```      SUBROUTINE CGELSX( M, N, NRHS, A, LDA, B, LDB, JPVT, RCOND, RANK,
\$                   WORK, RWORK, INFO )
*
*  -- LAPACK driver routine (version 3.1) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     November 2006
*
*     .. Scalar Arguments ..
INTEGER            INFO, LDA, LDB, M, N, NRHS, RANK
REAL               RCOND
*     ..
*     .. Array Arguments ..
INTEGER            JPVT( * )
REAL               RWORK( * )
COMPLEX            A( LDA, * ), B( LDB, * ), WORK( * )
*     ..
*
*  Purpose
*  =======
*
*  This routine is deprecated and has been replaced by routine CGELSY.
*
*  CGELSX computes the minimum-norm solution to a complex linear least
*  squares problem:
*      minimize || A * X - B ||
*  using a complete orthogonal factorization of A.  A is an M-by-N
*  matrix which may be rank-deficient.
*
*  Several right hand side vectors b and solution vectors x can be
*  handled in a single call; they are stored as the columns of the
*  M-by-NRHS right hand side matrix B and the N-by-NRHS solution
*  matrix X.
*
*  The routine first computes a QR factorization with column pivoting:
*      A * P = Q * [ R11 R12 ]
*                  [  0  R22 ]
*  with R11 defined as the largest leading submatrix whose estimated
*  condition number is less than 1/RCOND.  The order of R11, RANK,
*  is the effective rank of A.
*
*  Then, R22 is considered to be negligible, and R12 is annihilated
*  by unitary transformations from the right, arriving at the
*  complete orthogonal factorization:
*     A * P = Q * [ T11 0 ] * Z
*                 [  0  0 ]
*  The minimum-norm solution is then
*     X = P * Z' [ inv(T11)*Q1'*B ]
*                [        0       ]
*  where Q1 consists of the first RANK columns of Q.
*
*  Arguments
*  =========
*
*  M       (input) INTEGER
*          The number of rows of the matrix A.  M >= 0.
*
*  N       (input) INTEGER
*          The number of columns of the matrix A.  N >= 0.
*
*  NRHS    (input) INTEGER
*          The number of right hand sides, i.e., the number of
*          columns of matrices B and X. NRHS >= 0.
*
*  A       (input/output) COMPLEX array, dimension (LDA,N)
*          On entry, the M-by-N matrix A.
*          On exit, A has been overwritten by details of its
*          complete orthogonal factorization.
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A.  LDA >= max(1,M).
*
*  B       (input/output) COMPLEX array, dimension (LDB,NRHS)
*          On entry, the M-by-NRHS right hand side matrix B.
*          On exit, the N-by-NRHS solution matrix X.
*          If m >= n and RANK = n, the residual sum-of-squares for
*          the solution in the i-th column is given by the sum of
*          squares of elements N+1:M in that column.
*
*  LDB     (input) INTEGER
*          The leading dimension of the array B. LDB >= max(1,M,N).
*
*  JPVT    (input/output) INTEGER array, dimension (N)
*          On entry, if JPVT(i) .ne. 0, the i-th column of A is an
*          initial column, otherwise it is a free column.  Before
*          the QR factorization of A, all initial columns are
*          permuted to the leading positions; only the remaining
*          free columns are moved as a result of column pivoting
*          during the factorization.
*          On exit, if JPVT(i) = k, then the i-th column of A*P
*          was the k-th column of A.
*
*  RCOND   (input) REAL
*          RCOND is used to determine the effective rank of A, which
*          is defined as the order of the largest leading triangular
*          submatrix R11 in the QR factorization with pivoting of A,
*          whose estimated condition number < 1/RCOND.
*
*  RANK    (output) INTEGER
*          The effective rank of A, i.e., the order of the submatrix
*          R11.  This is the same as the order of the submatrix T11
*          in the complete orthogonal factorization of A.
*
*  WORK    (workspace) COMPLEX array, dimension
*                      (min(M,N) + max( N, 2*min(M,N)+NRHS )),
*
*  RWORK   (workspace) REAL array, dimension (2*N)
*
*  INFO    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -i, the i-th argument had an illegal value
*
*  =====================================================================
*
*     .. Parameters ..
INTEGER            IMAX, IMIN
PARAMETER          ( IMAX = 1, IMIN = 2 )
REAL               ZERO, ONE, DONE, NTDONE
PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0, DONE = ZERO,
\$                   NTDONE = ONE )
COMPLEX            CZERO, CONE
PARAMETER          ( CZERO = ( 0.0E+0, 0.0E+0 ),
\$                   CONE = ( 1.0E+0, 0.0E+0 ) )
*     ..
*     .. Local Scalars ..
INTEGER            I, IASCL, IBSCL, ISMAX, ISMIN, J, K, MN
REAL               ANRM, BIGNUM, BNRM, SMAX, SMAXPR, SMIN, SMINPR,
\$                   SMLNUM
COMPLEX            C1, C2, S1, S2, T1, T2
*     ..
*     .. External Subroutines ..
EXTERNAL           CGEQPF, CLAIC1, CLASCL, CLASET, CLATZM, CTRSM,
*     ..
*     .. External Functions ..
