1 SUBROUTINE CHPT21( ITYPE, UPLO, N, KBAND, AP, D, E, U, LDU, VP,
2 $ TAU, WORK, RWORK, 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, LDU, N
11 * ..
12 * .. Array Arguments ..
13 REAL D( * ), E( * ), RESULT( 2 ), RWORK( * )
14 COMPLEX AP( * ), TAU( * ), U( LDU, * ), VP( * ),
15 $ WORK( * )
16 * ..
17 *
18 * Purpose
19 * =======
20 *
21 * CHPT21 generally checks a decomposition of the form
22 *
23 * A = U S U*
24 *
25 * where * means conjugate transpose, A is hermitian, U is
26 * unitary, and S is diagonal (if KBAND=0) or (real) symmetric
27 * tridiagonal (if KBAND=1). If ITYPE=1, then U is represented as
28 * a dense matrix, otherwise the U is expressed as a product of
29 * Householder transformations, whose vectors are stored in the
30 * array "V" and whose scaling constants are in "TAU"; we shall
31 * use the letter "V" to refer to the product of Householder
32 * transformations (which should be equal to U).
33 *
34 * Specifically, if ITYPE=1, then:
35 *
36 * RESULT(1) = | A - U S U* | / ( |A| n ulp ) *and*
37 * RESULT(2) = | I - UU* | / ( n ulp )
38 *
39 * If ITYPE=2, then:
40 *
41 * RESULT(1) = | A - V S V* | / ( |A| n ulp )
42 *
43 * If ITYPE=3, then:
44 *
45 * RESULT(1) = | I - UV* | / ( n ulp )
46 *
47 * Packed storage means that, for example, if UPLO='U', then the columns
48 * of the upper triangle of A are stored one after another, so that
49 * A(1,j+1) immediately follows A(j,j) in the array AP. Similarly, if
50 * UPLO='L', then the columns of the lower triangle of A are stored one
51 * after another in AP, so that A(j+1,j+1) immediately follows A(n,j)
52 * in the array AP. This means that A(i,j) is stored in:
53 *
54 * AP( i + j*(j-1)/2 ) if UPLO='U'
55 *
56 * AP( i + (2*n-j)*(j-1)/2 ) if UPLO='L'
57 *
58 * The array VP bears the same relation to the matrix V that A does to
59 * AP.
60 *
61 * For ITYPE > 1, the transformation U is expressed as a product
62 * of Householder transformations:
63 *
64 * If UPLO='U', then V = H(n-1)...H(1), where
65 *
66 * H(j) = I - tau(j) v(j) v(j)*
67 *
68 * and the first j-1 elements of v(j) are stored in V(1:j-1,j+1),
69 * (i.e., VP( j*(j+1)/2 + 1 : j*(j+1)/2 + j-1 ) ),
70 * the j-th element is 1, and the last n-j elements are 0.
71 *
72 * If UPLO='L', then V = H(1)...H(n-1), where
73 *
74 * H(j) = I - tau(j) v(j) v(j)*
75 *
76 * and the first j elements of v(j) are 0, the (j+1)-st is 1, and the
77 * (j+2)-nd through n-th elements are stored in V(j+2:n,j) (i.e.,
78 * in VP( (2*n-j)*(j-1)/2 + j+2 : (2*n-j)*(j-1)/2 + n ) .)
79 *
80 * Arguments
81 * =========
82 *
83 * ITYPE (input) INTEGER
84 * Specifies the type of tests to be performed.
85 * 1: U expressed as a dense unitary matrix:
86 * RESULT(1) = | A - U S U* | / ( |A| n ulp ) *and*
87 * RESULT(2) = | I - UU* | / ( n ulp )
88 *
89 * 2: U expressed as a product V of Housholder transformations:
90 * RESULT(1) = | A - V S V* | / ( |A| n ulp )
91 *
92 * 3: U expressed both as a dense unitary matrix and
93 * as a product of Housholder transformations:
94 * RESULT(1) = | I - UV* | / ( n ulp )
95 *
96 * UPLO (input) CHARACTER
97 * If UPLO='U', the upper triangle of A and V will be used and
98 * the (strictly) lower triangle will not be referenced.
