1 SUBROUTINE CHET22( ITYPE, UPLO, N, M, KBAND, A, LDA, D, E, U, LDU,
2 $ V, LDV, 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, LDA, LDU, LDV, M, N
11 * ..
12 * .. Array Arguments ..
13 REAL D( * ), E( * ), RESULT( 2 ), RWORK( * )
14 COMPLEX A( LDA, * ), TAU( * ), U( LDU, * ),
15 $ V( LDV, * ), WORK( * )
16 * ..
17 *
18 * Purpose
19 * =======
20 *
21 * CHET22 generally checks a decomposition of the form
22 *
23 * A U = U S
24 *
25 * where A is complex Hermitian, the columns of U are orthonormal,
26 * and S is diagonal (if KBAND=0) or symmetric tridiagonal (if
27 * KBAND=1). If ITYPE=1, then U is represented as a dense matrix,
28 * otherwise the U is expressed as a product of Householder
29 * transformations, whose vectors are stored in the array "V" and
30 * whose scaling constants are in "TAU"; we shall use the letter
31 * "V" to refer to the product of Householder transformations
32 * (which should be equal to U).
33 *
34 * Specifically, if ITYPE=1, then:
35 *
36 * RESULT(1) = | U' A U - S | / ( |A| m ulp ) *and*
37 * RESULT(2) = | I - U'U | / ( m ulp )
38 *
39 * Arguments
40 * =========
41 *
42 * ITYPE INTEGER
43 * Specifies the type of tests to be performed.
44 * 1: U expressed as a dense orthogonal matrix:
45 * RESULT(1) = | A - U S U' | / ( |A| n ulp ) *and*
46 * RESULT(2) = | I - UU' | / ( n ulp )
47 *
48 * UPLO CHARACTER
49 * If UPLO='U', the upper triangle of A will be used and the
50 * (strictly) lower triangle will not be referenced. If
51 * UPLO='L', the lower triangle of A will be used and the
52 * (strictly) upper triangle will not be referenced.
53 * Not modified.
54 *
55 * N INTEGER
56 * The size of the matrix. If it is zero, CHET22 does nothing.
57 * It must be at least zero.
58 * Not modified.
59 *
60 * M INTEGER
61 * The number of columns of U. If it is zero, CHET22 does
62 * nothing. It must be at least zero.
63 * Not modified.
64 *
65 * KBAND INTEGER
66 * The bandwidth of the matrix. It may only be zero or one.
67 * If zero, then S is diagonal, and E is not referenced. If
68 * one, then S is symmetric tri-diagonal.
69 * Not modified.
70 *
71 * A COMPLEX array, dimension (LDA , N)
72 * The original (unfactored) matrix. It is assumed to be
73 * symmetric, and only the upper (UPLO='U') or only the lower
74 * (UPLO='L') will be referenced.
75 * Not modified.
76 *
77 * LDA INTEGER
78 * The leading dimension of A. It must be at least 1
79 * and at least N.
80 * Not modified.
81 *
82 * D REAL array, dimension (N)
83 * The diagonal of the (symmetric tri-) diagonal matrix.
84 * Not modified.
85 *
86 * E REAL array, dimension (N)
87 * The off-diagonal of the (symmetric tri-) diagonal matrix.
88 * E(1) is ignored, E(2) is the (1,2) and (2,1) element, etc.
89 * Not referenced if KBAND=0.
90 * Not modified.
91 *
92 * U COMPLEX array, dimension (LDU, N)
93 * If ITYPE=1, this contains the orthogonal matrix in
94 * the decomposition, expressed as a dense matrix.
95 * Not modified.
96 *
97 * LDU INTEGER
98 * The leading dimension of U. LDU must be at least N and
99 * at least 1.
100 * Not modified.
101 *
102 * V COMPLEX array, dimension (LDV, N)
103 * If ITYPE=2 or 3, the lower triangle of this array contains
104 * the Householder vectors used to describe the orthogonal
105 * matrix in the decomposition. If ITYPE=1, then it is not
106 * referenced.
107 * Not modified.
108 *
109 * LDV INTEGER
110 * The leading dimension of V. LDV must be at least N and
111 * at least 1.
112 * Not modified.
