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|
SUBROUTINE PCLATTRS( UPLO, TRANS, DIAG, NORMIN, N, A, IA, JA,
$ DESCA, X, IX, JX, DESCX, SCALE, CNORM, INFO )
*
* -- ScaLAPACK routine (version 1.7) --
* University of Tennessee, Knoxville, Oak Ridge National Laboratory,
* and University of California, Berkeley.
* July 31, 2001
*
* .. Scalar Arguments ..
CHARACTER DIAG, NORMIN, TRANS, UPLO
INTEGER IA, INFO, IX, JA, JX, N
REAL SCALE
* ..
* .. Array Arguments ..
INTEGER DESCA( * ), DESCX( * )
REAL CNORM( * )
COMPLEX A( * ), X( * )
* ..
*
* Purpose
* =======
*
* PCLATTRS solves one of the triangular systems
*
* A * x = s*b, A**T * x = s*b, or A**H * x = s*b,
*
* with scaling to prevent overflow. Here A is an upper or lower
* triangular matrix, A**T denotes the transpose of A, A**H denotes the
* conjugate transpose of A, x and b are n-element vectors, and s is a
* scaling factor, usually less than or equal to 1, chosen so that the
* components of x will be less than the overflow threshold. If the
* unscaled problem will not cause overflow, the Level 2 PBLAS routine
* PCTRSV is called. If the matrix A is singular (A(j,j) = 0 for some j)
* then s is set to 0 and a non-trivial solution to A*x = 0 is returned.
*
* This is very slow relative to PCTRSV. This should only be used
* when scaling is necessary to control overflow, or when it is modified
* to scale better.
* 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 r x c.
* LOCr( K ) denotes the number of elements of K that a process
* would receive if K were distributed over the r 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 c 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
* =========
*
* UPLO (global input) CHARACTER*1
* Specifies whether the matrix A is upper or lower triangular.
* = 'U': Upper triangular
* = 'L': Lower triangular
*
* TRANS (global input) CHARACTER*1
* Specifies the operation applied to A.
* = 'N': Solve A * x = s*b (No transpose)
* = 'T': Solve A**T * x = s*b (Transpose)
* = 'C': Solve A**H * x = s*b (Conjugate transpose)
*
* DIAG (global input) CHARACTER*1
* Specifies whether or not the matrix A is unit triangular.
* = 'N': Non-unit triangular
* = 'U': Unit triangular
*
* NORMIN (global input) CHARACTER*1
* Specifies whether CNORM has been set or not.
* = 'Y': CNORM contains the column norms on entry
* = 'N': CNORM is not set on entry. On exit, the norms will
* be computed and stored in CNORM.
*
* N (global input) INTEGER
* The order of the matrix A. N >= 0.
*
* A (local input) COMPLEX array, dimension (DESCA(LLD_),*)
* The triangular matrix A. If UPLO = 'U', the leading n by n
* upper triangular part of the array A contains the upper
* triangular matrix, and the strictly lower triangular part of
* A is not referenced. If UPLO = 'L', the leading n by n lower
* triangular part of the array A contains the lower triangular
* matrix, and the strictly upper triangular part of A is not
* referenced. If DIAG = 'U', the diagonal elements of A are
* also not referenced and are assumed to be 1.
*
* IA (global input) pointer to INTEGER
* The global row index of the submatrix of the distributed
* matrix A to operate on.
*
* JA (global input) pointer to INTEGER
* The global column index of the submatrix of the distributed
* matrix A to operate on.
*
* DESCA (global and local input) INTEGER array of dimension DLEN_.
* The array descriptor for the distributed matrix A.
*
* X (local input/output) COMPLEX array,
* dimension (DESCX(LLD_),*)
* On entry, the right hand side b of the triangular system.
* On exit, X is overwritten by the solution vector x.
*
* IX (global input) pointer to INTEGER
* The global row index of the submatrix of the distributed
* matrix X to operate on.
*
* JX (global input) pointer to INTEGER
* The global column index of the submatrix of the distributed
* matrix X to operate on.
*
* DESCX (global and local input) INTEGER array of dimension DLEN_.
* The array descriptor for the distributed matrix X.
*
* SCALE (global output) REAL
* The scaling factor s for the triangular system
* A * x = s*b, A**T * x = s*b, or A**H * x = s*b.
* If SCALE = 0, the matrix A is singular or badly scaled, and
* the vector x is an exact or approximate solution to A*x = 0.
*
* CNORM (global input or global output) REAL array,
* dimension (N)
* If NORMIN = 'Y', CNORM is an input argument and CNORM(j)
* contains the norm of the off-diagonal part of the j-th column
* of A. If TRANS = 'N', CNORM(j) must be greater than or equal
* to the infinity-norm, and if TRANS = 'T' or 'C', CNORM(j)
* must be greater than or equal to the 1-norm.
*
* If NORMIN = 'N', CNORM is an output argument and CNORM(j)
* returns the 1-norm of the offdiagonal part of the j-th column
* of A.
*
* INFO (global output) INTEGER
* = 0: successful exit
* < 0: if INFO = -k, the k-th argument had an illegal value
*
* Further Details
* ======= =======
*
* A rough bound on x is computed; if that is less than overflow, PCTRSV
* is called, otherwise, specific code is used which checks for possible
* overflow or divide-by-zero at every operation.
*
* A columnwise scheme is used for solving A*x = b. The basic algorithm
* if A is lower triangular is
*
* x[1:n] := b[1:n]
* for j = 1, ..., n
* x(j) := x(j) / A(j,j)
* x[j+1:n] := x[j+1:n] - x(j) * A[j+1:n,j]
* end
*
* Define bounds on the components of x after j iterations of the loop:
* M(j) = bound on x[1:j]
* G(j) = bound on x[j+1:n]
* Initially, let M(0) = 0 and G(0) = max{x(i), i=1,...,n}.
