 LAPACK  3.10.0 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.```

Definition at line 125 of file dstt21.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  DOUBLE PRECISION AD( * ), AE( * ), RESULT( 2 ), SD( * ),
137  \$ SE( * ), U( LDU, * ), WORK( * )
138 * ..
139 *
140 * =====================================================================
141 *
142 * .. Parameters ..
143  DOUBLE PRECISION ZERO, ONE
144  parameter( zero = 0.0d0, one = 1.0d0 )
145 * ..
146 * .. Local Scalars ..
147  INTEGER J
148  DOUBLE PRECISION ANORM, TEMP1, TEMP2, ULP, UNFL, WNORM
149 * ..
150 * .. External Functions ..
151  DOUBLE PRECISION DLAMCH, DLANGE, DLANSY
152  EXTERNAL dlamch, dlange, dlansy
153 * ..
154 * .. External Subroutines ..
155  EXTERNAL dgemm, dlaset, dsyr, dsyr2
156 * ..
157 * .. Intrinsic Functions ..
158  INTRINSIC abs, dble, max, min
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 = dlamch( 'Safe minimum' )
170  ulp = dlamch( 'Precision' )
171 *
172 * Do Test 1
173 *
174 * Copy A & Compute its 1-Norm:
175 *
176  CALL dlaset( '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 dsyr( '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 dsyr2( '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 = dlansy( '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, dble( n ) ) / ( n*ulp )
214  END IF
215  END IF
216 *
217 * Do Test 2
218 *
219 * Compute UU' - I
220 *
221  CALL dgemm( '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( dble( n ), dlange( '1', n, n, work, n,
229  \$ work( n**2+1 ) ) ) / ( n*ulp )
230 *
231  RETURN
232 *
233 * End of DSTT21
234 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
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:110
subroutine dsyr(UPLO, N, ALPHA, X, INCX, A, LDA)
DSYR
Definition: dsyr.f:132
subroutine dsyr2(UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA)
DSYR2
Definition: dsyr2.f:147
subroutine dgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DGEMM
Definition: dgemm.f:187
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:114
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,...
Definition: dlansy.f:122
Here is the call graph for this function:
Here is the caller graph for this function: