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| # Variables: | 44 |
| # Callers: | 1 |
| # Callings: | 1 |
| # Words: | 143 |
| # Keywords: | 95 |
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..
.. Array Arguments ..
..
Purpose
=======
PDLAED0 computes all eigenvalues and corresponding eigenvectors of a
symmetric tridiagonal matrix using the divide and conquer method.
Arguments
=========
N (global input) INTEGER
The order of the tridiagonal matrix T. N >= 0.
D (global input/output) DOUBLE PRECISION array, dimension (N)
On entry, the diagonal elements of the tridiagonal matrix.
On exit, if INFO = 0, the eigenvalues in descending order.
E (global input/output) DOUBLE PRECISION array, dimension (N-1)
On entry, the subdiagonal elements of the tridiagonal matrix.
On exit, E has been destroyed.
Q (local output) DOUBLE PRECISION array,
global dimension (N, N),
local dimension ( LLD_Q, LOCc(JQ+N-1))
Q contains the orthonormal eigenvectors of the symmetric
tridiagonal matrix.
On output, Q is distributed across the P processes in block
cyclic format.
IQ (global input) INTEGER
Q's global row index, which points to the beginning of the
submatrix which is to be operated on.
JQ (global input) INTEGER
Q's global column index, which points to the beginning of
the submatrix which is to be operated on.
DESCQ (global and local input) INTEGER array of dimension DLEN_.
The array descriptor for the distributed matrix Z.
WORK (local workspace ) DOUBLE PRECISION array, dimension (LWORK)
LWORK = 6*N + 2*NP*NQ, with
NP = NUMROC( N, MB_Q, MYROW, IQROW, NPROW )
NQ = NUMROC( N, NB_Q, MYCOL, IQCOL, NPCOL )
IQROW = INDXG2P( IQ, NB_Q, MYROW, RSRC_Q, NPROW )
IQCOL = INDXG2P( JQ, MB_Q, MYCOL, CSRC_Q, NPCOL )
IWORK (local workspace/output) INTEGER array, dimension (LIWORK)
LIWORK = 2 + 7*N + 8*NPCOL
INFO (global output) INTEGER
= 0: successful exit
< 0: If the i-th argument is an array and the j-entry had
an illegal value, then INFO = -(i*100+j), if the i-th
argument is a scalar and had an illegal value, then
INFO = -i.
> 0: The algorithm failed to compute the INFO/(N+1) th
eigenvalue while working on the submatrix lying in
global rows and columns mod(INFO,N+1).
=====================================================================
.. Parameters ..
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001 SUBROUTINE PDLAED0( N , D , E , Q , IQ , JQ , DESCQ , WORK , IWORK , INFO )
002
003 * -- ScaLAPACK auxiliary routine(version 1.7) --
004 * University of Tennessee , Knoxville , Oak Ridge National Laboratory ,
005 * and University of California , Berkeley.
006 * December 31 , 1998
007
008 * .. Scalar Arguments ..
009 INTEGER INFO , IQ , JQ , N
010 INTEGER BLOCK_CYCLIC_2D , DLEN_ , DTYPE_ , CTXT_ , M_ , N_ ,
011 $MB_ , NB_ , RSRC_ , CSRC_ , LLD_
012 PARAMETER( BLOCK_CYCLIC_2D = 1 , DLEN_ = 9 , DTYPE_ = 1 ,
013 $CTXT_ = 2 , M_ = 3 , N_ = 4 , MB_ = 5 , NB_ = 6 ,
014 $RSRC_ = 7 , CSRC_ = 8 , LLD_ = 9 )
015 * ..
016 * .. Local Scalars ..
017 INTEGER I , ID , IDCOL , IDROW , IID , IINFO , IIQ , IM1 , IM2 ,
018 $IPQ , IQCOL , IQROW , J , JJD , JJQ , LDQ , MATSIZ ,
019 $MYCOL , MYROW , N1 , NB , NBL , NBL1 , NPCOL , NPROW ,
020 $SUBPBS , TSUBPBS
021 * ..