*
* Then for iteration j+1 we have
* M(j+1) <= G(j) / | A(j+1,j+1) |
* G(j+1) <= G(j) + M(j+1) * | A[j+2:n,j+1] |
* <= G(j) ( 1 + CNORM(j+1) / | A(j+1,j+1) | )
*
* where CNORM(j+1) is greater than or equal to the infinity-norm of
* column j+1 of A, not counting the diagonal. Hence
*
* G(j) <= G(0) product ( 1 + CNORM(i) / | A(i,i) | )
* 1<=i<=j
* and
*
* |x(j)| <= ( G(0) / |A(j,j)| ) product ( 1 + CNORM(i) / |A(i,i)| )
* 1<=i< j
*
* Since |x(j)| <= M(j), we use the Level 2 PBLAS routine PCTRSV if the
* reciprocal of the largest M(j), j=1,..,n, is larger than
* max(underflow, 1/overflow).
*
* The bound on x(j) is also used to determine when a step in the
* columnwise method can be performed without fear of overflow. If
* the computed bound is greater than a large constant, x is scaled to
* prevent overflow, but if the bound overflows, x is set to 0, x(j) to
* 1, and scale to 0, and a non-trivial solution to A*x = 0 is found.
*
* Similarly, a row-wise scheme is used to solve A**T *x = b or
* A**H *x = b. The basic algorithm for A upper triangular is
*
* for j = 1, ..., n
* x(j) := ( b(j) - A[1:j-1,j]' * x[1:j-1] ) / A(j,j)
* end
*
* We simultaneously compute two bounds
* G(j) = bound on ( b(i) - A[1:i-1,i]' * x[1:i-1] ), 1<=i<=j
* M(j) = bound on x(i), 1<=i<=j
*
* The initial values are G(0) = 0, M(0) = max{b(i), i=1,..,n}, and we
* add the constraint G(j) >= G(j-1) and M(j) >= M(j-1) for j >= 1.
* Then the bound on x(j) is
*
* M(j) <= M(j-1) * ( 1 + CNORM(j) ) / | A(j,j) |
*
* <= M(0) * product ( ( 1 + CNORM(i) ) / |A(i,i)| )
* 1<=i<=j
*
* and we can safely call PCTRSV if 1/M(n) and 1/G(n) are both greater
* than max(underflow, 1/overflow).
*
* Last modified by: Mark R. Fahey, August 2000
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO, HALF, ONE, TWO
PARAMETER ( ZERO = 0.0E+0, HALF = 0.5E+0, ONE = 1.0E+0,
$ TWO = 2.0E+0 )
COMPLEX CZERO, CONE
PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ),
$ CONE = ( 1.0E+0, 0.0E+0 ) )
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 )
* ..
* .. Local Scalars ..
LOGICAL NOTRAN, NOUNIT, UPPER
INTEGER CONTXT, CSRC, I, ICOL, ICOLX, IMAX, IROW,
$ IROWX, ITMP1, ITMP1X, ITMP2, ITMP2X, J, JFIRST,
$ JINC, JLAST, LDA, LDX, MB, MYCOL, MYROW, NB,
$ NPCOL, NPROW, RSRC
REAL BIGNUM, GROW, REC, SMLNUM, TJJ, TMAX, TSCAL,
$ XBND, XJ, CR, CI
REAL XMAX( 1 )
COMPLEX CSUMJ, TJJS, USCAL, XJTMP, ZDUM
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER ISAMAX
REAL PSLAMCH
EXTERNAL LSAME, ISAMAX, PSLAMCH
* ..
* .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO, SGSUM2D, SSCAL, INFOG2L,
$ PSCASUM, PSLABAD, PXERBLA, PCAMAX, PCAXPY,
$ PCDOTC, PCDOTU, PCSSCAL, PCLASET, PCSCAL,
$ PCTRSV, CGEBR2D, CGEBS2D, SLADIV
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, REAL, CMPLX, CONJG, AIMAG, MAX, MIN
* ..
* .. Statement Functions ..
REAL CABS1, CABS2
* ..
* .. Statement Function definitions ..
CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) )
CABS2( ZDUM ) = ABS( REAL( ZDUM ) / 2.E0 ) +
$ ABS( AIMAG( ZDUM ) / 2.E0 )
* ..
* .. Executable Statements ..
*
INFO = 0
UPPER = LSAME( UPLO, 'U' )
NOTRAN = LSAME( TRANS, 'N' )
NOUNIT = LSAME( DIAG, 'N' )
*
CONTXT = DESCA( CTXT_ )
RSRC = DESCA( RSRC_ )
CSRC = DESCA( CSRC_ )
MB = DESCA( MB_ )
NB = DESCA( NB_ )
LDA = DESCA( LLD_ )
LDX = DESCX( LLD_ )
*
* Test the input parameters.
*
IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
INFO = -1
ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) .AND. .NOT.
$ LSAME( TRANS, 'C' ) ) THEN
INFO = -2
ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
INFO = -3
ELSE IF( .NOT.LSAME( NORMIN, 'Y' ) .AND. .NOT.
$ LSAME( NORMIN, 'N' ) ) THEN
INFO = -4
ELSE IF( N.LT.0 ) THEN
INFO = -5
END IF
*
CALL BLACS_GRIDINFO( CONTXT, NPROW, NPCOL, MYROW, MYCOL )
*
IF( INFO.NE.0 ) THEN
CALL PXERBLA( CONTXT, 'PCLATTRS', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
*
* Determine machine dependent parameters to control overflow.
*
SMLNUM = PSLAMCH( CONTXT, 'Safe minimum' )
BIGNUM = ONE / SMLNUM
CALL PSLABAD( CONTXT, SMLNUM, BIGNUM )
SMLNUM = SMLNUM / PSLAMCH( CONTXT, 'Precision' )
BIGNUM = ONE / SMLNUM
SCALE = ONE
*
*
IF( LSAME( NORMIN, 'N' ) ) THEN
*
* Compute the 1-norm of each column, not including the diagonal.
*
IF( UPPER ) THEN
*
* A is upper triangular.
*
CNORM( 1 ) = ZERO
DO 10 J = 2, N
CALL PSCASUM( J-1, CNORM( J ), A, IA, JA+J-1, DESCA, 1 )
10 CONTINUE
ELSE
*
* A is lower triangular.
