1 SUBROUTINE DSYT21( ITYPE, UPLO, N, KBAND, A, LDA, D, E, U, LDU, V,
2 $ LDV, TAU, WORK, RESULT )
3 *
4 * -- LAPACK test routine (version 3.1) --
5 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
6 * November 2006
7 *
8 * .. Scalar Arguments ..
9 CHARACTER UPLO
10 INTEGER ITYPE, KBAND, LDA, LDU, LDV, N
11 * ..
12 * .. Array Arguments ..
13 DOUBLE PRECISION A( LDA, * ), D( * ), E( * ), RESULT( 2 ),
14 $ TAU( * ), U( LDU, * ), V( LDV, * ), WORK( * )
15 * ..
16 *
17 * Purpose
18 * =======
19 *
20 * DSYT21 generally checks a decomposition of the form
21 *
22 * A = U S U'
23 *
24 * where ' means transpose, A is symmetric, U is orthogonal, and S is
25 * diagonal (if KBAND=0) or symmetric tridiagonal (if KBAND=1).
26 *
27 * If ITYPE=1, then U is represented as a dense matrix; otherwise U is
28 * expressed as a product of Householder transformations, whose vectors
29 * are stored in the array "V" and whose scaling constants are in "TAU".
30 * We shall use the letter "V" to refer to the product of Householder
31 * transformations (which should be equal to U).
32 *
33 * Specifically, if ITYPE=1, then:
34 *
35 * RESULT(1) = | A - U S U' | / ( |A| n ulp ) *and*
36 * RESULT(2) = | I - UU' | / ( n ulp )
37 *
38 * If ITYPE=2, then:
39 *
40 * RESULT(1) = | A - V S V' | / ( |A| n ulp )
41 *
42 * If ITYPE=3, then:
43 *
44 * RESULT(1) = | I - VU' | / ( n ulp )
45 *
46 * For ITYPE > 1, the transformation U is expressed as a product
47 * V = H(1)...H(n-2), where H(j) = I - tau(j) v(j) v(j)' and each
48 * vector v(j) has its first j elements 0 and the remaining n-j elements
49 * stored in V(j+1:n,j).
50 *
51 * Arguments
52 * =========
53 *
54 * ITYPE (input) INTEGER
55 * Specifies the type of tests to be performed.
56 * 1: U expressed as a dense orthogonal matrix:
57 * RESULT(1) = | A - U S U' | / ( |A| n ulp ) *and*
58 * RESULT(2) = | I - UU' | / ( n ulp )
59 *
60 * 2: U expressed as a product V of Housholder transformations:
61 * RESULT(1) = | A - V S V' | / ( |A| n ulp )
62 *
63 * 3: U expressed both as a dense orthogonal matrix and
64 * as a product of Housholder transformations:
65 * RESULT(1) = | I - VU' | / ( n ulp )
66 *
67 * UPLO (input) CHARACTER
68 * If UPLO='U', the upper triangle of A and V will be used and
69 * the (strictly) lower triangle will not be referenced.
70 * If UPLO='L', the lower triangle of A and V will be used and
71 * the (strictly) upper triangle will not be referenced.
72 *
73 * N (input) INTEGER
74 * The size of the matrix. If it is zero, DSYT21 does nothing.
75 * It must be at least zero.
76 *
77 * KBAND (input) INTEGER
78 * The bandwidth of the matrix. It may only be zero or one.
79 * If zero, then S is diagonal, and E is not referenced. If
80 * one, then S is symmetric tri-diagonal.
81 *
82 * A (input) DOUBLE PRECISION array, dimension (LDA, N)
83 * The original (unfactored) matrix. It is assumed to be
84 * symmetric, and only the upper (UPLO='U') or only the lower
85 * (UPLO='L') will be referenced.
86 *
87 * LDA (input) INTEGER
88 * The leading dimension of A. It must be at least 1
89 * and at least N.
90 *
91 * D (input) DOUBLE PRECISION array, dimension (N)
92 * The diagonal of the (symmetric tri-) diagonal matrix.
93 *
94 * E (input) DOUBLE PRECISION array, dimension (N-1)
95 * The off-diagonal of the (symmetric tri-) diagonal matrix.