113 *
114 * TAU COMPLEX array, dimension (N)
115 * If ITYPE >= 2, then TAU(j) is the scalar factor of
116 * v(j) v(j)' in the Householder transformation H(j) of
117 * the product U = H(1)...H(n-2)
118 * If ITYPE < 2, then TAU is not referenced.
119 * Not modified.
120 *
121 * WORK COMPLEX array, dimension (2*N**2)
122 * Workspace.
123 * Modified.
124 *
125 * RWORK REAL array, dimension (N)
126 * Workspace.
127 * Modified.
128 *
129 * RESULT REAL array, dimension (2)
130 * The values computed by the two tests described above. The
131 * values are currently limited to 1/ulp, to avoid overflow.
132 * RESULT(1) is always modified. RESULT(2) is modified only
133 * if LDU is at least N.
134 * Modified.
135 *
136 * =====================================================================
137 *
138 * .. Parameters ..
139 REAL ZERO, ONE
140 PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 )
141 COMPLEX CZERO, CONE
142 PARAMETER ( CZERO = ( 0.0E0, 0.0E0 ),
143 $ CONE = ( 1.0E0, 0.0E0 ) )
144 * ..
145 * .. Local Scalars ..
146 INTEGER J, JJ, JJ1, JJ2, NN, NNP1
147 REAL ANORM, ULP, UNFL, WNORM
148 * ..
149 * .. External Functions ..
150 REAL CLANHE, SLAMCH
151 EXTERNAL CLANHE, SLAMCH
152 * ..
153 * .. External Subroutines ..
154 EXTERNAL CGEMM, CHEMM
155 * ..
156 * .. Intrinsic Functions ..
157 INTRINSIC MAX, MIN, REAL
158 * ..
159 * .. Executable Statements ..
160 *
161 RESULT( 1 ) = ZERO
162 RESULT( 2 ) = ZERO
163 IF( N.LE.0 .OR. M.LE.0 )
164 $ RETURN
165 *
166 UNFL = SLAMCH( 'Safe minimum' )
167 ULP = SLAMCH( 'Precision' )
168 *
169 * Do Test 1
170 *
171 * Norm of A:
172 *
173 ANORM = MAX( CLANHE( '1', UPLO, N, A, LDA, RWORK ), UNFL )
174 *
175 * Compute error matrix:
176 *
177 * ITYPE=1: error = U' A U - S
178 *
179 CALL CHEMM( 'L', UPLO, N, M, CONE, A, LDA, U, LDU, CZERO, WORK,
180 $ N )
181 NN = N*N
182 NNP1 = NN + 1
183 CALL CGEMM( 'C', 'N', M, M, N, CONE, U, LDU, WORK, N, CZERO,
184 $ WORK( NNP1 ), N )
185 DO 10 J = 1, M
186 JJ = NN + ( J-1 )*N + J
187 WORK( JJ ) = WORK( JJ ) - D( J )
188 10 CONTINUE
189 IF( KBAND.EQ.1 .AND. N.GT.1 ) THEN
190 DO 20 J = 2, M
191 JJ1 = NN + ( J-1 )*N + J - 1
192 JJ2 = NN + ( J-2 )*N + J
193 WORK( JJ1 ) = WORK( JJ1 ) - E( J-1 )
194 WORK( JJ2 ) = WORK( JJ2 ) - E( J-1 )
195 20 CONTINUE
196 END IF
197 WNORM = CLANHE( '1', UPLO, M, WORK( NNP1 ), N, RWORK )
198 *
199 IF( ANORM.GT.WNORM ) THEN
200 RESULT( 1 ) = ( WNORM / ANORM ) / ( M*ULP )
201 ELSE
202 IF( ANORM.LT.ONE ) THEN
203 RESULT( 1 ) = ( MIN( WNORM, M*ANORM ) / ANORM ) / ( M*ULP )
204 ELSE
205 RESULT( 1 ) = MIN( WNORM / ANORM, REAL( M ) ) / ( M*ULP )
206 END IF
207 END IF
208 *
209 * Do Test 2
210 *
211 * Compute U'U - I
212 *
213 IF( ITYPE.EQ.1 )
214 $ CALL CUNT01( 'Columns', N, M, U, LDU, WORK, 2*N*N, RWORK,
215 $ RESULT( 2 ) )
216 *
217 RETURN
218 *
219 * End of CHET22
220 *
221 END
2 $ V, LDV, 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, LDA, LDU, LDV, M, N
11 * ..
