1 SUBROUTINE ZPBT01( UPLO, N, KD, A, LDA, AFAC, LDAFAC, RWORK,
2 $ RESID )
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 KD, LDA, LDAFAC, N
11 DOUBLE PRECISION RESID
12 * ..
13 * .. Array Arguments ..
14 DOUBLE PRECISION RWORK( * )
15 COMPLEX*16 A( LDA, * ), AFAC( LDAFAC, * )
16 * ..
17 *
18 * Purpose
19 * =======
20 *
21 * ZPBT01 reconstructs a Hermitian positive definite band matrix A from
22 * its L*L' or U'*U factorization and computes the residual
23 * norm( L*L' - A ) / ( N * norm(A) * EPS ) or
24 * norm( U'*U - A ) / ( N * norm(A) * EPS ),
25 * where EPS is the machine epsilon, L' is the conjugate transpose of
26 * L, and U' is the conjugate transpose of U.
27 *
28 * Arguments
29 * =========
30 *
31 * UPLO (input) CHARACTER*1
32 * Specifies whether the upper or lower triangular part of the
33 * Hermitian matrix A is stored:
34 * = 'U': Upper triangular
35 * = 'L': Lower triangular
36 *
37 * N (input) INTEGER
38 * The number of rows and columns of the matrix A. N >= 0.
39 *
40 * KD (input) INTEGER
41 * The number of super-diagonals of the matrix A if UPLO = 'U',
42 * or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
43 *
44 * A (input) COMPLEX*16 array, dimension (LDA,N)
45 * The original Hermitian band matrix A. If UPLO = 'U', the
46 * upper triangular part of A is stored as a band matrix; if
47 * UPLO = 'L', the lower triangular part of A is stored. The
48 * columns of the appropriate triangle are stored in the columns
49 * of A and the diagonals of the triangle are stored in the rows
50 * of A. See ZPBTRF for further details.
51 *
52 * LDA (input) INTEGER.
53 * The leading dimension of the array A. LDA >= max(1,KD+1).
54 *
55 * AFAC (input) COMPLEX*16 array, dimension (LDAFAC,N)
56 * The factored form of the matrix A. AFAC contains the factor
57 * L or U from the L*L' or U'*U factorization in band storage
58 * format, as computed by ZPBTRF.
59 *
60 * LDAFAC (input) INTEGER
61 * The leading dimension of the array AFAC.
62 * LDAFAC >= max(1,KD+1).
63 *
64 * RWORK (workspace) DOUBLE PRECISION array, dimension (N)
65 *
66 * RESID (output) DOUBLE PRECISION
67 * If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
68 * If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )
69 *
70 * =====================================================================
71 *
72 *
73 * .. Parameters ..
74 DOUBLE PRECISION ZERO, ONE
75 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
76 * ..
77 * .. Local Scalars ..
78 INTEGER I, J, K, KC, KLEN, ML, MU
79 DOUBLE PRECISION AKK, ANORM, EPS
80 * ..
81 * .. External Functions ..
82 LOGICAL LSAME
83 DOUBLE PRECISION DLAMCH, ZLANHB
84 COMPLEX*16 ZDOTC
85 EXTERNAL LSAME, DLAMCH, ZLANHB, ZDOTC
86 * ..
87 * .. External Subroutines ..
88 EXTERNAL ZDSCAL, ZHER, ZTRMV
89 * ..
90 * .. Intrinsic Functions ..
91 INTRINSIC DBLE, DIMAG, MAX, MIN
92 * ..
93 * .. Executable Statements ..
94 *
95 * Quick exit if N = 0.
96 *
97 IF( N.LE.0 ) THEN
98 RESID = ZERO
99 RETURN
100 END IF
101 *
102 * Exit with RESID = 1/EPS if ANORM = 0.
103 *
104 EPS = DLAMCH( 'Epsilon' )
105 ANORM = ZLANHB( '1', UPLO, N, KD, A, LDA, RWORK )
106 IF( ANORM.LE.ZERO ) THEN
107 RESID = ONE / EPS
108 RETURN
109 END IF
110 *
111 * Check the imaginary parts of the diagonal elements and return with
112 * an error code if any are nonzero.
113 *
114 IF( LSAME( UPLO, 'U' ) ) THEN
115 DO 10 J = 1, N
116 IF( DIMAG( AFAC( KD+1, J ) ).NE.ZERO ) THEN
117 RESID = ONE / EPS
118 RETURN
119 END IF
120 10 CONTINUE
121 ELSE
122 DO 20 J = 1, N
123 IF( DIMAG( AFAC( 1, J ) ).NE.ZERO ) THEN
124 RESID = ONE / EPS
125 RETURN
126 END IF
127 20 CONTINUE
128 END IF
129 *
130 * Compute the product U'*U, overwriting U.
131 *
132 IF( LSAME( UPLO, 'U' ) ) THEN
133 DO 30 K = N, 1, -1
134 KC = MAX( 1, KD+2-K )
135 KLEN = KD + 1 - KC
136 *
137 * Compute the (K,K) element of the result.
