] SE SE is DOUBLE PRECISION array, dimension (N-1) The off-diagonal of the (symmetric tri-) diagonal matrix S. Not referenced if KBSND=0. If KBAND=1, then AE(1) is the (1,2) and (2,1) element, SE(2) is the (2,3) and (3,2) element, etc. [in] U U is COMPLEX*16 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 (N**2) [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. RESULT(1) is always modified.

Definition at line 131 of file zstt21.f.

133*
134* -- LAPACK test routine --
135* -- LAPACK is a software package provided by Univ. of Tennessee, --
136* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
137*
138* .. Scalar Arguments ..
139 INTEGER KBAND, LDU, N
140* ..
141* .. Array Arguments ..
142 DOUBLE PRECISION AD( * ), AE( * ), RESULT( 2 ), RWORK( * ),
143 \$ SD( * ), SE( * )
144 COMPLEX*16 U( LDU, * ), WORK( * )
145* ..
146*
147* =====================================================================
148*
149* .. Parameters ..
150 DOUBLE PRECISION ZERO, ONE
151 parameter( zero = 0.0d+0, one = 1.0d+0 )
152 COMPLEX*16 CZERO, CONE
153 parameter( czero = ( 0.0d+0, 0.0d+0 ),
154 \$ cone = ( 1.0d+0, 0.0d+0 ) )
155* ..
156* .. Local Scalars ..
157 INTEGER J
158 DOUBLE PRECISION ANORM, TEMP1, TEMP2, ULP, UNFL, WNORM
159* ..
160* .. External Functions ..
161 DOUBLE PRECISION DLAMCH, ZLANGE, ZLANHE
162 EXTERNAL dlamch, zlange, zlanhe
163* ..
164* .. External Subroutines ..
165 EXTERNAL zgemm, zher, zher2, zlaset
166* ..
167* .. Intrinsic Functions ..
168 INTRINSIC abs, dble, dcmplx, max, min
169* ..
170* .. Executable Statements ..
171*
172* 1) Constants
173*
174 result( 1 ) = zero
175 result( 2 ) = zero
176 IF( n.LE.0 )
177 \$ RETURN
178*
179 unfl = dlamch( 'Safe minimum' )
180 ulp = dlamch( 'Precision' )
181*
182* Do Test 1
183*
184* Copy A & Compute its 1-Norm:
185*
186 CALL zlaset( 'Full', n, n, czero, czero, work, n )
187*
188 anorm = zero
189 temp1 = zero
190*
191 DO 10 j = 1, n - 1
192 work( ( n+1 )*( j-1 )+1 ) = ad( j )
193 work( ( n+1 )*( j-1 )+2 ) = ae( j )
194 temp2 = abs( ae( j ) )
195 anorm = max( anorm, abs( ad( j ) )+temp1+temp2 )
196 temp1 = temp2
197 10 CONTINUE
198*
199 work( n**2 ) = ad( n )
200 anorm = max( anorm, abs( ad( n ) )+temp1, unfl )
201*
202* Norm of A - USU*
203*
204 DO 20 j = 1, n
205 CALL zher( 'L', n, -sd( j ), u( 1, j ), 1, work, n )
206 20 CONTINUE
207*
208 IF( n.GT.1 .AND. kband.EQ.1 ) THEN
209 DO 30 j = 1, n - 1
210 CALL zher2( 'L', n, -dcmplx( se( j ) ), u( 1, j ), 1,
211 \$ u( 1, j+1 ), 1, work, n )
212 30 CONTINUE
213 END IF
214*
215 wnorm = zlanhe( '1', 'L', n, work, n, rwork )
216*
217 IF( anorm.GT.wnorm ) THEN
218 result( 1 ) = ( wnorm / anorm ) / ( n*ulp )
219 ELSE
220 IF( anorm.LT.one ) THEN
221 result( 1 ) = ( min( wnorm, n*anorm ) / anorm ) / ( n*ulp )
222 ELSE
223 result( 1 ) = min( wnorm / anorm, dble( n ) ) / ( n*ulp )
224 END IF
225 END IF
226*
227* Do Test 2
228*
229* Compute U U**H - I
230*
231 CALL zgemm( 'N', 'C', n, n, n, cone, u, ldu, u, ldu, czero, work,
232 \$ n )
233*
234 DO 40 j = 1, n
235 work( ( n+1 )*( j-1 )+1 ) = work( ( n+1 )*( j-1 )+1 ) - cone
236 40 CONTINUE
237*
238 result( 2 ) = min( dble( n ), zlange( '1', n, n, work, n,
239 \$ rwork ) ) / ( n*ulp )
240*
241 RETURN
242*
243* End of ZSTT21
244*
subroutine zgemm(transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
ZGEMM
Definition zgemm.f:188
subroutine zher2(uplo, n, alpha, x, incx, y, incy, a, lda)
ZHER2
Definition zher2.f:150
subroutine zher(uplo, n, alpha, x, incx, a, lda)
ZHER
Definition zher.f:135
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
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 zlanhe(norm, uplo, n, a, lda, work)
ZLANHE returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition zlanhe.f:124
subroutine zlaset(uplo, m, n, alpha, beta, a, lda)
ZLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition zlaset.f:106
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