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..
.. Array Arguments ..
..
Purpose
=======
PZHEEVX computes selected eigenvalues and, optionally, eigenvectors
of a complex hermitian matrix A by calling the recommended sequence
of ScaLAPACK routines. Eigenvalues/vectors can be selected by
specifying a range of values or a range of indices for the desired
eigenvalues.
Notes
=====
Each global data object is described by an associated description
vector. This vector stores the information required to establish
the mapping between an object element and its corresponding process
and memory location.
Let A be a generic term for any 2D block cyclicly distributed array.
Such a global array has an associated description vector DESCA.
In the following comments, the character _ should be read as
"of the global array".
NOTATION STORED IN EXPLANATION
--------------- -------------- --------------------------------------
DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case,
DTYPE_A = 1.
CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating
the BLACS process grid A is distribu-
ted over. The context itself is glo-
bal, but the handle (the integer
value) may vary.
M_A (global) DESCA( M_ ) The number of rows in the global
array A.
N_A (global) DESCA( N_ ) The number of columns in the global
array A.
MB_A (global) DESCA( MB_ ) The blocking factor used to distribute
the rows of the array.
NB_A (global) DESCA( NB_ ) The blocking factor used to distribute
the columns of the array.
RSRC_A (global) DESCA( RSRC_ ) The process row over which the first
row of the array A is distributed.
CSRC_A (global) DESCA( CSRC_ ) The process column over which the
first column of the array A is
distributed.
LLD_A (local) DESCA( LLD_ ) The leading dimension of the local
array. LLD_A >= MAX(1,LOCr(M_A)).
Let K be the number of rows or columns of a distributed matrix,
and assume that its process grid has dimension p x q.
LOCr( K ) denotes the number of elements of K that a process
would receive if K were distributed over the p processes of its
process column.
Similarly, LOCc( K ) denotes the number of elements of K that a
process would receive if K were distributed over the q processes of
its process row.
The values of LOCr() and LOCc() may be determined via a call to the
ScaLAPACK tool function, NUMROC:
LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ),
LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ).
An upper bound for these quantities may be computed by:
LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A
LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A
PZHEEVX assumes IEEE 754 standard compliant arithmetic. To port
to a system which does not have IEEE 754 arithmetic, modify
the appropriate SLmake.inc file to include the compiler switch
-DNO_IEEE. This switch only affects the compilation of pdlaiect.c.
Arguments
=========
NP = the number of rows local to a given process.
NQ = the number of columns local to a given process.
JOBZ (global input) CHARACTER*1
Specifies whether or not to compute the eigenvectors:
= 'N': Compute eigenvalues only.
= 'V': Compute eigenvalues and eigenvectors.
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.
UPLO (global 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 (global input) INTEGER
The number of rows and columns of the matrix A. N >= 0.
A (local input/workspace) block cyclic COMPLEX*16 array,
global dimension (N, N),
local dimension ( LLD_A, LOCc(JA+N-1) )
On entry, the Hermitian matrix A. If UPLO = 'U', only the
upper triangular part of A is used to define the elements of
the Hermitian matrix. If UPLO = 'L', only the lower
triangular part of A is used to define the elements of the
Hermitian matrix.
On exit, the lower triangle (if UPLO='L') or the upper
triangle (if UPLO='U') of A, including the diagonal, is
destroyed.
IA (global input) INTEGER
A's global row index, which points to the beginning of the
submatrix which is to be operated on.
JA (global input) INTEGER
A's global column index, which points to the beginning of
the submatrix which is to be operated on.
DESCA (global and local input) INTEGER array of dimension DLEN_.
The array descriptor for the distributed matrix A.
If DESCA( CTXT_ ) is incorrect, PZHEEVX cannot guarantee
correct error reporting.
VL (global input) DOUBLE PRECISION
If RANGE='V', the lower bound of the interval to be searched
for eigenvalues. Not referenced if RANGE = 'A' or 'I'.
VU (global input) DOUBLE PRECISION
If RANGE='V', the upper bound of the interval to be searched
for eigenvalues. Not referenced if RANGE = 'A' or 'I'.
IL (global input) 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'.
IU (global input) 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'.
ABSTOL (global input) DOUBLE PRECISION
If JOBZ='V', setting ABSTOL to PDLAMCH( CONTEXT, 'U') yields
the most orthogonal eigenvectors.
The absolute error tolerance for the eigenvalues.
An approximate eigenvalue is accepted as converged
when it is determined to lie in an interval [a,b]
of width less than or equal to
ABSTOL + EPS * max( |a|,|b| ) ,
where EPS is the machine precision. If ABSTOL is less than
or equal to zero, then EPS*norm(T) will be used in its place,
where norm(T) is the 1-norm of the tridiagonal matrix
obtained by reducing A to tridiagonal form.
Eigenvalues will be computed most accurately when ABSTOL is
set to twice the underflow threshold 2*PDLAMCH('S') not zero.
If this routine returns with ((MOD(INFO,2).NE.0) .OR.
(MOD(INFO/8,2).NE.0)), indicating that some eigenvalues or
eigenvectors did not converge, try setting ABSTOL to
2*PDLAMCH('S').
See "Computing Small Singular Values of Bidiagonal Matrices
with Guaranteed High Relative Accuracy," by Demmel and
Kahan, LAPACK Working Note #3.
See "On the correctness of Parallel Bisection in Floating
Point" by Demmel, Dhillon and Ren, LAPACK Working Note #70
M (global output) INTEGER
Total number of eigenvalues found. 0 <= M <= N.
NZ (global output) INTEGER
Total number of eigenvectors computed. 0 <= NZ <= M.
The number of columns of Z that are filled.
If JOBZ .NE. 'V', NZ is not referenced.
If JOBZ .EQ. 'V', NZ = M unless the user supplies
insufficient space and PZHEEVX is not able to detect this
before beginning computation. To get all the eigenvectors
requested, the user must supply both sufficient
space to hold the eigenvectors in Z (M .LE. DESCZ(N_))
and sufficient workspace to compute them. (See LWORK below.)
PZHEEVX is always able to detect insufficient space without
computation unless RANGE .EQ. 'V'.
W (global output) DOUBLE PRECISION array, dimension (N)
On normal exit, the first M entries contain the selected
eigenvalues in ascending order.
ORFAC (global input) DOUBLE PRECISION
Specifies which eigenvectors should be reorthogonalized.
Eigenvectors that correspond to eigenvalues which are within
tol=ORFAC*norm(A) of each other are to be reorthogonalized.
However, if the workspace is insufficient (see LWORK),
tol may be decreased until all eigenvectors to be
reorthogonalized can be stored in one process.
No reorthogonalization will be done if ORFAC equals zero.
A default value of 10^-3 is used if ORFAC is negative.
ORFAC should be identical on all processes.
Z (local output) COMPLEX*16 array,
global dimension (N, N),
local dimension ( LLD_Z, LOCc(JZ+N-1) )
If JOBZ = 'V', then on normal exit the first M columns of Z
contain the orthonormal eigenvectors of the matrix
corresponding to the selected eigenvalues. If an eigenvector
fails to converge, then that column of Z contains the latest
approximation to the eigenvector, and the index of the
eigenvector is returned in IFAIL.
If JOBZ = 'N', then Z is not referenced.
IZ (global input) INTEGER
Z's global row index, which points to the beginning of the
submatrix which is to be operated on.
JZ (global input) INTEGER
Z's global column index, which points to the beginning of
the submatrix which is to be operated on.
DESCZ (global and local input) INTEGER array of dimension DLEN_.
The array descriptor for the distributed matrix Z.
DESCZ( CTXT_ ) must equal DESCA( CTXT_ )
WORK (local workspace/output) COMPLEX*16 array,
dimension (LWORK)
WORK(1) returns workspace adequate workspace to allow
optimal performance.
LWORK (local input) INTEGER
Size of WORK array. If only eigenvalues are requested:
LWORK >= N + MAX( NB * ( NP0 + 1 ), 3 )
If eigenvectors are requested:
LWORK >= N + ( NP0 + MQ0 + NB ) * NB
with NQ0 = NUMROC( NN, NB, 0, 0, NPCOL ).
For optimal performance, greater workspace is needed, i.e.
LWORK >= MAX( LWORK, NHETRD_LWORK )
Where LWORK is as defined above, and
NHETRD_LWORK = N + 2*( ANB+1 )*( 4*NPS+2 ) +
( NPS + 1 ) * NPS
ICTXT = DESCA( CTXT_ )
ANB = PJLAENV( ICTXT, 3, 'PZHETTRD', 'L', 0, 0, 0, 0 )
SQNPC = SQRT( DBLE( NPROW * NPCOL ) )
NPS = MAX( NUMROC( N, 1, 0, 0, SQNPC ), 2*ANB )
NUMROC is a ScaLAPACK tool functions;
PJLAENV is a ScaLAPACK envionmental inquiry function
MYROW, MYCOL, NPROW and NPCOL can be determined by calling
the subroutine BLACS_GRIDINFO.
If LWORK = -1, then LWORK is global input and a workspace
query is assumed; the routine only calculates the
optimal size for all work arrays. Each of these
values is returned in the first entry of the corresponding
work array, and no error message is issued by PXERBLA.
RWORK (local workspace/output) DOUBLE PRECISION array,
dimension max(3,LRWORK)
On return, WORK(1) contains the optimal amount of
workspace required for efficient execution.
if JOBZ='N' RWORK(1) = optimal amount of workspace
required to compute eigenvalues efficiently
if JOBZ='V' RWORK(1) = optimal amount of workspace
required to compute eigenvalues and eigenvectors
efficiently with no guarantee on orthogonality.
If RANGE='V', it is assumed that all eigenvectors
may be required.
LRWORK (local input) INTEGER
Size of RWORK
See below for definitions of variables used to define LRWORK.
If no eigenvectors are requested (JOBZ = 'N') then
LRWORK >= 5 * NN + 4 * N
If eigenvectors are requested (JOBZ = 'V' ) then
the amount of workspace required to guarantee that all
eigenvectors are computed is:
LRWORK >= 4*N + MAX( 5*NN, NP0 * MQ0 ) +
ICEIL( NEIG, NPROW*NPCOL)*NN
The computed eigenvectors may not be orthogonal if the
minimal workspace is supplied and ORFAC is too small.
