SUBROUTINE PCUNMBR( VECT, SIDE, TRANS, M, N, K, A, IA, JA, DESCA, \$ TAU, C, IC, JC, DESCC, WORK, LWORK, INFO ) * * -- ScaLAPACK routine (version 1.7) -- * University of Tennessee, Knoxville, Oak Ridge National Laboratory, * and University of California, Berkeley. * May 1, 1997 * * .. Scalar Arguments .. CHARACTER SIDE, TRANS, VECT INTEGER IA, IC, INFO, JA, JC, K, LWORK, M, N * .. * .. Array Arguments .. INTEGER DESCA( * ), DESCC( * ) COMPLEX A( * ), C( * ), TAU( * ), WORK( * ) * .. * * Purpose * ======= * * If VECT = 'Q', PCUNMBR overwrites the general complex distributed * M-by-N matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with * * SIDE = 'L' SIDE = 'R' * TRANS = 'N': Q * sub( C ) sub( C ) * Q * TRANS = 'C': Q**H * sub( C ) sub( C ) * Q**H * * If VECT = 'P', PCUNMBR overwrites sub( C ) with * * SIDE = 'L' SIDE = 'R' * TRANS = 'N': P * sub( C ) sub( C ) * P * TRANS = 'C': P**H * sub( C ) sub( C ) * P**H * * Here Q and P**H are the unitary distributed matrices determined by * PCGEBRD when reducing a complex distributed matrix A(IA:*,JA:*) to * bidiagonal form: A(IA:*,JA:*) = Q * B * P**H. Q and P**H are defined * as products of elementary reflectors H(i) and G(i) respectively. * * Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the * order of the unitary matrix Q or P**H that is applied. * * If VECT = 'Q', A(IA:*,JA:*) is assumed to have been an NQ-by-K * matrix: * if nq >= k, Q = H(1) H(2) . . . H(k); * if nq < k, Q = H(1) H(2) . . . H(nq-1). * * If VECT = 'P', A(IA:*,JA:*) is assumed to have been a K-by-NQ * matrix: * if k < nq, P = G(1) G(2) . . . G(k); * if k >= nq, P = G(1) G(2) . . . G(nq-1). * * 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 * ========= * * VECT (global input) CHARACTER * = 'Q': apply Q or Q**H; * = 'P': apply P or P**H. * * SIDE (global input) CHARACTER * = 'L': apply Q, Q**H, P or P**H from the Left; * = 'R': apply Q, Q**H, P or P**H from the Right. * * TRANS (global input) CHARACTER * = 'N': No transpose, apply Q or P; * = 'C': Conjugate transpose, apply Q**H or P**H. * * M (global input) INTEGER * The number of rows to be operated on i.e the number of rows * of the distributed submatrix sub( C ). 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( C ). N >= 0. * * K (global input) INTEGER * If VECT = 'Q', the number of columns in the original * distributed matrix reduced by PCGEBRD. * If VECT = 'P', the number of rows in the original * distributed matrix reduced by PCGEBRD. * K >= 0. * * A (local input) COMPLEX pointer into the local memory * to an array of dimension (LLD_A,LOCc(JA+MIN(NQ,K)-1)) if * VECT='Q', and (LLD_A,LOCc(JA+NQ-1)) if