022 * .. External Subroutines ..
023 EXTERNAL BLACS_GRIDINFO , DGEBR2D , DGEBS2D , DGERV2D ,
024 $DGESD2D , DSTEQR , INFOG2L , PDLAED1 , PXERBLA
025 * ..
026 * .. External Functions ..
027 * ..
028 * .. Intrinsic Functions ..
029 INTRINSIC ABS , MIN
030 * ..
031 * .. Executable Statements ..
032
033 * This is just to keep ftnchek and toolpack / 1 happy
034 IF( BLOCK_CYCLIC_2D*CSRC_*CTXT_*DLEN_*DTYPE_*LLD_*MB_*M_*NB_*N_*
034  
035 $ RSRC_.LT.0 )RETURN
036
037 * Test the input parameters.
038
039 CALL BLACS_GRIDINFO( DESCQ( CTXT_ ) , NPROW , NPCOL , MYROW , MYCOL )
040 INFO = 0
041 IF( DESCQ( NB_ ).GT.N .OR. N.LT.2 )
041
042 $ INFO = - 1
043 IF( INFO.NE.0 ) THEN
043
044 CALL PXERBLA( DESCQ( CTXT_ ) , 'PDLAED0' , - INFO )
045 RETURN
046 END IF
047
048 NB = DESCQ( NB_ )
049 LDQ = DESCQ( LLD_ )
050 CALL INFOG2L( IQ , JQ , DESCQ , NPROW , NPCOL , MYROW , MYCOL , IIQ , JJQ ,
051 $ IQROW , IQCOL )
052
053 * Determine the size and placement of the submatrices , and save in
054 * the leading elements of IWORK.
055
056 TSUBPBS =( N - 1 ) / NB + 1
057 IWORK( 1 ) = TSUBPBS
058 SUBPBS = 1
059 10 CONTINUE
060 IF( IWORK( SUBPBS ).GT.1 ) THEN
060
061 DO 20 J = SUBPBS , 1 , - 1
061
062 IWORK( 2*J ) =( IWORK( J ) + 1 ) / 2
063 IWORK( 2*J - 1 ) = IWORK( J ) / 2
064 20 CONTINUE
064
065 SUBPBS = 2*SUBPBS
066 GO TO 10
067 END IF
068 DO 30 J = 2 , SUBPBS
068
069 IWORK( J ) = IWORK( J ) + IWORK( J - 1 )
070 30 CONTINUE
071
072 * Divide the matrix into TSUBPBS submatrices of size at most NB
073 * using rank - 1 modifications(cuts).
074
075 DO 40 I = NB + 1 , N , NB
075
076 IM1 = I - 1
077 D( IM1 ) = D( IM1 ) - ABS( E( IM1 ) )
078 D( I ) = D( I ) - ABS( E( IM1 ) )
079 40 CONTINUE
080
081 * Solve each submatrix eigenproblem at the bottom of the divide and
082 * conquer tree. D is the same on each process.
083
084 DO 50 ID = 1 , N , NB
084
085 CALL INFOG2L( IQ - 1 + ID , JQ - 1 + ID , DESCQ , NPROW , NPCOL , MYROW ,
086 $ MYCOL , IID , JJD , IDROW , IDCOL )
087 MATSIZ = MIN( NB , N - ID + 1 )
088 IF( MYROW.EQ.IDROW .AND. MYCOL.EQ.IDCOL ) THEN
088
089 IPQ = IID + ( JJD - 1 )*LDQ
090 CALL DSTEQR( 'I' , MATSIZ , D( ID ) , E( ID ) , Q( IPQ ) , LDQ ,
091 $ WORK , INFO )
092 IF( INFO.NE.0 ) THEN
092
093 CALL PXERBLA( DESCQ( CTXT_ ) , 'DSTEQR' , - INFO )
094 RETURN
095 END IF
096 IF( MYROW.NE.IQROW .OR. MYCOL.NE.IQCOL ) THEN
096
097 CALL DGESD2D( DESCQ( CTXT_ ) , MATSIZ , 1 , D( ID ) , MATSIZ ,
098 $ IQROW , IQCOL )
099 END IF
100 ELSE IF( MYROW.EQ.IQROW .AND. MYCOL.EQ.IQCOL ) THEN
100
101 CALL DGERV2D( DESCQ( CTXT_ ) , MATSIZ , 1 , D( ID ) , MATSIZ ,
102 $ IDROW , IDCOL )
103 END IF
104 50 CONTINUE
105
106 IF( MYROW.EQ.IQROW .AND. MYCOL.EQ.IQCOL ) THEN
106
107 CALL DGEBS2D( DESCQ( CTXT_ ) , 'A' , ' ' , N , 1 , D , N )
108 ELSE
108
109 CALL DGEBR2D( DESCQ( CTXT_ ) , 'A' , ' ' , N , 1 , D , N , IQROW ,
110 $ IQCOL )
111 END IF
112
113 * Successively merge eigensystems of adjacent submatrices
114 * into eigensystem for the corresponding larger matrix.