96 * E(1) is the (1,2) and (2,1) element, E(2) is the (2,3) and
97 * (3,2) element, etc.
98 * Not referenced if KBAND=0.
99 *
100 * U (input) DOUBLE PRECISION array, dimension (LDU, N)
101 * If ITYPE=1 or 3, this contains the orthogonal matrix in
102 * the decomposition, expressed as a dense matrix. If ITYPE=2,
103 * then it is not referenced.
104 *
105 * LDU (input) INTEGER
106 * The leading dimension of U. LDU must be at least N and
107 * at least 1.
108 *
109 * V (input) DOUBLE PRECISION array, dimension (LDV, N)
110 * If ITYPE=2 or 3, the columns of this array contain the
111 * Householder vectors used to describe the orthogonal matrix
112 * in the decomposition. If UPLO='L', then the vectors are in
113 * the lower triangle, if UPLO='U', then in the upper
114 * triangle.
115 * *NOTE* If ITYPE=2 or 3, V is modified and restored. The
116 * subdiagonal (if UPLO='L') or the superdiagonal (if UPLO='U')
117 * is set to one, and later reset to its original value, during
118 * the course of the calculation.
119 * If ITYPE=1, then it is neither referenced nor modified.
120 *
121 * LDV (input) INTEGER
122 * The leading dimension of V. LDV must be at least N and
123 * at least 1.
124 *
125 * TAU (input) DOUBLE PRECISION array, dimension (N)
126 * If ITYPE >= 2, then TAU(j) is the scalar factor of
127 * v(j) v(j)' in the Householder transformation H(j) of
128 * the product U = H(1)...H(n-2)
129 * If ITYPE < 2, then TAU is not referenced.
130 *
131 * WORK (workspace) DOUBLE PRECISION array, dimension (2*N**2)
132 *
133 * RESULT (output) DOUBLE PRECISION array, dimension (2)
134 * The values computed by the two tests described above. The
135 * values are currently limited to 1/ulp, to avoid overflow.
136 * RESULT(1) is always modified. RESULT(2) is modified only
137 * if ITYPE=1.
138 *
139 * =====================================================================
140 *
141 * .. Parameters ..
142 DOUBLE PRECISION ZERO, ONE, TEN
143 PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, TEN = 10.0D0 )
144 * ..
145 * .. Local Scalars ..
146 LOGICAL LOWER
147 CHARACTER CUPLO
148 INTEGER IINFO, J, JCOL, JR, JROW
149 DOUBLE PRECISION ANORM, ULP, UNFL, VSAVE, WNORM
150 * ..
151 * .. External Functions ..
152 LOGICAL LSAME
153 DOUBLE PRECISION DLAMCH, DLANGE, DLANSY
154 EXTERNAL LSAME, DLAMCH, DLANGE, DLANSY
155 * ..
156 * .. External Subroutines ..
157 EXTERNAL DGEMM, DLACPY, DLARFY, DLASET, DORM2L, DORM2R,
158 $ DSYR, DSYR2
159 * ..
160 * .. Intrinsic Functions ..
161 INTRINSIC DBLE, MAX, MIN
162 * ..
163 * .. Executable Statements ..