If you want to guarantee orthogonality (at the cost
of potentially poor performance) you should add
the following to LRWORK:
(CLUSTERSIZE-1)*N
where CLUSTERSIZE is the number of eigenvalues in the
largest cluster, where a cluster is defined as a set of
close eigenvalues: { W(K),...,W(K+CLUSTERSIZE-1) |
W(J+1) <= W(J) + ORFAC*2*norm(A) }
Variable definitions:
NEIG = number of eigenvectors requested
NB = DESCA( MB_ ) = DESCA( NB_ ) =
DESCZ( MB_ ) = DESCZ( NB_ )
NN = MAX( N, NB, 2 )
DESCA( RSRC_ ) = DESCA( NB_ ) = DESCZ( RSRC_ ) =
DESCZ( CSRC_ ) = 0
NP0 = NUMROC( NN, NB, 0, 0, NPROW )
MQ0 = NUMROC( MAX( NEIG, NB, 2 ), NB, 0, 0, NPCOL )
ICEIL( X, Y ) is a ScaLAPACK function returning
ceiling(X/Y)
When LRWORK is too small:
If LRWORK is too small to guarantee orthogonality,
PZHEEVX attempts to maintain orthogonality in
the clusters with the smallest
spacing between the eigenvalues.
If LRWORK is too small to compute all the eigenvectors
requested, no computation is performed and INFO=-25
is returned. Note that when RANGE='V', PZHEEVX does
not know how many eigenvectors are requested until
the eigenvalues are computed. Therefore, when RANGE='V'
and as long as LRWORK is large enough to allow PZHEEVX to
compute the eigenvalues, PZHEEVX will compute the
eigenvalues and as many eigenvectors as it can.
Relationship between workspace, orthogonality & performance:
If CLUSTERSIZE >= N/SQRT(NPROW*NPCOL), then providing
enough space to compute all the eigenvectors
orthogonally will cause serious degradation in
performance. In the limit (i.e. CLUSTERSIZE = N-1)
PZSTEIN will perform no better than ZSTEIN on 1
processor.
For CLUSTERSIZE = N/SQRT(NPROW*NPCOL) reorthogonalizing
all eigenvectors will increase the total execution time
by a factor of 2 or more.
For CLUSTERSIZE > N/SQRT(NPROW*NPCOL) execution time will
grow as the square of the cluster size, all other factors
remaining equal and assuming enough workspace. Less
workspace means less reorthogonalization but faster
execution.
If LRWORK = -1, then LRWORK is global input and a workspace
query is assumed; the routine only calculates the size
required for optimal performance for all work arrays. Each of
these values is returned in the first entry of the
corresponding work arrays, and no error message is issued by
PXERBLA.
IWORK (local workspace) INTEGER array
On return, IWORK(1) contains the amount of integer workspace
required.
LIWORK (local input) INTEGER
size of IWORK
LIWORK >= 6 * NNP
Where:
NNP = MAX( N, NPROW*NPCOL + 1, 4 )
If LIWORK = -1, then LIWORK is global input and a workspace
query is assumed; the routine only calculates the minimum
and optimal size for all work arrays. Each of these
values is returned in the first entry of the corresponding
work array, and no error message is issued by PXERBLA.
IFAIL (global output) INTEGER array, dimension (N)
If JOBZ = 'V', then on normal exit, the first M elements of
IFAIL are zero. If (MOD(INFO,2).NE.0) on exit, then
IFAIL contains the
indices of the eigenvectors that failed to converge.
If JOBZ = 'N', then IFAIL is not referenced.
ICLUSTR (global output) integer array, dimension (2*NPROW*NPCOL)
This array contains indices of eigenvectors corresponding to
a cluster of eigenvalues that could not be reorthogonalized
due to insufficient workspace (see LWORK, ORFAC and INFO).
Eigenvectors corresponding to clusters of eigenvalues indexed
ICLUSTR(2*I-1) to ICLUSTR(2*I), could not be
reorthogonalized due to lack of workspace. Hence the
eigenvectors corresponding to these clusters may not be
orthogonal. ICLUSTR() is a zero terminated array.
(ICLUSTR(2*K).NE.0 .AND. ICLUSTR(2*K+1).EQ.0) if and only if
K is the number of clusters
ICLUSTR is not referenced if JOBZ = 'N'
GAP (global output) DOUBLE PRECISION array,
dimension (NPROW*NPCOL)
This array contains the gap between eigenvalues whose
eigenvectors could not be reorthogonalized. The output
values in this array correspond to the clusters indicated
by the array ICLUSTR. As a result, the dot product between
eigenvectors correspoding to the I^th cluster may be as high
as ( C * n ) / GAP(I) where C is a small constant.
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: if (MOD(INFO,2).NE.0), then one or more eigenvectors
failed to converge. Their indices are stored
in IFAIL. Ensure ABSTOL=2.0*PDLAMCH( 'U' )
Send e-mail to scalapack@cs.utk.edu
if (MOD(INFO/2,2).NE.0),then eigenvectors corresponding
to one or more clusters of eigenvalues could not be
reorthogonalized because of insufficient workspace.
The indices of the clusters are stored in the array
ICLUSTR.
if (MOD(INFO/4,2).NE.0), then space limit prevented
PZHEEVX from computing all of the eigenvectors
between VL and VU. The number of eigenvectors
computed is returned in NZ.
if (MOD(INFO/8,2).NE.0), then PZSTEBZ failed to compute
eigenvalues. Ensure ABSTOL=2.0*PDLAMCH( 'U' )
Send e-mail to scalapack@cs.utk.edu
Alignment requirements
======================
The distributed submatrices A(IA:*, JA:*) and C(IC:IC+M-1,JC:JC+N-1)
must verify some alignment properties, namely the following
expressions should be true:
( MB_A.EQ.NB_A.EQ.MB_Z .AND. IROFFA.EQ.IROFFZ .AND. IROFFA.EQ.0 .AND.
IAROW.EQ.IZROW )
where
IROFFA = MOD( IA-1, MB_A ) and ICOFFA = MOD( JA-1, NB_A ).
=====================================================================
Differences between PZHEEVX and ZHEEVX
======================================
A, LDA -> A, IA, JA, DESCA
Z, LDZ -> Z, IZ, JZ, DESCZ
WORKSPACE needs are larger for PZHEEVX.
LIWORK parameter added
ORFAC, ICLUSTER() and GAP() parameters added
meaning of INFO is changed
Functional differences:
PZHEEVX does not promise orthogonality for eigenvectors associated
with tighly clustered eigenvalues.
PZHEEVX does not reorthogonalize eigenvectors
that are on different processes. The extent of reorthogonalization
is controlled by the input parameter LWORK.
Version 1.4 limitations:
DESCA(MB_) = DESCA(NB_)
DESCA(M_) = DESCZ(M_)
DESCA(N_) = DESCZ(N_)
DESCA(MB_) = DESCZ(MB_)
DESCA(NB_) = DESCZ(NB_)
DESCA(RSRC_) = DESCZ(RSRC_)
.. Parameters ..
|
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001 SUBROUTINE PZHEEVX( JOBZ , RANGE , UPLO , N , A , IA , JA , DESCA , VL ,
002 $VU , IL , IU , ABSTOL , M , NZ , W , ORFAC , Z , IZ ,
003 $JZ , DESCZ , WORK , LWORK , RWORK , LRWORK , IWORK ,
004 $LIWORK , IFAIL , ICLUSTR , GAP , INFO )
005
006 * -- ScaLAPACK routine(version 1.7) --
007 * University of Tennessee , Knoxville , Oak Ridge National Laboratory ,
008 * and University of California , Berkeley.
009 * May 25 , 2001
010
011 * .. Scalar Arguments ..
012 CHARACTER JOBZ , RANGE , UPLO
013 INTEGER IA , IL , INFO , IU , IZ , JA , JZ , LIWORK , LRWORK ,
014 $LWORK , M , N , NZ
015 DOUBLE PRECISION ABSTOL , ORFAC , VL , VU
016 INTEGER BLOCK_CYCLIC_2D , DLEN_ , DTYPE_ , CTXT_ , M_ , N_ ,
017 $MB_ , NB_ , RSRC_ , CSRC_ , LLD_
018 PARAMETER( BLOCK_CYCLIC_2D = 1 , DLEN_ = 9 , DTYPE_ = 1 ,
019 $CTXT_ = 2 , M_ = 3 , N_ = 4 , MB_ = 5 , NB_ = 6 ,
020 $RSRC_ = 7 , CSRC_ = 8 , LLD_ = 9 )
021 DOUBLE PRECISION ZERO , ONE , TEN , FIVE
022 PARAMETER( ZERO = 0.0D + 0 , ONE = 1.0D + 0 , TEN = 10.0D + 0 ,
023 $FIVE = 5.0D + 0 )
024 INTEGER IERREIN , IERRCLS , IERRSPC , IERREBZ
025 PARAMETER( IERREIN = 1 , IERRCLS = 2 , IERRSPC = 4 ,
026 $IERREBZ = 8 )
027 * ..
028 * .. Local Scalars ..
029 LOGICAL ALLEIG , INDEIG , LOWER , LQUERY , QUICKRETURN ,
030 $VALEIG , WANTZ
031 CHARACTER ORDER
032 INTEGER ANB , CSRC_A , I , IAROW , ICOFFA , ICTXT , IINFO ,
033 $INDD , INDD2 , INDE , INDE2 , INDIBL , INDISP ,
034 $INDRWORK , INDTAU , INDWORK , IROFFA , IROFFZ ,
035 $ISCALE , ISIZESTEBZ , ISIZESTEIN , IZROW ,
036 $LALLWORK , LIWMIN , LLRWORK , LLWORK , LRWMIN ,
037 $LRWOPT , LWMIN , LWOPT , MAXEIGS , MB_A , MQ0 ,
038 $MYCOL , MYROW , NB , NB_A , NEIG , NHETRD_LWOPT , NN ,
039 $NNP , NP0 , NPCOL , NPROCS , NPROW , NPS , NQ0 ,
040 $NSPLIT , NZZ , OFFSET , RSRC_A , RSRC_Z , SIZEHEEVX ,
041 $SIZESTEIN , SQNPC
042 DOUBLE PRECISION ABSTLL , ANRM , BIGNUM , EPS , RMAX , RMIN , SAFMIN ,
043 $SIGMA , SMLNUM , VLL , VUU
044 * ..
045 * .. Local Arrays ..
046 INTEGER IDUM1( 4 ) , IDUM2( 4 )
047 * ..