99 * If UPLO='L', the lower triangle of A and V will be used and
100 * the (strictly) upper triangle will not be referenced.
101 *
102 * N (input) INTEGER
103 * The size of the matrix. If it is zero, CHPT21 does nothing.
104 * It must be at least zero.
105 *
106 * KBAND (input) INTEGER
107 * The bandwidth of the matrix. It may only be zero or one.
108 * If zero, then S is diagonal, and E is not referenced. If
109 * one, then S is symmetric tri-diagonal.
110 *
111 * AP (input) COMPLEX array, dimension (N*(N+1)/2)
112 * The original (unfactored) matrix. It is assumed to be
113 * hermitian, and contains the columns of just the upper
114 * triangle (UPLO='U') or only the lower triangle (UPLO='L'),
115 * packed one after another.
116 *
117 * D (input) REAL array, dimension (N)
118 * The diagonal of the (symmetric tri-) diagonal matrix.
119 *
120 * E (input) REAL array, dimension (N)
121 * The off-diagonal of the (symmetric tri-) diagonal matrix.
122 * E(1) is the (1,2) and (2,1) element, E(2) is the (2,3) and
123 * (3,2) element, etc.
124 * Not referenced if KBAND=0.
125 *
126 * U (input) COMPLEX array, dimension (LDU, N)
127 * If ITYPE=1 or 3, this contains the unitary matrix in
128 * the decomposition, expressed as a dense matrix. If ITYPE=2,
129 * then it is not referenced.
130 *
131 * LDU (input) INTEGER
132 * The leading dimension of U. LDU must be at least N and
133 * at least 1.
134 *
135 * VP (input) REAL array, dimension (N*(N+1)/2)
136 * If ITYPE=2 or 3, the columns of this array contain the
137 * Householder vectors used to describe the unitary matrix
138 * in the decomposition, as described in purpose.
139 * *NOTE* If ITYPE=2 or 3, V is modified and restored. The
140 * subdiagonal (if UPLO='L') or the superdiagonal (if UPLO='U')
141 * is set to one, and later reset to its original value, during
142 * the course of the calculation.
143 * If ITYPE=1, then it is neither referenced nor modified.
144 *
145 * TAU (input) COMPLEX array, dimension (N)
146 * If ITYPE >= 2, then TAU(j) is the scalar factor of
147 * v(j) v(j)* in the Householder transformation H(j) of
148 * the product U = H(1)...H(n-2)
149 * If ITYPE < 2, then TAU is not referenced.
150 *
151 * WORK (workspace) COMPLEX array, dimension (N**2)
152 * Workspace.
153 *
154 * RWORK (workspace) REAL array, dimension (N)
155 * Workspace.
156 *
157 * RESULT (output) REAL array, dimension (2)
158 * The values computed by the two tests described above. The
159 * values are currently limited to 1/ulp, to avoid overflow.
160 * RESULT(1) is always modified. RESULT(2) is modified only
161 * if ITYPE=1.
162 *
163 * =====================================================================
164 *
165 * .. Parameters ..
166 REAL ZERO, ONE, TEN
167 PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0, TEN = 10.0E+0 )
168 REAL HALF
169 PARAMETER ( HALF = 1.0E+0 / 2.0E+0 )
170 COMPLEX CZERO, CONE
171 PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ),
172 $ CONE = ( 1.0E+0, 0.0E+0 ) )
173 * ..
174 * .. Local Scalars ..
175 LOGICAL LOWER
176 CHARACTER CUPLO
177 INTEGER IINFO, J, JP, JP1, JR, LAP
178 REAL ANORM, ULP, UNFL, WNORM
179 COMPLEX TEMP, VSAVE
180 * ..
181 * .. External Functions ..
182 LOGICAL LSAME
183 REAL CLANGE, CLANHP, SLAMCH
184 COMPLEX CDOTC
185 EXTERNAL LSAME, CLANGE, CLANHP, SLAMCH, CDOTC
186 * ..
187 * .. External Subroutines ..
