1 SUBROUTINE ZHPT01( UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID )
2 *
3 * -- LAPACK test routine (version 3.1) --
4 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
5 * November 2006
6 *
7 * .. Scalar Arguments ..
8 CHARACTER UPLO
9 INTEGER LDC, N
10 DOUBLE PRECISION RESID
11 * ..
12 * .. Array Arguments ..
13 INTEGER IPIV( * )
14 DOUBLE PRECISION RWORK( * )
15 COMPLEX*16 A( * ), AFAC( * ), C( LDC, * )
16 * ..
17 *
18 * Purpose
19 * =======
20 *
21 * ZHPT01 reconstructs a Hermitian indefinite packed matrix A from its
22 * block L*D*L' or U*D*U' factorization and computes the residual
23 * norm( C - A ) / ( N * norm(A) * EPS ),
24 * where C is the reconstructed matrix, EPS is the machine epsilon,
25 * L' is the conjugate transpose of L, and U' is the conjugate transpose
26 * 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 * A (input) COMPLEX*16 array, dimension (N*(N+1)/2)
41 * The original Hermitian matrix A, stored as a packed
42 * triangular matrix.
43 *
44 * AFAC (input) COMPLEX*16 array, dimension (N*(N+1)/2)
45 * The factored form of the matrix A, stored as a packed
46 * triangular matrix. AFAC contains the block diagonal matrix D
47 * and the multipliers used to obtain the factor L or U from the
48 * block L*D*L' or U*D*U' factorization as computed by ZHPTRF.
49 *
50 * IPIV (input) INTEGER array, dimension (N)
51 * The pivot indices from ZHPTRF.
52 *
53 * C (workspace) COMPLEX*16 array, dimension (LDC,N)
54 *
55 * LDC (integer) INTEGER
56 * The leading dimension of the array C. LDC >= max(1,N).
57 *
58 * RWORK (workspace) DOUBLE PRECISION array, dimension (N)
59 *
60 * RESID (output) DOUBLE PRECISION
61 * If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS )
62 * If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )
63 *
64 * =====================================================================
65 *
66 * .. Parameters ..
67 DOUBLE PRECISION ZERO, ONE
68 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
69 COMPLEX*16 CZERO, CONE
70 PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ),
71 $ CONE = ( 1.0D+0, 0.0D+0 ) )
72 * ..
73 * .. Local Scalars ..
74 INTEGER I, INFO, J, JC
75 DOUBLE PRECISION ANORM, EPS
76 * ..
77 * .. External Functions ..
78 LOGICAL LSAME
79 DOUBLE PRECISION DLAMCH, ZLANHE, ZLANHP
80 EXTERNAL LSAME, DLAMCH, ZLANHE, ZLANHP
81 * ..
82 * .. External Subroutines ..
83 EXTERNAL ZLASET, ZLAVHP
84 * ..
85 * .. Intrinsic Functions ..
86 INTRINSIC DBLE, DIMAG
87 * ..
88 * .. Executable Statements ..
89 *
90 * Quick exit if N = 0.
91 *
92 IF( N.LE.0 ) THEN
93 RESID = ZERO
94 RETURN
95 END IF
96 *
97 * Determine EPS and the norm of A.
98 *
99 EPS = DLAMCH( 'Epsilon' )
100 ANORM = ZLANHP( '1', UPLO, N, A, RWORK )
101 *
102 * Check the imaginary parts of the diagonal elements and return with
103 * an error code if any are nonzero.
104 *
105 JC = 1
106 IF( LSAME( UPLO, 'U' ) ) THEN
107 DO 10 J = 1, N
108 IF( DIMAG( AFAC( JC ) ).NE.ZERO ) THEN
109 RESID = ONE / EPS
110 RETURN
111 END IF
112 JC = JC + J + 1
113 10 CONTINUE
114 ELSE
115 DO 20 J = 1, N
116 IF( DIMAG( AFAC( JC ) ).NE.ZERO ) THEN
117 RESID = ONE / EPS
118 RETURN
119 END IF
120 JC = JC + N - J + 1
121 20 CONTINUE
122 END IF
123 *
124 * Initialize C to the identity matrix.