115
116 * while( SUBPBS > 1 )
117
118 60 CONTINUE
119 IF( SUBPBS.GT.1 ) THEN
119
120 IM2 = SUBPBS - 2
121 DO 80 I = 0 , IM2 , 2
121
122 IF( I.EQ.0 ) THEN
122
123 NBL = IWORK( 2 )
124 NBL1 = IWORK( 1 )
125 IF( NBL1.EQ.0 )
125
126 $ GO TO 70
127 ID = 1
128 MATSIZ = MIN( N , NBL*NB )
129 N1 = NBL1*NB
130 ELSE
130
131 NBL = IWORK( I + 2 ) - IWORK( I )
132 NBL1 = NBL / 2
133 IF( NBL1.EQ.0 )
133
134 $ GO TO 70
135 ID = IWORK( I )*NB + 1
136 MATSIZ = MIN( NB*NBL , N - ID + 1 )
137 N1 = NBL1*NB
138 END IF
139
140 * Merge lower order eigensystems(of size N1 and MATSIZ - N1)
141 * into an eigensystem of size MATSIZ.
142
143 CALL PDLAED1 ( MATSIZ , N1 , D( ID ) , ID , Q , IQ , JQ , DESCQ ,
144 $ E( ID + N1 - 1 ) , WORK , IWORK( SUBPBS + 1 ) , IINFO )
145 IF( IINFO.NE.0 ) THEN
145
146 INFO = IINFO*( N + 1 ) + ID
147 END IF
148
149 70 CONTINUE
150 IWORK( I / 2 + 1 ) = IWORK( I + 2 )
151 80 CONTINUE
152 SUBPBS = SUBPBS / 2
153
154 GO TO 60
155 END IF
156
157 * end while
158
159 90 CONTINUE
160 RETURN
161
162 * End of PDLAED0
163
164 END24
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Variables in Routine PDLAED0()
| Summary Report |
| Data Type | Quantity | Size(byte) |
| INTEGER | 43 | 172 |
| REAL | 1 | 4 |
| TOTAL | 44 | 176 |
List of Variables
INTEGER
| BLOCK_CYCLIC_2D | CSRC_ | CTXT_ | DLEN_ | DTYPE_ |
| I | ID | IDCOL | IDROW | IID |
| IINFO | IIQ | IM1 | IM2 | INFO |
| IPQ | IQ | IQCOL | IQROW | IWORK |
| J | JJD | JJQ | JQ | LDQ |
| LLD_ | M_ | MATSIZ | MB_ | MYCOL |
| MYROW | N | N_ | N1 | NB |
| NB_ | NBL | NBL1 | NPCOL | NPROW |
| RSRC_ | SUBPBS | TSUBPBS | | |
REAL
Variables Dependence Graph
Put the mouse over a right hand side variable to display the corresponding line of the dependence | | - | | - | - | | D | <--- | IM1D( IM1 ) = D( IM1 ) - ABS( E( IM1 ) ){2D( I ) = D( I ) - ABS( E( IM1 ) )}, DD( IM1 ) = D( IM1 ) - ABS( E( IM1 ) ){2D( I ) = D( I ) - ABS( E( IM1 ) )}, ID( I ) = D( I ) - ABS( E( IM1 ) ) |
| I | <--- | IM2DO 80 I = 0, IM2, 2, NDO 40 I = NB + 1, N, NB, NBDO 40 I = NB + 1, N, NB |
| ID | <--- | IWORKID = IWORK( I )*NB + 1, NDO 50 ID = 1, N, NB, NBID = IWORK( I )*NB + 1{2DO 50 ID = 1, N, NB}, IID = IWORK( I )*NB + 1 |
| IM1 | <--- | IIM1 = I - 1 |
| IM2 | <--- | SUBPBSIM2 = SUBPBS - 2 |
| INFO | <--- | IINFOINFO = IINFO*( N+1 ) + ID, NINFO = IINFO*( N+1 ) + ID, IDINFO = IINFO*( N+1 ) + ID |
| IPQ | <--- | IIDIPQ = IID + ( JJD-1 )*LDQ, JJDIPQ = IID + ( JJD-1 )*LDQ, LDQIPQ = IID + ( JJD-1 )*LDQ |
| IWORK | <--- | IWORKIWORK( I / 2+1 ) = IWORK( I+2 ){2IWORK( 2*J ) = ( IWORK( J )+1 ) / 2, 3IWORK( 2*J-1 ) = IWORK( J ) / 2, 4IWORK( J ) = IWORK( J ) + IWORK( J-1 )}, JIWORK( 2*J ) = ( IWORK( J )+1 ) / 2{2IWORK( 2*J-1 ) = IWORK( J ) / 2, 3IWORK( J ) = IWORK( J ) + IWORK( J-1 )}, TSUBPBSIWORK( 1 ) = TSUBPBS, IIWORK( I / 2+1 ) = IWORK( I+2 ) |
| J | <--- | SUBPBSDO 20 J = SUBPBS, 1, -1{2DO 30 J = 2, SUBPBS} |
| LDQ | <--- | LLD_LDQ = DESCQ( LLD_ ) |
| MATSIZ | <--- | NMATSIZ = MIN( N, NBL*NB ){2MATSIZ = MIN( NB*NBL, N-ID+1 ), 3MATSIZ = MIN( NB, N-ID+1 )}, NBMATSIZ = MIN( N, NBL*NB ){2MATSIZ = MIN( NB*NBL, N-ID+1 ), 3MATSIZ = MIN( NB, N-ID+1 )}, NBLMATSIZ = MIN( N, NBL*NB ){2MATSIZ = MIN( NB*NBL, N-ID+1 )}, IDMATSIZ = MIN( NB*NBL, N-ID+1 ){2MATSIZ = MIN( NB, N-ID+1 )} |
| N1 | <--- | NBN1 = NBL1*NB{2N1 = NBL1*NB}, NBL1N1 = NBL1*NB{2N1 = NBL1*NB} |
| NB | <--- | NB_NB = DESCQ( NB_ ) |
| NBL | <--- | IWORKNBL = IWORK( 2 ){2NBL = IWORK( I+2 ) - IWORK( I )}, INBL = IWORK( I+2 ) - IWORK( I ) |
| NBL1 | <--- | IWORKNBL1 = IWORK( 1 ), NBLNBL1 = NBL / 2 |
| SUBPBS | <--- | SUBPBSSUBPBS = SUBPBS / 2{2SUBPBS = 2*SUBPBS} |
| TSUBPBS | <--- | NTSUBPBS = ( N-1 ) / NB + 1, NBTSUBPBS = ( N-1 ) / NB + 1 |
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Analysis elements of the routine PDLAED0()
Put the mouse over each element to display detailed matching information
 Assigned variables |
| | | BLOCK_CYCLIC_2D , CSRC_ , CTXT_ , DLEN_ , DTYPE_ , I , ID , IM1 , IM2 , INFO , IPQ , IWORK , J , LDQ , LLD_ , M_ , MATSIZ , MB_ , N_ , N1 , NB , NB_ , NBL , NBL1 , RSRC_ , SUBPBS , TSUBPBS |
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| Active variables |
