Routine PCGEBD2() Documented By Universal Report

Routine: PCGEBD2()

File: SRC\pcgebd2.f

# lines:	453
# code:	453
# comment:	0
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# Variables:	45
# Callers:	1
# Callings:	4
# Words:	229
# Keywords:	116

..
     .. Array Arguments ..
     ..
  Purpose
  =======
  PCGEBD2 reduces a complex general M-by-N distributed matrix
  sub( A ) = A(IA:IA+M-1,JA:JA+N-1) to upper or lower bidiagonal
  form B by an unitary transformation: Q' * sub( A ) * P = B.
  If M >= N, B is upper bidiagonal; if M < N, B is lower bidiagonal.
  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
  Arguments
  =========
  M       (global input) INTEGER
          The number of rows to be operated on, i.e. the number of rows
          of the distributed submatrix sub( A ). M >= 0.
  N       (global input) INTEGER
          The number of columns to be operated on, i.e. the number of
          columns of the distributed submatrix sub( A ). N >= 0.
  A       (local input/local output) COMPLEX pointer into the
          local memory to an array of dimension (LLD_A,LOCc(JA+N-1)).
          On entry, this array contains the local pieces of the
          general distributed matrix sub( A ). On exit, if M >= N,
          the diagonal and the first superdiagonal of sub( A ) are
          overwritten with the upper bidiagonal matrix B; the elements
          below the diagonal, with the array TAUQ, represent the
          unitary matrix Q as a product of elementary reflectors, and
          the elements above the first superdiagonal, with the array
          TAUP, represent the orthogonal matrix P as a product of
          elementary reflectors. If M < N, the diagonal and the first
          subdiagonal are overwritten with the lower bidiagonal
          matrix B; the elements below the first subdiagonal, with the
          array TAUQ, represent the unitary matrix Q as a product of
          elementary reflectors, and the elements above the diagonal,
          with the array TAUP, represent the orthogonal matrix P as a
          product of elementary reflectors. See Further Details.
  IA      (global input) INTEGER
          The row index in the global array A indicating the first
          row of sub( A ).
  JA      (global input) INTEGER
          The column index in the global array A indicating the
          first column of sub( A ).
  DESCA   (global and local input) INTEGER array of dimension DLEN_.
          The array descriptor for the distributed matrix A.
  D       (local output) REAL array, dimension
          LOCc(JA+MIN(M,N)-1) if M >= N; LOCr(IA+MIN(M,N)-1) otherwise.
          The distributed diagonal elements of the bidiagonal matrix
          B: D(i) = A(i,i). D is tied to the distributed matrix A.
  E       (local output) REAL array, dimension
          LOCr(IA+MIN(M,N)-1) if M >= N; LOCc(JA+MIN(M,N)-2) otherwise.
          The distributed off-diagonal elements of the bidiagonal
          distributed matrix B:
          if m >= n, E(i) = A(i,i+1) for i = 1,2,...,n-1;
          if m < n, E(i) = A(i+1,i) for i = 1,2,...,m-1.
          E is tied to the distributed matrix A.
  TAUQ    (local output) COMPLEX array dimension
          LOCc(JA+MIN(M,N)-1). The scalar factors of the elementary
          reflectors which represent the unitary matrix Q. TAUQ is
          tied to the distributed matrix A. See Further Details.
  TAUP    (local output) COMPLEX array, dimension
          LOCr(IA+MIN(M,N)-1). The scalar factors of the elementary
          reflectors which represent the unitary matrix P. TAUP is
          tied to the distributed matrix A. See Further Details.
  WORK    (local workspace/local output) COMPLEX array,
                                                  dimension (LWORK)
          On exit, WORK(1) returns the minimal and optimal LWORK.
  LWORK   (local or global input) INTEGER
          The dimension of the array WORK.
          LWORK is local input and must be at least
          LWORK >= MAX( MpA0, NqA0 )
          where NB = MB_A = NB_A, IROFFA = MOD( IA-1, NB )
          IAROW = INDXG2P( IA, NB, MYROW, RSRC_A, NPROW ),
          IACOL = INDXG2P( JA, NB, MYCOL, CSRC_A, NPCOL ),
          MpA0 = NUMROC( M+IROFFA, NB, MYROW, IAROW, NPROW ),
          NqA0 = NUMROC( N+IROFFA, NB, MYCOL, IACOL, NPCOL ).
          INDXG2P and NUMROC are ScaLAPACK tool functions;
          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 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.
  INFO    (local 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.
  Further Details
  ===============
  The matrices Q and P are represented as products of elementary
  reflectors:
  If m >= n,
     Q = H(1) H(2) . . . H(n)  and  P = G(1) G(2) . . . G(n-1)
  Each H(i) and G(i) has the form:
     H(i) = I - tauq * v * v'  and G(i) = I - taup * u * u'
  where tauq and taup are complex scalars, and v and u are complex
  vectors;
  v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in
  A(ia+i:ia+m-1,ja+i-1);
  u(1:i) = 0, u(i+1) = 1, and u(i+2:n) is stored on exit in
  A(ia+i-1,ja+i+1:ja+n-1);
  tauq is stored in TAUQ(ja+i-1) and taup in TAUP(ia+i-1).
  If m < n,
     Q = H(1) H(2) . . . H(m-1)  and  P = G(1) G(2) . . . G(m)
  Each H(i) and G(i) has the form:
     H(i) = I - tauq * v * v'  and G(i) = I - taup * u * u'
  where tauq and taup are complex scalars, and v and u are complex
  vectors;
  v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in
  A(ia+i+1:ia+m-1,ja+i-1);
  u(1:i-1) = 0, u(i) = 1, and u(i+1:n) is stored on exit in
  A(ia+i-1,ja+i:ja+n-1);
  tauq is stored in TAUQ(ja+i-1) and taup in TAUP(ia+i-1).
  The contents of sub( A ) on exit are illustrated by the following
  examples:
  m = 6 and n = 5 (m > n):          m = 5 and n = 6 (m < n):
    (  d   e   u1  u1  u1 )           (  d   u1  u1  u1  u1  u1 )
    (  v1  d   e   u2  u2 )           (  e   d   u2  u2  u2  u2 )
    (  v1  v2  d   e   u3 )           (  v1  e   d   u3  u3  u3 )
    (  v1  v2  v3  d   e  )           (  v1  v2  e   d   u4  u4 )
    (  v1  v2  v3  v4  d  )           (  v1  v2  v3  e   d   u5 )
    (  v1  v2  v3  v4  v5 )
  where d and e denote diagonal and off-diagonal elements of B, vi
  denotes an element of the vector defining H(i), and ui an element of
  the vector defining G(i).
  Alignment requirements
  ======================
  The distributed submatrix sub( A ) must verify some alignment proper-
  ties, namely the following expressions should be true:
                  ( MB_A.EQ.NB_A .AND. IROFFA.EQ.ICOFFA )
  =====================================================================
     .. Parameters ..