164 *
165 RESULT( 1 ) = ZERO
166 IF( ITYPE.EQ.1 )
167 $ RESULT( 2 ) = ZERO
168 IF( N.LE.0 )
169 $ RETURN
170 *
171 IF( LSAME( UPLO, 'U' ) ) THEN
172 LOWER = .FALSE.
173 CUPLO = 'U'
174 ELSE
175 LOWER = .TRUE.
176 CUPLO = 'L'
177 END IF
178 *
179 UNFL = DLAMCH( 'Safe minimum' )
180 ULP = DLAMCH( 'Epsilon' )*DLAMCH( 'Base' )
181 *
182 * Some Error Checks
183 *
184 IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
185 RESULT( 1 ) = TEN / ULP
186 RETURN
187 END IF
188 *
189 * Do Test 1
190 *
191 * Norm of A:
192 *
193 IF( ITYPE.EQ.3 ) THEN
194 ANORM = ONE
195 ELSE
196 ANORM = MAX( DLANSY( '1', CUPLO, N, A, LDA, WORK ), UNFL )
197 END IF
198 *
199 * Compute error matrix:
200 *
201 IF( ITYPE.EQ.1 ) THEN
202 *
203 * ITYPE=1: error = A - U S U'
204 *
205 CALL DLASET( 'Full', N, N, ZERO, ZERO, WORK, N )
206 CALL DLACPY( CUPLO, N, N, A, LDA, WORK, N )
207 *
208 DO 10 J = 1, N
209 CALL DSYR( CUPLO, N, -D( J ), U( 1, J ), 1, WORK, N )
210 10 CONTINUE
211 *
212 IF( N.GT.1 .AND. KBAND.EQ.1 ) THEN
213 DO 20 J = 1, N - 1
214 CALL DSYR2( CUPLO, N, -E( J ), U( 1, J ), 1, U( 1, J+1 ),
215 $ 1, WORK, N )
216 20 CONTINUE
217 END IF
218 WNORM = DLANSY( '1', CUPLO, N, WORK, N, WORK( N**2+1 ) )
219 *
220 ELSE IF( ITYPE.EQ.2 ) THEN
221 *
222 * ITYPE=2: error = V S V' - A
223 *
224 CALL DLASET( 'Full', N, N, ZERO, ZERO, WORK, N )
225 *
226 IF( LOWER ) THEN
227 WORK( N**2 ) = D( N )
228 DO 40 J = N - 1, 1, -1
229 IF( KBAND.EQ.1 ) THEN
230 WORK( ( N+1 )*( J-1 )+2 ) = ( ONE-TAU( J ) )*E( J )
231 DO 30 JR = J + 2, N
232 WORK( ( J-1 )*N+JR ) = -TAU( J )*E( J )*V( JR, J )
233 30 CONTINUE
234 END IF
235 *
236 VSAVE = V( J+1, J )
237 V( J+1, J ) = ONE
238 CALL DLARFY( 'L', N-J, V( J+1, J ), 1, TAU( J ),
239 $ WORK( ( N+1 )*J+1 ), N, WORK( N**2+1 ) )
240 V( J+1, J ) = VSAVE
241 WORK( ( N+1 )*( J-1 )+1 ) = D( J )
242 40 CONTINUE
243 ELSE
244 WORK( 1 ) = D( 1 )
245 DO 60 J = 1, N - 1
246 IF( KBAND.EQ.1 ) THEN
247 WORK( ( N+1 )*J ) = ( ONE-TAU( J ) )*E( J )
248 DO 50 JR = 1, J - 1
249 WORK( J*N+JR ) = -TAU( J )*E( J )*V( JR, J+1 )
250 50 CONTINUE
251 END IF
252 *
253 VSAVE = V( J, J+1 )
254 V( J, J+1 ) = ONE
255 CALL DLARFY( 'U', J, V( 1, J+1 ), 1, TAU( J ), WORK, N,
256 $ WORK( N**2+1 ) )
257 V( J, J+1 ) = VSAVE
258 WORK( ( N+1 )*J+1 ) = D( J+1 )
259 60 CONTINUE
260 END IF
261 *
262 DO 90 JCOL = 1, N
263 IF( LOWER ) THEN
264 DO 70 JROW = JCOL, N
265 WORK( JROW+N*( JCOL-1 ) ) = WORK( JROW+N*( JCOL-1 ) )
266 $ - A( JROW, JCOL )
267 70 CONTINUE
268 ELSE
269 DO 80 JROW = 1, JCOL
270 WORK( JROW+N*( JCOL-1 ) ) = WORK( JROW+N*( JCOL-1 ) )
271 $ - A( JROW, JCOL )
272 80 CONTINUE
273 END IF
274 90 CONTINUE
275 WNORM = DLANSY( '1', CUPLO, N, WORK, N, WORK( N**2+1 ) )
276 *
277 ELSE IF( ITYPE.EQ.3 ) THEN
278 *
279 * ITYPE=3: error = U V' - I
280 *
281 IF( N.LT.2 )
282 $ RETURN