048 * .. External Functions ..
049 LOGICAL LSAME
050 INTEGER ICEIL , INDXG2P , NUMROC , PJLAENV
051 DOUBLE PRECISION PDLAMCH , PZLANHE
052 EXTERNAL LSAME , ICEIL , INDXG2P , NUMROC , PJLAENV ,
053 $PDLAMCH , PZLANHE
054 * ..
055 * .. External Subroutines ..
056 EXTERNAL BLACS_GRIDINFO , CHK1MAT , DGEBR2D , DGEBS2D ,
057 $DLASRT , DSCAL , IGAMN2D , PCHK1MAT , PCHK2MAT ,
058 $PDLARED1D , PDSTEBZ , PXERBLA , PZELGET , PZHENTRD ,
059 $PZLASCL , PZSTEIN , PZUNMTR
060 * ..
061 * .. Intrinsic Functions ..
062 INTRINSIC ABS , DBLE , DCMPLX , ICHAR , INT , MAX , MIN , MOD ,
063 $SQRT
064 * ..
065 * .. Executable Statements ..
066 * This is just to keep ftnchek and toolpack / 1 happy
067 IF( BLOCK_CYCLIC_2D*CSRC_*CTXT_*DLEN_*DTYPE_*LLD_*MB_*M_*NB_*N_*
067  
068 $ RSRC_.LT.0 )RETURN
069
070 QUICKRETURN =( N.EQ.0 )
071
072 * Test the input arguments.
073
074 ICTXT = DESCA( CTXT_ )
075 CALL BLACS_GRIDINFO( ICTXT , NPROW , NPCOL , MYROW , MYCOL )
076 INFO = 0
077
078 WANTZ = LSAME( JOBZ , 'V' )
079 IF( NPROW.EQ. - 1 ) THEN
079
080 INFO = - ( 800 + CTXT_ )
081 ELSE IF( WANTZ ) THEN
081
082 IF( ICTXT.NE.DESCZ( CTXT_ ) ) THEN
082
083 INFO = - ( 2100 + CTXT_ )
084 END IF
085 END IF
086 IF( INFO.EQ.0 ) THEN
086
087 CALL CHK1MAT( N , 4 , N , 4 , IA , JA , DESCA , 8 , INFO )
088 IF( WANTZ )
088
089 $ CALL CHK1MAT( N , 4 , N , 4 , IZ , JZ , DESCZ , 21 , INFO )
090
091 IF( INFO.EQ.0 ) THEN
092
093 * Get machine constants.
094
094
095 SAFMIN = PDLAMCH( ICTXT , 'Safe minimum' )
096 EPS = PDLAMCH( ICTXT , 'Precision' )
097 SMLNUM = SAFMIN / EPS
098 BIGNUM = ONE / SMLNUM
099 RMIN = SQRT( SMLNUM )
100 RMAX = MIN( SQRT( BIGNUM ) , ONE / SQRT( SQRT( SAFMIN ) ) )
101
102 NPROCS = NPROW*NPCOL
103 LOWER = LSAME( UPLO , 'L' )
104 ALLEIG = LSAME( RANGE , 'A' )
105 VALEIG = LSAME( RANGE , 'V' )
106 INDEIG = LSAME( RANGE , 'I' )
107
108 * Set up pointers into the WORK array
109
110 INDTAU = 1
111 INDWORK = INDTAU + N
112 LLWORK = LWORK - INDWORK + 1
113
114 * Set up pointers into the RWORK array
115
116 INDE = 1
117 INDD = INDE + N
118 INDD2 = INDD + N
119 INDE2 = INDD2 + N
120 INDRWORK = INDE2 + N
121 LLRWORK = LRWORK - INDRWORK + 1
122
123 * Set up pointers into the IWORK array
124
125 ISIZESTEIN = 3*N + NPROCS + 1
126 ISIZESTEBZ = MAX( 4*N , 14 , NPROCS )
127 INDIBL =( MAX( ISIZESTEIN , ISIZESTEBZ ) ) + 1
128 INDISP = INDIBL + N
129
130 * Compute the total amount of space needed
131
132 LQUERY = .FALSE.
133 IF( LWORK.EQ. - 1 .OR. LIWORK.EQ. - 1 .OR. LRWORK.EQ. - 1 )
133
134 $ LQUERY = .TRUE.
135
136 NNP = MAX( N , NPROCS + 1 , 4 )
137 LIWMIN = 6*NNP
138
139 NPROCS = NPROW*NPCOL
140 NB_A = DESCA( NB_ )
141 MB_A = DESCA( MB_ )
142 NB = NB_A
143 NN = MAX( N , NB , 2 )
144
145 RSRC_A = DESCA( RSRC_ )
146 CSRC_A = DESCA( CSRC_ )
147 IROFFA = MOD( IA - 1 , MB_A )
148 ICOFFA = MOD( JA - 1 , NB_A )
149 IAROW = INDXG2P( 1 , NB_A , MYROW , RSRC_A , NPROW )
150 NP0 = NUMROC( N + IROFFA , NB , 0 , 0 , NPROW )
151 MQ0 = NUMROC( N + ICOFFA , NB , 0 , 0 , NPCOL )
152 IF( WANTZ ) THEN
152
153 RSRC_Z = DESCZ( RSRC_ )
154 IROFFZ = MOD( IZ - 1 , MB_A )
155 IZROW = INDXG2P( 1 , NB_A , MYROW , RSRC_Z , NPROW )
156 END IF
157
158 IF(( .NOT.WANTZ ) .OR.( VALEIG .AND.( .NOT.LQUERY ) ) )
158
159 $ THEN
160 LWMIN = N + MAX( NB*( NP0 + 1 ) , 3 )
161 LWOPT = LWMIN
162 LRWMIN = 5*NN + 4*N
163 IF( WANTZ ) THEN
163
164 MQ0 = NUMROC( MAX( N , NB , 2 ) , NB , 0 , 0 , NPCOL )
165 LRWOPT = 4*N + MAX( 5*NN , NP0*MQ0 ) +
166 $ ICEIL( N , NPROW*NPCOL )*NN
167 ELSE
167
168 LRWOPT = LRWMIN
169 END IF
170 NEIG = 0
171 ELSE
171
172 IF( ALLEIG .OR. VALEIG ) THEN
172
173 NEIG = N
174 ELSE IF( INDEIG ) THEN
174
175 NEIG = IU - IL + 1
176 END IF
177 MQ0 = NUMROC( MAX( NEIG , NB , 2 ) , NB , 0 , 0 , NPCOL )
178 NQ0 = NUMROC( NN , NB , 0 , 0 , NPCOL )
179 LWMIN = N + ( NP0 + NQ0 + NB )*NB
180 LRWMIN = 4*N + MAX( 5*NN , NP0*MQ0 ) +
181 $ ICEIL( NEIG , NPROW*NPCOL )*NN
182 LRWOPT = LRWMIN
183 LWOPT = LWMIN
184
185 END IF
186
187 * Compute how much workspace is needed to use the
188 * new TRD code
189
190 ANB = PJLAENV( ICTXT , 3 , 'PZHETTRD' , 'L' , 0 , 0 , 0 , 0 )
191 SQNPC = INT( SQRT( DBLE( NPROW*NPCOL ) ) )
192 NPS = MAX( NUMROC( N , 1 , 0 , 0 , SQNPC ) , 2*ANB )
193 NHETRD_LWOPT = 2*( ANB + 1 )*( 4*NPS + 2 ) + ( NPS + 2 )*NPS
194 LWOPT = MAX( LWOPT , N + NHETRD_LWOPT )
195
196 END IF
197 IF( INFO.EQ.0 ) THEN
197
198 IF( MYROW.EQ.0 .AND. MYCOL.EQ.0 ) THEN
198
199 RWORK( 1 ) = ABSTOL
200 IF( VALEIG ) THEN
200
201 RWORK( 2 ) = VL
202 RWORK( 3 ) = VU
203 ELSE
203
204 RWORK( 2 ) = ZERO
205 RWORK( 3 ) = ZERO
206 END IF
207 CALL DGEBS2D( ICTXT , 'ALL' , ' ' , 3 , 1 , RWORK , 3 )
208 ELSE
208
209 CALL DGEBR2D( ICTXT , 'ALL' , ' ' , 3 , 1 , RWORK , 3 , 0 , 0 )
210 END IF
211 IF( .NOT.( WANTZ .OR. LSAME( JOBZ , 'N' ) ) ) THEN
211
212 INFO = - 1
213 ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN
213
214 INFO = - 2
215 ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO , 'U' ) ) ) THEN
215
216 INFO = - 3
217 ELSE IF( VALEIG .AND. N.GT.0 .AND. VU.LE.VL ) THEN
217
218 INFO = - 10
219 ELSE IF( INDEIG .AND.( IL.LT.1 .OR. IL.GT.MAX( 1 , N ) ) )
219
220 $ THEN
221 INFO = - 11
222 ELSE IF( INDEIG .AND.( IU.LT.MIN( N , IL ) .OR. IU.GT.N ) )
222
223 $ THEN
224 INFO = - 12
225 ELSE IF( LWORK.LT.LWMIN .AND. LWORK.NE. - 1 ) THEN
225
226 INFO = - 23
227 ELSE IF( LRWORK.LT.LRWMIN .AND. LRWORK.NE. - 1 ) THEN
227
228 INFO = - 25
229 ELSE IF( LIWORK.LT.LIWMIN .AND. LIWORK.NE. - 1 ) THEN
229
230 INFO = - 27
231 ELSE IF( VALEIG .AND.( ABS( RWORK( 2 ) - VL ).GT.FIVE*EPS*
231
232 $ ABS( VL ) ) ) THEN
233 INFO = - 9
234 ELSE IF( VALEIG .AND.( ABS( RWORK( 3 ) - VU ).GT.FIVE*EPS*
234
235 $ ABS( VU ) ) ) THEN
236 INFO = - 10
237 ELSE IF( ABS( RWORK( 1 ) - ABSTOL ).GT.FIVE*EPS*
237
238 $ ABS( ABSTOL ) ) THEN
239 INFO = - 13
240 ELSE IF( IROFFA.NE.0 ) THEN
240
241 INFO = - 6
242 ELSE IF( DESCA( MB_ ).NE.DESCA( NB_ ) ) THEN
242
243 INFO = - ( 800 + NB_ )
244 END IF
245 IF( WANTZ ) THEN
245
246 IF( IROFFA.NE.IROFFZ ) THEN
246
247 INFO = - 19
248 ELSE IF( IAROW.NE.IZROW ) THEN
248
249 INFO = - 19
250 ELSE IF( DESCA( M_ ).NE.DESCZ( M_ ) ) THEN
250
251 INFO = - ( 2100 + M_ )
252 ELSE IF( DESCA( N_ ).NE.DESCZ( N_ ) ) THEN
252
253 INFO = - ( 2100 + N_ )
254 ELSE IF( DESCA( MB_ ).NE.DESCZ( MB_ ) ) THEN
254