*
DO 20 J = 1, N - 1
CALL PSCASUM( N-J, CNORM( J ), A, IA+J, JA+J-1, DESCA,
$ 1 )
20 CONTINUE
CNORM( N ) = ZERO
END IF
CALL SGSUM2D( CONTXT, 'Row', ' ', N, 1, CNORM, 1, -1, -1 )
END IF
*
* Scale the column norms by TSCAL if the maximum element in CNORM is
* greater than BIGNUM/2.
*
IMAX = ISAMAX( N, CNORM, 1 )
TMAX = CNORM( IMAX )
IF( TMAX.LE.BIGNUM*HALF ) THEN
TSCAL = ONE
ELSE
TSCAL = HALF / ( SMLNUM*TMAX )
CALL SSCAL( N, TSCAL, CNORM, 1 )
END IF
*
* Compute a bound on the computed solution vector to see if the
* Level 2 PBLAS routine PCTRSV can be used.
*
XMAX( 1 ) = ZERO
CALL PCAMAX( N, ZDUM, IMAX, X, IX, JX, DESCX, 1 )
XMAX( 1 ) = CABS2( ZDUM )
CALL SGSUM2D( CONTXT, 'Row', ' ', 1, 1, XMAX, 1, -1, -1 )
XBND = XMAX( 1 )
*
IF( NOTRAN ) THEN
*
* Compute the growth in A * x = b.
*
IF( UPPER ) THEN
JFIRST = N
JLAST = 1
JINC = -1
ELSE
JFIRST = 1
JLAST = N
JINC = 1
END IF
*
IF( TSCAL.NE.ONE ) THEN
GROW = ZERO
GO TO 50
END IF
*
IF( NOUNIT ) THEN
*
* A is non-unit triangular.
*
* Compute GROW = 1/G(j) and XBND = 1/M(j).
* Initially, G(0) = max{x(i), i=1,...,n}.
*
GROW = HALF / MAX( XBND, SMLNUM )
XBND = GROW
DO 30 J = JFIRST, JLAST, JINC
*
* Exit the loop if the growth factor is too small.
*
IF( GROW.LE.SMLNUM )
$ GO TO 50
*
* TJJS = A( J, J )
CALL INFOG2L( IA+J-1, JA+J-1, DESCA, NPROW, NPCOL, MYROW,
$ MYCOL, IROW, ICOL, ITMP1, ITMP2 )
IF( ( MYROW.EQ.ITMP1 ) .AND. ( MYCOL.EQ.ITMP2 ) ) THEN
TJJS = A( ( ICOL-1 )*LDA+IROW )
CALL CGEBS2D( CONTXT, 'All', ' ', 1, 1, TJJS, 1 )
ELSE
CALL CGEBR2D( CONTXT, 'All', ' ', 1, 1, TJJS, 1,
$ ITMP1, ITMP2 )
END IF
TJJ = CABS1( TJJS )
*
IF( TJJ.GE.SMLNUM ) THEN
*
* M(j) = G(j-1) / abs(A(j,j))
*
XBND = MIN( XBND, MIN( ONE, TJJ )*GROW )
ELSE
*
* M(j) could overflow, set XBND to 0.
*
XBND = ZERO
END IF
*
IF( TJJ+CNORM( J ).GE.SMLNUM ) THEN
*
* G(j) = G(j-1)*( 1 + CNORM(j) / abs(A(j,j)) )
*
GROW = GROW*( TJJ / ( TJJ+CNORM( J ) ) )
ELSE
*
* G(j) could overflow, set GROW to 0.
*
GROW = ZERO
END IF
30 CONTINUE
GROW = XBND
ELSE
*
* A is unit triangular.
*
* Compute GROW = 1/G(j), where G(0) = max{x(i), i=1,...,n}.
*
GROW = MIN( ONE, HALF / MAX( XBND, SMLNUM ) )
DO 40 J = JFIRST, JLAST, JINC
*
* Exit the loop if the growth factor is too small.
*
IF( GROW.LE.SMLNUM )
$ GO TO 50
*
* G(j) = G(j-1)*( 1 + CNORM(j) )
*
GROW = GROW*( ONE / ( ONE+CNORM( J ) ) )
40 CONTINUE
END IF
50 CONTINUE
*
ELSE
*
* Compute the growth in A**T * x = b or A**H * x = b.
*
IF( UPPER ) THEN
JFIRST = 1
JLAST = N
JINC = 1
ELSE
JFIRST = N
JLAST = 1
JINC = -1
END IF
*
IF( TSCAL.NE.ONE ) THEN
GROW = ZERO
GO TO 80
END IF
*
IF( NOUNIT ) THEN
*
* A is non-unit triangular.
*
* Compute GROW = 1/G(j) and XBND = 1/M(j).
* Initially, M(0) = max{x(i), i=1,...,n}.
*
GROW = HALF / MAX( XBND, SMLNUM )
XBND = GROW
DO 60 J = JFIRST, JLAST, JINC
*
* Exit the loop if the growth factor is too small.
*
IF( GROW.LE.SMLNUM )
$ GO TO 80
*
* G(j) = max( G(j-1), M(j-1)*( 1 + CNORM(j) ) )
*
XJ = ONE + CNORM( J )
GROW = MIN( GROW, XBND / XJ )
*
* TJJS = A( J, J )
CALL INFOG2L( IA+J-1, JA+J-1, DESCA, NPROW, NPCOL, MYROW,
$ MYCOL, IROW, ICOL, ITMP1, ITMP2 )
IF( ( MYROW.EQ.ITMP1 ) .AND. ( MYCOL.EQ.ITMP2 ) ) THEN
TJJS = A( ( ICOL-1 )*LDA+IROW )
CALL CGEBS2D( CONTXT, 'All', ' ', 1, 1, TJJS, 1 )
ELSE
CALL CGEBR2D( CONTXT, 'All', ' ', 1, 1, TJJS, 1,
$ ITMP1, ITMP2 )
END IF
TJJ = CABS1( TJJS )
*
IF( TJJ.GE.SMLNUM ) THEN
*
* M(j) = M(j-1)*( 1 + CNORM(j) ) / abs(A(j,j))
*
IF( XJ.GT.TJJ )
$ XBND = XBND*( TJJ / XJ )
ELSE
*
* M(j) could overflow, set XBND to 0.