188 EXTERNAL CAXPY, CCOPY, CGEMM, CHPMV, CHPR, CHPR2,
189 $ CLACPY, CLASET, CUPMTR
190 * ..
191 * .. Intrinsic Functions ..
192 INTRINSIC CMPLX, MAX, MIN, REAL
193 * ..
194 * .. Executable Statements ..
195 *
196 * Constants
197 *
198 RESULT( 1 ) = ZERO
199 IF( ITYPE.EQ.1 )
200 $ RESULT( 2 ) = ZERO
201 IF( N.LE.0 )
202 $ RETURN
203 *
204 LAP = ( N*( N+1 ) ) / 2
205 *
206 IF( LSAME( UPLO, 'U' ) ) THEN
207 LOWER = .FALSE.
208 CUPLO = 'U'
209 ELSE
210 LOWER = .TRUE.
211 CUPLO = 'L'
212 END IF
213 *
214 UNFL = SLAMCH( 'Safe minimum' )
215 ULP = SLAMCH( 'Epsilon' )*SLAMCH( 'Base' )
216 *
217 * Some Error Checks
218 *
219 IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
220 RESULT( 1 ) = TEN / ULP
221 RETURN
222 END IF
223 *
224 * Do Test 1
225 *
226 * Norm of A:
227 *
228 IF( ITYPE.EQ.3 ) THEN
229 ANORM = ONE
230 ELSE
231 ANORM = MAX( CLANHP( '1', CUPLO, N, AP, RWORK ), UNFL )
232 END IF
233 *
234 * Compute error matrix:
235 *
236 IF( ITYPE.EQ.1 ) THEN
237 *
238 * ITYPE=1: error = A - U S U*
239 *
240 CALL CLASET( 'Full', N, N, CZERO, CZERO, WORK, N )
241 CALL CCOPY( LAP, AP, 1, WORK, 1 )
242 *
243 DO 10 J = 1, N
244 CALL CHPR( CUPLO, N, -D( J ), U( 1, J ), 1, WORK )
245 10 CONTINUE
246 *
247 IF( N.GT.1 .AND. KBAND.EQ.1 ) THEN
248 DO 20 J = 1, N - 1
249 CALL CHPR2( CUPLO, N, -CMPLX( E( J ) ), U( 1, J ), 1,
250 $ U( 1, J-1 ), 1, WORK )
251 20 CONTINUE
252 END IF
253 WNORM = CLANHP( '1', CUPLO, N, WORK, RWORK )
254 *
255 ELSE IF( ITYPE.EQ.2 ) THEN
256 *
257 * ITYPE=2: error = V S V* - A
258 *
259 CALL CLASET( 'Full', N, N, CZERO, CZERO, WORK, N )
260 *
261 IF( LOWER ) THEN
262 WORK( LAP ) = D( N )
263 DO 40 J = N - 1, 1, -1
264 JP = ( ( 2*N-J )*( J-1 ) ) / 2
265 JP1 = JP + N - J
266 IF( KBAND.EQ.1 ) THEN
267 WORK( JP+J+1 ) = ( CONE-TAU( J ) )*E( J )
268 DO 30 JR = J + 2, N
269 WORK( JP+JR ) = -TAU( J )*E( J )*VP( JP+JR )
270 30 CONTINUE
271 END IF
272 *
273 IF( TAU( J ).NE.CZERO ) THEN
274 VSAVE = VP( JP+J+1 )
275 VP( JP+J+1 ) = CONE
276 CALL CHPMV( 'L', N-J, CONE, WORK( JP1+J+1 ),
277 $ VP( JP+J+1 ), 1, CZERO, WORK( LAP+1 ), 1 )
278 TEMP = -HALF*TAU( J )*CDOTC( N-J, WORK( LAP+1 ), 1,
279 $ VP( JP+J+1 ), 1 )
280 CALL CAXPY( N-J, TEMP, VP( JP+J+1 ), 1, WORK( LAP+1 ),
281 $ 1 )
282 CALL CHPR2( 'L', N-J, -TAU( J ), VP( JP+J+1 ), 1,