255 INFO = - ( 2100 + MB_ )
256 ELSE IF( DESCA( NB_ ).NE.DESCZ( NB_ ) ) THEN
256
257 INFO = - ( 2100 + NB_ )
258 ELSE IF( DESCA( RSRC_ ).NE.DESCZ( RSRC_ ) ) THEN
258
259 INFO = - ( 2100 + RSRC_ )
260 ELSE IF( DESCA( CSRC_ ).NE.DESCZ( CSRC_ ) ) THEN
260
261 INFO = - ( 2100 + CSRC_ )
262 ELSE IF( ICTXT.NE.DESCZ( CTXT_ ) ) THEN
262
263 INFO = - ( 2100 + CTXT_ )
264 END IF
265 END IF
266 END IF
267 IF( WANTZ ) THEN
267
268 IDUM1( 1 ) = ICHAR( 'V' )
269 ELSE
269
270 IDUM1( 1 ) = ICHAR( 'N' )
271 END IF
272 IDUM2( 1 ) = 1
273 IF( LOWER ) THEN
273
274 IDUM1( 2 ) = ICHAR( 'L' )
275 ELSE
275
276 IDUM1( 2 ) = ICHAR( 'U' )
277 END IF
278 IDUM2( 2 ) = 2
279 IF( ALLEIG ) THEN
279
280 IDUM1( 3 ) = ICHAR( 'A' )
281 ELSE IF( INDEIG ) THEN
281
282 IDUM1( 3 ) = ICHAR( 'I' )
283 ELSE
283
284 IDUM1( 3 ) = ICHAR( 'V' )
285 END IF
286 IDUM2( 3 ) = 3
287 IF( LQUERY ) THEN
287
288 IDUM1( 4 ) = - 1
289 ELSE
289
290 IDUM1( 4 ) = 1
291 END IF
292 IDUM2( 4 ) = 4
293 IF( WANTZ ) THEN
293
294 CALL PCHK2MAT( N , 4 , N , 4 , IA , JA , DESCA , 8 , N , 4 , N , 4 , IZ ,
295 $ JZ , DESCZ , 21 , 4 , IDUM1 , IDUM2 , INFO )
296 ELSE
296
297 CALL PCHK1MAT( N , 4 , N , 4 , IA , JA , DESCA , 8 , 4 , IDUM1 ,
298 $ IDUM2 , INFO )
299 END IF
300 WORK( 1 ) = DCMPLX( LWOPT )
301 RWORK( 1 ) = DBLE( LRWOPT )
302 IWORK( 1 ) = LIWMIN
303 END IF
304
305 IF( INFO.NE.0 ) THEN
305
306 CALL PXERBLA( ICTXT , 'PZHEEVX' , - INFO )
307 RETURN
308 ELSE IF( LQUERY ) THEN
308
309 RETURN
310 END IF
311
312 * Quick return if possible
313
314 IF( QUICKRETURN ) THEN
314
315 IF( WANTZ ) THEN
315
316 NZ = 0
317 ICLUSTR( 1 ) = 0
318 END IF
319 M = 0
320 WORK( 1 ) = DCMPLX( LWOPT )
321 RWORK( 1 ) = DBLE( LRWMIN )
322 IWORK( 1 ) = LIWMIN
323 RETURN
324 END IF
325
326 * Scale matrix to allowable range , if necessary.
327
328 ABSTLL = ABSTOL
329 ISCALE = 0
330 IF( VALEIG ) THEN
330
331 VLL = VL
332 VUU = VU
333 ELSE
333
334 VLL = ZERO
335 VUU = ZERO
336 END IF
337
338 ANRM = PZLANHE( 'M' , UPLO , N , A , IA , JA , DESCA ,
339 $ RWORK( INDRWORK ) )
340
341 IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
341
342 ISCALE = 1
343 SIGMA = RMIN / ANRM
344 ANRM = ANRM*SIGMA
345 ELSE IF( ANRM.GT.RMAX ) THEN
345
346 ISCALE = 1
347 SIGMA = RMAX / ANRM
348 ANRM = ANRM*SIGMA
349 END IF
350
351 IF( ISCALE.EQ.1 ) THEN
351
352 CALL PZLASCL ( UPLO , ONE , SIGMA , N , N , A , IA , JA , DESCA , IINFO )
353 IF( ABSTOL.GT.0 )
353
354 $ ABSTLL = ABSTOL*SIGMA
355 IF( VALEIG ) THEN
355
356 VLL = VL*SIGMA
357 VUU = VU*SIGMA
358 IF( VUU.EQ.VLL ) THEN
358
359 VUU = VUU + 2*MAX( ABS( VUU )*EPS , SAFMIN )
360 END IF
361 END IF
362 END IF
363
364 * Call PZHENTRD to reduce Hermitian matrix to tridiagonal form.
365
366 LALLWORK = LLRWORK
367
368 CALL PZHENTRD ( UPLO , N , A , IA , JA , DESCA , RWORK( INDD ) ,
369 $ RWORK( INDE ) , WORK( INDTAU ) , WORK( INDWORK ) ,
370 $ LLWORK , RWORK( INDRWORK ) , LLRWORK , IINFO )
371
372 * Copy the values of D , E to all processes
373
374 * Here PxLARED1D is used to redistribute the tridiagonal matrix.
375 * PxLARED1D , however , doesn't yet work with arbritary matrix
376 * distributions so we have PxELGET as a backup.
377
378 OFFSET = 0
379 IF( IA.EQ.1 .AND. JA.EQ.1 .AND. RSRC_A.EQ.0 .AND. CSRC_A.EQ.0 )
379
380 $ THEN
381 CALL PDLARED1D ( N , IA , JA , DESCA , RWORK( INDD ) ,
382 $ RWORK( INDD2 ) , RWORK( INDRWORK ) , LLRWORK )
383
384 CALL PDLARED1D ( N , IA , JA , DESCA , RWORK( INDE ) ,
385 $ RWORK( INDE2 ) , RWORK( INDRWORK ) , LLRWORK )
386 IF( .NOT.LOWER )
386
387 $ OFFSET = 1
388 ELSE
388
389 DO 10 I = 1 , N
389
390 CALL PZELGET( 'A' , ' ' , WORK( INDD2 + I - 1 ) , A , I + IA - 1 ,
391 $ I + JA - 1 , DESCA )
392 RWORK( INDD2 + I - 1 ) = DBLE( WORK( INDD2 + I - 1 ) )
393 10 CONTINUE
393
394 IF( LSAME( UPLO , 'U' ) ) THEN
394
395 DO 20 I = 1 , N - 1
395
396 CALL PZELGET( 'A' , ' ' , WORK( INDE2 + I - 1 ) , A , I + IA - 1 ,
397 $ I + JA , DESCA )
398 RWORK( INDE2 + I - 1 ) = DBLE( WORK( INDE2 + I - 1 ) )
399 20 CONTINUE
399
400 ELSE
400
401 DO 30 I = 1 , N - 1
401
402 CALL PZELGET( 'A' , ' ' , WORK( INDE2 + I - 1 ) , A , I + IA ,
403 $ I + JA - 1 , DESCA )
404 RWORK( INDE2 + I - 1 ) = DBLE( WORK( INDE2 + I - 1 ) )
405 30 CONTINUE
405
406 END IF
407 END IF
408
409 * Call PDSTEBZ and , if eigenvectors are desired , PZSTEIN.
410
411 IF( WANTZ ) THEN
411
412 ORDER = 'B'
413 ELSE
413
414 ORDER = 'E'
415 END IF
416
417 CALL PDSTEBZ ( ICTXT , RANGE , ORDER , N , VLL , VUU , IL , IU , ABSTLL ,
418 $ RWORK( INDD2 ) , RWORK( INDE2 + OFFSET ) , M , NSPLIT , W ,
419 $ IWORK( INDIBL ) , IWORK( INDISP ) , RWORK( INDRWORK ) ,
420 $ LLRWORK , IWORK( 1 ) , ISIZESTEBZ , IINFO )
421
422 * IF PDSTEBZ fails , the error propogates to INFO , but
423 * we do not propogate the eigenvalue(s) which failed because :
424 * 1) This should never happen if the user specifies
425 * ABSTOL = 2 * PDLAMCH( 'U' )
426 * 2) PDSTEIN will confirm / deny whether the eigenvalues are
427 * close enough.
428
429 IF( IINFO.NE.0 ) THEN
429
430 INFO = INFO + IERREBZ
431 DO 40 I = 1 , M
431
432 IWORK( INDIBL + I - 1 ) = ABS( IWORK( INDIBL + I - 1 ) )
433 40 CONTINUE
433
434 END IF
435 IF( WANTZ ) THEN
436
436
437 IF( VALEIG ) THEN
438
439 * Compute the maximum number of eigenvalues that we can
440 * compute in the
441 * workspace that we have , and that we can store in Z.
442
443 * Loop through the possibilities looking for the largest
444 * NZ that we can feed to PZSTEIN and PZUNMTR
445
446 * Since all processes must end up with the same value
447 * of NZ , we first compute the minimum of LALLWORK
448
448
449 CALL IGAMN2D( ICTXT , 'A' , ' ' , 1 , 1 , LALLWORK , 1 , 1 , 1 , - 1 ,
450 $ - 1 , - 1 )
451
452 MAXEIGS = DESCZ( N_ )
453
454 DO 50 NZ = MIN( MAXEIGS , M ) , 0 , - 1
454
455 MQ0 = NUMROC( NZ , NB , 0 , 0 , NPCOL )
456 SIZESTEIN = ICEIL( NZ , NPROCS )*N + MAX( 5*N , NP0*MQ0 )
457 SIZEHEEVX = SIZESTEIN
458 IF( SIZEHEEVX.LE.LALLWORK )
458
459 $ GO TO 60
460 50 CONTINUE
461 60 CONTINUE
462 ELSE
462
463 NZ = M
464 END IF
465 NZ = MAX( NZ , 0 )
466 IF( NZ.NE.M ) THEN
466
467 INFO = INFO + IERRSPC
468
469 DO 70 I = 1 , M
469
470 IFAIL( I ) = 0
471 70 CONTINUE
472
473 * The following code handles a rare special case
474 * - NZ .NE. M means that we don't have enough room to store
475 * all the vectors.