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001        SUBROUTINE PCGEBD2( M , N , A , IA , JA , DESCA , D , E , TAUQ , TAUP ,
002       $WORK , LWORK , INFO )
003  
004  *     -- ScaLAPACK auxiliary routine(version 1.7) --
005  *     University of Tennessee , Knoxville , Oak Ridge National Laboratory ,
006  *     and University of California , Berkeley.
007  *     May 1 , 1997
008  
009  *     .. Scalar Arguments ..
010        INTEGER IA , INFO , JA , LWORK , M , N
011        INTEGER BLOCK_CYCLIC_2D , CSRC_ , CTXT_ , DLEN_ , DTYPE_ ,
012       $LLD_ , MB_ , M_ , NB_ , N_ , RSRC_
013        PARAMETER( BLOCK_CYCLIC_2D = 1 , DLEN_ = 9 , DTYPE_ = 1 ,
014       $CTXT_ = 2 , M_ = 3 , N_ = 4 , MB_ = 5 , NB_ = 6 ,
015       $RSRC_ = 7 , CSRC_ = 8 , LLD_ = 9 )
016        COMPLEX ONE , ZERO
017        PARAMETER( ONE =( 1.0E + 0 , 0.0E + 0 ) ,
018       $ZERO =( 0.0E + 0 , 0.0E + 0 ) )
019  *     ..
020  *     .. Local Scalars ..
021        LOGICAL LQUERY
022        INTEGER I , IACOL , IAROW , ICOFFA , ICTXT , II , IROFFA , J ,
023       $JJ , K , LWMIN , MPA0 , MYCOL , MYROW , NPCOL , NPROW ,
024       $NQA0
025        COMPLEX ALPHA
026  *     ..
027  *     .. Local Arrays ..
028        INTEGER DESCD( DLEN_ ) , DESCE( DLEN_ )
029  *     ..
030  *     .. External Subroutines ..
031        EXTERNAL BLACS_ABORT , BLACS_GRIDINFO , CGEBR2D ,
032       $CGEBS2D , CHK1MAT , CLARFG , DESCSET , INFOG2L ,
033       $PCELSET , PCLACGV , PCLARF , PCLARFC ,
034       $PCLARFG , PSELSET , PXERBLA , SGEBR2D ,
035       $SGEBS2D
036  *     ..
037  *     .. External Functions ..
038        INTEGER INDXG2P , NUMROC
039        EXTERNAL INDXG2P , NUMROC
040  *     ..
041  *     .. Intrinsic Functions ..
042        INTRINSIC CMPLX , MAX , MIN , MOD , REAL
043  *     ..
044  *     .. Executable Statements ..
045  
046  *     Test the input parameters
047  
048        ICTXT = DESCA( CTXT_ )
049        CALL BLACS_GRIDINFO( ICTXT , NPROW , NPCOL , MYROW , MYCOL )
050  
051  *     Test the input parameters
052  
053        INFO = 0
054        IF( NPROW.EQ. - 1 ) THEN
054               
055            INFO = - (600 + CTXT_)
056        ELSE
056               
057            CALL CHK1MAT( M , 1 , N , 2 , IA , JA , DESCA , 6 , INFO )
058            IF( INFO.EQ.0 ) THEN
058                   
059                IROFFA = MOD( IA - 1 , DESCA( MB_ ) )
060                ICOFFA = MOD( JA - 1 , DESCA( NB_ ) )
061                IAROW = INDXG2P( IA , DESCA( MB_ ) , MYROW , DESCA( RSRC_ ) ,
062       $        NPROW )
063                IACOL = INDXG2P( JA , DESCA( NB_ ) , MYCOL , DESCA( CSRC_ ) ,
064       $        NPCOL )
065                MPA0 = NUMROC( M + IROFFA , DESCA( MB_ ) , MYROW , IAROW , NPROW )
066                NQA0 = NUMROC( N + ICOFFA , DESCA( NB_ ) , MYCOL , IACOL , NPCOL )
067                LWMIN = MAX( MPA0 , NQA0 )
068  
069                WORK( 1 ) = CMPLX( REAL( LWMIN ) )
070                LQUERY =( LWORK.EQ. - 1 )
071                IF( IROFFA.NE.ICOFFA ) THEN
071                       
072                    INFO = - 5
073                ELSE IF( DESCA( MB_ ).NE.DESCA( NB_ ) ) THEN
073                       
074                    INFO = - (600 + NB_)
075                ELSE IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
075                       
076                    INFO = - 12
077                END IF
078            END IF
079        END IF
080  
081        IF( INFO.LT.0 ) THEN
081               