12 * .. Array Arguments ..
13 REAL D( * ), E( * ), RESULT( 2 ), RWORK( * )
14 COMPLEX A( LDA, * ), TAU( * ), U( LDU, * ),
15 $ V( LDV, * ), WORK( * )
16 * ..
17 *
18 * Purpose
19 * =======
20 *
21 * CHET22 generally checks a decomposition of the form
22 *
23 * A U = U S
24 *
25 * where A is complex Hermitian, the columns of U are orthonormal,
26 * and S is diagonal (if KBAND=0) or symmetric tridiagonal (if
27 * KBAND=1). If ITYPE=1, then U is represented as a dense matrix,
28 * otherwise the U is expressed as a product of Householder
29 * transformations, whose vectors are stored in the array "V" and
30 * whose scaling constants are in "TAU"; we shall use the letter
31 * "V" to refer to the product of Householder transformations
32 * (which should be equal to U).
33 *
34 * Specifically, if ITYPE=1, then:
35 *
36 * RESULT(1) = | U' A U - S | / ( |A| m ulp ) *and*
37 * RESULT(2) = | I - U'U | / ( m ulp )
38 *
39 * Arguments
40 * =========
41 *
42 * ITYPE INTEGER
43 * Specifies the type of tests to be performed.
44 * 1: U expressed as a dense orthogonal matrix:
45 * RESULT(1) = | A - U S U' | / ( |A| n ulp ) *and*
46 * RESULT(2) = | I - UU' | / ( n ulp )
47 *
48 * UPLO CHARACTER
49 * If UPLO='U', the upper triangle of A will be used and the
50 * (strictly) lower triangle will not be referenced. If
51 * UPLO='L', the lower triangle of A will be used and the
52 * (strictly) upper triangle will not be referenced.
53 * Not modified.
54 *
55 * N INTEGER
56 * The size of the matrix. If it is zero, CHET22 does nothing.
57 * It must be at least zero.
58 * Not modified.
59 *
60 * M INTEGER
61 * The number of columns of U. If it is zero, CHET22 does
62 * nothing. It must be at least zero.
63 * Not modified.
64 *
65 * KBAND INTEGER
66 * The bandwidth of the matrix. It may only be zero or one.
67 * If zero, then S is diagonal, and E is not referenced. If
68 * one, then S is symmetric tri-diagonal.
69 * Not modified.
70 *
71 * A COMPLEX array, dimension (LDA , N)
72 * The original (unfactored) matrix. It is assumed to be
73 * symmetric, and only the upper (UPLO='U') or only the lower
74 * (UPLO='L') will be referenced.
75 * Not modified.
76 *
77 * LDA INTEGER
78 * The leading dimension of A. It must be at least 1
79 * and at least N.
80 * Not modified.
81 *
82 * D REAL array, dimension (N)
83 * The diagonal of the (symmetric tri-) diagonal matrix.
84 * Not modified.
85 *
86 * E REAL array, dimension (N)
87 * The off-diagonal of the (symmetric tri-) diagonal matrix.
88 * E(1) is ignored, E(2) is the (1,2) and (2,1) element, etc.
89 * Not referenced if KBAND=0.
90 * Not modified.
91 *
92 * U COMPLEX array, dimension (LDU, N)
93 * If ITYPE=1, this contains the orthogonal matrix in
94 * the decomposition, expressed as a dense matrix.
95 * Not modified.
96 *
97 * LDU INTEGER
98 * The leading dimension of U. LDU must be at least N and
99 * at least 1.
100 * Not modified.
101 *
102 * V COMPLEX array, dimension (LDV, N)
103 * If ITYPE=2 or 3, the lower triangle of this array contains
104 * the Householder vectors used to describe the orthogonal
105 * matrix in the decomposition. If ITYPE=1, then it is not
106 * referenced.
107 * Not modified.
108 *
109 * LDV INTEGER
110 * The leading dimension of V. LDV must be at least N and
111 * at least 1.
112 * Not modified.