125 *
126 CALL ZLASET( 'Full', N, N, CZERO, CONE, C, LDC )
127 *
128 * Call ZLAVHP to form the product D * U' (or D * L' ).
129 *
130 CALL ZLAVHP( UPLO, 'Conjugate', 'Non-unit', N, N, AFAC, IPIV, C,
131 $ LDC, INFO )
132 *
133 * Call ZLAVHP again to multiply by U ( or L ).
134 *
135 CALL ZLAVHP( UPLO, 'No transpose', 'Unit', N, N, AFAC, IPIV, C,
136 $ LDC, INFO )
137 *
138 * Compute the difference C - A .
139 *
140 IF( LSAME( UPLO, 'U' ) ) THEN
141 JC = 0
142 DO 40 J = 1, N
143 DO 30 I = 1, J - 1
144 C( I, J ) = C( I, J ) - A( JC+I )
145 30 CONTINUE
146 C( J, J ) = C( J, J ) - DBLE( A( JC+J ) )
147 JC = JC + J
148 40 CONTINUE
149 ELSE
150 JC = 1
151 DO 60 J = 1, N
152 C( J, J ) = C( J, J ) - DBLE( A( JC ) )
153 DO 50 I = J + 1, N
154 C( I, J ) = C( I, J ) - A( JC+I-J )
155 50 CONTINUE
156 JC = JC + N - J + 1
157 60 CONTINUE
158 END IF
159 *
160 * Compute norm( C - A ) / ( N * norm(A) * EPS )
161 *
162 RESID = ZLANHE( '1', UPLO, N, C, LDC, RWORK )
163 *
164 IF( ANORM.LE.ZERO ) THEN
165 IF( RESID.NE.ZERO )
166 $ RESID = ONE / EPS
167 ELSE
168 RESID = ( ( RESID / DBLE( N ) ) / ANORM ) / EPS
169 END IF
170 *
171 RETURN
172 *
173 * End of ZHPT01
174 *
175 END
2 *
3 * -- LAPACK test routine (version 3.1) --
4 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
5 * November 2006
6 *
7 * .. Scalar Arguments ..
8 CHARACTER UPLO
9 INTEGER LDC, N
10 DOUBLE PRECISION RESID
11 * ..
12 * .. Array Arguments ..
13 INTEGER IPIV( * )
14 DOUBLE PRECISION RWORK( * )
15 COMPLEX*16 A( * ), AFAC( * ), C( LDC, * )
16 * ..
17 *
18 * Purpose
19 * =======
20 *
21 * ZHPT01 reconstructs a Hermitian indefinite packed matrix A from its
22 * block L*D*L' or U*D*U' factorization and computes the residual
23 * norm( C - A ) / ( N * norm(A) * EPS ),
24 * where C is the reconstructed matrix, EPS is the machine epsilon,
25 * L' is the conjugate transpose of L, and U' is the conjugate transpose
26 * 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 * A (input) COMPLEX*16 array, dimension (N*(N+1)/2)
41 * The original Hermitian matrix A, stored as a packed
42 * triangular matrix.
43 *
44 * AFAC (input) COMPLEX*16 array, dimension (N*(N+1)/2)
45 * The factored form of the matrix A, stored as a packed
46 * triangular matrix. AFAC contains the block diagonal matrix D
47 * and the multipliers used to obtain the factor L or U from the
48 * block L*D*L' or U*D*U' factorization as computed by ZHPTRF.
49 *
50 * IPIV (input) INTEGER array, dimension (N)
51 * The pivot indices from ZHPTRF.
52 *
53 * C (workspace) COMPLEX*16 array, dimension (LDC,N)
54 *
55 * LDC (integer) INTEGER
56 * The leading dimension of the array C. LDC >= max(1,N).
57 *
58 * RWORK (workspace) DOUBLE PRECISION array, dimension (N)
59 *
60 * RESID (output) DOUBLE PRECISION
61 * If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS )
62 * If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )
63 *
64 * =====================================================================
65 *
66 * .. Parameters ..
