LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ sget36()

 subroutine sget36 ( real RMAX, integer LMAX, integer, dimension( 3 ) NINFO, integer KNT, integer NIN )

SGET36

Purpose:
``` SGET36 tests STREXC, a routine for moving blocks (either 1 by 1 or
2 by 2) on the diagonal of a matrix in real Schur form.  Thus, SLAEXC
computes an orthogonal matrix Q such that

Q' * T1 * Q  = T2

and where one of the diagonal blocks of T1 (the one at row IFST) has
been moved to position ILST.

The test code verifies that the residual Q'*T1*Q-T2 is small, that T2
is in Schur form, and that the final position of the IFST block is
ILST (within +-1).

The test matrices are read from a file with logical unit number NIN.```
Parameters
 [out] RMAX ``` RMAX is REAL Value of the largest test ratio.``` [out] LMAX ``` LMAX is INTEGER Example number where largest test ratio achieved.``` [out] NINFO ``` NINFO is INTEGER array, dimension (3) NINFO(J) is the number of examples where INFO=J.``` [out] KNT ``` KNT is INTEGER Total number of examples tested.``` [in] NIN ``` NIN is INTEGER Input logical unit number.```

Definition at line 87 of file sget36.f.

88 *
89 * -- LAPACK test routine --
90 * -- LAPACK is a software package provided by Univ. of Tennessee, --
91 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
92 *
93 * .. Scalar Arguments ..
94  INTEGER KNT, LMAX, NIN
95  REAL RMAX
96 * ..
97 * .. Array Arguments ..
98  INTEGER NINFO( 3 )
99 * ..
100 *
101 * =====================================================================
102 *
103 * .. Parameters ..
104  REAL ZERO, ONE
105  parameter( zero = 0.0e0, one = 1.0e0 )
106  INTEGER LDT, LWORK
107  parameter( ldt = 10, lwork = 2*ldt*ldt )
108 * ..
109 * .. Local Scalars ..
110  INTEGER I, IFST, IFST1, IFST2, IFSTSV, ILST, ILST1,
111  \$ ILST2, ILSTSV, INFO1, INFO2, J, LOC, N
112  REAL EPS, RES
113 * ..
114 * .. Local Arrays ..
115  REAL Q( LDT, LDT ), RESULT( 2 ), T1( LDT, LDT ),
116  \$ T2( LDT, LDT ), TMP( LDT, LDT ), WORK( LWORK )
117 * ..
118 * .. External Functions ..
119  REAL SLAMCH
120  EXTERNAL slamch
121 * ..
122 * .. External Subroutines ..
123  EXTERNAL shst01, slacpy, slaset, strexc
124 * ..
125 * .. Intrinsic Functions ..
126  INTRINSIC abs, sign
127 * ..
128 * .. Executable Statements ..
129 *
130  eps = slamch( 'P' )
131  rmax = zero
132  lmax = 0
133  knt = 0
134  ninfo( 1 ) = 0
135  ninfo( 2 ) = 0
136  ninfo( 3 ) = 0
137 *
138 * Read input data until N=0
139 *
140  10 CONTINUE
141  READ( nin, fmt = * )n, ifst, ilst
142  IF( n.EQ.0 )
143  \$ RETURN
144  knt = knt + 1
145  DO 20 i = 1, n
146  READ( nin, fmt = * )( tmp( i, j ), j = 1, n )
147  20 CONTINUE
148  CALL slacpy( 'F', n, n, tmp, ldt, t1, ldt )
149  CALL slacpy( 'F', n, n, tmp, ldt, t2, ldt )
150  ifstsv = ifst
151  ilstsv = ilst
152  ifst1 = ifst
153  ilst1 = ilst
154  ifst2 = ifst
155  ilst2 = ilst
156  res = zero
157 *
158 * Test without accumulating Q
159 *
160  CALL slaset( 'Full', n, n, zero, one, q, ldt )
161  CALL strexc( 'N', n, t1, ldt, q, ldt, ifst1, ilst1, work, info1 )
162  DO 40 i = 1, n
163  DO 30 j = 1, n
164  IF( i.EQ.j .AND. q( i, j ).NE.one )
165  \$ res = res + one / eps
166  IF( i.NE.j .AND. q( i, j ).NE.zero )
167  \$ res = res + one / eps
168  30 CONTINUE
169  40 CONTINUE
170 *
171 * Test with accumulating Q
172 *
173  CALL slaset( 'Full', n, n, zero, one, q, ldt )
174  CALL strexc( 'V', n, t2, ldt, q, ldt, ifst2, ilst2, work, info2 )
175 *
176 * Compare T1 with T2
177 *
178  DO 60 i = 1, n
179  DO 50 j = 1, n
180  IF( t1( i, j ).NE.t2( i, j ) )
181  \$ res = res + one / eps
182  50 CONTINUE
183  60 CONTINUE
184  IF( ifst1.NE.ifst2 )
185  \$ res = res + one / eps
186  IF( ilst1.NE.ilst2 )
187  \$ res = res + one / eps
188  IF( info1.NE.info2 )
189  \$ res = res + one / eps
190 *
191 * Test for successful reordering of T2
192 *
193  IF( info2.NE.0 ) THEN
194  ninfo( info2 ) = ninfo( info2 ) + 1
195  ELSE
196  IF( abs( ifst2-ifstsv ).GT.1 )
197  \$ res = res + one / eps
198  IF( abs( ilst2-ilstsv ).GT.1 )
199  \$ res = res + one / eps
200  END IF
201 *
202 * Test for small residual, and orthogonality of Q
203 *
204  CALL shst01( n, 1, n, tmp, ldt, t2, ldt, q, ldt, work, lwork,
205  \$ result )
206  res = res + result( 1 ) + result( 2 )
207 *
208 * Test for T2 being in Schur form
209 *
210  loc = 1
211  70 CONTINUE
212  IF( t2( loc+1, loc ).NE.zero ) THEN
213 *
214 * 2 by 2 block
215 *
216  IF( t2( loc, loc+1 ).EQ.zero .OR. t2( loc, loc ).NE.
217  \$ t2( loc+1, loc+1 ) .OR. sign( one, t2( loc, loc+1 ) ).EQ.
218  \$ sign( one, t2( loc+1, loc ) ) )res = res + one / eps
219  DO 80 i = loc + 2, n
220  IF( t2( i, loc ).NE.zero )
221  \$ res = res + one / res
222  IF( t2( i, loc+1 ).NE.zero )
223  \$ res = res + one / res
224  80 CONTINUE
225  loc = loc + 2
226  ELSE
227 *
228 * 1 by 1 block
229 *
230  DO 90 i = loc + 1, n
231  IF( t2( i, loc ).NE.zero )
232  \$ res = res + one / res
233  90 CONTINUE
234  loc = loc + 1
235  END IF
236  IF( loc.LT.n )
237  \$ GO TO 70
238  IF( res.GT.rmax ) THEN
239  rmax = res
240  lmax = knt
241  END IF
242  GO TO 10
243 *
244 * End of SGET36
245 *
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
subroutine slacpy(UPLO, M, N, A, LDA, B, LDB)
SLACPY copies all or part of one two-dimensional array to another.
Definition: slacpy.f:103
subroutine strexc(COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, WORK, INFO)
STREXC
Definition: strexc.f:148
subroutine shst01(N, ILO, IHI, A, LDA, H, LDH, Q, LDQ, WORK, LWORK, RESULT)
SHST01
Definition: shst01.f:134
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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