113 *
114 * TAU COMPLEX array, dimension (N)
115 * If ITYPE >= 2, then TAU(j) is the scalar factor of
116 * v(j) v(j)' in the Householder transformation H(j) of
117 * the product U = H(1)...H(n-2)
118 * If ITYPE < 2, then TAU is not referenced.
119 * Not modified.
120 *
121 * WORK COMPLEX array, dimension (2*N**2)
122 * Workspace.
123 * Modified.
124 *
125 * RWORK REAL array, dimension (N)
126 * Workspace.
127 * Modified.
128 *
129 * RESULT REAL array, dimension (2)
130 * The values computed by the two tests described above. The
131 * values are currently limited to 1/ulp, to avoid overflow.
132 * RESULT(1) is always modified. RESULT(2) is modified only
133 * if LDU is at least N.
134 * Modified.
135 *
136 * =====================================================================
137 *
138 * .. Parameters ..
139 REAL ZERO, ONE
140 PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 )
141 COMPLEX CZERO, CONE
142 PARAMETER ( CZERO = ( 0.0E0, 0.0E0 ),
143 $ CONE = ( 1.0E0, 0.0E0 ) )
144 * ..
145 * .. Local Scalars ..
146 INTEGER J, JJ, JJ1, JJ2, NN, NNP1
147 REAL ANORM, ULP, UNFL, WNORM
148 * ..
149 * .. External Functions ..
150 REAL CLANHE, SLAMCH
151 EXTERNAL CLANHE, SLAMCH
152 * ..
153 * .. External Subroutines ..
154 EXTERNAL CGEMM, CHEMM
155 * ..
156 * .. Intrinsic Functions ..
157 INTRINSIC MAX, MIN, REAL
158 * ..
159 * .. Executable Statements ..
160 *
161 RESULT( 1 ) = ZERO
162 RESULT( 2 ) = ZERO
163 IF( N.LE.0 .OR. M.LE.0 )
164 $ RETURN
165 *
166 UNFL = SLAMCH( 'Safe minimum' )
167 ULP = SLAMCH( 'Precision' )
168 *
169 * Do Test 1
170 *
171 * Norm of A:
172 *
173 ANORM = MAX( CLANHE( '1', UPLO, N, A, LDA, RWORK ), UNFL )
174 *
175 * Compute error matrix:
176 *
177 * ITYPE=1: error = U' A U - S
178 *
179 CALL CHEMM( 'L', UPLO, N, M, CONE, A, LDA, U, LDU, CZERO, WORK,
180 $ N )
181 NN = N*N
182 NNP1 = NN + 1
183 CALL CGEMM( 'C', 'N', M, M, N, CONE, U, LDU, WORK, N, CZERO,
184 $ WORK( NNP1 ), N )
185 DO 10 J = 1, M
186 JJ = NN + ( J-1 )*N + J
187 WORK( JJ ) = WORK( JJ ) - D( J )
188 10 CONTINUE
189 IF( KBAND.EQ.1 .AND. N.GT.1 ) THEN
190 DO 20 J = 2, M
191 JJ1 = NN + ( J-1 )*N + J - 1
192 JJ2 = NN + ( J-2 )*N + J
193 WORK( JJ1 ) = WORK( JJ1 ) - E( J-1 )
194 WORK( JJ2 ) = WORK( JJ2 ) - E( J-1 )
195 20 CONTINUE
196 END IF
197 WNORM = CLANHE( '1', UPLO, M, WORK( NNP1 ), N, RWORK )
198 *
199 IF( ANORM.GT.WNORM ) THEN
200 RESULT( 1 ) = ( WNORM / ANORM ) / ( M*ULP )
201 ELSE
202 IF( ANORM.LT.ONE ) THEN
203 RESULT( 1 ) = ( MIN( WNORM, M*ANORM ) / ANORM ) / ( M*ULP )
204 ELSE
205 RESULT( 1 ) = MIN( WNORM / ANORM, REAL( M ) ) / ( M*ULP )
206 END IF
207 END IF
208 *
209 * Do Test 2
210 *
211 * Compute U'U - I
212 *
213 IF( ITYPE.EQ.1 )
214 $ CALL CUNT01( 'Columns', N, M, U, LDU, WORK, 2*N*N, RWORK,
215 $ RESULT( 2 ) )
216 *
217 RETURN
218 *
219 * End of CHET22
220 *
221 END