082            CALL PXERBLA( ICTXT , 'PCGEBD2' , - INFO )
083            CALL BLACS_ABORT( ICTXT , 1 )
084            RETURN
085        ELSE IF( LQUERY ) THEN
085               
086            RETURN
087        END IF
088  
089        CALL INFOG2L( IA , JA , DESCA , NPROW , NPCOL , MYROW , MYCOL , II , JJ ,
090       $IAROW , IACOL )
091  
092        IF( M.EQ.1 .AND. N.EQ.1 ) THEN
092               
093            IF( MYCOL.EQ.IACOL ) THEN
093                   
094                IF( MYROW.EQ.IAROW ) THEN
094                       
095                    I = II + (JJ - 1)*DESCA( LLD_ )
096                    CALL CLARFG( 1 , A( I ) , A( I ) , 1 , TAUQ( JJ ) )
097                    D( JJ ) = REAL( A( I ) )
098                    CALL SGEBS2D( ICTXT , 'Columnwise' , ' ' , 1 , 1 , D( JJ ) ,
099       $            1 )
100                    CALL CGEBS2D( ICTXT , 'Columnwise' , ' ' , 1 , 1 , TAUQ( JJ ) ,
101       $            1 )
102                ELSE
102                       
103                    CALL SGEBR2D( ICTXT , 'Columnwise' , ' ' , 1 , 1 , D( JJ ) ,
104       $            1 , IAROW , IACOL )
105                    CALL CGEBR2D( ICTXT , 'Columnwise' , ' ' , 1 , 1 , TAUQ( JJ ) ,
106       $            1 , IAROW , IACOL )
107                END IF
108            END IF
109            IF( MYROW.EQ.IAROW )
109                   
110       $        TAUP( II ) = ZERO
111                RETURN
112            END IF
113  
114            ALPHA = ZERO
115  
116            IF( M.GE.N ) THEN
117  
118  *             Reduce to upper bidiagonal form
119  
119                   
120                CALL DESCSET( DESCD , 1 , JA + MIN(M , N) - 1 , 1 , DESCA( NB_ ) , MYROW ,
121       $        DESCA( CSRC_ ) , DESCA( CTXT_ ) , 1 )
122                CALL DESCSET( DESCE , IA + MIN(M , N) - 1 , 1 , DESCA( MB_ ) , 1 ,
123       $        DESCA( RSRC_ ) , MYCOL , DESCA( CTXT_ ) ,
124       $        DESCA( LLD_ ) )
125                DO 10 K = 1 , N
125                       
126                    I = IA + K - 1
127                    J = JA + K - 1
128  
129  *                 Generate elementary reflector H(j) to annihilate
130  *                 A(ia + i : ia + m - 1 , j)
131  
132                    CALL PCLARFG ( M - K + 1 , ALPHA , I , J , A , MIN( I + 1 , M + IA - 1 ) ,
133       $            J , DESCA , 1 , TAUQ )
134                    CALL PSELSET( D , 1 , J , DESCD , REAL( ALPHA ) )
135                    CALL PCELSET( A , I , J , DESCA , ONE )
136  
137  *                 Apply H(i) to A(i : ia + m - 1 , i + 1 : ja + n - 1) from the left
138  
139                    CALL PCLARFC ( 'Left' , M - K + 1 , N - K , A , I , J , DESCA , 1 , TAUQ ,
140       $            A , I , J + 1 , DESCA , WORK )
141                    CALL PCELSET( A , I , J , DESCA , CMPLX( REAL( ALPHA ) ) )
142  
143                    IF( K.LT.N ) THEN
144  
145  *                     Generate elementary reflector G(i) to annihilate
146  *                     A(i , ja + j + 1 : ja + n - 1)
147  
147                           
148                        CALL PCLACGV ( N - K , A , I , J + 1 , DESCA , DESCA( M_ ) )
149                        CALL PCLARFG ( N - K , ALPHA , I , J + 1 , A , I ,
150       $                MIN( J + 2 , JA + N - 1 ) , DESCA , DESCA( M_ ) ,
151       $                TAUP )
152                        CALL PSELSET( E , I , 1 , DESCE , REAL( ALPHA ) )
153                        CALL PCELSET( A , I , J + 1 , DESCA , ONE )
154  