476 * - NSPLIT .GT. 1 means that the matrix split
477 * In this case , we cannot simply take the first NZ eigenvalues
478 * because PDSTEBZ sorts the eigenvalues by block when
479 * a split occurs. So , we have to make another call to
480 * PDSTEBZ with a new upper limit - VUU.
481
481
482 IF( NSPLIT.GT.1 ) THEN
482
483 CALL DLASRT( 'I' , M , W , IINFO )
484 NZZ = 0
485 IF( NZ.GT.0 ) THEN
486
486
487 VUU = W( NZ ) - TEN*( EPS*ANRM + SAFMIN )
488 IF( VLL.GE.VUU ) THEN
488
489 NZZ = 0
490 ELSE
490
491 CALL PDSTEBZ ( ICTXT , RANGE , ORDER , N , VLL , VUU , IL ,
492 $ IU , ABSTLL , RWORK( INDD2 ) ,
493 $ RWORK( INDE2 + OFFSET ) , NZZ , NSPLIT ,
494 $ W , IWORK( INDIBL ) , IWORK( INDISP ) ,
495 $ RWORK( INDRWORK ) , LLRWORK ,
496 $ IWORK( 1 ) , ISIZESTEBZ , IINFO )
497 END IF
498
499 IF( MOD( INFO / IERREBZ , 1 ).EQ.0 ) THEN
499
500 IF( NZZ.GT.NZ .OR. IINFO.NE.0 ) THEN
500
501 INFO = INFO + IERREBZ
502 END IF
503 END IF
504 END IF
505 NZ = MIN( NZ , NZZ )
506
507 END IF
508 END IF
509 CALL PZSTEIN ( N , RWORK( INDD2 ) , RWORK( INDE2 + OFFSET ) , NZ , W ,
510 $IWORK( INDIBL ) , IWORK( INDISP ) , ORFAC , Z , IZ ,
511 $JZ , DESCZ , RWORK( INDRWORK ) , LALLWORK ,
512 $IWORK( 1 ) , ISIZESTEIN , IFAIL , ICLUSTR , GAP ,
513 $IINFO )
514
515 IF( IINFO.GE.NZ + 1 )
515
516 $ INFO = INFO + IERRCLS
517 IF( MOD( IINFO , NZ + 1 ).NE.0 )
517
518 $ INFO = INFO + IERREIN
519
520 * Z = Q * Z
521
522 IF( NZ.GT.0 ) THEN
522
523 CALL PZUNMTR ( 'L' , UPLO , 'N' , N , NZ , A , IA , JA , DESCA ,
524 $ WORK( INDTAU ) , Z , IZ , JZ , DESCZ ,
525 $ WORK( INDWORK ) , LLWORK , IINFO )
526 END IF
527
528 END IF
529
530 * If matrix was scaled , then rescale eigenvalues appropriately.
531
532 IF( ISCALE.EQ.1 ) THEN
532
533 CALL DSCAL( M , ONE / SIGMA , W , 1 )
534 END IF
535
536 WORK( 1 ) = DCMPLX( LWOPT )
537 RWORK( 1 ) = DBLE( LRWOPT )
538 IWORK( 1 ) = LIWMIN
539
540 RETURN
541
542 * End of PZHEEVX
543
544 END69
101
|
|
Variables in Routine PZHEEVX()
| Summary Report |
| Data Type | Quantity | Size(byte) |
| CHARACTER | 4 | 4 |
| DOUBLE PRECISION | 21 | 84 |
| INTEGER | 92 | 396 |
| LOGICAL | 8 | 8 |
| REAL | 2 | 8 |
| TOTAL | 127 | 500 |
List of Variables
CHARACTER
DOUBLE PRECISION
| ABSTLL | ABSTOL | ANRM | BIGNUM | EPS |
| FIVE | ONE | ORFAC | PDLAMCH | PZLANHE |
| RMAX | RMIN | SAFMIN | SIGMA | SMLNUM |
| TEN | VL | VLL | VU | VUU |
| ZERO | | | | |
INTEGER
| ANB | BLOCK_CYCLIC_2D | CSRC_ | CSRC_A | CTXT_ |
| DLEN_ | DTYPE_ | I | IA | IAROW |
| ICEIL | ICLUSTR | ICOFFA | ICTXT | IDUM1( 4 ) |
| IDUM2( 4 ) | IERRCLS | IERREBZ | IERREIN | IERRSPC |
| IFAIL | IINFO | IL | INDD | INDD2 |
| INDE | INDE2 | INDIBL | INDISP | INDRWORK |
| INDTAU | INDWORK | INDXG2P | INFO | IROFFA |
| IROFFZ | ISCALE | ISIZESTEBZ | ISIZESTEIN | IU |
| IWORK | IZ | IZROW | JA | JZ |
| LALLWORK | LIWMIN | LIWORK | LLD_ | LLRWORK |
| LLWORK | LRWMIN | LRWOPT | LRWORK | LWMIN |
| LWOPT | LWORK | M | M_ | MAXEIGS |
| MB_ | MB_A | MQ0 | MYCOL | MYROW |
| N | N_ | NB | NB_ | NB_A |
| NEIG | NHETRD_LWOPT | NN | NNP | NP0 |
| NPCOL | NPROCS | NPROW | NPS | NQ0 |
| NSPLIT | NUMROC | NZ | NZZ | OFFSET |
| PJLAENV | RSRC_ | RSRC_A | RSRC_Z | SIZEHEEVX |
| SIZESTEIN | SQNPC | | | |
LOGICAL
| ALLEIG | INDEIG | LOWER | LQUERY | LSAME |
| QUICKRETURN | VALEIG | WANTZ | | |
REAL
Variables Dependence Graph
Put the mouse over a right hand side variable to display the corresponding line of the dependence | | - | | - | - | | ABSTLL | <--- | ABSTOLABSTLL = ABSTOL |
| ALLEIG | <--- | RANGEALLEIG = LSAME( RANGE, 'A' ), LSAMEALLEIG = LSAME( RANGE, 'A' ) |
| ANB | <--- | PJLAENVANB = PJLAENV( ICTXT, 3, 'PZHETTRD', 'L', 0, 0, 0, 0 ), ICTXTANB = PJLAENV( ICTXT, 3, 'PZHETTRD', 'L', 0, 0, 0, 0 ) |
| ANRM | <--- | PZLANHEANRM = PZLANHE( 'M', UPLO, N, A, IA, JA, DESCA,, RWORKANRM = PZLANHE( 'M', UPLO, N, A, IA, JA, DESCA,, SIGMAANRM = ANRM*SIGMA{2ANRM = ANRM*SIGMA}, UPLOANRM = PZLANHE( 'M', UPLO, N, A, IA, JA, DESCA,, IAANRM = PZLANHE( 'M', UPLO, N, A, IA, JA, DESCA,, INDRWORKANRM = PZLANHE( 'M', UPLO, N, A, IA, JA, DESCA,, ANRMANRM = ANRM*SIGMA{2ANRM = ANRM*SIGMA}, JAANRM = PZLANHE( 'M', UPLO, N, A, IA, JA, DESCA,, MANRM = PZLANHE( 'M', UPLO, N, A, IA, JA, DESCA,, NANRM = PZLANHE( 'M', UPLO, N, A, IA, JA, DESCA, |
| BIGNUM | <--- | SMLNUMBIGNUM = ONE / SMLNUM, ONEBIGNUM = ONE / SMLNUM |
| CSRC_A | <--- | CSRC_CSRC_A = DESCA( CSRC_ ) |
| EPS | <--- | PDLAMCHEPS = PDLAMCH( ICTXT, 'Precision' ), ICTXTEPS = PDLAMCH( ICTXT, 'Precision' ) |
| I | <--- | MDO 40 I = 1, M{2DO 70 I = 1, M}, NDO 10 I = 1, N{2DO 20 I = 1, N - 1, 3DO 30 I = 1, N - 1} |
| IAROW | <--- | RSRC_AIAROW = INDXG2P( 1, NB_A, MYROW, RSRC_A, NPROW ), INDXG2PIAROW = INDXG2P( 1, NB_A, MYROW, RSRC_A, NPROW ), MYROWIAROW = INDXG2P( 1, NB_A, MYROW, RSRC_A, NPROW ), NB_AIAROW = INDXG2P( 1, NB_A, MYROW, RSRC_A, NPROW ), NPROWIAROW = INDXG2P( 1, NB_A, MYROW, RSRC_A, NPROW ) |
| ICOFFA | <--- | JAICOFFA = MOD( JA-1, NB_A ), NB_AICOFFA = MOD( JA-1, NB_A ) |
| ICTXT | <--- | CTXT_ICTXT = DESCA( CTXT_ ) |
| IDUM1 | <--- | IIDUM1( 3 ) = ICHAR( 'I' ), NIDUM1( 1 ) = ICHAR( 'N' ) |
| INDD | <--- | INDEINDD = INDE + N, NINDD = INDE + N |
| INDD2 | <--- | INDDINDD2 = INDD + N, NINDD2 = INDD + N |
| INDE2 | <--- | INDD2INDE2 = INDD2 + N, NINDE2 = INDD2 + N |
| INDEIG | <--- | RANGEINDEIG = LSAME( RANGE, 'I' ), IINDEIG = LSAME( RANGE, 'I' ), LSAMEINDEIG = LSAME( RANGE, 'I' ) |