283 CALL DLACPY( ' ', N, N, U, LDU, WORK, N )
284 IF( LOWER ) THEN
285 CALL DORM2R( 'R', 'T', N, N-1, N-1, V( 2, 1 ), LDV, TAU,
286 $ WORK( N+1 ), N, WORK( N**2+1 ), IINFO )
287 ELSE
288 CALL DORM2L( 'R', 'T', N, N-1, N-1, V( 1, 2 ), LDV, TAU,
289 $ WORK, N, WORK( N**2+1 ), IINFO )
290 END IF
291 IF( IINFO.NE.0 ) THEN
292 RESULT( 1 ) = TEN / ULP
293 RETURN
294 END IF
295 *
296 DO 100 J = 1, N
297 WORK( ( N+1 )*( J-1 )+1 ) = WORK( ( N+1 )*( J-1 )+1 ) - ONE
298 100 CONTINUE
299 *
300 WNORM = DLANGE( '1', N, N, WORK, N, WORK( N**2+1 ) )
301 END IF
302 *
303 IF( ANORM.GT.WNORM ) THEN
304 RESULT( 1 ) = ( WNORM / ANORM ) / ( N*ULP )
305 ELSE
306 IF( ANORM.LT.ONE ) THEN
307 RESULT( 1 ) = ( MIN( WNORM, N*ANORM ) / ANORM ) / ( N*ULP )
308 ELSE
309 RESULT( 1 ) = MIN( WNORM / ANORM, DBLE( N ) ) / ( N*ULP )
310 END IF
311 END IF
312 *
313 * Do Test 2
314 *
315 * Compute UU' - I
316 *
317 IF( ITYPE.EQ.1 ) THEN
318 CALL DGEMM( 'N', 'C', N, N, N, ONE, U, LDU, U, LDU, ZERO, WORK,
319 $ N )
320 *
321 DO 110 J = 1, N
322 WORK( ( N+1 )*( J-1 )+1 ) = WORK( ( N+1 )*( J-1 )+1 ) - ONE
323 110 CONTINUE
324 *
325 RESULT( 2 ) = MIN( DLANGE( '1', N, N, WORK, N,
326 $ WORK( N**2+1 ) ), DBLE( N ) ) / ( N*ULP )
327 END IF
328 *
329 RETURN
330 *
331 * End of DSYT21
332 *
333 END
2 $ LDV, TAU, WORK, RESULT )
3 *
4 * -- LAPACK test routine (version 3.1) --
5 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
6 * November 2006
7 *
8 * .. Scalar Arguments ..
9 CHARACTER UPLO
10 INTEGER ITYPE, KBAND, LDA, LDU, LDV, N
11 * ..
12 * .. Array Arguments ..
13 DOUBLE PRECISION A( LDA, * ), D( * ), E( * ), RESULT( 2 ),
14 $ TAU( * ), U( LDU, * ), V( LDV, * ), WORK( * )
15 * ..
16 *
17 * Purpose
18 * =======
19 *
20 * DSYT21 generally checks a decomposition of the form
21 *
22 * A = U S U'
23 *
24 * where ' means transpose, A is symmetric, U is orthogonal, and S is
25 * diagonal (if KBAND=0) or symmetric tridiagonal (if KBAND=1).
26 *
27 * If ITYPE=1, then U is represented as a dense matrix; otherwise U is
28 * expressed as a product of Householder transformations, whose vectors
29 * are stored in the array "V" and whose scaling constants are in "TAU".
30 * We shall use the letter "V" to refer to the product of Householder
31 * transformations (which should be equal to U).
32 *
33 * Specifically, if ITYPE=1, then:
34 *
35 * RESULT(1) = | A - U S U' | / ( |A| n ulp ) *and*
36 * RESULT(2) = | I - UU' | / ( n ulp )
37 *
38 * If ITYPE=2, then:
39 *
40 * RESULT(1) = | A - V S V' | / ( |A| n ulp )
41 *
42 * If ITYPE=3, then:
43 *
44 * RESULT(1) = | I - VU' | / ( n ulp )
45 *
46 * For ITYPE > 1, the transformation U is expressed as a product
47 * V = H(1)...H(n-2), where H(j) = I - tau(j) v(j) v(j)' and each
48 * vector v(j) has its first j elements 0 and the remaining n-j elements
49 * stored in V(j+1:n,j).