67 DOUBLE PRECISION ZERO, ONE
68 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
69 COMPLEX*16 CZERO, CONE
70 PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ),
71 $ CONE = ( 1.0D+0, 0.0D+0 ) )
72 * ..
73 * .. Local Scalars ..
74 INTEGER I, INFO, J, JC
75 DOUBLE PRECISION ANORM, EPS
76 * ..
77 * .. External Functions ..
78 LOGICAL LSAME
79 DOUBLE PRECISION DLAMCH, ZLANHE, ZLANHP
80 EXTERNAL LSAME, DLAMCH, ZLANHE, ZLANHP
81 * ..
82 * .. External Subroutines ..
83 EXTERNAL ZLASET, ZLAVHP
84 * ..
85 * .. Intrinsic Functions ..
86 INTRINSIC DBLE, DIMAG
87 * ..
88 * .. Executable Statements ..
89 *
90 * Quick exit if N = 0.
91 *
92 IF( N.LE.0 ) THEN
93 RESID = ZERO
94 RETURN
95 END IF
96 *
97 * Determine EPS and the norm of A.
98 *
99 EPS = DLAMCH( 'Epsilon' )
100 ANORM = ZLANHP( '1', UPLO, N, A, RWORK )
101 *
102 * Check the imaginary parts of the diagonal elements and return with
103 * an error code if any are nonzero.
104 *
105 JC = 1
106 IF( LSAME( UPLO, 'U' ) ) THEN
107 DO 10 J = 1, N
108 IF( DIMAG( AFAC( JC ) ).NE.ZERO ) THEN
109 RESID = ONE / EPS
110 RETURN
111 END IF
112 JC = JC + J + 1
113 10 CONTINUE
114 ELSE
115 DO 20 J = 1, N
116 IF( DIMAG( AFAC( JC ) ).NE.ZERO ) THEN
117 RESID = ONE / EPS
118 RETURN
119 END IF
120 JC = JC + N - J + 1
121 20 CONTINUE
122 END IF
123 *
124 * Initialize C to the identity matrix.
125 *
126 CALL ZLASET( 'Full', N, N, CZERO, CONE, C, LDC )
127 *
128 * Call ZLAVHP to form the product D * U' (or D * L' ).
129 *
130 CALL ZLAVHP( UPLO, 'Conjugate', 'Non-unit', N, N, AFAC, IPIV, C,
131 $ LDC, INFO )
132 *
133 * Call ZLAVHP again to multiply by U ( or L ).
134 *
135 CALL ZLAVHP( UPLO, 'No transpose', 'Unit', N, N, AFAC, IPIV, C,
136 $ LDC, INFO )
137 *
138 * Compute the difference C - A .
139 *
140 IF( LSAME( UPLO, 'U' ) ) THEN
141 JC = 0
142 DO 40 J = 1, N
143 DO 30 I = 1, J - 1
144 C( I, J ) = C( I, J ) - A( JC+I )
145 30 CONTINUE
146 C( J, J ) = C( J, J ) - DBLE( A( JC+J ) )
147 JC = JC + J
148 40 CONTINUE
149 ELSE
150 JC = 1
151 DO 60 J = 1, N
152 C( J, J ) = C( J, J ) - DBLE( A( JC ) )
153 DO 50 I = J + 1, N
154 C( I, J ) = C( I, J ) - A( JC+I-J )
155 50 CONTINUE
156 JC = JC + N - J + 1
157 60 CONTINUE
158 END IF
159 *
160 * Compute norm( C - A ) / ( N * norm(A) * EPS )
161 *
162 RESID = ZLANHE( '1', UPLO, N, C, LDC, RWORK )
163 *
164 IF( ANORM.LE.ZERO ) THEN
165 IF( RESID.NE.ZERO )
166 $ RESID = ONE / EPS
167 ELSE
168 RESID = ( ( RESID / DBLE( N ) ) / ANORM ) / EPS
169 END IF
170 *
171 RETURN
172 *
173 * End of ZHPT01
174 *
175 END