VECT = 'P'. NQ = M * if SIDE = 'L', and NQ = N otherwise. The vectors which * define the elementary reflectors H(i) and G(i), whose * products determine the matrices Q and P, as returned by * PCGEBRD. * If VECT = 'Q', LLD_A >= max(1,LOCr(IA+NQ-1)); * if VECT = 'P', LLD_A >= max(1,LOCr(IA+MIN(NQ,K)-1)). * * 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. * * TAU (local input) COMPLEX array, dimension * LOCc(JA+MIN(NQ,K)-1) if VECT = 'Q', LOCr(IA+MIN(NQ,K)-1) if * VECT = 'P', TAU(i) must contain the scalar factor of the * elementary reflector H(i) or G(i), which determines Q or P, * as returned by PDGEBRD in its array argument TAUQ or TAUP. * TAU is tied to the distributed matrix A. * * C (local input/local output) COMPLEX pointer into the * local memory to an array of dimension (LLD_C,LOCc(JC+N-1)). * On entry, the local pieces of the distributed matrix sub(C). * On exit, if VECT='Q', sub( C ) is overwritten by Q*sub( C ) * or Q'*sub( C ) or sub( C )*Q' or sub( C )*Q; if VECT='P, * sub( C ) is overwritten by P*sub( C ) or P'*sub( C ) or * sub( C )*P or sub( C )*P'. * * IC (global input) INTEGER * The row index in the global array C indicating the first * row of sub( C ). * * JC (global input) INTEGER * The column index in the global array C indicating the * first column of sub( C ). * * DESCC (global and local input) INTEGER array of dimension DLEN_. * The array descriptor for the distributed matrix C. * * 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 * If SIDE = 'L', * NQ = M; * if( (VECT = 'Q' and NQ >= K) or (VECT <> 'Q' and NQ > K) ), * IAA=IA; JAA=JA; MI=M; NI=N; ICC=IC; JCC=JC; * else * IAA=IA+1; JAA=JA; MI=M-1; NI=N; ICC=IC+1; JCC=JC; * end if * else if SIDE = 'R', * NQ = N; * if( (VECT = 'Q' and NQ >= K) or (VECT <> 'Q' and NQ > K) ), * IAA=IA; JAA=JA; MI=M; NI=N; ICC=IC; JCC=JC; * else * IAA=IA; JAA=JA+1; MI=M; NI=N-1; ICC=IC; JCC=JC+1; * end if * end if * * If VECT = 'Q', * If SIDE = 'L', * LWORK >= MAX( (NB_A*(NB_A-1))/2, (NqC0 + MpC0)*NB_A ) + * NB_A * NB_A * else if SIDE = 'R', * LWORK >= MAX( (NB_A*(NB_A-1))/2, ( NqC0 + MAX( NpA0 + * NUMROC( NUMROC( NI+ICOFFC, NB_A, 0, 0, NPCOL ), * NB_A, 0, 0, LCMQ ), MpC0 ) )*NB_A ) + * NB_A * NB_A * end if * else if VECT <> 'Q', * if SIDE = 'L', * LWORK >= MAX( (MB_A*(MB_A-1))/2, ( MpC0 + MAX( MqA0 + * NUMROC( NUMROC( MI+IROFFC, MB_A, 0, 0, NPROW ), * MB_A, 0, 0, LCMP ), NqC0 ) )*MB_A ) + * MB_A * MB_A * else if SIDE = 'R', * LWORK >= MAX( (MB_A*(MB_A-1))/2, (MpC0 + NqC0)*MB_A ) + * MB_A * MB_A * end if * end if * * where LCMP = LCM / NPROW, LCMQ = LCM / NPCOL, with * LCM = ICLM( NPROW, NPCOL ), * * IROFFA = MOD( IAA-1, MB_A ), ICOFFA = MOD( JAA-1, NB_A ), * IAROW = INDXG2P( IAA, MB_A, MYROW, RSRC_A, NPROW ), * IACOL = INDXG2P( JAA, NB_A, MYCOL, CSRC_A, NPCOL ), * MqA0 = NUMROC( MI+ICOFFA, NB_A, MYCOL, IACOL, NPCOL ), * NpA0 = NUMROC( NI+IROFFA, MB_A, MYROW, IAROW, NPROW ), * * IROFFC = MOD( ICC-1, MB_C ), ICOFFC = MOD( JCC-1, NB_C ), * ICROW = INDXG2P( ICC, MB_C, MYROW, RSRC_C, NPROW ), * ICCOL = INDXG2P( JCC, NB_C, MYCOL, CSRC_C, NPCOL ), * MpC0 = NUMROC( MI+IROFFC, MB_C, MYROW, ICROW, NPROW ), * NqC0 = NUMROC( NI+ICOFFC, NB_C, MYCOL, ICCOL, 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 (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. * * 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: * * If VECT = 'Q', * If SIDE = 'L', * ( MB_A.EQ.MB_C .AND. IROFFA.EQ.IROFFC .AND. IAROW.EQ.ICROW ) * If SIDE = 'R', * ( MB_A.EQ.NB_C .AND. IROFFA.EQ.ICOFFC ) * else * If SIDE = 'L', * ( MB_A.EQ.MB_C .AND. ICOFFA.EQ.IROFFC ) * If SIDE = 'R', * ( NB_A.EQ.NB_C .AND. ICOFFA.EQ.ICOFFC .AND. IACOL.EQ.ICCOL ) * end if * * ===================================================================== * * .. Parameters .. INTEGER BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_, \$ LLD_, MB_, M_, NB_, N_, RSRC_ 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 APPLYQ, LEFT, LQUERY, NOTRAN CHARACTER TRANST INTEGER IAA, IACOL, IAROW, ICC, ICCOL, ICOFFA, ICOFFC, \$ ICROW, ICTXT, IINFO, IROFFA, IROFFC, JAA, JCC, \$ LCM, LCMP, LCMQ, LWMIN, MI, MPC0, MQA0, MYCOL, \$ MYROW, NI, NPA0, NPCOL, NPROW, NQ, NQC0 * .. * .. Local Arrays .. INTEGER IDUM1( 5 ), IDUM2( 5 ) * .. * .. External Subroutines .. EXTERNAL BLACS_GRIDINFO, CHK1MAT, PCHK2MAT, PCUNMLQ, \$ PCUNMQR, PXERBLA * .. * .. External Functions .. LOGICAL LSAME INTEGER ILCM, INDXG2P, NUMROC EXTERNAL ILCM, INDXG2P, LSAME, NUMROC * .. * .. Intrinsic Functions .. INTRINSIC CMPLX, ICHAR, MAX, MOD, REAL * .. * .. Executable Statements .. * * Get grid parameters * ICTXT = DESCA( CTXT_ ) CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL ) * * Test the input parameters * INFO = 0 IF( NPROW.EQ.-1 ) THEN INFO = -(1000+CTXT_) ELSE APPLYQ = LSAME( VECT, 'Q' ) LEFT = LSAME( SIDE, 'L' ) NOTRAN = LSAME( TRANS, 'N' ) * * NQ is the order of Q or P * IF( LEFT ) THEN NQ = M IF( ( APPLYQ .AND. NQ.GE.K ) .OR. \$ ( .NOT.APPLYQ .AND. NQ.GT.K ) ) THEN IAA = IA JAA = JA MI = M NI = N ICC = IC JCC = JC ELSE IAA = IA + 1 JAA = JA MI = M - 1 NI = N ICC = IC + 1 JCC = JC END IF * IF( APPLYQ ) THEN CALL CHK1MAT( M, 4, K, 6, IA, JA, DESCA, 10, INFO ) ELSE CALL CHK1MAT( K, 6, M, 4, IA, JA, DESCA, 10, INFO ) END IF ELSE NQ = N IF( ( APPLYQ .AND. NQ.GE.K ) .OR. \$ ( .NOT.APPLYQ .AND. NQ.GT.K ) ) THEN IAA = IA JAA = JA MI = M NI = N ICC = IC JCC = JC ELSE IAA = IA JAA = JA + 1 MI = M NI = N - 1 ICC = IC JCC = JC + 1 END IF * IF( APPLYQ ) THEN CALL CHK1MAT( N, 5, K, 6, IA, JA, DESCA, 10, INFO ) ELSE CALL CHK1MAT( K, 6, N, 5, IA, JA, DESCA, 10, INFO ) END IF END IF CALL CHK1MAT( M, 4, N, 5, IC, JC, DESCC, 15, INFO ) * IF( INFO.EQ.0 ) THEN IROFFA = MOD( IAA-1, DESCA( MB_ ) ) ICOFFA = MOD( JAA-1, DESCA( NB_ ) ) IROFFC = MOD( ICC-1, DESCC( MB_ ) ) ICOFFC = MOD( JCC-1, DESCC( NB_ ) ) IACOL = INDXG2P( JAA, DESCA( NB_ ), MYCOL, DESCA( CSRC_ ), \$ NPCOL ) IAROW = INDXG2P( IAA, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), \$ NPROW ) ICROW = INDXG2P( ICC, DESCC( MB_ ), MYROW, DESCC( RSRC_ ), \$ NPROW ) ICCOL = INDXG2P( JCC, DESCC( NB_ ), MYCOL, DESCC( CSRC_ ), \$ NPCOL ) MPC0 = NUMROC( MI+IROFFC, DESCC( MB_ ), MYROW, ICROW, \$ NPROW ) NQC0 = NUMROC( NI+ICOFFC, DESCC( NB_ ), MYCOL, ICCOL, \$ NPCOL ) * IF( APPLYQ ) THEN IF( LEFT ) THEN LWMIN = MAX( ( DESCA( NB_ ) * ( DESCA( NB_ ) - 1 ) ) \$ / 2, ( MPC0 + NQC0 ) * DESCA( NB_ ) ) + \$ DESCA( NB_ ) * DESCA( NB_ ) ELSE NPA0 = NUMROC( NI+IROFFA, DESCA( MB_ ), MYROW, IAROW, \$ NPROW ) LCM = ILCM( NPROW, NPCOL ) LCMQ = LCM / NPCOL LWMIN = MAX( ( DESCA( NB_ ) * ( DESCA( NB_ ) - 1 ) ) \$ / 2, ( NQC0 + MAX( NPA0 + NUMROC( NUMROC( \$ NI+ICOFFC, DESCA( NB_ ), 0, 0, NPCOL ), \$ DESCA( NB_ ), 0, 0, LCMQ ), MPC0 ) ) * \$ DESCA( NB_ ) ) + DESCA( NB_ ) * DESCA( NB_ ) END IF ELSE * IF( LEFT ) THEN MQA0 = NUMROC( MI+ICOFFA, DESCA( NB_ ), MYCOL, IACOL, \$ NPCOL ) LCM = ILCM( NPROW, NPCOL ) LCMP = LCM / NPROW LWMIN = MAX( ( DESCA( MB_ ) * ( DESCA( MB_ ) - 1 ) ) \$ / 2, ( MPC0 + MAX( MQA0 + NUMROC( NUMROC( \$ MI+IROFFC, DESCA( MB_ ), 0, 0, NPROW ), \$ DESCA( MB_ ), 0, 0, LCMP ), NQC0 ) ) * \$ DESCA( MB_ ) ) + DESCA( MB_ ) * DESCA( MB_ ) ELSE LWMIN = MAX( ( DESCA( MB_ ) * ( DESCA( MB_ ) - 1 ) ) \$ / 2, ( MPC0 + NQC0 ) * DESCA( MB_ ) ) + \$ DESCA( MB_ ) * DESCA( MB_ ) END IF * END IF * WORK( 1 ) = CMPLX( REAL( LWMIN ) ) LQUERY = ( LWORK.EQ.-1 ) IF( .NOT.APPLYQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN INFO = -1 ELSE IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN INFO = -2 ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN INFO = -3 ELSE IF( K.LT.0 ) THEN INFO = -6 ELSE IF( APPLYQ .AND. .NOT.LEFT .AND. \$ DESCA( MB_ ).NE.DESCC( NB_ ) ) THEN INFO = -(1000+NB_) ELSE IF( APPLYQ .AND. LEFT .AND. IROFFA.NE.IROFFC ) THEN INFO = -13 ELSE IF( APPLYQ .AND. LEFT .AND. IAROW.NE.ICROW ) THEN INFO = -13 ELSE IF( .NOT.APPLYQ .AND. LEFT .AND. \$ ICOFFA.NE.IROFFC ) THEN INFO = -13 ELSE IF( .NOT.APPLYQ .AND. .NOT.LEFT .AND. \$ IACOL.NE.ICCOL ) THEN INFO = -14 ELSE IF( APPLYQ .AND. .NOT.LEFT .AND. \$ IROFFA.NE.ICOFFC ) THEN INFO = -14 ELSE IF( .NOT.APPLYQ .AND. .NOT.LEFT .AND. \$ ICOFFA.NE.ICOFFC ) THEN INFO = -14 ELSE IF( APPLYQ .AND. LEFT .AND. \$ DESCA( MB_ ).NE.DESCC( MB_ ) ) THEN INFO = -(1500+MB_) ELSE IF( .NOT.APPLYQ .AND. LEFT .AND. \$ DESCA( MB_ ).NE.DESCC( MB_ ) ) THEN INFO = -(1500+MB_) ELSE IF( APPLYQ .AND. .NOT.LEFT .AND. \$ DESCA( MB_ ).NE.DESCC( NB_ ) ) THEN INFO = -(1500+NB_) ELSE IF( .NOT.APPLYQ .AND. .NOT.LEFT .AND. \$ DESCA( NB_ ).NE.DESCC( NB_ ) ) THEN INFO = -(1500+NB_) ELSE IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN INFO = -17 END IF END IF * IF( APPLYQ ) THEN IDUM1( 1 ) = ICHAR( 'Q' ) ELSE IDUM1( 1 ) = ICHAR( 'P' ) END IF IDUM2( 1 ) = 1 IF( LEFT ) THEN IDUM1( 2 ) = ICHAR( 'L' ) ELSE IDUM1( 2 ) = ICHAR( 'R' ) END IF IDUM2( 2 ) = 2 IF( NOTRAN ) THEN IDUM1( 3 ) = ICHAR( 'N' ) ELSE IDUM1( 3 ) = ICHAR( 'C' ) END IF IDUM2( 3 ) = 3 IDUM1( 4 ) = K IDUM2( 4 ) = 6 IF( LWORK.EQ.-1 ) THEN IDUM1( 5 ) = -1 ELSE IDUM1( 5 ) = 1 END IF IDUM2( 5 ) = 17 IF( APPLYQ ) THEN IF( LEFT ) THEN CALL PCHK2MAT( M, 4, K, 6, IA, JA, DESCA, 10, M, 4, N, \$ 5, IC, JC, DESCC, 15, 5, IDUM1, IDUM2, \$ INFO ) ELSE CALL PCHK2MAT( N, 5, K, 6, IA, JA, DESCA, 10, M, 4, N, \$ 5, IC, JC, DESCC, 15, 5, IDUM1, IDUM2, \$ INFO ) END IF ELSE IF( LEFT ) THEN CALL PCHK2MAT( K, 6, M, 4, IA, JA, DESCA, 10, M, 4, N, \$ 5, IC, JC, DESCC, 15, 5, IDUM1, IDUM2, \$ INFO ) ELSE CALL PCHK2MAT( K, 6, N, 5, IA, JA, DESCA, 10, M, 4, N, \$ 5, IC, JC, DESCC, 15, 5, IDUM1, IDUM2, \$ INFO ) END IF END IF END IF * IF( INFO.NE.0 ) THEN CALL PXERBLA( ICTXT, 'PCUNMBR', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( M.EQ.0 .OR. N.EQ.0 ) \$ RETURN * IF( APPLYQ ) THEN * * Apply Q * IF( NQ.GE.K ) THEN * * Q was determined by a call to PCGEBRD with nq >= k * CALL PCUNMQR( SIDE, TRANS, M, N, K, A, IA, JA, DESCA, TAU, \$ C, IC, JC, DESCC, WORK, LWORK, IINFO ) ELSE IF( NQ.GT.1 ) THEN * * Q was determined by a call to PCGEBRD with nq < k * CALL PCUNMQR( SIDE, TRANS, MI, NI, NQ-1, A, IA+1, JA, DESCA, \$ TAU, C, ICC, JCC, DESCC, WORK, LWORK, IINFO ) END IF ELSE * * Apply P * IF( NOTRAN ) THEN TRANST = 'C' ELSE TRANST = 'N' END IF IF( NQ.GT.K ) THEN * * P was determined by a call to PCGEBRD with nq > k * CALL PCUNMLQ( SIDE, TRANST, M, N, K, A, IA, JA, DESCA, TAU, \$ C, IC, JC, DESCC, WORK, LWORK, IINFO ) ELSE IF( NQ.GT.1 ) THEN * * P was determined by a call to PCGEBRD with nq <= k * CALL PCUNMLQ( SIDE, TRANST, MI, NI, NQ-1, A, IA, JA+1, \$ DESCA, TAU, C, ICC, JCC, DESCC, WORK, LWORK, \$ IINFO ) END IF END IF * WORK( 1 ) = CMPLX( REAL( LWMIN ) ) * RETURN * * End of PCUNMBR * END