155  *                     Apply G(i) to A(i + 1 : ia + m - 1 , i + 1 : ja + n - 1) from the right
156  
157                        CALL PCLARF ( 'Right' , M - K , N - K , A , I , J + 1 , DESCA ,
158       $                DESCA( M_ ) , TAUP , A , I + 1 , J + 1 , DESCA ,
159       $                WORK )
160                        CALL PCELSET( A , I , J + 1 , DESCA , CMPLX( REAL( ALPHA ) ) )
161                        CALL PCLACGV ( N - K , A , I , J + 1 , DESCA , DESCA( M_ ) )
162                    ELSE
162                           
163                        CALL PCELSET( TAUP , I , 1 , DESCE , ZERO )
164                    END IF
165     10         CONTINUE
166  
166               
167            ELSE
168  
169  *             Reduce to lower bidiagonal form
170  
170                   
171                CALL DESCSET( DESCD , IA + MIN(M , N) - 1 , 1 , DESCA( MB_ ) , 1 ,
172       $        DESCA( RSRC_ ) , MYCOL , DESCA( CTXT_ ) ,
173       $        DESCA( LLD_ ) )
174                CALL DESCSET( DESCE , 1 , JA + MIN(M , N) - 1 , 1 , DESCA( NB_ ) , MYROW ,
175       $        DESCA( CSRC_ ) , DESCA( CTXT_ ) , 1 )
176                DO 20 K = 1 , M
176                       
177                    I = IA + K - 1
178                    J = JA + K - 1
179  
180  *                 Generate elementary reflector G(i) to annihilate
181  *                 A(i , ja + j : ja + n - 1)
182  
183                    CALL PCLACGV ( N - K + 1 , A , I , J , DESCA , DESCA( M_ ) )
184                    CALL PCLARFG ( N - K + 1 , ALPHA , I , J , A , I ,
185       $            MIN( J + 1 , JA + N - 1 ) , DESCA , DESCA( M_ ) , TAUP )
186                    CALL PSELSET( D , I , 1 , DESCD , REAL( ALPHA ) )
187                    CALL PCELSET( A , I , J , DESCA , ONE )
188  
189  *                 Apply G(i) to A(i : ia + m - 1 , j : ja + n - 1) from the right
190  
191                    CALL PCLARF ( 'Right' , M - K , N - K + 1 , A , I , J , DESCA ,
192       $            DESCA( M_ ) , TAUP , A , MIN( I + 1 , IA + M - 1 ) , J ,
193       $            DESCA , WORK )
194                    CALL PCELSET( A , I , J , DESCA , CMPLX( REAL( ALPHA ) ) )
195                    CALL PCLACGV ( N - K + 1 , A , I , J , DESCA , DESCA( M_ ) )
196  
197                    IF( K.LT.M ) THEN
198  
199  *                     Generate elementary reflector H(i) to annihilate
200  *                     A(i + 2 : ia + m - 1 , j)
201  
201                           
202                        CALL PCLARFG ( M - K , ALPHA , I + 1 , J , A ,
203       $                MIN( I + 2 , IA + M - 1 ) , J , DESCA , 1 , TAUQ )
204                        CALL PSELSET( E , 1 , J , DESCE , REAL( ALPHA ) )
205                        CALL PCELSET( A , I + 1 , J , DESCA , ONE )
206  
207  *                     Apply H(i) to A(i + 1 : ia + m - 1 , j + 1 : ja + n - 1) from the left
208  
209                        CALL PCLARFC ( 'Left' , M - K , N - K , A , I + 1 , J , DESCA , 1 ,
210       $                TAUQ , A , I + 1 , J + 1 , DESCA , WORK )
211                        CALL PCELSET( A , I + 1 , J , DESCA , CMPLX( REAL( ALPHA ) ) )
212                    ELSE
212                           
213                        CALL PCELSET( TAUQ , 1 , J , DESCE , ZERO )
214                    END IF
215     20         CONTINUE
215               
216            END IF
217  
218            WORK( 1 ) = CMPLX( REAL( LWMIN ) )
219  
220            RETURN
221  
222  *         End of PCGEBD2
223  
224        END3439