50 *
51 * Arguments
52 * =========
53 *
54 * ITYPE (input) INTEGER
55 * Specifies the type of tests to be performed.
56 * 1: U expressed as a dense orthogonal matrix:
57 * RESULT(1) = | A - U S U' | / ( |A| n ulp ) *and*
58 * RESULT(2) = | I - UU' | / ( n ulp )
59 *
60 * 2: U expressed as a product V of Housholder transformations:
61 * RESULT(1) = | A - V S V' | / ( |A| n ulp )
62 *
63 * 3: U expressed both as a dense orthogonal matrix and
64 * as a product of Housholder transformations:
65 * RESULT(1) = | I - VU' | / ( n ulp )
66 *
67 * UPLO (input) CHARACTER
68 * If UPLO='U', the upper triangle of A and V will be used and
69 * the (strictly) lower triangle will not be referenced.
70 * If UPLO='L', the lower triangle of A and V will be used and
71 * the (strictly) upper triangle will not be referenced.
72 *
73 * N (input) INTEGER
74 * The size of the matrix. If it is zero, DSYT21 does nothing.
75 * It must be at least zero.
76 *
77 * KBAND (input) INTEGER
78 * The bandwidth of the matrix. It may only be zero or one.
79 * If zero, then S is diagonal, and E is not referenced. If
80 * one, then S is symmetric tri-diagonal.
81 *
82 * A (input) DOUBLE PRECISION array, dimension (LDA, N)
83 * The original (unfactored) matrix. It is assumed to be
84 * symmetric, and only the upper (UPLO='U') or only the lower
85 * (UPLO='L') will be referenced.
86 *
87 * LDA (input) INTEGER
88 * The leading dimension of A. It must be at least 1
89 * and at least N.
90 *
91 * D (input) DOUBLE PRECISION array, dimension (N)
92 * The diagonal of the (symmetric tri-) diagonal matrix.
93 *
94 * E (input) DOUBLE PRECISION array, dimension (N-1)
95 * The off-diagonal of the (symmetric tri-) diagonal matrix.
96 * E(1) is the (1,2) and (2,1) element, E(2) is the (2,3) and
97 * (3,2) element, etc.
98 * Not referenced if KBAND=0.
99 *
100 * U (input) DOUBLE PRECISION array, dimension (LDU, N)
101 * If ITYPE=1 or 3, this contains the orthogonal matrix in
102 * the decomposition, expressed as a dense matrix. If ITYPE=2,
103 * then it is not referenced.
104 *
105 * LDU (input) INTEGER
106 * The leading dimension of U. LDU must be at least N and
107 * at least 1.
108 *
109 * V (input) DOUBLE PRECISION array, dimension (LDV, N)
110 * If ITYPE=2 or 3, the columns of this array contain the
111 * Householder vectors used to describe the orthogonal matrix
112 * in the decomposition. If UPLO='L', then the vectors are in
113 * the lower triangle, if UPLO='U', then in the upper
114 * triangle.
115 * *NOTE* If ITYPE=2 or 3, V is modified and restored. The
116 * subdiagonal (if UPLO='L') or the superdiagonal (if UPLO='U')
117 * is set to one, and later reset to its original value, during
118 * the course of the calculation.
119 * If ITYPE=1, then it is neither referenced nor modified.
120 *
121 * LDV (input) INTEGER
122 * The leading dimension of V. LDV must be at least N and
123 * at least 1.
124 *
125 * TAU (input) DOUBLE PRECISION array, dimension (N)
126 * If ITYPE >= 2, then TAU(j) is the scalar factor of
127 * v(j) v(j)' in the Householder transformation H(j) of
128 * the product U = H(1)...H(n-2)
129 * If ITYPE < 2, then TAU is not referenced.
130 *
131 * WORK (workspace) DOUBLE PRECISION array, dimension (2*N**2)
132 *
133 * RESULT (output) DOUBLE PRECISION array, dimension (2)
134 * The values computed by the two tests described above. The
135 * values are currently limited to 1/ulp, to avoid overflow.
136 * RESULT(1) is always modified. RESULT(2) is modified only
137 * if ITYPE=1.
138 *
139 * =====================================================================
140 *
141 * .. Parameters ..