283 $ WORK( LAP+1 ), 1, WORK( JP1+J+1 ) )
284 *
285 VP( JP+J+1 ) = VSAVE
286 END IF
287 WORK( JP+J ) = D( J )
288 40 CONTINUE
289 ELSE
290 WORK( 1 ) = D( 1 )
291 DO 60 J = 1, N - 1
292 JP = ( J*( J-1 ) ) / 2
293 JP1 = JP + J
294 IF( KBAND.EQ.1 ) THEN
295 WORK( JP1+J ) = ( CONE-TAU( J ) )*E( J )
296 DO 50 JR = 1, J - 1
297 WORK( JP1+JR ) = -TAU( J )*E( J )*VP( JP1+JR )
298 50 CONTINUE
299 END IF
300 *
301 IF( TAU( J ).NE.CZERO ) THEN
302 VSAVE = VP( JP1+J )
303 VP( JP1+J ) = CONE
304 CALL CHPMV( 'U', J, CONE, WORK, VP( JP1+1 ), 1, CZERO,
305 $ WORK( LAP+1 ), 1 )
306 TEMP = -HALF*TAU( J )*CDOTC( J, WORK( LAP+1 ), 1,
307 $ VP( JP1+1 ), 1 )
308 CALL CAXPY( J, TEMP, VP( JP1+1 ), 1, WORK( LAP+1 ),
309 $ 1 )
310 CALL CHPR2( 'U', J, -TAU( J ), VP( JP1+1 ), 1,
311 $ WORK( LAP+1 ), 1, WORK )
312 VP( JP1+J ) = VSAVE
313 END IF
314 WORK( JP1+J+1 ) = D( J+1 )
315 60 CONTINUE
316 END IF
317 *
318 DO 70 J = 1, LAP
319 WORK( J ) = WORK( J ) - AP( J )
320 70 CONTINUE
321 WNORM = CLANHP( '1', CUPLO, N, WORK, RWORK )
322 *
323 ELSE IF( ITYPE.EQ.3 ) THEN
324 *
325 * ITYPE=3: error = U V* - I
326 *
327 IF( N.LT.2 )
328 $ RETURN
329 CALL CLACPY( ' ', N, N, U, LDU, WORK, N )
330 CALL CUPMTR( 'R', CUPLO, 'C', N, N, VP, TAU, WORK, N,
331 $ WORK( N**2+1 ), IINFO )
332 IF( IINFO.NE.0 ) THEN
333 RESULT( 1 ) = TEN / ULP
334 RETURN
335 END IF
336 *
337 DO 80 J = 1, N
338 WORK( ( N+1 )*( J-1 )+1 ) = WORK( ( N+1 )*( J-1 )+1 ) - CONE
339 80 CONTINUE
340 *
341 WNORM = CLANGE( '1', N, N, WORK, N, RWORK )
342 END IF
343 *
344 IF( ANORM.GT.WNORM ) THEN
345 RESULT( 1 ) = ( WNORM / ANORM ) / ( N*ULP )
346 ELSE
347 IF( ANORM.LT.ONE ) THEN
348 RESULT( 1 ) = ( MIN( WNORM, N*ANORM ) / ANORM ) / ( N*ULP )
349 ELSE
350 RESULT( 1 ) = MIN( WNORM / ANORM, REAL( N ) ) / ( N*ULP )
351 END IF
352 END IF
353 *
354 * Do Test 2
355 *
356 * Compute UU* - I
357 *
358 IF( ITYPE.EQ.1 ) THEN
359 CALL CGEMM( 'N', 'C', N, N, N, CONE, U, LDU, U, LDU, CZERO,
360 $ WORK, N )
361 *
362 DO 90 J = 1, N
363 WORK( ( N+1 )*( J-1 )+1 ) = WORK( ( N+1 )*( J-1 )+1 ) - CONE
364 90 CONTINUE
365 *
366 RESULT( 2 ) = MIN( CLANGE( '1', N, N, WORK, N, RWORK ),
367 $ REAL( N ) ) / ( N*ULP )
368 END IF
369 *
370 RETURN
371 *
372 * End of CHPT21
373 *
374 END
2 $ TAU, WORK, RWORK, 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, LDU, N
11 * ..
