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
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
|
SUBROUTINE PZLASIZEHEEVR( WKNOWN, RANGE, N, DESCA, VL, VU, IL, IU,
$ ISEED, WIN, MAXSIZE, VECSIZE, VALSIZE )
*
* -- ScaLAPACK routine (@(MODE)version *TBA*) --
* University of California, Berkeley and
* University of Tennessee, Knoxville.
* October 21, 2006
*
IMPLICIT NONE
*
* .. Scalar Arguments ..
LOGICAL WKNOWN
CHARACTER RANGE
INTEGER IL, IU, MAXSIZE, N, VALSIZE, VECSIZE
DOUBLE PRECISION VL, VU
* ..
* .. Array Arguments ..
INTEGER DESCA( * ), ISEED( 4 )
DOUBLE PRECISION WIN( * )
* ..
*
* Purpose
* =======
*
* PZLASIZEHEEVR computes the amount of memory needed by PZHEEVR
* to ensure:
* 1) Orthogonal Eigenvectors
* 2) Eigenpairs with small residual norms
*
* Arguments
* =========
*
* WKNOWN (global input) INTEGER
* .FALSE.: WIN does not contain the eigenvalues
* .TRUE.: WIN does contain the eigenvalues
*
* RANGE (global input) CHARACTER*1
* = 'A': all eigenvalues will be found.
* = 'V': all eigenvalues in the interval [VL,VU]
* will be found.
* = 'I': the IL-th through IU-th eigenvalues will be found.
*
* N (global input) INTEGER
* Size of the matrix to be tested. (global size)
*
* DESCA (global input) INTEGER array dimension ( DLEN_ )
*
* VL (global input/output ) DOUBLE PRECISION
* If RANGE='V', the lower bound of the interval to be searched
* for eigenvalues. Not referenced if RANGE = 'A' or 'I'.
* If VL > VU, RANGE='V' and WKNOWN = .TRUE., VL is set
* to a random value near an entry in WIN
*
* VU (global input/output ) DOUBLE PRECISION
* If RANGE='V', the upper bound of the interval to be searched
* for eigenvalues. Not referenced if RANGE = 'A' or 'I'.
* If VL > VU, RANGE='V' and WKNOWN = .TRUE., VU is set
* to a random value near an entry in WIN
*
* IL (global input/output ) INTEGER
* If RANGE='I', the index (from smallest to largest) of the
* smallest eigenvalue to be returned. IL >= 1.
* Not referenced if RANGE = 'A' or 'V'.
* If IL < 0, RANGE='I' and WKNOWN = .TRUE., IL is set
* to a random value from 1 to N
*
* IU (global input/output ) INTEGER
* If RANGE='I', the index (from smallest to largest) of the
* largest eigenvalue to be returned. min(IL,N) <= IU <= N.
* Not referenced if RANGE = 'A' or 'V'.
* If IU < 0, RANGE='I' and WKNOWN = .TRUE., IU is set
* to a random value from IL to N
*
* ISEED (global input/output) INTEGER array, dimension (4)
* On entry, the seed of the random number generator; the array
* elements must be between 0 and 4095, and ISEED(4) must be
* odd.
* On exit, the seed is updated.
* ISEED is not touched unless IL, IU, VL or VU are modified.
*
* WIN (global input) DOUBLE PRECISION array, dimension (N)
* If WKNOWN=1, WIN contains the eigenvalues of the matrix.
*
* MAXSIZE (global output) INTEGER
* Workspace required to guarantee that PZHEEVR will return
* orthogonal eigenvectors. IF WKNOWN=0, MAXSIZE is set to a
* a value which guarantees orthogonality no matter what the
* spectrum is. If WKNOWN=1, MAXSIZE is set to a value which
* guarantees orthogonality on a matrix with eigenvalues given
* by WIN.
*
* VECSIZE (global output) INTEGER
* Workspace required to guarantee that PZHEEVR
* will compute eigenvectors.
*
* VALSIZE (global output) INTEGER
* Workspace required to guarantee that PZHEEVR
* will compute eigenvalues.
*
*
* .. Parameters ..
INTEGER CTXT_, MB_
PARAMETER ( CTXT_ = 2, MB_ = 5 )
DOUBLE PRECISION TWENTY
PARAMETER ( TWENTY = 20.0D0 )
* ..
* .. Local Scalars ..
*
INTEGER ILMIN, IUMAX,
$ MQ0, MYCOL, MYIL, MYIU, MYROW, NB, NEIG, NN,
$ NP0, NPCOL, NPROW
DOUBLE PRECISION ANORM, EPS, SAFMIN
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER ICEIL, NUMROC
DOUBLE PRECISION DLARAN, PDLAMCH
EXTERNAL LSAME, ICEIL, NUMROC, DLARAN, PDLAMCH
* ..
* .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, DBLE, INT, MAX
* ..
* .. Executable Statements ..
*
CALL BLACS_GRIDINFO( DESCA( CTXT_ ), NPROW, NPCOL, MYROW, MYCOL )
EPS = PDLAMCH( DESCA( CTXT_ ), 'Precision' )
SAFMIN = PDLAMCH( DESCA( CTXT_ ), 'Safe Minimum' )
NB = DESCA( MB_ )
NN = MAX( N, NB, 2 )
NP0 = NUMROC( NN, NB, 0, 0, NPROW )
VALSIZE = 3 + 5*N + MAX( 12*NN, NB*( NP0+1 ) )
IF( WKNOWN ) THEN
ANORM = SAFMIN / EPS
IF( N.GE.1 )
$ ANORM = MAX( ABS( WIN( 1 ) ), ABS( WIN( N ) ), ANORM )
IF( LSAME( RANGE, 'I' ) ) THEN
IF( IL.LT.0 )
$ IL = INT( DLARAN( ISEED )*DBLE( N ) ) + 1
IF( IU.LT.0 )
$ IU = INT( DLARAN( ISEED )*DBLE( N-IL ) ) + IL
IF( N.EQ.0 )
$ IU = 0
ELSE IF( LSAME( RANGE, 'V' ) ) THEN
IF( VL.GT.VU ) THEN
MYIL = INT( DLARAN( ISEED )*DBLE( N ) ) + 1
MYIU = INT( DLARAN( ISEED )*DBLE( N-MYIL ) ) + MYIL
VL = WIN( MYIL ) - TWENTY*EPS*ABS( WIN( MYIL ) )
VU = WIN( MYIU ) + TWENTY*EPS*ABS( WIN( MYIU ) )
VU = MAX( VU, VL+EPS*TWENTY*ABS( VL )+SAFMIN )
END IF
END IF
*
END IF
IF( LSAME( RANGE, 'V' ) ) THEN
* We do not know how many eigenvalues will be computed
ILMIN = 1
IUMAX = N
ELSE IF( LSAME( RANGE, 'I' ) ) THEN
ILMIN = IL
IUMAX = IU
ELSE IF( LSAME( RANGE, 'A' ) ) THEN
ILMIN = 1
IUMAX = N
END IF
*
NEIG = IUMAX - ILMIN + 1
*
MQ0 = NUMROC( MAX( NEIG, NB, 2 ), NB, 0, 0, NPCOL )
*
VECSIZE = 3 + 5*N + MAX( 18*NN, NP0*MQ0+2*NB*NB ) +
$ (2 + ICEIL( NEIG, NPROW*NPCOL ))*NN
VALSIZE = MAX(3, VALSIZE)
VECSIZE = MAX(3, VECSIZE)
MAXSIZE = VECSIZE
*
RETURN
*
* End of PZLASIZEHEEVR
*
END
|