| INDIBL | <--- | ISIZESTEBZINDIBL = ( MAX( ISIZESTEIN, ISIZESTEBZ ) ) + 1, ISIZESTEININDIBL = ( MAX( ISIZESTEIN, ISIZESTEBZ ) ) + 1 |
| INDISP | <--- | INDIBLINDISP = INDIBL + N, NINDISP = INDIBL + N |
| INDRWORK | <--- | INDE2INDRWORK = INDE2 + N, NINDRWORK = INDE2 + N |
| INDWORK | <--- | INDTAUINDWORK = INDTAU + N, NINDWORK = INDTAU + N |
| INFO | <--- | CTXT_INFO = -( 2100+CTXT_ ){2INFO = -( 800+CTXT_ ), 3INFO = -( 2100+CTXT_ )}, RSRC_INFO = -( 2100+RSRC_ ), IERREBZINFO = INFO + IERREBZ{2INFO = INFO + IERREBZ}, IERRSPCINFO = INFO + IERRSPC, INFOINFO = INFO + IERREBZ{2INFO = INFO + IERRSPC, 3INFO = INFO + IERREBZ}, M_INFO = -( 2100+M_ ), MB_INFO = -( 2100+MB_ ), N_INFO = -( 2100+N_ ), CSRC_INFO = -( 2100+CSRC_ ), NB_INFO = -( 800+NB_ ){2INFO = -( 2100+NB_ )} |
| IROFFA | <--- | IAIROFFA = MOD( IA-1, MB_A ), MB_AIROFFA = MOD( IA-1, MB_A ) |
| IROFFZ | <--- | IZIROFFZ = MOD( IZ-1, MB_A ), MB_AIROFFZ = MOD( IZ-1, MB_A ) |
| ISIZESTEBZ | <--- | NISIZESTEBZ = MAX( 4*N, 14, NPROCS ), NPROCSISIZESTEBZ = MAX( 4*N, 14, NPROCS ) |
| ISIZESTEIN | <--- | NISIZESTEIN = 3*N + NPROCS + 1, NPROCSISIZESTEIN = 3*N + NPROCS + 1 |
| IWORK | <--- | IIWORK( INDIBL+I-1 ) = ABS( IWORK( INDIBL+I-1 ) ), INDIBLIWORK( INDIBL+I-1 ) = ABS( IWORK( INDIBL+I-1 ) ), IWORKIWORK( INDIBL+I-1 ) = ABS( IWORK( INDIBL+I-1 ) ), LIWMINIWORK( 1 ) = LIWMIN{2IWORK( 1 ) = LIWMIN, 3IWORK( 1 ) = LIWMIN} |
| IZROW | <--- | RSRC_ZIZROW = INDXG2P( 1, NB_A, MYROW, RSRC_Z, NPROW ), INDXG2PIZROW = INDXG2P( 1, NB_A, MYROW, RSRC_Z, NPROW ), MYROWIZROW = INDXG2P( 1, NB_A, MYROW, RSRC_Z, NPROW ), NB_AIZROW = INDXG2P( 1, NB_A, MYROW, RSRC_Z, NPROW ), NPROWIZROW = INDXG2P( 1, NB_A, MYROW, RSRC_Z, NPROW ) |
| LALLWORK | <--- | LLRWORKLALLWORK = LLRWORK |
| LIWMIN | <--- | NNPLIWMIN = 6*NNP |
| LLRWORK | <--- | INDRWORKLLRWORK = LRWORK - INDRWORK + 1, LRWORKLLRWORK = LRWORK - INDRWORK + 1 |
| LLWORK | <--- | INDWORKLLWORK = LWORK - INDWORK + 1, LWORKLLWORK = LWORK - INDWORK + 1 |
| LOWER | <--- | UPLOLOWER = LSAME( UPLO, 'L' ), LSAMELOWER = LSAME( UPLO, 'L' ) |
| LRWMIN | <--- | ICEILLRWMIN = 4*N + MAX( 5*NN, NP0*MQ0 ) +, MQ0LRWMIN = 4*N + MAX( 5*NN, NP0*MQ0 ) +, NLRWMIN = 5*NN + 4*N{2LRWMIN = 4*N + MAX( 5*NN, NP0*MQ0 ) +}, NEIGLRWMIN = 4*N + MAX( 5*NN, NP0*MQ0 ) +, NNLRWMIN = 5*NN + 4*N{2LRWMIN = 4*N + MAX( 5*NN, NP0*MQ0 ) +}, NP0LRWMIN = 4*N + MAX( 5*NN, NP0*MQ0 ) +, NPCOLLRWMIN = 4*N + MAX( 5*NN, NP0*MQ0 ) +, NPROWLRWMIN = 4*N + MAX( 5*NN, NP0*MQ0 ) + |
| LRWOPT | <--- | ICEILLRWOPT = 4*N + MAX( 5*NN, NP0*MQ0 ) +, LRWMINLRWOPT = LRWMIN{2LRWOPT = LRWMIN}, MQ0LRWOPT = 4*N + MAX( 5*NN, NP0*MQ0 ) +, NLRWOPT = 4*N + MAX( 5*NN, NP0*MQ0 ) +, NNLRWOPT = 4*N + MAX( 5*NN, NP0*MQ0 ) +, NP0LRWOPT = 4*N + MAX( 5*NN, NP0*MQ0 ) +, NPCOLLRWOPT = 4*N + MAX( 5*NN, NP0*MQ0 ) +, NPROWLRWOPT = 4*N + MAX( 5*NN, NP0*MQ0 ) + |
| LWMIN | <--- | NLWMIN = N + MAX( NB*( NP0+1 ), 3 ){2LWMIN = N + ( NP0+NQ0+NB )*NB}, NBLWMIN = N + MAX( NB*( NP0+1 ), 3 ){2LWMIN = N + ( NP0+NQ0+NB )*NB}, NP0LWMIN = N + MAX( NB*( NP0+1 ), 3 ){2LWMIN = N + ( NP0+NQ0+NB )*NB}, NQ0LWMIN = N + ( NP0+NQ0+NB )*NB |
| LWOPT | <--- | LWMINLWOPT = LWMIN{2LWOPT = LWMIN}, LWOPTLWOPT = MAX( LWOPT, N+NHETRD_LWOPT ), NLWOPT = MAX( LWOPT, N+NHETRD_LWOPT ), NHETRD_LWOPTLWOPT = MAX( LWOPT, N+NHETRD_LWOPT ) |
| MAXEIGS | <--- | N_MAXEIGS = DESCZ( N_ ) |
| MB_A | <--- | MB_MB_A = DESCA( MB_ ) |
| MQ0 | <--- | ICOFFAMQ0 = NUMROC( N+ICOFFA, NB, 0, 0, NPCOL ), NMQ0 = NUMROC( N+ICOFFA, NB, 0, 0, NPCOL ){2MQ0 = NUMROC( MAX( N, NB, 2 ), NB, 0, 0, NPCOL )}, NBMQ0 = NUMROC( N+ICOFFA, NB, 0, 0, NPCOL ){2MQ0 = NUMROC( MAX( N, NB, 2 ), NB, 0, 0, NPCOL ), 3MQ0 = NUMROC( MAX( NEIG, NB, 2 ), NB, 0, 0, NPCOL ), 4MQ0 = NUMROC( NZ, NB, 0, 0, NPCOL )}, NEIGMQ0 = NUMROC( MAX( NEIG, NB, 2 ), NB, 0, 0, NPCOL ), NPCOLMQ0 = NUMROC( N+ICOFFA, NB, 0, 0, NPCOL ){2MQ0 = NUMROC( MAX( N, NB, 2 ), NB, 0, 0, NPCOL ), 3MQ0 = NUMROC( MAX( NEIG, NB, 2 ), NB, 0, 0, NPCOL ), 4MQ0 = NUMROC( NZ, NB, 0, 0, NPCOL )}, NUMROCMQ0 = NUMROC( N+ICOFFA, NB, 0, 0, NPCOL ){2MQ0 = NUMROC( MAX( N, NB, 2 ), NB, 0, 0, NPCOL ), 3MQ0 = NUMROC( MAX( NEIG, NB, 2 ), NB, 0, 0, NPCOL ), 4MQ0 = NUMROC( NZ, NB, 0, 0, NPCOL )}, NZMQ0 = NUMROC( NZ, NB, 0, 0, NPCOL ) |
| NB | <--- | NB_ANB = NB_A |
| NB_A | <--- | NB_NB_A = DESCA( NB_ ) |
| NEIG | <--- | ILNEIG = IU - IL + 1, IUNEIG = IU - IL + 1, NNEIG = N |
| NHETRD_LWOPT | <--- | ANBNHETRD_LWOPT = 2*( ANB+1 )*( 4*NPS+2 ) + ( NPS+2 )*NPS, NPSNHETRD_LWOPT = 2*( ANB+1 )*( 4*NPS+2 ) + ( NPS+2 )*NPS |
| NN | <--- | NNN = MAX( N, NB, 2 ), NBNN = MAX( N, NB, 2 ) |
| NNP | <--- | NNNP = MAX( N, NPROCS+1, 4 ), NPROCSNNP = MAX( N, NPROCS+1, 4 ) |
| NP0 | <--- | IROFFANP0 = NUMROC( N+IROFFA, NB, 0, 0, NPROW ), NNP0 = NUMROC( N+IROFFA, NB, 0, 0, NPROW ), NBNP0 = NUMROC( N+IROFFA, NB, 0, 0, NPROW ), NPROWNP0 = NUMROC( N+IROFFA, NB, 0, 0, NPROW ), NUMROCNP0 = NUMROC( N+IROFFA, NB, 0, 0, NPROW ) |
| NPROCS | <--- | NPCOLNPROCS = NPROW*NPCOL{2NPROCS = NPROW*NPCOL}, NPROWNPROCS = NPROW*NPCOL{2NPROCS = NPROW*NPCOL} |
| NPS | <--- | SQNPCNPS = MAX( NUMROC( N, 1, 0, 0, SQNPC ), 2*ANB ), ANBNPS = MAX( NUMROC( N, 1, 0, 0, SQNPC ), 2*ANB ), NNPS = MAX( NUMROC( N, 1, 0, 0, SQNPC ), 2*ANB ), NUMROCNPS = MAX( NUMROC( N, 1, 0, 0, SQNPC ), 2*ANB ) |
| NQ0 | <--- | NBNQ0 = NUMROC( NN, NB, 0, 0, NPCOL ), NNNQ0 = NUMROC( NN, NB, 0, 0, NPCOL ), NPCOLNQ0 = NUMROC( NN, NB, 0, 0, NPCOL ), NUMROCNQ0 = NUMROC( NN, NB, 0, 0, NPCOL ) |