*
XBND = ZERO
END IF
60 CONTINUE
GROW = MIN( GROW, XBND )
ELSE
*
* A is unit triangular.
*
* Compute GROW = 1/G(j), where G(0) = max{x(i), i=1,...,n}.
*
GROW = MIN( ONE, HALF / MAX( XBND, SMLNUM ) )
DO 70 J = JFIRST, JLAST, JINC
*
* Exit the loop if the growth factor is too small.
*
IF( GROW.LE.SMLNUM )
$ GO TO 80
*
* G(j) = ( 1 + CNORM(j) )*G(j-1)
*
XJ = ONE + CNORM( J )
GROW = GROW / XJ
70 CONTINUE
END IF
80 CONTINUE
END IF
*
IF( ( GROW*TSCAL ).GT.SMLNUM ) THEN
*
* Use the Level 2 PBLAS solve if the reciprocal of the bound on
* elements of X is not too small.
*
CALL PCTRSV( UPLO, TRANS, DIAG, N, A, IA, JA, DESCA, X, IX, JX,
$ DESCX, 1 )
ELSE
*
* Use a Level 1 PBLAS solve, scaling intermediate results.
*
IF( XMAX( 1 ).GT.BIGNUM*HALF ) THEN
*
* Scale X so that its components are less than or equal to
* BIGNUM in absolute value.
*
SCALE = ( BIGNUM*HALF ) / XMAX( 1 )
CALL PCSSCAL( N, SCALE, X, IX, JX, DESCX, 1 )
XMAX( 1 ) = BIGNUM
ELSE
XMAX( 1 ) = XMAX( 1 )*TWO
END IF
*
IF( NOTRAN ) THEN
*
* Solve A * x = b
*
DO 100 J = JFIRST, JLAST, JINC
*
* Compute x(j) = b(j) / A(j,j), scaling x if necessary.
*
* XJ = CABS1( X( J ) )
CALL INFOG2L( IX+J-1, JX, DESCX, NPROW, NPCOL, MYROW,
$ MYCOL, IROWX, ICOLX, ITMP1X, ITMP2X )
IF( ( MYROW.EQ.ITMP1X ) .AND. ( MYCOL.EQ.ITMP2X ) ) THEN
XJTMP = X( IROWX )
CALL CGEBS2D( CONTXT, 'All', ' ', 1, 1, XJTMP, 1 )
ELSE
CALL CGEBR2D( CONTXT, 'All', ' ', 1, 1, XJTMP, 1,
$ ITMP1X, ITMP2X )
END IF
XJ = CABS1( XJTMP )
IF( NOUNIT ) THEN
* TJJS = A( J, J )*TSCAL
CALL INFOG2L( IA+J-1, JA+J-1, DESCA, NPROW, NPCOL,
$ MYROW, MYCOL, IROW, ICOL, ITMP1, ITMP2 )
IF( ( MYROW.EQ.ITMP1 ) .AND. ( MYCOL.EQ.ITMP2 ) ) THEN
TJJS = A( ( ICOL-1 )*LDA+IROW )*TSCAL
CALL CGEBS2D( CONTXT, 'All', ' ', 1, 1, TJJS, 1 )
ELSE
CALL CGEBR2D( CONTXT, 'All', ' ', 1, 1, TJJS, 1,
$ ITMP1, ITMP2 )
END IF
ELSE
TJJS = TSCAL
IF( TSCAL.EQ.ONE )
$ GO TO 90
END IF
TJJ = CABS1( TJJS )
IF( TJJ.GT.SMLNUM ) THEN
*
* abs(A(j,j)) > SMLNUM:
*
IF( TJJ.LT.ONE ) THEN
IF( XJ.GT.TJJ*BIGNUM ) THEN
*
* Scale x by 1/b(j).
*
REC = ONE / XJ
CALL PCSSCAL( N, REC, X, IX, JX, DESCX, 1 )
XJTMP = XJTMP*REC
SCALE = SCALE*REC
XMAX( 1 ) = XMAX( 1 )*REC
END IF
END IF
* X( J ) = CLADIV( X( J ), TJJS )
* XJ = CABS1( X( J ) )
CALL SLADIV( REAL( XJTMP ), AIMAG( XJTMP ),
$ REAL( TJJS ), AIMAG( TJJS ), CR, CI )
XJTMP = CMPLX( CR, CI )
XJ = CABS1( XJTMP )
IF( ( MYROW.EQ.ITMP1X ) .AND. ( MYCOL.EQ.ITMP2X ) )
$ THEN
X( IROWX ) = XJTMP
END IF
ELSE IF( TJJ.GT.ZERO ) THEN
*
* 0 < abs(A(j,j)) <= SMLNUM:
*
IF( XJ.GT.TJJ*BIGNUM ) THEN
*
* Scale x by (1/abs(x(j)))*abs(A(j,j))*BIGNUM
* to avoid overflow when dividing by A(j,j).
*
REC = ( TJJ*BIGNUM ) / XJ
IF( CNORM( J ).GT.ONE ) THEN
*
* Scale by 1/CNORM(j) to avoid overflow when
* multiplying x(j) times column j.
*
REC = REC / CNORM( J )
END IF
CALL PCSSCAL( N, REC, X, IX, JX, DESCX, 1 )
XJTMP = XJTMP*REC
SCALE = SCALE*REC
XMAX( 1 ) = XMAX( 1 )*REC
END IF
* X( J ) = CLADIV( X( J ), TJJS )
* XJ = CABS1( X( J ) )
CALL SLADIV( REAL( XJTMP ), AIMAG( XJTMP ),
$ REAL( TJJS ), AIMAG( TJJS ), CR, CI )
XJTMP = CMPLX( CR, CI )
XJ = CABS1( XJTMP )
IF( ( MYROW.EQ.ITMP1X ) .AND. ( MYCOL.EQ.ITMP2X ) )
$ THEN
X( IROWX ) = XJTMP
END IF
ELSE
*
* A(j,j) = 0: Set x(1:n) = 0, x(j) = 1, and
* scale = 0, and compute a solution to A*x = 0.