12 * .. Array Arguments ..
13 REAL D( * ), E( * ), RESULT( 2 ), RWORK( * )
14 COMPLEX AP( * ), TAU( * ), U( LDU, * ), VP( * ),
15 $ WORK( * )
16 * ..
17 *
18 * Purpose
19 * =======
20 *
21 * CHPT21 generally checks a decomposition of the form
22 *
23 * A = U S U*
24 *
25 * where * means conjugate transpose, A is hermitian, U is
26 * unitary, and S is diagonal (if KBAND=0) or (real) symmetric
27 * tridiagonal (if KBAND=1). If ITYPE=1, then U is represented as
28 * a dense matrix, otherwise the U is expressed as a product of
29 * Householder transformations, whose vectors are stored in the
30 * array "V" and whose scaling constants are in "TAU"; we shall
31 * use the letter "V" to refer to the product of Householder
32 * transformations (which should be equal to U).
33 *
34 * Specifically, if ITYPE=1, then:
35 *
36 * RESULT(1) = | A - U S U* | / ( |A| n ulp ) *and*
37 * RESULT(2) = | I - UU* | / ( n ulp )
38 *
39 * If ITYPE=2, then:
40 *
41 * RESULT(1) = | A - V S V* | / ( |A| n ulp )
42 *
43 * If ITYPE=3, then:
44 *
45 * RESULT(1) = | I - UV* | / ( n ulp )
46 *
47 * Packed storage means that, for example, if UPLO='U', then the columns
48 * of the upper triangle of A are stored one after another, so that
49 * A(1,j+1) immediately follows A(j,j) in the array AP. Similarly, if
50 * UPLO='L', then the columns of the lower triangle of A are stored one
51 * after another in AP, so that A(j+1,j+1) immediately follows A(n,j)
52 * in the array AP. This means that A(i,j) is stored in:
53 *
54 * AP( i + j*(j-1)/2 ) if UPLO='U'
55 *
56 * AP( i + (2*n-j)*(j-1)/2 ) if UPLO='L'
57 *
58 * The array VP bears the same relation to the matrix V that A does to
59 * AP.
60 *
61 * For ITYPE > 1, the transformation U is expressed as a product
62 * of Householder transformations:
63 *
64 * If UPLO='U', then V = H(n-1)...H(1), where
65 *
66 * H(j) = I - tau(j) v(j) v(j)*
67 *
68 * and the first j-1 elements of v(j) are stored in V(1:j-1,j+1),
69 * (i.e., VP( j*(j+1)/2 + 1 : j*(j+1)/2 + j-1 ) ),
70 * the j-th element is 1, and the last n-j elements are 0.
71 *
72 * If UPLO='L', then V = H(1)...H(n-1), where
73 *
74 * H(j) = I - tau(j) v(j) v(j)*
75 *
76 * and the first j elements of v(j) are 0, the (j+1)-st is 1, and the
77 * (j+2)-nd through n-th elements are stored in V(j+2:n,j) (i.e.,
78 * in VP( (2*n-j)*(j-1)/2 + j+2 : (2*n-j)*(j-1)/2 + n ) .)
79 *
80 * Arguments
81 * =========
82 *
83 * ITYPE (input) INTEGER
84 * Specifies the type of tests to be performed.
85 * 1: U expressed as a dense unitary matrix:
86 * RESULT(1) = | A - U S U* | / ( |A| n ulp ) *and*
87 * RESULT(2) = | I - UU* | / ( n ulp )
88 *
89 * 2: U expressed as a product V of Housholder transformations:
90 * RESULT(1) = | A - V S V* | / ( |A| n ulp )
91 *
92 * 3: U expressed both as a dense unitary matrix and
93 * as a product of Housholder transformations:
94 * RESULT(1) = | I - UV* | / ( n ulp )
95 *
96 * UPLO (input) CHARACTER
97 * If UPLO='U', the upper triangle of A and V will be used and
98 * the (strictly) lower triangle will not be referenced.