138 *
139 AKK = ZDOTC( KLEN+1, AFAC( KC, K ), 1, AFAC( KC, K ), 1 )
140 AFAC( KD+1, K ) = AKK
141 *
142 * Compute the rest of column K.
143 *
144 IF( KLEN.GT.0 )
145 $ CALL ZTRMV( 'Upper', 'Conjugate', 'Non-unit', KLEN,
146 $ AFAC( KD+1, K-KLEN ), LDAFAC-1,
147 $ AFAC( KC, K ), 1 )
148 *
149 30 CONTINUE
150 *
151 * UPLO = 'L': Compute the product L*L', overwriting L.
152 *
153 ELSE
154 DO 40 K = N, 1, -1
155 KLEN = MIN( KD, N-K )
156 *
157 * Add a multiple of column K of the factor L to each of
158 * columns K+1 through N.
159 *
160 IF( KLEN.GT.0 )
161 $ CALL ZHER( 'Lower', KLEN, ONE, AFAC( 2, K ), 1,
162 $ AFAC( 1, K+1 ), LDAFAC-1 )
163 *
164 * Scale column K by the diagonal element.
165 *
166 AKK = AFAC( 1, K )
167 CALL ZDSCAL( KLEN+1, AKK, AFAC( 1, K ), 1 )
168 *
169 40 CONTINUE
170 END IF
171 *
172 * Compute the difference L*L' - A or U'*U - A.
173 *
174 IF( LSAME( UPLO, 'U' ) ) THEN
175 DO 60 J = 1, N
176 MU = MAX( 1, KD+2-J )
177 DO 50 I = MU, KD + 1
178 AFAC( I, J ) = AFAC( I, J ) - A( I, J )
179 50 CONTINUE
180 60 CONTINUE
181 ELSE
182 DO 80 J = 1, N
183 ML = MIN( KD+1, N-J+1 )
184 DO 70 I = 1, ML
185 AFAC( I, J ) = AFAC( I, J ) - A( I, J )
186 70 CONTINUE
187 80 CONTINUE
188 END IF
189 *
190 * Compute norm( L*L' - A ) / ( N * norm(A) * EPS )
191 *
192 RESID = ZLANHB( '1', UPLO, N, KD, AFAC, LDAFAC, RWORK )
193 *
194 RESID = ( ( RESID / DBLE( N ) ) / ANORM ) / EPS
195 *
196 RETURN
197 *
198 * End of ZPBT01
199 *
200 END
2 $ RESID )
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 KD, LDA, LDAFAC, N
11 DOUBLE PRECISION RESID
12 * ..
13 * .. Array Arguments ..
14 DOUBLE PRECISION RWORK( * )
15 COMPLEX*16 A( LDA, * ), AFAC( LDAFAC, * )
16 * ..
17 *
18 * Purpose
19 * =======
20 *
21 * ZPBT01 reconstructs a Hermitian positive definite band matrix A from
22 * its L*L' or U'*U factorization and computes the residual
23 * norm( L*L' - A ) / ( N * norm(A) * EPS ) or
24 * norm( U'*U - A ) / ( N * norm(A) * EPS ),
25 * where EPS is the machine epsilon, L' is the conjugate transpose of
26 * L, and U' is the conjugate transpose of U.
27 *
28 * Arguments
29 * =========
30 *
31 * UPLO (input) CHARACTER*1
32 * Specifies whether the upper or lower triangular part of the
33 * Hermitian matrix A is stored:
34 * = 'U': Upper triangular
35 * = 'L': Lower triangular
36 *
37 * N (input) INTEGER
38 * The number of rows and columns of the matrix A. N >= 0.
39 *
40 * KD (input) INTEGER
41 * The number of super-diagonals of the matrix A if UPLO = 'U',
42 * or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
43 *
44 * A (input) COMPLEX*16 array, dimension (LDA,N)
45 * The original Hermitian band matrix A. If UPLO = 'U', the
46 * upper triangular part of A is stored as a band matrix; if
47 * UPLO = 'L', the lower triangular part of A is stored. The
48 * columns of the appropriate triangle are stored in the columns
49 * of A and the diagonals of the triangle are stored in the rows
50 * of A. See ZPBTRF for further details.
51 *
52 * LDA (input) INTEGER.
53 * The leading dimension of the array A. LDA >= max(1,KD+1).
54 *
55 * AFAC (input) COMPLEX*16 array, dimension (LDAFAC,N)
56 * The factored form of the matrix A. AFAC contains the factor
57 * L or U from the L*L' or U'*U factorization in band storage
58 * format, as computed by ZPBTRF.
59 *
60 * LDAFAC (input) INTEGER
61 * The leading dimension of the array AFAC.
62 * LDAFAC >= max(1,KD+1).