| NZ | <--- | MDO 50 NZ = MIN( MAXEIGS, M ), 0, -1{2NZ = M}, MAXEIGSDO 50 NZ = MIN( MAXEIGS, M ), 0, -1, NZNZ = MAX( NZ, 0 ){2NZ = MIN( NZ, NZZ )}, NZZNZ = MIN( NZ, NZZ ) |
| RMAX | <--- | SAFMINRMAX = MIN( SQRT( BIGNUM ), ONE / SQRT( SQRT( SAFMIN ) ) ), BIGNUMRMAX = MIN( SQRT( BIGNUM ), ONE / SQRT( SQRT( SAFMIN ) ) ), ONERMAX = MIN( SQRT( BIGNUM ), ONE / SQRT( SQRT( SAFMIN ) ) ) |
| RMIN | <--- | SMLNUMRMIN = SQRT( SMLNUM ) |
| RSRC_A | <--- | RSRC_RSRC_A = DESCA( RSRC_ ) |
| RSRC_Z | <--- | RSRC_RSRC_Z = DESCZ( RSRC_ ) |
| RWORK | <--- | VLRWORK( 2 ) = VL, VURWORK( 3 ) = VU, WORKRWORK( INDD2+I-1 ) = DBLE( WORK( INDD2+I-1 ) ){2RWORK( INDE2+I-1 ) = DBLE( WORK( INDE2+I-1 ) ), 3RWORK( INDE2+I-1 ) = DBLE( WORK( INDE2+I-1 ) )}, ZERORWORK( 2 ) = ZERO{2RWORK( 3 ) = ZERO}, IRWORK( INDD2+I-1 ) = DBLE( WORK( INDD2+I-1 ) ){2RWORK( INDE2+I-1 ) = DBLE( WORK( INDE2+I-1 ) ), 3RWORK( INDE2+I-1 ) = DBLE( WORK( INDE2+I-1 ) )}, ABSTOLRWORK( 1 ) = ABSTOL, INDD2RWORK( INDD2+I-1 ) = DBLE( WORK( INDD2+I-1 ) ), INDE2RWORK( INDE2+I-1 ) = DBLE( WORK( INDE2+I-1 ) ){2RWORK( INDE2+I-1 ) = DBLE( WORK( INDE2+I-1 ) )}, LRWMINRWORK( 1 ) = DBLE( LRWMIN ), LRWOPTRWORK( 1 ) = DBLE( LRWOPT ){2RWORK( 1 ) = DBLE( LRWOPT )} |
| SAFMIN | <--- | PDLAMCHSAFMIN = PDLAMCH( ICTXT, 'Safe minimum' ), ICTXTSAFMIN = PDLAMCH( ICTXT, 'Safe minimum' ) |
| SIGMA | <--- | RMAXSIGMA = RMAX / ANRM, RMINSIGMA = RMIN / ANRM, ANRMSIGMA = RMIN / ANRM{2SIGMA = RMAX / ANRM} |
| SIZEHEEVX | <--- | SIZESTEINSIZEHEEVX = SIZESTEIN |
| SIZESTEIN | <--- | ICEILSIZESTEIN = ICEIL( NZ, NPROCS )*N + MAX( 5*N, NP0*MQ0 ), MQ0SIZESTEIN = ICEIL( NZ, NPROCS )*N + MAX( 5*N, NP0*MQ0 ), NSIZESTEIN = ICEIL( NZ, NPROCS )*N + MAX( 5*N, NP0*MQ0 ), NP0SIZESTEIN = ICEIL( NZ, NPROCS )*N + MAX( 5*N, NP0*MQ0 ), NPROCSSIZESTEIN = ICEIL( NZ, NPROCS )*N + MAX( 5*N, NP0*MQ0 ), NZSIZESTEIN = ICEIL( NZ, NPROCS )*N + MAX( 5*N, NP0*MQ0 ) |
| SMLNUM | <--- | SAFMINSMLNUM = SAFMIN / EPS, EPSSMLNUM = SAFMIN / EPS |
| SQNPC | <--- | NPCOLSQNPC = INT( SQRT( DBLE( NPROW*NPCOL ) ) ), NPROWSQNPC = INT( SQRT( DBLE( NPROW*NPCOL ) ) ) |
| VALEIG | <--- | RANGEVALEIG = LSAME( RANGE, 'V' ), LSAMEVALEIG = LSAME( RANGE, 'V' ) |
| VLL | <--- | SIGMAVLL = VL*SIGMA, VLVLL = VL{2VLL = VL*SIGMA}, ZEROVLL = ZERO |
| VUU | <--- | SAFMINVUU = VUU + 2*MAX( ABS( VUU )*EPS, SAFMIN ){2VUU = W( NZ ) - TEN*( EPS*ANRM+SAFMIN )}, SIGMAVUU = VU*SIGMA, TENVUU = W( NZ ) - TEN*( EPS*ANRM+SAFMIN ), VUVUU = VU{2VUU = VU*SIGMA}, VUUVUU = VUU + 2*MAX( ABS( VUU )*EPS, SAFMIN ), ZEROVUU = ZERO, EPSVUU = VUU + 2*MAX( ABS( VUU )*EPS, SAFMIN ){2VUU = W( NZ ) - TEN*( EPS*ANRM+SAFMIN )}, ANRMVUU = W( NZ ) - TEN*( EPS*ANRM+SAFMIN ), NZVUU = W( NZ ) - TEN*( EPS*ANRM+SAFMIN ) |
| WANTZ | <--- | JOBZWANTZ = LSAME( JOBZ, 'V' ), LSAMEWANTZ = LSAME( JOBZ, 'V' ) |
| WORK | <--- | LWOPTWORK( 1 ) = DCMPLX( LWOPT ){2WORK( 1 ) = DCMPLX( LWOPT ), 3WORK( 1 ) = DCMPLX( LWOPT )} |
|
|
Analysis elements of the routine PZHEEVX()
Put the mouse over each element to display detailed matching information
 Assigned variables |
| | | ABSTLL , ABSTOL , ALLEIG , ANB , ANRM , BIGNUM , BLOCK_CYCLIC_2D , CSRC_ , CSRC_A , CTXT_ , DLEN_ , DTYPE_ , EPS , FIVE , I , IAROW , ICLUSTR , ICOFFA , ICTXT , IDUM1 , IDUM2 , IERRCLS , IERREBZ , IERREIN , IERRSPC , INDD , INDD2 , INDE , INDE2 , INDEIG , INDIBL , INDISP , INDRWORK , INDTAU , INDWORK , INFO , IROFFA , IROFFZ , ISCALE , ISIZESTEBZ , ISIZESTEIN , IWORK , IZROW , LALLWORK , LIWMIN , LLD_ , LLRWORK , LLWORK , LOWER , LQUERY , LRWMIN , LRWOPT , LWMIN , LWOPT , M , M_ , MAXEIGS , MB_ , MB_A , MQ0 , N_ , NB , NB_ , NB_A , NEIG , NHETRD_LWOPT , NN , NNP , NP0 , NPROCS , NPS , NQ0 , NZ , NZZ , OFFSET , ONE , ORDER , QUICKRETURN , RMAX , RMIN , RSRC_ , RSRC_A , RSRC_Z , RWORK , SAFMIN , SIGMA , SIZEHEEVX , SIZESTEIN , SMLNUM , SQNPC , TEN , VALEIG , VLL , VUU , WANTZ , WORK , Z , ZERO |
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| Active variables |
| | | A , ABSTLL , ABSTOL , ALLEIG , ANB , ANRM , BIGNUM , BLOCK_CYCLIC_2D , CSRC_ , CSRC_A , CTXT_ , DESCA , DESCZ , DLEN_ , DTYPE_ , EPS , FIVE , GAP , I , IA , IAROW , ICEIL , ICLUSTR , ICOFFA , ICTXT , IDUM1 , IDUM2 , IERRCLS , IERREBZ , IERREIN , IERRSPC , IFAIL , IINFO , IL , INDD , INDD2 , INDE , INDE2 , INDEIG , INDIBL , INDISP , INDRWORK , INDTAU , INDWORK , INDXG2P , INFO , IROFFA , IROFFZ , ISCALE , ISIZESTEBZ , ISIZESTEIN , IU , IWORK , IZ , IZROW , JA , JOBZ , JZ , LALLWORK , LIWMIN , LIWORK , LLD_ , LLRWORK , LLWORK , LOWER , LQUERY , LRWMIN , LRWOPT , LRWORK , LSAME , LWMIN , LWOPT , LWORK , M , M_ , MAXEIGS , MB_ , MB_A , MQ0 , MYCOL , MYROW , N , N_ , NB , NB_ , NB_A , NEIG , NHETRD_LWOPT , NN , NNP , NP0 , NPCOL , NPROCS , NPROW , NPS , NQ0 , NSPLIT , NUMROC , NZ , NZZ , OFFSET , ONE , ORDER , ORFAC , PDLAMCH , PJLAENV , PZLANHE , QUICKRETURN , RANGE , RMAX , RMIN , RSRC_ , RSRC_A , RSRC_Z , RWORK , SAFMIN , SIGMA , SIZEHEEVX , SIZESTEIN , SMLNUM , SQNPC , TEN , UPLO , VALEIG , VL , VLL , VU , VUU , W , WANTZ , WORK , Z , ZERO |
|
| Allocated variables [ statement : associated variable ] |
| |  new | : a |
|
| Accessed arrays [ array name : associated index ] |
| | DESCA | : CSRC_ , CSRC_ , CTXT_ , M_ , MB_ , MB_ , MB_ , N_ , NB_ , NB_ , NB_ , RSRC_ , RSRC_ |
| | DESCZ | : CSRC_ , CTXT_ , CTXT_ , M_ , MB_ , N_ , N_ , NB_ , RSRC_ , RSRC_ |
| | ICEIL | : N, NPROW*NPCOL , NEIG, NPROW*NPCOL , NZ, NPROCS |
| | ICLUSTR | : 1 |
| | IDUM1 | : 1 , 1 , 2 , 2 , 3 , 3 , 3 , 4 , 4 , 4 |
| | IDUM2 | : 1 , 2 , 3 , 4 , 4 |
