LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
Loading...
Searching...
No Matches

◆ cstt21()

subroutine cstt21 ( integer  N,
integer  KBAND,
real, dimension( * )  AD,
real, dimension( * )  AE,
real, dimension( * )  SD,
real, dimension( * )  SE,
complex, dimension( ldu, * )  U,
integer  LDU,
complex, dimension( * )  WORK,
real, dimension( * )  RWORK,
real, dimension( 2 )  RESULT 
)

CSTT21

Purpose:
 CSTT21  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, CSTT21 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 REAL array, dimension (N)
          The diagonal of the original (unfactored) matrix A.  A is
          assumed to be real symmetric tridiagonal.
[in]AE
          AE is REAL 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 REAL array, dimension (N)
          The diagonal of the real (symmetric tri-) diagonal matrix S.
[in]SE
          SE is REAL 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 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 array, dimension (N**2)
[out]RWORK
          RWORK is REAL array, dimension (N)
[out]RESULT
          RESULT is REAL 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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 131 of file cstt21.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 REAL AD( * ), AE( * ), RESULT( 2 ), RWORK( * ),
143 $ SD( * ), SE( * )
144 COMPLEX U( LDU, * ), WORK( * )
145* ..
146*
147* =====================================================================
148*
149* .. Parameters ..
150 REAL ZERO, ONE
151 parameter( zero = 0.0e+0, one = 1.0e+0 )
152 COMPLEX CZERO, CONE
153 parameter( czero = ( 0.0e+0, 0.0e+0 ),
154 $ cone = ( 1.0e+0, 0.0e+0 ) )
155* ..
156* .. Local Scalars ..
157 INTEGER J
158 REAL ANORM, TEMP1, TEMP2, ULP, UNFL, WNORM
159* ..
160* .. External Functions ..
161 REAL CLANGE, CLANHE, SLAMCH
162 EXTERNAL clange, clanhe, slamch
163* ..
164* .. External Subroutines ..
165 EXTERNAL cgemm, cher, cher2, claset
166* ..
167* .. Intrinsic Functions ..
168 INTRINSIC abs, cmplx, max, min, real
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 = slamch( 'Safe minimum' )
180 ulp = slamch( 'Precision' )
181*
182* Do Test 1
183*
184* Copy A & Compute its 1-Norm:
185*
186 CALL claset( '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 - U S U**H
203*
204 DO 20 j = 1, n
205 CALL cher( '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 cher2( 'L', n, -cmplx( se( j ) ), u( 1, j ), 1,
211 $ u( 1, j+1 ), 1, work, n )
212 30 CONTINUE
213 END IF
214*
215 wnorm = clanhe( '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, real( n ) ) / ( n*ulp )
224 END IF
225 END IF
226*
227* Do Test 2
228*
229* Compute U U**H - I
230*
231 CALL cgemm( '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( real( n ), clange( '1', n, n, work, n,
239 $ rwork ) ) / ( n*ulp )
240*
241 RETURN
242*
243* End of CSTT21
244*
subroutine cher2(UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA)
CHER2
Definition: cher2.f:150
subroutine cher(UPLO, N, ALPHA, X, INCX, A, LDA)
CHER
Definition: cher.f:135
subroutine cgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
CGEMM
Definition: cgemm.f:187
real function clange(NORM, M, N, A, LDA, WORK)
CLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: clange.f:115
real function clanhe(NORM, UPLO, N, A, LDA, WORK)
CLANHE returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: clanhe.f:124
subroutine claset(UPLO, M, N, ALPHA, BETA, A, LDA)
CLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: claset.f:106
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
Here is the call graph for this function:
Here is the caller graph for this function: