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SUBROUTINE PSLAED1( N, N1, D, ID, Q, IQ, JQ, DESCQ, RHO, WORK,
$ IWORK, INFO )
*
* -- ScaLAPACK auxiliary routine (version 1.7) --
* University of Tennessee, Knoxville, Oak Ridge National Laboratory,
* and University of California, Berkeley.
* December 31, 1998
*
* .. Scalar Arguments ..
INTEGER ID, INFO, IQ, JQ, N, N1
REAL RHO
* ..
* .. Array Arguments ..
INTEGER DESCQ( * ), IWORK( * )
REAL D( * ), Q( * ), WORK( * )
* ..
*
* Purpose
* =======
*
* PSLAED1 computes the updated eigensystem of a diagonal
* matrix after modification by a rank-one symmetric matrix,
* in parallel.
*
* T = Q(in) ( D(in) + RHO * Z*Z' ) Q'(in) = Q(out) * D(out) * Q'(out)
*
* where Z = Q'u, u is a vector of length N with ones in the
* N1 and N1 + 1 th elements and zeros elsewhere.
*
* The eigenvectors of the original matrix are stored in Q, and the
* eigenvalues are in D. The algorithm consists of three stages:
*
* The first stage consists of deflating the size of the problem
* when there are multiple eigenvalues or if there is a zero in
* the Z vector. For each such occurence the dimension of the
* secular equation problem is reduced by one. This stage is
* performed by the routine PSLAED2.
*
* The second stage consists of calculating the updated
* eigenvalues. This is done by finding the roots of the secular
* equation via the routine SLAED4 (as called by PSLAED3).
* This routine also calculates the eigenvectors of the current
* problem.
*
* The final stage consists of computing the updated eigenvectors
* directly using the updated eigenvalues. The eigenvectors for
* the current problem are multiplied with the eigenvectors from
* the overall problem.
*
* Arguments
* =========
*
* N (global input) INTEGER
* The order of the tridiagonal matrix T. N >= 0.
*
*
* N1 (input) INTEGER
* The location of the last eigenvalue in the leading
* sub-matrix.
* min(1,N) <= N1 <= N.
*
* D (global input/output) REAL array, dimension (N)
* On entry,the eigenvalues of the rank-1-perturbed matrix.
* On exit, the eigenvalues of the repaired matrix.
*
* ID (global input) INTEGER
* Q's global row/col index, which points to the beginning
* of the submatrix which is to be operated on.
*
* Q (local output) REAL array,
* global dimension (N, N),
* local dimension ( LLD_Q, LOCc(JQ+N-1))
* Q contains the orthonormal eigenvectors of the symmetric
* tridiagonal matrix.
*
* 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.
*
* RHO (input) REAL
* The subdiagonal entry used to create the rank-1 modification.
*
* WORK (local workspace/output) REAL array,
* dimension 6*N + 2*NP*NQ
*
* IWORK (local workspace/output) INTEGER array,
* dimension 7*N + 8*NPCOL + 2
*
* 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 ith eigenvalue.
*
* =====================================================================
*
* .. Parameters ..
*
INTEGER BLOCK_CYCLIC_2D, DLEN_, DTYPE_, CTXT_, M_, N_,
$ MB_, NB_, RSRC_, CSRC_, LLD_
PARAMETER ( BLOCK_CYCLIC_2D = 1, DLEN_ = 9, DTYPE_ = 1,
$ CTXT_ = 2, M_ = 3, N_ = 4, MB_ = 5, NB_ = 6,
$ RSRC_ = 7, CSRC_ = 8, LLD_ = 9 )
REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
* ..
* .. Local Scalars ..
INTEGER COL, COLTYP, IBUF, ICTOT, ICTXT, IDLMDA, IIQ,
$ INDCOL, INDROW, INDX, INDXC, INDXP, INDXR, INQ,
$ IPQ, IPQ2, IPSM, IPU, IPWORK, IQ1, IQ2, IQCOL,
$ IQQ, IQROW, IW, IZ, J, JC, JJ2C, JJC, JJQ, JNQ,
$ K, LDQ, LDQ2, LDU, MYCOL, MYROW, NB, NN, NN1,
$ NN2, NP, NPCOL, NPROW, NQ
* ..
* .. Local Arrays ..
INTEGER DESCQ2( DLEN_ ), DESCU( DLEN_ )
* ..
* .. External Functions ..
INTEGER NUMROC
EXTERNAL NUMROC
* ..
* .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO, DESCINIT, INFOG1L, INFOG2L,
$ PSGEMM, PSLAED2, PSLAED3, PSLAEDZ, PSLASET,
$ PXERBLA, SCOPY
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN
* ..
* .. Executable Statements ..
*
* This is just to keep ftnchek and toolpack/1 happy
IF( BLOCK_CYCLIC_2D*CSRC_*CTXT_*DLEN_*DTYPE_*LLD_*MB_*M_*NB_*N_*
$ RSRC_.LT.0 )RETURN
*
*
* Test the input parameters.