63 *
64 * RWORK (workspace) DOUBLE PRECISION array, dimension (N)
65 *
66 * RESID (output) DOUBLE PRECISION
67 * If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
68 * If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )
69 *
70 * =====================================================================
71 *
72 *
73 * .. Parameters ..
74 DOUBLE PRECISION ZERO, ONE
75 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
76 * ..
77 * .. Local Scalars ..
78 INTEGER I, J, K, KC, KLEN, ML, MU
79 DOUBLE PRECISION AKK, ANORM, EPS
80 * ..
81 * .. External Functions ..
82 LOGICAL LSAME
83 DOUBLE PRECISION DLAMCH, ZLANHB
84 COMPLEX*16 ZDOTC
85 EXTERNAL LSAME, DLAMCH, ZLANHB, ZDOTC
86 * ..
87 * .. External Subroutines ..
88 EXTERNAL ZDSCAL, ZHER, ZTRMV
89 * ..
90 * .. Intrinsic Functions ..
91 INTRINSIC DBLE, DIMAG, MAX, MIN
92 * ..
93 * .. Executable Statements ..
94 *
95 * Quick exit if N = 0.
96 *
97 IF( N.LE.0 ) THEN
98 RESID = ZERO
99 RETURN
100 END IF
101 *
102 * Exit with RESID = 1/EPS if ANORM = 0.
103 *
104 EPS = DLAMCH( 'Epsilon' )
105 ANORM = ZLANHB( '1', UPLO, N, KD, A, LDA, RWORK )
106 IF( ANORM.LE.ZERO ) THEN
107 RESID = ONE / EPS
108 RETURN
109 END IF
110 *
111 * Check the imaginary parts of the diagonal elements and return with
112 * an error code if any are nonzero.
113 *
114 IF( LSAME( UPLO, 'U' ) ) THEN
115 DO 10 J = 1, N
116 IF( DIMAG( AFAC( KD+1, J ) ).NE.ZERO ) THEN
117 RESID = ONE / EPS
118 RETURN
119 END IF
120 10 CONTINUE
121 ELSE
122 DO 20 J = 1, N
123 IF( DIMAG( AFAC( 1, J ) ).NE.ZERO ) THEN
124 RESID = ONE / EPS
125 RETURN
126 END IF
127 20 CONTINUE
128 END IF
129 *
130 * Compute the product U'*U, overwriting U.
131 *
132 IF( LSAME( UPLO, 'U' ) ) THEN
133 DO 30 K = N, 1, -1
134 KC = MAX( 1, KD+2-K )
135 KLEN = KD + 1 - KC
136 *
137 * Compute the (K,K) element of the result.
138 *
139 AKK = ZDOTC( KLEN+1, AFAC( KC, K ), 1, AFAC( KC, K ), 1 )
140 AFAC( KD+1, K ) = AKK
141 *
142 * Compute the rest of column K.
143 *
144 IF( KLEN.GT.0 )
145 $ CALL ZTRMV( 'Upper', 'Conjugate', 'Non-unit', KLEN,
146 $ AFAC( KD+1, K-KLEN ), LDAFAC-1,
147 $ AFAC( KC, K ), 1 )
148 *
149 30 CONTINUE
150 *
151 * UPLO = 'L': Compute the product L*L', overwriting L.
152 *
153 ELSE
154 DO 40 K = N, 1, -1
155 KLEN = MIN( KD, N-K )
156 *
157 * Add a multiple of column K of the factor L to each of
158 * columns K+1 through N.
159 *
160 IF( KLEN.GT.0 )
161 $ CALL ZHER( 'Lower', KLEN, ONE, AFAC( 2, K ), 1,
162 $ AFAC( 1, K+1 ), LDAFAC-1 )
163 *
164 * Scale column K by the diagonal element.
165 *
166 AKK = AFAC( 1, K )
167 CALL ZDSCAL( KLEN+1, AKK, AFAC( 1, K ), 1 )
168 *
169 40 CONTINUE
170 END IF
171 *
172 * Compute the difference L*L' - A or U'*U - A.
173 *
174 IF( LSAME( UPLO, 'U' ) ) THEN
175 DO 60 J = 1, N
176 MU = MAX( 1, KD+2-J )
177 DO 50 I = MU, KD + 1
178 AFAC( I, J ) = AFAC( I, J ) - A( I, J )
179 50 CONTINUE
180 60 CONTINUE
181 ELSE
182 DO 80 J = 1, N
183 ML = MIN( KD+1, N-J+1 )
184 DO 70 I = 1, ML
185 AFAC( I, J ) = AFAC( I, J ) - A( I, J )
186 70 CONTINUE
187 80 CONTINUE
188 END IF
189 *
190 * Compute norm( L*L' - A ) / ( N * norm(A) * EPS )
191 *
192 RESID = ZLANHB( '1', UPLO, N, KD, AFAC, LDAFAC, RWORK )
193 *
194 RESID = ( ( RESID / DBLE( N ) ) / ANORM ) / EPS
195 *
196 RETURN
197 *
198 * End of ZPBT01
199 *
200 END