LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ dstt21()

 subroutine dstt21 ( integer N, integer KBAND, double precision, dimension( * ) AD, double precision, dimension( * ) AE, double precision, dimension( * ) SD, double precision, dimension( * ) SE, double precision, dimension( ldu, * ) U, integer LDU, double precision, dimension( * ) WORK, double precision, dimension( 2 ) RESULT )

DSTT21

Purpose:
``` DSTT21 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, DSTT21 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 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 (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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (N*(N+1))` [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.```
Date
December 2016

Definition at line 129 of file dstt21.f.

129 *
130 * -- LAPACK test routine (version 3.7.0) --
131 * -- LAPACK is a software package provided by Univ. of Tennessee, --
132 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
133 * December 2016
134 *
135 * .. Scalar Arguments ..
136  INTEGER kband, ldu, n
137 * ..
138 * .. Array Arguments ..
139  DOUBLE PRECISION ad( * ), ae( * ), result( 2 ), sd( * ),
140  \$ se( * ), u( ldu, * ), work( * )
141 * ..
142 *
143 * =====================================================================
144 *
145 * .. Parameters ..
146  DOUBLE PRECISION zero, one
147  parameter( zero = 0.0d0, one = 1.0d0 )
148 * ..
149 * .. Local Scalars ..
150  INTEGER j
151  DOUBLE PRECISION anorm, temp1, temp2, ulp, unfl, wnorm
152 * ..
153 * .. External Functions ..
154  DOUBLE PRECISION dlamch, dlange, dlansy
155  EXTERNAL dlamch, dlange, dlansy
156 * ..
157 * .. External Subroutines ..
158  EXTERNAL dgemm, dlaset, dsyr, dsyr2
159 * ..
160 * .. Intrinsic Functions ..
161  INTRINSIC abs, dble, max, min
162 * ..
163 * .. Executable Statements ..
164 *
165 * 1) Constants
166 *
167  result( 1 ) = zero
168  result( 2 ) = zero
169  IF( n.LE.0 )
170  \$ RETURN
171 *
172  unfl = dlamch( 'Safe minimum' )
173  ulp = dlamch( 'Precision' )
174 *
175 * Do Test 1
176 *
177 * Copy A & Compute its 1-Norm:
178 *
179  CALL dlaset( 'Full', n, n, zero, zero, work, n )
180 *
181  anorm = zero
182  temp1 = zero
183 *
184  DO 10 j = 1, n - 1
185  work( ( n+1 )*( j-1 )+1 ) = ad( j )
186  work( ( n+1 )*( j-1 )+2 ) = ae( j )
187  temp2 = abs( ae( j ) )
188  anorm = max( anorm, abs( ad( j ) )+temp1+temp2 )
189  temp1 = temp2
190  10 CONTINUE
191 *
192  work( n**2 ) = ad( n )
193  anorm = max( anorm, abs( ad( n ) )+temp1, unfl )
194 *
195 * Norm of A - USU'
196 *
197  DO 20 j = 1, n
198  CALL dsyr( 'L', n, -sd( j ), u( 1, j ), 1, work, n )
199  20 CONTINUE
200 *
201  IF( n.GT.1 .AND. kband.EQ.1 ) THEN
202  DO 30 j = 1, n - 1
203  CALL dsyr2( 'L', n, -se( j ), u( 1, j ), 1, u( 1, j+1 ), 1,
204  \$ work, n )
205  30 CONTINUE
206  END IF
207 *
208  wnorm = dlansy( '1', 'L', n, work, n, work( n**2+1 ) )
209 *
210  IF( anorm.GT.wnorm ) THEN
211  result( 1 ) = ( wnorm / anorm ) / ( n*ulp )
212  ELSE
213  IF( anorm.LT.one ) THEN
214  result( 1 ) = ( min( wnorm, n*anorm ) / anorm ) / ( n*ulp )
215  ELSE
216  result( 1 ) = min( wnorm / anorm, dble( n ) ) / ( n*ulp )
217  END IF
218  END IF
219 *
220 * Do Test 2
221 *
222 * Compute UU' - I
223 *
224  CALL dgemm( 'N', 'C', n, n, n, one, u, ldu, u, ldu, zero, work,
225  \$ n )
226 *
227  DO 40 j = 1, n
228  work( ( n+1 )*( j-1 )+1 ) = work( ( n+1 )*( j-1 )+1 ) - one
229  40 CONTINUE
230 *
231  result( 2 ) = min( dble( n ), dlange( '1', n, n, work, n,
232  \$ work( n**2+1 ) ) ) / ( n*ulp )
233 *
234  RETURN
235 *
236 * End of DSTT21
237 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
double precision function dlansy(NORM, UPLO, N, A, LDA, WORK)
DLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix.
Definition: dlansy.f:124
subroutine dsyr(UPLO, N, ALPHA, X, INCX, A, LDA)
DSYR
Definition: dsyr.f:134
subroutine dlaset(UPLO, M, N, ALPHA, BETA, A, LDA)
DLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values...
Definition: dlaset.f:112
subroutine dgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DGEMM
Definition: dgemm.f:189
double precision function dlange(NORM, M, N, A, LDA, WORK)
DLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: dlange.f:116
subroutine dsyr2(UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA)
DSYR2
Definition: dsyr2.f:149
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