LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ sstt21()

subroutine sstt21 ( integer  N,
integer  KBAND,
real, dimension( * )  AD,
real, dimension( * )  AE,
real, dimension( * )  SD,
real, dimension( * )  SE,
real, dimension( ldu, * )  U,
integer  LDU,
real, dimension( * )  WORK,
real, dimension( 2 )  RESULT 
)

SSTT21

Purpose:
 SSTT21 checks a decomposition of the form

    A = U S U'

 where ' means transpose, A is symmetric tridiagonal, U is orthogonal,
 and S is diagonal (if KBAND=0) or symmetric tridiagonal (if KBAND=1).
 Two tests are performed:

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

    RESULT(2) = | I - UU' | / ( n ulp )
Parameters
[in]N
          N is INTEGER
          The size of the matrix.  If it is zero, SSTT21 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 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 (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 REAL array, dimension (LDU, N)
          The orthogonal matrix in the decomposition.
[in]LDU
          LDU is INTEGER
          The leading dimension of U.  LDU must be at least N.
[out]WORK
          WORK is REAL array, dimension (N*(N+1))
[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 125 of file sstt21.f.

127 *
128 * -- LAPACK test routine --
129 * -- LAPACK is a software package provided by Univ. of Tennessee, --
130 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
131 *
132 * .. Scalar Arguments ..
133  INTEGER KBAND, LDU, N
134 * ..
135 * .. Array Arguments ..
136  REAL AD( * ), AE( * ), RESULT( 2 ), SD( * ),
137  $ SE( * ), U( LDU, * ), WORK( * )
138 * ..
139 *
140 * =====================================================================
141 *
142 * .. Parameters ..
143  REAL ZERO, ONE
144  parameter( zero = 0.0e0, one = 1.0e0 )
145 * ..
146 * .. Local Scalars ..
147  INTEGER J
148  REAL ANORM, TEMP1, TEMP2, ULP, UNFL, WNORM
149 * ..
150 * .. External Functions ..
151  REAL SLAMCH, SLANGE, SLANSY
152  EXTERNAL slamch, slange, slansy
153 * ..
154 * .. External Subroutines ..
155  EXTERNAL sgemm, slaset, ssyr, ssyr2
156 * ..
157 * .. Intrinsic Functions ..
158  INTRINSIC abs, max, min, real
159 * ..
160 * .. Executable Statements ..
161 *
162 * 1) Constants
163 *
164  result( 1 ) = zero
165  result( 2 ) = zero
166  IF( n.LE.0 )
167  $ RETURN
168 *
169  unfl = slamch( 'Safe minimum' )
170  ulp = slamch( 'Precision' )
171 *
172 * Do Test 1
173 *
174 * Copy A & Compute its 1-Norm:
175 *
176  CALL slaset( 'Full', n, n, zero, zero, work, n )
177 *
178  anorm = zero
179  temp1 = zero
180 *
181  DO 10 j = 1, n - 1
182  work( ( n+1 )*( j-1 )+1 ) = ad( j )
183  work( ( n+1 )*( j-1 )+2 ) = ae( j )
184  temp2 = abs( ae( j ) )
185  anorm = max( anorm, abs( ad( j ) )+temp1+temp2 )
186  temp1 = temp2
187  10 CONTINUE
188 *
189  work( n**2 ) = ad( n )
190  anorm = max( anorm, abs( ad( n ) )+temp1, unfl )
191 *
192 * Norm of A - USU'
193 *
194  DO 20 j = 1, n
195  CALL ssyr( 'L', n, -sd( j ), u( 1, j ), 1, work, n )
196  20 CONTINUE
197 *
198  IF( n.GT.1 .AND. kband.EQ.1 ) THEN
199  DO 30 j = 1, n - 1
200  CALL ssyr2( 'L', n, -se( j ), u( 1, j ), 1, u( 1, j+1 ), 1,
201  $ work, n )
202  30 CONTINUE
203  END IF
204 *
205  wnorm = slansy( '1', 'L', n, work, n, work( n**2+1 ) )
206 *
207  IF( anorm.GT.wnorm ) THEN
208  result( 1 ) = ( wnorm / anorm ) / ( n*ulp )
209  ELSE
210  IF( anorm.LT.one ) THEN
211  result( 1 ) = ( min( wnorm, n*anorm ) / anorm ) / ( n*ulp )
212  ELSE
213  result( 1 ) = min( wnorm / anorm, real( n ) ) / ( n*ulp )
214  END IF
215  END IF
216 *
217 * Do Test 2
218 *
219 * Compute UU' - I
220 *
221  CALL sgemm( 'N', 'C', n, n, n, one, u, ldu, u, ldu, zero, work,
222  $ n )
223 *
224  DO 40 j = 1, n
225  work( ( n+1 )*( j-1 )+1 ) = work( ( n+1 )*( j-1 )+1 ) - one
226  40 CONTINUE
227 *
228  result( 2 ) = min( real( n ), slange( '1', n, n, work, n,
229  $ work( n**2+1 ) ) ) / ( n*ulp )
230 *
231  RETURN
232 *
233 * End of SSTT21
234 *
subroutine slaset(UPLO, M, N, ALPHA, BETA, A, LDA)
SLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: slaset.f:110
real function slange(NORM, M, N, A, LDA, WORK)
SLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: slange.f:114
real function slansy(NORM, UPLO, N, A, LDA, WORK)
SLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: slansy.f:122
subroutine ssyr(UPLO, N, ALPHA, X, INCX, A, LDA)
SSYR
Definition: ssyr.f:132
subroutine ssyr2(UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA)
SSYR2
Definition: ssyr2.f:147
subroutine sgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
SGEMM
Definition: sgemm.f:187
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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