99 * If UPLO='L', the lower triangle of A and V will be used and
100 * the (strictly) upper triangle will not be referenced.
101 *
102 * N (input) INTEGER
103 * The size of the matrix. If it is zero, CHPT21 does nothing.
104 * It must be at least zero.
105 *
106 * KBAND (input) INTEGER
107 * The bandwidth of the matrix. It may only be zero or one.
108 * If zero, then S is diagonal, and E is not referenced. If
109 * one, then S is symmetric tri-diagonal.
110 *
111 * AP (input) COMPLEX array, dimension (N*(N+1)/2)
112 * The original (unfactored) matrix. It is assumed to be
113 * hermitian, and contains the columns of just the upper
114 * triangle (UPLO='U') or only the lower triangle (UPLO='L'),
115 * packed one after another.
116 *
117 * D (input) REAL array, dimension (N)
118 * The diagonal of the (symmetric tri-) diagonal matrix.
119 *
120 * E (input) REAL array, dimension (N)
121 * The off-diagonal of the (symmetric tri-) diagonal matrix.
122 * E(1) is the (1,2) and (2,1) element, E(2) is the (2,3) and
123 * (3,2) element, etc.
124 * Not referenced if KBAND=0.
125 *
126 * U (input) COMPLEX array, dimension (LDU, N)
127 * If ITYPE=1 or 3, this contains the unitary matrix in
128 * the decomposition, expressed as a dense matrix. If ITYPE=2,
129 * then it is not referenced.
130 *
131 * LDU (input) INTEGER
132 * The leading dimension of U. LDU must be at least N and
133 * at least 1.
134 *
135 * VP (input) REAL array, dimension (N*(N+1)/2)
136 * If ITYPE=2 or 3, the columns of this array contain the
137 * Householder vectors used to describe the unitary matrix
138 * in the decomposition, as described in purpose.
139 * *NOTE* If ITYPE=2 or 3, V is modified and restored. The
140 * subdiagonal (if UPLO='L') or the superdiagonal (if UPLO='U')
141 * is set to one, and later reset to its original value, during
142 * the course of the calculation.
143 * If ITYPE=1, then it is neither referenced nor modified.
144 *
145 * TAU (input) COMPLEX array, dimension (N)
146 * If ITYPE >= 2, then TAU(j) is the scalar factor of
147 * v(j) v(j)* in the Householder transformation H(j) of
148 * the product U = H(1)...H(n-2)
149 * If ITYPE < 2, then TAU is not referenced.
150 *
151 * WORK (workspace) COMPLEX array, dimension (N**2)
152 * Workspace.
153 *
154 * RWORK (workspace) REAL array, dimension (N)
155 * Workspace.
156 *
157 * RESULT (output) REAL array, dimension (2)
158 * The values computed by the two tests described above. The
159 * values are currently limited to 1/ulp, to avoid overflow.
160 * RESULT(1) is always modified. RESULT(2) is modified only
161 * if ITYPE=1.
162 *
163 * =====================================================================
164 *
165 * .. Parameters ..
166 REAL ZERO, ONE, TEN
167 PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0, TEN = 10.0E+0 )
168 REAL HALF
169 PARAMETER ( HALF = 1.0E+0 / 2.0E+0 )
170 COMPLEX CZERO, CONE
171 PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ),
172 $ CONE = ( 1.0E+0, 0.0E+0 ) )
173 * ..
174 * .. Local Scalars ..
175 LOGICAL LOWER
176 CHARACTER CUPLO
177 INTEGER IINFO, J, JP, JP1, JR, LAP
178 REAL ANORM, ULP, UNFL, WNORM
179 COMPLEX TEMP, VSAVE
180 * ..
181 * .. External Functions ..
182 LOGICAL LSAME
183 REAL CLANGE, CLANHP, SLAMCH
184 COMPLEX CDOTC
185 EXTERNAL LSAME, CLANGE, CLANHP, SLAMCH, CDOTC
186 * ..
187 * .. External Subroutines ..