| | IFAIL | : I |
| | INDXG2P | : 1, NB_A, MYROW, RSRC_A, NPROW , 1, NB_A, MYROW, RSRC_Z, NPROW |
| | IWORK | : 1 , 1 , 1 , 1 , 1 , 1 , INDIBL , INDIBL , INDIBL , INDIBL+I-1 , INDISP , INDISP , INDISP |
| | LSAME | : JOBZ, 'N' , JOBZ, 'V' , RANGE, 'A' , RANGE, 'I' , RANGE, 'V' , UPLO, 'L' , UPLO, 'U' , UPLO, 'U' |
| | NUMROC | : MAX( N, NB, 2 ), NB, 0, 0, NPCOL , MAX( NEIG, NB, 2 ), NB, 0, 0, NPCOL , N, 1, 0, 0, SQNPC , N+ICOFFA, NB, 0, 0, NPCOL , N+IROFFA, NB, 0, 0, NPROW , NN, NB, 0, 0, NPCOL , NZ, NB, 0, 0, NPCOL |
| | PDLAMCH | : ICTXT, 'Precision' , ICTXT, 'Safe minimum' , 'U' |
| | PJLAENV | : ICTXT, 3, 'PZHETTRD', 'L', 0, 0, 0, 0 |
| | RWORK | : 1 , 1 , 1 , 1 , 1 , 2 , 2 , 2 , 3 , 3 , 3 , INDD , INDD , INDD2 , INDD2 , INDD2 , INDD2 , INDD2+I-1 , INDE , INDE , INDE2 , INDE2+I-1 , INDE2+I-1 , INDE2+OFFSET , INDE2+OFFSET , INDE2+OFFSET , INDRWORK , INDRWORK , INDRWORK , INDRWORK , INDRWORK , INDRWORK , INDRWORK |
| | W | : NZ |
| | WORK | : 1 , 1 , 1 , INDD2+I-1 , INDD2+I-1 , INDE2+I-1 , INDE2+I-1 , INDE2+I-1 , INDE2+I-1 , INDTAU , INDTAU , INDWORK , INDWORK |
|
| Conditional statements [ statement : associated predicate ] |
| | do | : ( 10 I = 1 , N ) , ( 20 I = 1 , N - 1 ) , ( 30 I = 1 , N - 1 ) , ( not propogate the eigenvalue(s) which failed because : ) , ( 40 I = 1 , M ) , ( 50 NZ = MIN( MAXEIGS , M ) , 0 , - 1 ) , ( 70 I = 1 , M ) |
| | for | : ( the largest ) |
| | if | : ( BLOCK_CYCLIC_2D*CSRC_*CTXT_*DLEN_*DTYPE_*LLD_*MB_*M_*NB_*N_* ) , ( NPROW.EQ. - 1 ) , ( WANTZ ) , ( (ICTXT.NE.DESCZ( CTXT_ ) ) ) , ( INFO.EQ.0 ) , ( WANTZ ) , ( INFO.EQ.0 ) , ( LWORK.EQ. - 1 .OR. LIWORK.EQ. - 1 .OR. LRWORK.EQ. - 1 ) , ( WANTZ ) , ( (( .NOT.WANTZ ) .OR. ( VALEIG .AND. ( .NOT.LQUERY ) ) ) ) , ( WANTZ ) , ( ALLEIG .OR. VALEIG ) , ( INDEIG ) , ( INFO.EQ.0 ) , ( MYROW.EQ.0 .AND. MYCOL.EQ.0 ) , ( VALEIG ) , ( (.NOT.( WANTZ .OR. LSAME( JOBZ , 'N' ) ) ) ) , ( (.NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) ) , ( (.NOT.( LOWER .OR. LSAME( UPLO , 'U' ) ) ) ) , ( VALEIG .AND. N.GT.0 .AND. VU.LE.VL ) , ( (INDEIG .AND. ( IL.LT.1 .OR. IL.GT.MAX( 1 , N ) ) ) ) , ( (INDEIG .AND. ( IU.LT.MIN( N , IL ) .OR. IU.GT.N ) ) ) , ( LWORK.LT.LWMIN .AND. LWORK.NE. - 1 ) , ( LRWORK.LT.LRWMIN .AND. LRWORK.NE. - 1 ) , ( LIWORK.LT.LIWMIN .AND. LIWORK.NE. - 1 ) , ( (VALEIG .AND. ( ABS( RWORK( 2 ) - VL ).GT.FIVE*EPS* ) , ( (VALEIG .AND. ( ABS( RWORK( 3 ) - VU ).GT.FIVE*EPS* ) , ( (ABS( RWORK( 1 ) - ABSTOL ).GT.FIVE*EPS* ) , ( IROFFA.NE.0 ) , ( (DESCA( MB_ ).NE.DESCA( NB_ ) ) ) , ( WANTZ ) , ( IROFFA.NE.IROFFZ ) , ( IAROW.NE.IZROW ) , ( (DESCA( M_ ).NE.DESCZ( M_ ) ) ) , ( (DESCA( N_ ).NE.DESCZ( N_ ) ) ) , ( (DESCA( MB_ ).NE.DESCZ( MB_ ) ) ) , ( (DESCA( NB_ ).NE.DESCZ( NB_ ) ) ) , ( (DESCA( RSRC_ ).NE.DESCZ( RSRC_ ) ) ) , ( (DESCA( CSRC_ ).NE.DESCZ( CSRC_ ) ) ) , ( (ICTXT.NE.DESCZ( CTXT_ ) ) ) , ( WANTZ ) , ( LOWER ) , ( ALLEIG ) , ( INDEIG ) , ( LQUERY ) , ( WANTZ ) , ( INFO.NE.0 ) , ( LQUERY ) , ( possible ) , ( QUICKRETURN ) , ( WANTZ ) , ( necessary. ) , ( VALEIG ) , ( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) , ( ANRM.GT.RMAX ) , ( ISCALE.EQ.1 ) , ( ABSTOL.GT.0 ) , ( VALEIG ) , ( VUU.EQ.VLL ) , ( IA.EQ.1 .AND. JA.EQ.1 .AND. RSRC_A.EQ.0 .AND. CSRC_A.EQ.0 ) , ( .NOT.LOWER ) , ( (LSAME( UPLO , 'U' ) ) ) , ( eigenvectors are desired , PZSTEIN. ) , ( WANTZ ) , ( PDSTEBZ fails , the error propogates to INFO , but ) , ( the user specifies ) , ( IINFO.NE.0 ) , ( WANTZ ) , ( VALEIG ) , ( SIZEHEEVX.LE.LALLWORK ) , ( NZ.NE.M ) , ( NSPLIT.GT.1 ) , ( NZ.GT.0 ) , ( VLL.GE.VUU ) , ( (MOD( INFO / IERREBZ , 1 ).EQ.0 ) ) , ( NZZ.GT.NZ .OR. IINFO.NE.0 ) , ( IINFO.GE.NZ + 1 ) , ( (MOD( IINFO , NZ + 1 ).NE.0 ) ) , ( NZ.GT.0 ) , ( matrix was scaled , ) , ( ISCALE.EQ.1 ) |
|
| List of variables |
ABSTLL
ABSTOL
ALLEIG
ANB
ANRM
BIGNUM
BLOCK_CYCLIC_2D
| CSRC_
CSRC_A
CTXT_
DLEN_
DTYPE_
EPS
FIVE
I
| IA
IAROW
ICEIL
ICLUSTR
ICOFFA
ICTXT
IDUM1( 4 )
IDUM2( 4 )
| IERRCLS
IERREBZ
IERREIN
IERRSPC
IFAIL
IINFO
IL
INDD
| INDD2
INDE
INDE2
INDEIG
INDIBL
INDISP
INDRWORK
INDTAU
| INDWORK
INDXG2P
INFO
IROFFA
IROFFZ
ISCALE
ISIZESTEBZ
ISIZESTEIN
| IU
IWORK
IZ
IZROW
JA
JOBZ
JZ
LALLWORK
| LIWMIN
LIWORK
LLD_
LLRWORK
LLWORK
LOWER
LQUERY
LRWMIN
| LRWOPT
LRWORK
LSAME
LWMIN
LWOPT
LWORK
M
M_
| MAXEIGS
MB_
MB_A
MQ0
MYCOL
MYROW
N
N_
| NB
NB_
NB_A
NEIG
NHETRD_LWOPT
NN
NNP
NP0
| NPCOL
NPROCS
NPROW
NPS
NQ0
NSPLIT
NUMROC
NZ
| NZZ
OFFSET
ONE
ORDER
ORFAC
PDLAMCH
PJLAENV
PZLANHE
| QUICKRETURN
RANGE
RMAX
RMIN
RSRC_
RSRC_A
RSRC_Z
RWORK
| SAFMIN
SIGMA
SIZEHEEVX
SIZESTEIN
SMLNUM
SQNPC
TEN
UPLO
| VALEIG
VL
VLL
VU
VUU
WANTZ
WORK
ZERO | | close
| |
ABSTLL
ABSTOL
ALLEIG
ANB
ANRM
BIGNUM
BLOCK_CYCLIC_2D
CSRC_
CSRC_A
CTXT_
DLEN_
DTYPE_
EPS
FIVE
I
IA
IAROW
ICEIL
ICLUSTR
ICOFFA
ICTXT
IDUM1( 4 )
IDUM2( 4 )
IERRCLS
IERREBZ
IERREIN
IERRSPC
IFAIL
IINFO
IL
INDD
INDD2
INDE
INDE2
INDEIG
INDIBL
INDISP
INDRWORK
INDTAU
INDWORK
INDXG2P
INFO
IROFFA
IROFFZ
ISCALE
ISIZESTEBZ
ISIZESTEIN
IU
IWORK
IZ
IZROW
JA
JOBZ
JZ
LALLWORK
LIWMIN
LIWORK
LLD_
LLRWORK
LLWORK
LOWER
LQUERY
LRWMIN
LRWOPT
LRWORK
LSAME
LWMIN
LWOPT
LWORK
M
M_
MAXEIGS
MB_
MB_A
MQ0
MYCOL
MYROW
N
N_
NB
NB_
NB_A
NEIG
NHETRD_LWOPT
NN
NNP
NP0
NPCOL
NPROCS
NPROW
NPS
NQ0
NSPLIT
NUMROC
NZ
NZZ
OFFSET
ONE
ORDER
ORFAC
PDLAMCH
PJLAENV
PZLANHE
QUICKRETURN
RANGE
RMAX
RMIN
RSRC_
RSRC_A
RSRC_Z
RWORK
SAFMIN
SIGMA
SIZEHEEVX
SIZESTEIN
SMLNUM
SQNPC
TEN
UPLO
VALEIG
VL
VLL
VU
VUU
WANTZ
WORK
ZERO
313#523#600#219#540#507#230#292#572
| |