*
CALL BLACS_GRIDINFO( DESCQ( CTXT_ ), NPROW, NPCOL, MYROW, MYCOL )
INFO = 0
IF( NPROW.EQ.-1 ) THEN
INFO = -( 600+CTXT_ )
ELSE IF( N.LT.0 ) THEN
INFO = -1
ELSE IF( ID.GT.DESCQ( N_ ) ) THEN
INFO = -4
ELSE IF( N1.GE.N ) THEN
INFO = -2
END IF
IF( INFO.NE.0 ) THEN
CALL PXERBLA( DESCQ( CTXT_ ), 'PSLAED1', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
*
* The following values are integer pointers which indicate
* the portion of the workspace used by a particular array
* in PSLAED2 and PSLAED3.
*
ICTXT = DESCQ( CTXT_ )
NB = DESCQ( NB_ )
LDQ = DESCQ( LLD_ )
*
CALL INFOG2L( IQ-1+ID, JQ-1+ID, DESCQ, NPROW, NPCOL, MYROW, MYCOL,
$ IIQ, JJQ, IQROW, IQCOL )
*
NP = NUMROC( N, DESCQ( MB_ ), MYROW, IQROW, NPROW )
NQ = NUMROC( N, DESCQ( NB_ ), MYCOL, IQCOL, NPCOL )
*
LDQ2 = MAX( NP, 1 )
LDU = LDQ2
*
IZ = 1
IDLMDA = IZ + N
IW = IDLMDA + N
IPQ2 = IW + N
IPU = IPQ2 + LDQ2*NQ
IBUF = IPU + LDU*NQ
* (IBUF est de taille 3*N au maximum)
*
ICTOT = 1
IPSM = ICTOT + NPCOL*4
INDX = IPSM + NPCOL*4
INDXC = INDX + N
INDXP = INDXC + N
INDCOL = INDXP + N
COLTYP = INDCOL + N
INDROW = COLTYP + N
INDXR = INDROW + N
*
CALL DESCINIT( DESCQ2, N, N, NB, NB, IQROW, IQCOL, ICTXT, LDQ2,
$ INFO )
CALL DESCINIT( DESCU, N, N, NB, NB, IQROW, IQCOL, ICTXT, LDU,
$ INFO )
*
* Form the z-vector which consists of the last row of Q_1 and the
* first row of Q_2.
*
IPWORK = IDLMDA
CALL PSLAEDZ( N, N1, ID, Q, IQ, JQ, LDQ, DESCQ, WORK( IZ ),
$ WORK( IPWORK ) )
*
* Deflate eigenvalues.
*
IPQ = IIQ + ( JJQ-1 )*LDQ
CALL PSLAED2( ICTXT, K, N, N1, NB, D, IQROW, IQCOL, Q( IPQ ), LDQ,
$ RHO, WORK( IZ ), WORK( IW ), WORK( IDLMDA ),
$ WORK( IPQ2 ), LDQ2, WORK( IBUF ), IWORK( ICTOT ),
$ IWORK( IPSM ), NPCOL, IWORK( INDX ), IWORK( INDXC ),
$ IWORK( INDXP ), IWORK( INDCOL ), IWORK( COLTYP ),
$ NN, NN1, NN2, IQ1, IQ2 )
*
* Solve Secular Equation.
*
IF( K.NE.0 ) THEN
CALL PSLASET( 'A', N, N, ZERO, ONE, WORK( IPU ), 1, 1, DESCU )
CALL PSLAED3( ICTXT, K, N, NB, D, IQROW, IQCOL, RHO,
$ WORK( IDLMDA ), WORK( IW ), WORK( IZ ),
$ WORK( IPU ), LDQ2, WORK( IBUF ), IWORK( INDX ),
$ IWORK( INDCOL ), IWORK( INDROW ), IWORK( INDXR ),
$ IWORK( INDXC ), IWORK( ICTOT ), NPCOL, INFO )
*
* Compute the updated eigenvectors.
*
IQQ = MIN( IQ1, IQ2 )
IF( NN1.GT.0 ) THEN
INQ = IQ - 1 + ID
JNQ = JQ - 1 + ID + IQQ - 1
CALL PSGEMM( 'N', 'N', N1, NN, NN1, ONE, WORK( IPQ2 ), 1,
$ IQ1, DESCQ2, WORK( IPU ), IQ1, IQQ, DESCU,
$ ZERO, Q, INQ, JNQ, DESCQ )
END IF
IF( NN2.GT.0 ) THEN
INQ = IQ - 1 + ID + N1
JNQ = JQ - 1 + ID + IQQ - 1
CALL PSGEMM( 'N', 'N', N-N1, NN, NN2, ONE, WORK( IPQ2 ),
$ N1+1, IQ2, DESCQ2, WORK( IPU ), IQ2, IQQ,
$ DESCU, ZERO, Q, INQ, JNQ, DESCQ )
END IF
*
DO 10 J = K + 1, N
JC = IWORK( INDX+J-1 )
CALL INFOG1L( JQ-1+JC, NB, NPCOL, MYCOL, IQCOL, JJC, COL )
CALL INFOG1L( JC, NB, NPCOL, MYCOL, IQCOL, JJ2C, COL )
IF( MYCOL.EQ.COL ) THEN
IQ2 = IPQ2 + ( JJ2C-1 )*LDQ2
INQ = IPQ + ( JJC-1 )*LDQ
CALL SCOPY( NP, WORK( IQ2 ), 1, Q( INQ ), 1 )
END IF
10 CONTINUE
END IF
*
20 CONTINUE
RETURN
*
* End of PSLAED1
*
END
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