188 EXTERNAL CAXPY, CCOPY, CGEMM, CHPMV, CHPR, CHPR2,
189 $ CLACPY, CLASET, CUPMTR
190 * ..
191 * .. Intrinsic Functions ..
192 INTRINSIC CMPLX, MAX, MIN, REAL
193 * ..
194 * .. Executable Statements ..
195 *
196 * Constants
197 *
198 RESULT( 1 ) = ZERO
199 IF( ITYPE.EQ.1 )
200 $ RESULT( 2 ) = ZERO
201 IF( N.LE.0 )
202 $ RETURN
203 *
204 LAP = ( N*( N+1 ) ) / 2
205 *
206 IF( LSAME( UPLO, 'U' ) ) THEN
207 LOWER = .FALSE.
208 CUPLO = 'U'
209 ELSE
210 LOWER = .TRUE.
211 CUPLO = 'L'
212 END IF
213 *
214 UNFL = SLAMCH( 'Safe minimum' )
215 ULP = SLAMCH( 'Epsilon' )*SLAMCH( 'Base' )
216 *
217 * Some Error Checks
218 *
219 IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
220 RESULT( 1 ) = TEN / ULP
221 RETURN
222 END IF
223 *
224 * Do Test 1
225 *
226 * Norm of A:
227 *
228 IF( ITYPE.EQ.3 ) THEN
229 ANORM = ONE
230 ELSE
231 ANORM = MAX( CLANHP( '1', CUPLO, N, AP, RWORK ), UNFL )
232 END IF
233 *
234 * Compute error matrix:
235 *
236 IF( ITYPE.EQ.1 ) THEN
237 *
238 * ITYPE=1: error = A - U S U*
239 *
240 CALL CLASET( 'Full', N, N, CZERO, CZERO, WORK, N )
241 CALL CCOPY( LAP, AP, 1, WORK, 1 )
242 *
243 DO 10 J = 1, N
244 CALL CHPR( CUPLO, N, -D( J ), U( 1, J ), 1, WORK )
245 10 CONTINUE
246 *
247 IF( N.GT.1 .AND. KBAND.EQ.1 ) THEN
248 DO 20 J = 1, N - 1
249 CALL CHPR2( CUPLO, N, -CMPLX( E( J ) ), U( 1, J ), 1,
250 $ U( 1, J-1 ), 1, WORK )
251 20 CONTINUE
252 END IF
253 WNORM = CLANHP( '1', CUPLO, N, WORK, RWORK )
254 *
255 ELSE IF( ITYPE.EQ.2 ) THEN
256 *
257 * ITYPE=2: error = V S V* - A
258 *
259 CALL CLASET( 'Full', N, N, CZERO, CZERO, WORK, N )
260 *
261 IF( LOWER ) THEN
262 WORK( LAP ) = D( N )
263 DO 40 J = N - 1, 1, -1
264 JP = ( ( 2*N-J )*( J-1 ) ) / 2
265 JP1 = JP + N - J
266 IF( KBAND.EQ.1 ) THEN
267 WORK( JP+J+1 ) = ( CONE-TAU( J ) )*E( J )
268 DO 30 JR = J + 2, N
269 WORK( JP+JR ) = -TAU( J )*E( J )*VP( JP+JR )
270 30 CONTINUE
271 END IF
272 *
273 IF( TAU( J ).NE.CZERO ) THEN
274 VSAVE = VP( JP+J+1 )
275 VP( JP+J+1 ) = CONE
276 CALL CHPMV( 'L', N-J, CONE, WORK( JP1+J+1 ),
277 $ VP( JP+J+1 ), 1, CZERO, WORK( LAP+1 ), 1 )
278 TEMP = -HALF*TAU( J )*CDOTC( N-J, WORK( LAP+1 ), 1,
279 $ VP( JP+J+1 ), 1 )
280 CALL CAXPY( N-J, TEMP, VP( JP+J+1 ), 1, WORK( LAP+1 ),
281 $ 1 )
282 CALL CHPR2( 'L', N-J, -TAU( J ), VP( JP+J+1 ), 1,