142 DOUBLE PRECISION ZERO, ONE, TEN
143 PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, TEN = 10.0D0 )
144 * ..
145 * .. Local Scalars ..
146 LOGICAL LOWER
147 CHARACTER CUPLO
148 INTEGER IINFO, J, JCOL, JR, JROW
149 DOUBLE PRECISION ANORM, ULP, UNFL, VSAVE, WNORM
150 * ..
151 * .. External Functions ..
152 LOGICAL LSAME
153 DOUBLE PRECISION DLAMCH, DLANGE, DLANSY
154 EXTERNAL LSAME, DLAMCH, DLANGE, DLANSY
155 * ..
156 * .. External Subroutines ..
157 EXTERNAL DGEMM, DLACPY, DLARFY, DLASET, DORM2L, DORM2R,
158 $ DSYR, DSYR2
159 * ..
160 * .. Intrinsic Functions ..
161 INTRINSIC DBLE, MAX, MIN
162 * ..
163 * .. Executable Statements ..
164 *
165 RESULT( 1 ) = ZERO
166 IF( ITYPE.EQ.1 )
167 $ RESULT( 2 ) = ZERO
168 IF( N.LE.0 )
169 $ RETURN
170 *
171 IF( LSAME( UPLO, 'U' ) ) THEN
172 LOWER = .FALSE.
173 CUPLO = 'U'
174 ELSE
175 LOWER = .TRUE.
176 CUPLO = 'L'
177 END IF
178 *
179 UNFL = DLAMCH( 'Safe minimum' )
180 ULP = DLAMCH( 'Epsilon' )*DLAMCH( 'Base' )
181 *
182 * Some Error Checks
183 *
184 IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
185 RESULT( 1 ) = TEN / ULP
186 RETURN
187 END IF
188 *
189 * Do Test 1
190 *
191 * Norm of A:
192 *
193 IF( ITYPE.EQ.3 ) THEN
194 ANORM = ONE
195 ELSE
196 ANORM = MAX( DLANSY( '1', CUPLO, N, A, LDA, WORK ), UNFL )
197 END IF
198 *
199 * Compute error matrix:
200 *
201 IF( ITYPE.EQ.1 ) THEN
202 *
203 * ITYPE=1: error = A - U S U'
204 *
205 CALL DLASET( 'Full', N, N, ZERO, ZERO, WORK, N )
206 CALL DLACPY( CUPLO, N, N, A, LDA, WORK, N )
207 *
208 DO 10 J = 1, N
209 CALL DSYR( CUPLO, N, -D( J ), U( 1, J ), 1, WORK, N )
210 10 CONTINUE
211 *
212 IF( N.GT.1 .AND. KBAND.EQ.1 ) THEN
213 DO 20 J = 1, N - 1
214 CALL DSYR2( CUPLO, N, -E( J ), U( 1, J ), 1, U( 1, J+1 ),
215 $ 1, WORK, N )
216 20 CONTINUE
217 END IF
218 WNORM = DLANSY( '1', CUPLO, N, WORK, N, WORK( N**2+1 ) )
219 *
220 ELSE IF( ITYPE.EQ.2 ) THEN
221 *
222 * ITYPE=2: error = V S V' - A
223 *
224 CALL DLASET( 'Full', N, N, ZERO, ZERO, WORK, N )
225 *
226 IF( LOWER ) THEN
227 WORK( N**2 ) = D( N )
228 DO 40 J = N - 1, 1, -1
229 IF( KBAND.EQ.1 ) THEN
230 WORK( ( N+1 )*( J-1 )+2 ) = ( ONE-TAU( J ) )*E( J )
231 DO 30 JR = J + 2, N
232 WORK( ( J-1 )*N+JR ) = -TAU( J )*E( J )*V( JR, J )
233 30 CONTINUE
234 END IF
235 *
236 VSAVE = V( J+1, J )
237 V( J+1, J ) = ONE
238 CALL DLARFY( 'L', N-J, V( J+1, J ), 1, TAU( J ),