Variables in Routine PCGEBD2()

Summary Report
Data Type	Quantity	Size(byte)
COMPLEX	3	12
INTEGER	38	152
LOGICAL	1	1
REAL	3	12
TOTAL	45	177

List of Variables

COMPLEX

ALPHA ONE ZERO

INTEGER

BLOCK_CYCLIC_2D CSRC_ CTXT_ DESCD( DLEN_ ) DESCE( DLEN_ )
DLEN_ DTYPE_ I IA IACOL
IAROW ICOFFA ICTXT II INDXG2P
INFO IROFFA J JA JJ
K LLD_ LWMIN LWORK M
M_ MB_ MPA0 MYCOL MYROW
N N_ NB_ NPCOL NPROW
NQA0 NUMROC RSRC_

LOGICAL

LQUERY

REAL

D TAUP WORK

Variables Dependence Graph
Put the mouse over a right hand side variable to display the corresponding line of the dependence
-
- -
ALPHA <--- ZEROALPHA = ZERO

D <--- ID( JJ ) = REAL( A( I ) )

I <--- IAI = IA + K - 1{2I = IA + K - 1}, III = II+(JJ-1)*DESCA( LLD_ ), JJI = II+(JJ-1)*DESCA( LLD_ ), KI = IA + K - 1{2I = IA + K - 1}, LLD_I = II+(JJ-1)*DESCA( LLD_ )

IACOL <--- INDXG2P, JA, CSRC_, MYCOL, NB_, NPCOL

IAROW <--- IA, INDXG2P, MB_, MYROW, NPROW, RSRC_

ICOFFA <--- JAICOFFA = MOD( JA-1, DESCA( NB_ ) ), NB_ICOFFA = MOD( JA-1, DESCA( NB_ ) )

ICTXT <--- CTXT_ICTXT = DESCA( CTXT_ )

INFO <--- NB_INFO = -(600+NB_), CTXT_INFO = -(600+CTXT_)

IROFFA <--- IAIROFFA = MOD( IA-1, DESCA( MB_ ) ), MB_IROFFA = MOD( IA-1, DESCA( MB_ ) )

J <--- JAJ = JA + K - 1{2J = JA + K - 1}, KJ = JA + K - 1{2J = JA + K - 1}

K <--- MDO 20 K = 1, M, NDO 10 K = 1, N

LWMIN <--- MPA0LWMIN = MAX( MPA0, NQA0 ), NQA0LWMIN = MAX( MPA0, NQA0 )

MPA0 <--- IAROW, IROFFA, M, MB_, MYROW, NPROW, NUMROC

NQA0 <--- IACOL, ICOFFA, MYCOL, N, NB_, NPCOL, NUMROC

WORK <--- LWMINWORK( 1 ) = CMPLX( REAL( LWMIN ) ){2WORK( 1 ) = CMPLX( REAL( LWMIN ) )}