*
CALL PCLASET( ' ', N, 1, CZERO, CZERO, X, IX, JX,
$ DESCX )
IF( ( MYROW.EQ.ITMP1X ) .AND. ( MYCOL.EQ.ITMP2X ) )
$ THEN
X( IROWX ) = CONE
END IF
XJTMP = CONE
XJ = ONE
SCALE = ZERO
XMAX( 1 ) = ZERO
END IF
90 CONTINUE
*
* Scale x if necessary to avoid overflow when adding a
* multiple of column j of A.
*
IF( XJ.GT.ONE ) THEN
REC = ONE / XJ
IF( CNORM( J ).GT.( BIGNUM-XMAX( 1 ) )*REC ) THEN
*
* Scale x by 1/(2*abs(x(j))).
*
REC = REC*HALF
CALL PCSSCAL( N, REC, X, IX, JX, DESCX, 1 )
XJTMP = XJTMP*REC
SCALE = SCALE*REC
END IF
ELSE IF( XJ*CNORM( J ).GT.( BIGNUM-XMAX( 1 ) ) ) THEN
*
* Scale x by 1/2.
*
CALL PCSSCAL( N, HALF, X, IX, JX, DESCX, 1 )
XJTMP = XJTMP*HALF
SCALE = SCALE*HALF
END IF
*
IF( UPPER ) THEN
IF( J.GT.1 ) THEN
*
* Compute the update
* x(1:j-1) := x(1:j-1) - x(j) * A(1:j-1,j)
*
ZDUM = -XJTMP*TSCAL
CALL PCAXPY( J-1, ZDUM, A, IA, JA+J-1, DESCA, 1, X,
$ IX, JX, DESCX, 1 )
CALL PCAMAX( J-1, ZDUM, IMAX, X, IX, JX, DESCX, 1 )
XMAX( 1 ) = CABS1( ZDUM )
CALL SGSUM2D( CONTXT, 'Row', ' ', 1, 1, XMAX, 1,
$ -1, -1 )
END IF
ELSE
IF( J.LT.N ) THEN
*
* Compute the update
* x(j+1:n) := x(j+1:n) - x(j) * A(j+1:n,j)
*
ZDUM = -XJTMP*TSCAL
CALL PCAXPY( N-J, ZDUM, A, IA+J, JA+J-1, DESCA, 1,
$ X, IX+J, JX, DESCX, 1 )
CALL PCAMAX( N-J, ZDUM, I, X, IX+J, JX, DESCX, 1 )
XMAX( 1 ) = CABS1( ZDUM )
CALL SGSUM2D( CONTXT, 'Row', ' ', 1, 1, XMAX, 1,
$ -1, -1 )
END IF
END IF
100 CONTINUE
*
ELSE IF( LSAME( TRANS, 'T' ) ) THEN
*
* Solve A**T * x = b
*
DO 120 J = JFIRST, JLAST, JINC
*
* Compute x(j) = b(j) - sum A(k,j)*x(k).
* k<>j
*
* XJ = CABS1( X( J ) )
CALL INFOG2L( IX+J-1, JX, DESCX, NPROW, NPCOL, MYROW,
$ MYCOL, IROWX, ICOLX, ITMP1X, ITMP2X )
IF( ( MYROW.EQ.ITMP1X ) .AND. ( MYCOL.EQ.ITMP2X ) ) THEN
XJTMP = X( IROWX )
CALL CGEBS2D( CONTXT, 'All', ' ', 1, 1, XJTMP, 1 )
ELSE
CALL CGEBR2D( CONTXT, 'All', ' ', 1, 1, XJTMP, 1,
$ ITMP1X, ITMP2X )
END IF
XJ = CABS1( XJTMP )
USCAL = CMPLX( TSCAL )
REC = ONE / MAX( XMAX( 1 ), ONE )
IF( CNORM( J ).GT.( BIGNUM-XJ )*REC ) THEN
*
* If x(j) could overflow, scale x by 1/(2*XMAX).
*
REC = REC*HALF
IF( NOUNIT ) THEN
* TJJS = A( J, J )*TSCAL
CALL INFOG2L( IA+J-1, JA+J-1, DESCA, NPROW, NPCOL,
$ MYROW, MYCOL, IROW, ICOL, ITMP1,
$ ITMP2 )
IF( ( MYROW.EQ.ITMP1 ) .AND. ( MYCOL.EQ.ITMP2 ) )
$ THEN
TJJS = A( ( ICOL-1 )*LDA+IROW )*TSCAL
CALL CGEBS2D( CONTXT, 'All', ' ', 1, 1, TJJS,
$ 1 )
ELSE
CALL CGEBR2D( CONTXT, 'All', ' ', 1, 1, TJJS, 1,
$ ITMP1, ITMP2 )
END IF
ELSE
TJJS = TSCAL
END IF
TJJ = CABS1( TJJS )
IF( TJJ.GT.ONE ) THEN
*
* Divide by A(j,j) when scaling x if A(j,j) > 1.
*
REC = MIN( ONE, REC*TJJ )
CALL SLADIV( REAL( USCAL ), AIMAG( USCAL ),
$ REAL( TJJS ), AIMAG( TJJS ), CR, CI )
USCAL = CMPLX( CR, CI )
END IF
IF( REC.LT.ONE ) THEN
CALL PCSSCAL( N, REC, X, IX, JX, DESCX, 1 )
XJTMP = XJTMP*REC
SCALE = SCALE*REC
XMAX( 1 ) = XMAX( 1 )*REC
END IF
END IF
*
CSUMJ = CZERO
IF( USCAL.EQ.CONE ) THEN
*
* If the scaling needed for A in the dot product is 1,
* call PCDOTU to perform the dot product.
*
IF( UPPER ) THEN
CALL PCDOTU( J-1, CSUMJ, A, IA, JA+J-1, DESCA, 1,
$ X, IX, JX, DESCX, 1 )
ELSE IF( J.LT.N ) THEN
CALL PCDOTU( N-J, CSUMJ, A, IA+J, JA+J-1, DESCA, 1,
$ X, IX+J, JX, DESCX, 1 )
END IF
IF( MYCOL.EQ.ITMP2X ) THEN
CALL CGEBS2D( CONTXT, 'Row', ' ', 1, 1, CSUMJ, 1 )
ELSE
CALL CGEBR2D( CONTXT, 'Row', ' ', 1, 1, CSUMJ, 1,
$ MYROW, ITMP2X )
END IF
ELSE
*
* Otherwise, scale column of A by USCAL before dot
* product. Below is not the best way to do it.
