1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
|
SUBROUTINE ZSPT01( UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID )
*
* -- LAPACK test routine (version 3.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* September 30, 1994
*
* .. Scalar Arguments ..
CHARACTER UPLO
INTEGER LDC, N
DOUBLE PRECISION RESID
* ..
* .. Array Arguments ..
INTEGER IPIV( * )
DOUBLE PRECISION RWORK( * )
COMPLEX*16 A( * ), AFAC( * ), C( LDC, * )
* ..
*
* Purpose
* =======
*
* ZSPT01 reconstructs a symmetric indefinite packed matrix A from its
* diagonal pivoting factorization A = U*D*U' or A = L*D*L' and computes
* the residual
* norm( C - A ) / ( N * norm(A) * EPS ),
* where C is the reconstructed matrix and EPS is the machine epsilon.
*
* Arguments
* ==========
*
* UPLO (input) CHARACTER*1
* Specifies whether the upper or lower triangular part of the
* Hermitian matrix A is stored:
* = 'U': Upper triangular
* = 'L': Lower triangular
*
* N (input) INTEGER
* The order of the matrix A. N >= 0.
*
* A (input) COMPLEX*16 array, dimension (N*(N+1)/2)
* The original symmetric matrix A, stored as a packed
* triangular matrix.
*
* AFAC (input) COMPLEX*16 array, dimension (N*(N+1)/2)
* The factored form of the matrix A, stored as a packed
* triangular matrix. AFAC contains the block diagonal matrix D
* and the multipliers used to obtain the factor L or U from the
* L*D*L' or U*D*U' factorization as computed by ZSPTRF.
*
* IPIV (input) INTEGER array, dimension (N)
* The pivot indices from ZSPTRF.
*
* C (workspace) COMPLEX*16 array, dimension (LDC,N)
*
* LDC (integer) INTEGER
* The leading dimension of the array C. LDC >= max(1,N).
*
* RWORK (workspace) DOUBLE PRECISION array, dimension (N)
*
* RESID (output) DOUBLE PRECISION
* If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS )
* If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
COMPLEX*16 CZERO, CONE
PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ),
$ CONE = ( 1.0D+0, 0.0D+0 ) )
* ..
* .. Local Scalars ..
INTEGER I, INFO, J, JC
DOUBLE PRECISION ANORM, EPS
* ..
* .. External Functions ..
LOGICAL LSAME
DOUBLE PRECISION DLAMCH, ZLANSP, ZLANSY
EXTERNAL LSAME, DLAMCH, ZLANSP, ZLANSY
* ..
* .. External Subroutines ..
EXTERNAL ZLASET, ZLAVSP
* ..
* .. Intrinsic Functions ..
INTRINSIC DBLE
* ..
* .. Executable Statements ..
*
* Quick exit if N = 0.
*
IF( N.LE.0 ) THEN
RESID = ZERO
RETURN
END IF
*
* Determine EPS and the norm of A.
*
EPS = DLAMCH( 'Epsilon' )
ANORM = ZLANSP( '1', UPLO, N, A, RWORK )
*
* Initialize C to the identity matrix.
*
CALL ZLASET( 'Full', N, N, CZERO, CONE, C, LDC )
*
* Call ZLAVSP to form the product D * U' (or D * L' ).
*
CALL ZLAVSP( UPLO, 'Transpose', 'Non-unit', N, N, AFAC, IPIV, C,
$ LDC, INFO )
*
* Call ZLAVSP again to multiply by U ( or L ).
*
CALL ZLAVSP( UPLO, 'No transpose', 'Unit', N, N, AFAC, IPIV, C,
$ LDC, INFO )
*
* Compute the difference C - A .
*
IF( LSAME( UPLO, 'U' ) ) THEN
JC = 0
DO 20 J = 1, N
DO 10 I = 1, J
C( I, J ) = C( I, J ) - A( JC+I )
10 CONTINUE
JC = JC + J
20 CONTINUE
ELSE
JC = 1
DO 40 J = 1, N
DO 30 I = J, N
C( I, J ) = C( I, J ) - A( JC+I-J )
30 CONTINUE
JC = JC + N - J + 1
40 CONTINUE
END IF
*
* Compute norm( C - A ) / ( N * norm(A) * EPS )
*
RESID = ZLANSY( '1', UPLO, N, C, LDC, RWORK )
*
IF( ANORM.LE.ZERO ) THEN
IF( RESID.NE.ZERO )
$ RESID = ONE / EPS
ELSE
RESID = ( ( RESID / DBLE( N ) ) / ANORM ) / EPS
END IF
*
RETURN
*
* End of ZSPT01
*
END
|