239 $ WORK( ( N+1 )*J+1 ), N, WORK( N**2+1 ) )
240 V( J+1, J ) = VSAVE
241 WORK( ( N+1 )*( J-1 )+1 ) = D( J )
242 40 CONTINUE
243 ELSE
244 WORK( 1 ) = D( 1 )
245 DO 60 J = 1, N - 1
246 IF( KBAND.EQ.1 ) THEN
247 WORK( ( N+1 )*J ) = ( ONE-TAU( J ) )*E( J )
248 DO 50 JR = 1, J - 1
249 WORK( J*N+JR ) = -TAU( J )*E( J )*V( JR, J+1 )
250 50 CONTINUE
251 END IF
252 *
253 VSAVE = V( J, J+1 )
254 V( J, J+1 ) = ONE
255 CALL DLARFY( 'U', J, V( 1, J+1 ), 1, TAU( J ), WORK, N,
256 $ WORK( N**2+1 ) )
257 V( J, J+1 ) = VSAVE
258 WORK( ( N+1 )*J+1 ) = D( J+1 )
259 60 CONTINUE
260 END IF
261 *
262 DO 90 JCOL = 1, N
263 IF( LOWER ) THEN
264 DO 70 JROW = JCOL, N
265 WORK( JROW+N*( JCOL-1 ) ) = WORK( JROW+N*( JCOL-1 ) )
266 $ - A( JROW, JCOL )
267 70 CONTINUE
268 ELSE
269 DO 80 JROW = 1, JCOL
270 WORK( JROW+N*( JCOL-1 ) ) = WORK( JROW+N*( JCOL-1 ) )
271 $ - A( JROW, JCOL )
272 80 CONTINUE
273 END IF
274 90 CONTINUE
275 WNORM = DLANSY( '1', CUPLO, N, WORK, N, WORK( N**2+1 ) )
276 *
277 ELSE IF( ITYPE.EQ.3 ) THEN
278 *
279 * ITYPE=3: error = U V' - I
280 *
281 IF( N.LT.2 )
282 $ RETURN
283 CALL DLACPY( ' ', N, N, U, LDU, WORK, N )
284 IF( LOWER ) THEN
285 CALL DORM2R( 'R', 'T', N, N-1, N-1, V( 2, 1 ), LDV, TAU,
286 $ WORK( N+1 ), N, WORK( N**2+1 ), IINFO )
287 ELSE
288 CALL DORM2L( 'R', 'T', N, N-1, N-1, V( 1, 2 ), LDV, TAU,
289 $ WORK, N, WORK( N**2+1 ), IINFO )
290 END IF
291 IF( IINFO.NE.0 ) THEN
292 RESULT( 1 ) = TEN / ULP
293 RETURN
294 END IF
295 *
296 DO 100 J = 1, N
297 WORK( ( N+1 )*( J-1 )+1 ) = WORK( ( N+1 )*( J-1 )+1 ) - ONE
298 100 CONTINUE
299 *
300 WNORM = DLANGE( '1', N, N, WORK, N, WORK( N**2+1 ) )
301 END IF
302 *
303 IF( ANORM.GT.WNORM ) THEN
304 RESULT( 1 ) = ( WNORM / ANORM ) / ( N*ULP )
305 ELSE
306 IF( ANORM.LT.ONE ) THEN
307 RESULT( 1 ) = ( MIN( WNORM, N*ANORM ) / ANORM ) / ( N*ULP )
308 ELSE
309 RESULT( 1 ) = MIN( WNORM / ANORM, DBLE( N ) ) / ( N*ULP )
310 END IF
311 END IF
312 *
313 * Do Test 2
314 *
315 * Compute UU' - I
316 *
317 IF( ITYPE.EQ.1 ) THEN
318 CALL DGEMM( 'N', 'C', N, N, N, ONE, U, LDU, U, LDU, ZERO, WORK,
319 $ N )
320 *
321 DO 110 J = 1, N
322 WORK( ( N+1 )*( J-1 )+1 ) = WORK( ( N+1 )*( J-1 )+1 ) - ONE
323 110 CONTINUE
324 *
325 RESULT( 2 ) = MIN( DLANGE( '1', N, N, WORK, N,
326 $ WORK( N**2+1 ) ), DBLE( N ) ) / ( N*ULP )
327 END IF
328 *
329 RETURN
330 *
331 * End of DSYT21
332 *
333 END