| | | BLOCK_CYCLIC_2D , CSRC_ , CTXT_ , D , DESCQ , DLEN_ , DTYPE_ , E , I , ID , IDCOL , IDROW , IID , IINFO , IIQ , IM1 , IM2 , INFO , IPQ , IQ , IQCOL , IQROW , IWORK , J , JJD , JJQ , JQ , LDQ , LLD_ , M_ , MATSIZ , MB_ , MYCOL , MYROW , N , N_ , N1 , NB , NB_ , NBL , NBL1 , NPCOL , NPROW , Q , RSRC_ , SUBPBS , TSUBPBS , WORK |
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| Accessed arrays [ array name : associated index ] |
| |  D | : I , ID , ID , ID , ID , IM1 |
| | DESCQ | : CTXT_ , CTXT_ , CTXT_ , CTXT_ , CTXT_ , CTXT_ , CTXT_ , LLD_ , NB_ , NB_ |
| | E | : ID , ID+N1-1 , IM1 , IM1 |
| | IWORK | : 1 , 1 , 2 , 2*J , 2*J-1 , I / 2+1 , I , I , I+2 , I+2 , J , J , J , J-1 , SUBPBS , SUBPBS+1 |
| | Q | : IPQ |
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| Conditional statements [ statement : associated predicate ] |
| | do | : ( 20 J = SUBPBS , 1 , - 1 ) , ( 30 J = 2 , SUBPBS ) , ( 40 I = NB + 1 , N , NB ) , ( 50 ID = 1 , N , NB ) , ( 80 I = 0 , IM2 , 2 ) |
| | for | : ( the corresponding larger matrix. ) |
| | if | : ( BLOCK_CYCLIC_2D*CSRC_*CTXT_*DLEN_*DTYPE_*LLD_*MB_*M_*NB_*N_* ) , ( (DESCQ( NB_ ).GT.N .OR. N.LT.2 ) ) , ( INFO.NE.0 ) , ( (IWORK( SUBPBS ).GT.1 ) ) , ( MYROW.EQ.IDROW .AND. MYCOL.EQ.IDCOL ) , ( INFO.NE.0 ) , ( MYROW.NE.IQROW .OR. MYCOL.NE.IQCOL ) , ( MYROW.EQ.IQROW .AND. MYCOL.EQ.IQCOL ) , ( MYROW.EQ.IQROW .AND. MYCOL.EQ.IQCOL ) , ( SUBPBS.GT.1 ) , ( I.EQ.0 ) , ( NBL1.EQ.0 ) , ( NBL1.EQ.0 ) , ( IINFO.NE.0 ) |
| | while | : ( SUBPBS > 1 ) |
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| List of variables |
BLOCK_CYCLIC_2D
CSRC_
CTXT_
D
DLEN_
DTYPE_
I
| ID
IDCOL
IDROW
IID
IINFO
IIQ
IM1
IM2
| INFO
IPQ
IQ
IQCOL
IQROW
IWORK
J
JJD
| JJQ
JQ
LDQ
LLD_
M_
MATSIZ
MB_
MYCOL
| MYROW
N
N_
N1
NB
NB_
NBL
NBL1
| NPCOL
NPROW
RSRC_
SUBPBS
TSUBPBS | | close
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BLOCK_CYCLIC_2D
CSRC_
CTXT_
D
DLEN_
DTYPE_
I
ID
IDCOL
IDROW
IID
IINFO
IIQ
IM1
IM2
INFO
IPQ
IQ
IQCOL
IQROW
IWORK
J
JJD
JJQ
JQ
LDQ
LLD_
M_
MATSIZ
MB_
MYCOL
MYROW
N
N_
N1
NB
NB_
NBL
NBL1
NPCOL
NPROW
RSRC_
SUBPBS
TSUBPBS
212
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