283 $ WORK( LAP+1 ), 1, WORK( JP1+J+1 ) )
284 *
285 VP( JP+J+1 ) = VSAVE
286 END IF
287 WORK( JP+J ) = D( J )
288 40 CONTINUE
289 ELSE
290 WORK( 1 ) = D( 1 )
291 DO 60 J = 1, N - 1
292 JP = ( J*( J-1 ) ) / 2
293 JP1 = JP + J
294 IF( KBAND.EQ.1 ) THEN
295 WORK( JP1+J ) = ( CONE-TAU( J ) )*E( J )
296 DO 50 JR = 1, J - 1
297 WORK( JP1+JR ) = -TAU( J )*E( J )*VP( JP1+JR )
298 50 CONTINUE
299 END IF
300 *
301 IF( TAU( J ).NE.CZERO ) THEN
302 VSAVE = VP( JP1+J )
303 VP( JP1+J ) = CONE
304 CALL CHPMV( 'U', J, CONE, WORK, VP( JP1+1 ), 1, CZERO,
305 $ WORK( LAP+1 ), 1 )
306 TEMP = -HALF*TAU( J )*CDOTC( J, WORK( LAP+1 ), 1,
307 $ VP( JP1+1 ), 1 )
308 CALL CAXPY( J, TEMP, VP( JP1+1 ), 1, WORK( LAP+1 ),
309 $ 1 )
310 CALL CHPR2( 'U', J, -TAU( J ), VP( JP1+1 ), 1,
311 $ WORK( LAP+1 ), 1, WORK )
312 VP( JP1+J ) = VSAVE
313 END IF
314 WORK( JP1+J+1 ) = D( J+1 )
315 60 CONTINUE
316 END IF
317 *
318 DO 70 J = 1, LAP
319 WORK( J ) = WORK( J ) - AP( J )
320 70 CONTINUE
321 WNORM = CLANHP( '1', CUPLO, N, WORK, RWORK )
322 *
323 ELSE IF( ITYPE.EQ.3 ) THEN
324 *
325 * ITYPE=3: error = U V* - I
326 *
327 IF( N.LT.2 )
328 $ RETURN
329 CALL CLACPY( ' ', N, N, U, LDU, WORK, N )
330 CALL CUPMTR( 'R', CUPLO, 'C', N, N, VP, TAU, WORK, N,
331 $ WORK( N**2+1 ), IINFO )
332 IF( IINFO.NE.0 ) THEN
333 RESULT( 1 ) = TEN / ULP
334 RETURN
335 END IF
336 *
337 DO 80 J = 1, N
338 WORK( ( N+1 )*( J-1 )+1 ) = WORK( ( N+1 )*( J-1 )+1 ) - CONE
339 80 CONTINUE
340 *
341 WNORM = CLANGE( '1', N, N, WORK, N, RWORK )
342 END IF
343 *
344 IF( ANORM.GT.WNORM ) THEN
345 RESULT( 1 ) = ( WNORM / ANORM ) / ( N*ULP )
346 ELSE
347 IF( ANORM.LT.ONE ) THEN
348 RESULT( 1 ) = ( MIN( WNORM, N*ANORM ) / ANORM ) / ( N*ULP )
349 ELSE
350 RESULT( 1 ) = MIN( WNORM / ANORM, REAL( N ) ) / ( N*ULP )
351 END IF
352 END IF
353 *
354 * Do Test 2
355 *
356 * Compute UU* - I
357 *
358 IF( ITYPE.EQ.1 ) THEN
359 CALL CGEMM( 'N', 'C', N, N, N, CONE, U, LDU, U, LDU, CZERO,
360 $ WORK, N )
361 *
362 DO 90 J = 1, N
363 WORK( ( N+1 )*( J-1 )+1 ) = WORK( ( N+1 )*( J-1 )+1 ) - CONE
364 90 CONTINUE
365 *
366 RESULT( 2 ) = MIN( CLANGE( '1', N, N, WORK, N, RWORK ),
367 $ REAL( N ) ) / ( N*ULP )
368 END IF
369 *
370 RETURN
371 *
372 * End of CHPT21
373 *
374 END