*
IF( UPPER ) THEN
* DO 130 I = 1, J - 1
* CSUMJ = CSUMJ + ( A( I, J )*USCAL )*X( I )
* 130 CONTINUE
ZDUM = CONJG( USCAL )
CALL PCSCAL( J-1, ZDUM, A, IA, JA+J-1, DESCA, 1 )
CALL PCDOTU( J-1, CSUMJ, A, IA, JA+J-1, DESCA, 1,
$ X, IX, JX, DESCX, 1 )
CALL SLADIV( REAL( ZDUM ), AIMAG( ZDUM ),
$ REAL( USCAL ), AIMAG( USCAL ), CR, CI)
ZDUM = CMPLX( CR, CI )
CALL PCSCAL( J-1, ZDUM, A, IA, JA+J-1, DESCA, 1 )
ELSE IF( J.LT.N ) THEN
* DO 140 I = J + 1, N
* CSUMJ = CSUMJ + ( A( I, J )*USCAL )*X( I )
* 140 CONTINUE
ZDUM = CONJG( USCAL )
CALL PCSCAL( N-J, ZDUM, A, IA+J, JA+J-1, DESCA, 1 )
CALL PCDOTU( N-J, CSUMJ, A, IA+J, JA+J-1, DESCA, 1,
$ X, IX+J, JX, DESCX, 1 )
CALL SLADIV( REAL( ZDUM ), AIMAG( ZDUM ),
$ REAL( USCAL ), AIMAG( USCAL ), CR, CI)
ZDUM = CMPLX( CR, CI )
CALL PCSCAL( N-J, ZDUM, A, IA+J, JA+J-1, DESCA, 1 )
END IF
IF( MYCOL.EQ.ITMP2X ) THEN
CALL CGEBS2D( CONTXT, 'Row', ' ', 1, 1, CSUMJ, 1 )
ELSE
CALL CGEBR2D( CONTXT, 'Row', ' ', 1, 1, CSUMJ, 1,
$ MYROW, ITMP2X )
END IF
END IF
*
IF( USCAL.EQ.CMPLX( TSCAL ) ) THEN
*
* Compute x(j) := ( x(j) - CSUMJ ) / A(j,j) if 1/A(j,j)
* was not used to scale the dotproduct.
*
* X( J ) = X( J ) - CSUMJ
* XJ = CABS1( X( J ) )
XJTMP = XJTMP - CSUMJ
XJ = CABS1( XJTMP )
* IF( ( MYROW.EQ.ITMP1X ) .AND. ( MYCOL.EQ.ITMP2X ) )
* $ X( IROWX ) = XJTMP
IF( NOUNIT ) THEN
* TJJS = A( J, J )*TSCAL
CALL INFOG2L( IA+J-1, JA+J-1, DESCA, NPROW, NPCOL,
$ MYROW, MYCOL, IROW, ICOL, ITMP1,
$ ITMP2 )
IF( ( MYROW.EQ.ITMP1 ) .AND. ( MYCOL.EQ.ITMP2 ) )
$ THEN
TJJS = A( ( ICOL-1 )*LDA+IROW )*TSCAL
CALL CGEBS2D( CONTXT, 'All', ' ', 1, 1, TJJS,
$ 1 )
ELSE
CALL CGEBR2D( CONTXT, 'All', ' ', 1, 1, TJJS, 1,
$ ITMP1, ITMP2 )
END IF
ELSE
TJJS = TSCAL
IF( TSCAL.EQ.ONE )
$ GO TO 110
END IF
*
* Compute x(j) = x(j) / A(j,j), scaling if necessary.
*
TJJ = CABS1( TJJS )
IF( TJJ.GT.SMLNUM ) THEN
*
* abs(A(j,j)) > SMLNUM:
*
IF( TJJ.LT.ONE ) THEN
IF( XJ.GT.TJJ*BIGNUM ) THEN
*
* Scale X by 1/abs(x(j)).
*
REC = ONE / XJ
CALL PCSSCAL( N, REC, X, IX, JX, DESCX, 1 )
XJTMP = XJTMP*REC
SCALE = SCALE*REC
XMAX( 1 ) = XMAX( 1 )*REC
END IF
END IF
* X( J ) = CLADIV( X( J ), TJJS )
CALL SLADIV( REAL( XJTMP ), AIMAG( XJTMP ),
$ REAL( TJJS ), AIMAG( TJJS ), CR, CI )
XJTMP = CMPLX( CR, CI )
IF( ( MYROW.EQ.ITMP1X ) .AND. ( MYCOL.EQ.ITMP2X ) )
$ THEN
X( IROWX ) = XJTMP
END IF
ELSE IF( TJJ.GT.ZERO ) THEN
*
* 0 < abs(A(j,j)) <= SMLNUM:
*
IF( XJ.GT.TJJ*BIGNUM ) THEN
*
* Scale x by (1/abs(x(j)))*abs(A(j,j))*BIGNUM.
*
REC = ( TJJ*BIGNUM ) / XJ
CALL PCSSCAL( N, REC, X, IX, JX, DESCX, 1 )
XJTMP = XJTMP*REC
SCALE = SCALE*REC
XMAX( 1 ) = XMAX( 1 )*REC
END IF
* X( J ) = CLADIV( X( J ), TJJS )
CALL SLADIV( REAL( XJTMP ), AIMAG( XJTMP ),
$ REAL( TJJS ), AIMAG( TJJS ), CR, CI )
XJTMP = CMPLX( CR, CI )
IF( ( MYROW.EQ.ITMP1X ) .AND. ( MYCOL.EQ.ITMP2X ) )
$ THEN
X( IROWX ) = XJTMP
END IF
ELSE
*
* A(j,j) = 0: Set x(1:n) = 0, x(j) = 1, and
* scale = 0 and compute a solution to A**T *x = 0.
*
CALL PCLASET( ' ', N, 1, CZERO, CZERO, X, IX, JX,
$ DESCX )
IF( ( MYROW.EQ.ITMP1X ) .AND. ( MYCOL.EQ.ITMP2X ) )
$ THEN
X( IROWX ) = CONE
END IF
XJTMP = CONE
SCALE = ZERO
XMAX( 1 ) = ZERO
END IF
110 CONTINUE
ELSE
*
* Compute x(j) := x(j) / A(j,j) - CSUMJ if the dot
* product has already been divided by 1/A(j,j).
*
* X( J ) = CLADIV( X( J ), TJJS ) - CSUMJ
CALL SLADIV( REAL( XJTMP ), AIMAG( XJTMP ),
$ REAL( TJJS ), AIMAG( TJJS ), CR, CI )
XJTMP = CMPLX( CR, CI )
IF( ( MYROW.EQ.ITMP1X ) .AND. ( MYCOL.EQ.ITMP2X ) )
$ THEN
X( IROWX ) = XJTMP
END IF
END IF
XMAX( 1 ) = MAX( XMAX( 1 ), CABS1( XJTMP ) )
120 CONTINUE
*
ELSE
*
* Solve A**H * x = b
*
DO 140 J = JFIRST, JLAST, JINC
*
* Compute x(j) = b(j) - sum A(k,j)*x(k).
* k<>j
*
CALL INFOG2L( IX+J-1, JX, DESCX, NPROW, NPCOL, MYROW,
$ MYCOL, IROWX, ICOLX, ITMP1X, ITMP2X )
IF( ( MYROW.EQ.ITMP1X ) .AND. ( MYCOL.EQ.ITMP2X ) ) THEN
XJTMP = X( IROWX )
CALL CGEBS2D( CONTXT, 'All', ' ', 1, 1, XJTMP, 1 )
ELSE
CALL CGEBR2D( CONTXT, 'All', ' ', 1, 1, XJTMP, 1,
$ ITMP1X, ITMP2X )
END IF
XJ = CABS1( XJTMP )
USCAL = TSCAL
REC = ONE / MAX( XMAX( 1 ), ONE )
IF( CNORM( J ).GT.( BIGNUM-XJ )*REC ) THEN
*
* If x(j) could overflow, scale x by 1/(2*XMAX).
*
REC = REC*HALF
IF( NOUNIT ) THEN
* TJJS = CONJG( A( J, J ) )*TSCAL
CALL INFOG2L( IA+J-1, JA+J-1, DESCA, NPROW, NPCOL,
$ MYROW, MYCOL, IROW, ICOL, ITMP1,
$ ITMP2 )
IF( ( MYROW.EQ.ITMP1 ) .AND. ( MYCOL.EQ.ITMP2 ) )
$ THEN
TJJS = CONJG( A( ( ICOL-1 )*LDA+IROW ) )*TSCAL
CALL CGEBS2D( CONTXT, 'All', ' ', 1, 1, TJJS,
$ 1 )
ELSE
CALL CGEBR2D( CONTXT, 'All', ' ', 1, 1, TJJS, 1,
$ ITMP1, ITMP2 )
END IF
ELSE
TJJS = TSCAL
END IF
TJJ = CABS1( TJJS )
IF( TJJ.GT.ONE ) THEN
*
* Divide by A(j,j) when scaling x if A(j,j) > 1.
*
REC = MIN( ONE, REC*TJJ )
CALL SLADIV( REAL( USCAL ), AIMAG( USCAL ),
$ REAL( TJJS ), AIMAG( TJJS ), CR, CI )
USCAL = CMPLX( CR, CI )
END IF
IF( REC.LT.ONE ) THEN
CALL PCSSCAL( N, REC, X, IX, JX, DESCX, 1 )
XJTMP = XJTMP*REC
SCALE = SCALE*REC
XMAX( 1 ) = XMAX( 1 )*REC
END IF
END IF
*
CSUMJ = CZERO
IF( USCAL.EQ.CONE ) THEN
*
* If the scaling needed for A in the dot product is 1,
* call PCDOTC to perform the dot product.
*
IF( UPPER ) THEN
CALL PCDOTC( J-1, CSUMJ, A, IA, JA+J-1, DESCA, 1,
$ X, IX, JX, DESCX, 1 )
ELSE IF( J.LT.N ) THEN
CALL PCDOTC( N-J, CSUMJ, A, IA+J, JA+J-1, DESCA, 1,
$ X, IX+J, JX, DESCX, 1 )
END IF
IF( MYCOL.EQ.ITMP2X ) THEN
CALL CGEBS2D( CONTXT, 'Row', ' ', 1, 1, CSUMJ, 1 )
ELSE
CALL CGEBR2D( CONTXT, 'Row', ' ', 1, 1, CSUMJ, 1,
$ MYROW, ITMP2X )
END IF
ELSE
*
* Otherwise, scale column of A by USCAL before dot
* product. Below is not the best way to do it.
*
IF( UPPER ) THEN
* DO 180 I = 1, J - 1
* CSUMJ = CSUMJ + ( CONJG( A( I, J ) )*USCAL )*
* $ X( I )
* 180 CONTINUE
ZDUM = CONJG( USCAL )
CALL PCSCAL( J-1, ZDUM, A, IA, JA+J-1, DESCA, 1 )
CALL PCDOTC( J-1, CSUMJ, A, IA, JA+J-1, DESCA, 1,
$ X, IX, JX, DESCX, 1 )
CALL SLADIV( ONE, ZERO,
$ REAL( ZDUM ), AIMAG( ZDUM ), CR, CI )
ZDUM = CMPLX( CR, CI )
CALL PCSCAL( J-1, ZDUM, A, IA, JA+J-1, DESCA, 1 )
ELSE IF( J.LT.N ) THEN
* DO 190 I = J + 1, N
* CSUMJ = CSUMJ + ( CONJG( A( I, J ) )*USCAL )*
* $ X( I )
* 190 CONTINUE
ZDUM = CONJG( USCAL )
CALL PCSCAL( N-J, ZDUM, A, IA+J, JA+J-1, DESCA, 1 )
CALL PCDOTC( N-J, CSUMJ, A, IA+J, JA+J-1, DESCA, 1,
$ X, IX+J, JX, DESCX, 1 )
CALL SLADIV( ONE, ZERO,
$ REAL( ZDUM ), AIMAG( ZDUM ), CR, CI )
ZDUM = CMPLX( CR, CI )
CALL PCSCAL( N-J, ZDUM, A, IA+J, JA+J-1, DESCA, 1 )
END IF
IF( MYCOL.EQ.ITMP2X ) THEN
CALL CGEBS2D( CONTXT, 'Row', ' ', 1, 1, CSUMJ, 1 )
ELSE
CALL CGEBR2D( CONTXT, 'Row', ' ', 1, 1, CSUMJ, 1,
$ MYROW, ITMP2X )
END IF
END IF
*
IF( USCAL.EQ.CMPLX( TSCAL ) ) THEN
*
* Compute x(j) := ( x(j) - CSUMJ ) / A(j,j) if 1/A(j,j)
* was not used to scale the dotproduct.
*
* X( J ) = X( J ) - CSUMJ
* XJ = CABS1( X( J ) )
XJTMP = XJTMP - CSUMJ
XJ = CABS1( XJTMP )
* IF( ( MYROW.EQ.ITMP1X ) .AND. ( MYCOL.EQ.ITMP2X ) )
* $ X( IROWX ) = XJTMP
IF( NOUNIT ) THEN
* TJJS = CONJG( A( J, J ) )*TSCAL
CALL INFOG2L( IA+J-1, JA+J-1, DESCA, NPROW, NPCOL,
$ MYROW, MYCOL, IROW, ICOL, ITMP1,
$ ITMP2 )
IF( ( MYROW.EQ.ITMP1 ) .AND. ( MYCOL.EQ.ITMP2 ) )
$ THEN
TJJS = CONJG( A( ( ICOL-1 )*LDA+IROW ) )*TSCAL
CALL CGEBS2D( CONTXT, 'All', ' ', 1, 1, TJJS,
$ 1 )
ELSE
CALL CGEBR2D( CONTXT, 'All', ' ', 1, 1, TJJS, 1,
$ ITMP1, ITMP2 )
END IF
ELSE
TJJS = TSCAL
IF( TSCAL.EQ.ONE )
$ GO TO 130
END IF
*
* Compute x(j) = x(j) / A(j,j), scaling if necessary.
*
TJJ = CABS1( TJJS )
IF( TJJ.GT.SMLNUM ) THEN
*
* abs(A(j,j)) > SMLNUM:
*
IF( TJJ.LT.ONE ) THEN
IF( XJ.GT.TJJ*BIGNUM ) THEN
*
* Scale X by 1/abs(x(j)).
*
REC = ONE / XJ
CALL PCSSCAL( N, REC, X, IX, JX, DESCX, 1 )
XJTMP = XJTMP*REC
SCALE = SCALE*REC
XMAX( 1 ) = XMAX( 1 )*REC
END IF
END IF
* X( J ) = CLADIV( X( J ), TJJS )
CALL SLADIV( REAL( XJTMP ), AIMAG( XJTMP ),
$ REAL( TJJS ), AIMAG( TJJS ), CR, CI )
XJTMP = CMPLX( CR, CI )
IF( ( MYROW.EQ.ITMP1X ) .AND. ( MYCOL.EQ.ITMP2X ) )
$ X( IROWX ) = XJTMP
ELSE IF( TJJ.GT.ZERO ) THEN
*
* 0 < abs(A(j,j)) <= SMLNUM:
*
IF( XJ.GT.TJJ*BIGNUM ) THEN
*
* Scale x by (1/abs(x(j)))*abs(A(j,j))*BIGNUM.
*
REC = ( TJJ*BIGNUM ) / XJ
CALL PCSSCAL( N, REC, X, IX, JX, DESCX, 1 )
XJTMP = XJTMP*REC
SCALE = SCALE*REC
XMAX( 1 ) = XMAX( 1 )*REC
END IF
* X( J ) = CLADIV( X( J ), TJJS )
CALL SLADIV( REAL( XJTMP ), AIMAG( XJTMP ),
$ REAL( TJJS ), AIMAG( TJJS ), CR, CI )
XJTMP = CMPLX( CR, CI )
IF( ( MYROW.EQ.ITMP1X ) .AND. ( MYCOL.EQ.ITMP2X ) )
$ X( IROWX ) = XJTMP
ELSE
*
* A(j,j) = 0: Set x(1:n) = 0, x(j) = 1, and
* scale = 0 and compute a solution to A**H *x = 0.
*
CALL PCLASET( ' ', N, 1, CZERO, CZERO, X, IX, JX,
$ DESCX )
IF( ( MYROW.EQ.ITMP1X ) .AND. ( MYCOL.EQ.ITMP2X ) )
$ X( IROWX ) = CONE
XJTMP = CONE
SCALE = ZERO
XMAX( 1 ) = ZERO
END IF
130 CONTINUE
ELSE
*
* Compute x(j) := x(j) / A(j,j) - CSUMJ if the dot
* product has already been divided by 1/A(j,j).
*
* X( J ) = CLADIV( X( J ), TJJS ) - CSUMJ
CALL SLADIV( REAL( XJTMP ), AIMAG( XJTMP ),
$ REAL( TJJS ), AIMAG( TJJS ), CR, CI )
XJTMP = CMPLX( CR, CI )
IF( ( MYROW.EQ.ITMP1X ) .AND. ( MYCOL.EQ.ITMP2X ) )
$ X( IROWX ) = XJTMP
END IF
XMAX( 1 ) = MAX( XMAX( 1 ), CABS1( XJTMP ) )
140 CONTINUE
END IF
SCALE = SCALE / TSCAL
END IF
*
* Scale the column norms by 1/TSCAL for return.
*
IF( TSCAL.NE.ONE ) THEN
CALL SSCAL( N, ONE / TSCAL, CNORM, 1 )
END IF
*
RETURN
*
* End of PCLATTRS
*
END
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