REAL               CLANGE, SLAMCH
EXTERNAL           CLANGE, SLAMCH
*     ..
*     .. Intrinsic Functions ..
INTRINSIC          ABS, CONJG, MAX, MIN
*     ..
*     .. Executable Statements ..
*
MN = MIN( M, N )
ISMIN = MN + 1
ISMAX = 2*MN + 1
*
*     Test the input arguments.
*
INFO = 0
IF( M.LT.0 ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
INFO = -2
ELSE IF( NRHS.LT.0 ) THEN
INFO = -3
ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
INFO = -5
ELSE IF( LDB.LT.MAX( 1, M, N ) ) THEN
INFO = -7
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'CGELSX', -INFO )
RETURN
END IF
*
*     Quick return if possible
*
IF( MIN( M, N, NRHS ).EQ.0 ) THEN
RANK = 0
RETURN
END IF
*
*     Get machine parameters
*
SMLNUM = SLAMCH( 'S' ) / SLAMCH( 'P' )
BIGNUM = ONE / SMLNUM
*
*     Scale A, B if max elements outside range [SMLNUM,BIGNUM]
*
ANRM = CLANGE( 'M', M, N, A, LDA, RWORK )
IASCL = 0
IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN
*
*        Scale matrix norm up to SMLNUM
*
CALL CLASCL( 'G', 0, 0, ANRM, SMLNUM, M, N, A, LDA, INFO )
IASCL = 1
ELSE IF( ANRM.GT.BIGNUM ) THEN
*
*        Scale matrix norm down to BIGNUM
*
CALL CLASCL( 'G', 0, 0, ANRM, BIGNUM, M, N, A, LDA, INFO )
IASCL = 2
ELSE IF( ANRM.EQ.ZERO ) THEN
*
*        Matrix all zero. Return zero solution.
*
CALL CLASET( 'F', MAX( M, N ), NRHS, CZERO, CZERO, B, LDB )
RANK = 0
GO TO 100
END IF
*
BNRM = CLANGE( 'M', M, NRHS, B, LDB, RWORK )
IBSCL = 0
IF( BNRM.GT.ZERO .AND. BNRM.LT.SMLNUM ) THEN
*
*        Scale matrix norm up to SMLNUM
*
CALL CLASCL( 'G', 0, 0, BNRM, SMLNUM, M, NRHS, B, LDB, INFO )
IBSCL = 1
ELSE IF( BNRM.GT.BIGNUM ) THEN
*
*        Scale matrix norm down to BIGNUM
*
CALL CLASCL( 'G', 0, 0, BNRM, BIGNUM, M, NRHS, B, LDB, INFO )
IBSCL = 2
END IF
*
*     Compute QR factorization with column pivoting of A:
*        A * P = Q * R
*
CALL CGEQPF( M, N, A, LDA, JPVT, WORK( 1 ), WORK( MN+1 ), RWORK,
\$             INFO )
*
*     complex workspace MN+N. Real workspace 2*N. Details of Householder
*     rotations stored in WORK(1:MN).
*
*     Determine RANK using incremental condition estimation
*
WORK( ISMIN ) = CONE
WORK( ISMAX ) = CONE
SMAX = ABS( A( 1, 1 ) )
SMIN = SMAX
IF( ABS( A( 1, 1 ) ).EQ.ZERO ) THEN
RANK = 0
CALL CLASET( 'F', MAX( M, N ), NRHS, CZERO, CZERO, B, LDB )
GO TO 100
ELSE
RANK = 1
END IF
*
10 CONTINUE
IF( RANK.LT.MN ) THEN
I = RANK + 1
CALL CLAIC1( IMIN, RANK, WORK( ISMIN ), SMIN, A( 1, I ),
\$                A( I, I ), SMINPR, S1, C1 )
CALL CLAIC1( IMAX, RANK, WORK( ISMAX ), SMAX, A( 1, I ),
\$                A( I, I ), SMAXPR, S2, C2 )
*
IF( SMAXPR*RCOND.LE.SMINPR ) THEN
DO 20 I = 1, RANK
WORK( ISMIN+I-1 ) = S1*WORK( ISMIN+I-1 )
WORK( ISMAX+I-1 ) = S2*WORK( ISMAX+I-1 )
20       CONTINUE
WORK( ISMIN+RANK ) = C1
WORK( ISMAX+RANK ) = C2
SMIN = SMINPR
SMAX = SMAXPR
RANK = RANK + 1
GO TO 10
END IF
END IF
*
*     Logically partition R = [ R11 R12 ]
*                             [  0  R22 ]
*     where R11 = R(1:RANK,1:RANK)
*
*     [R11,R12] = [ T11, 0 ] * Y
*
IF( RANK.LT.N )
\$   CALL CTZRQF( RANK, N, A, LDA, WORK( MN+1 ), INFO )
*
*     Details of Householder rotations stored in WORK(MN+1:2*MN)
*
*     B(1:M,1:NRHS) := Q' * B(1:M,1:NRHS)
*
CALL CUNM2R( 'Left', 'Conjugate transpose', M, NRHS, MN, A, LDA,
\$             WORK( 1 ), B, LDB, WORK( 2*MN+1 ), INFO )
*
*     workspace NRHS
*
*      B(1:RANK,1:NRHS) := inv(T11) * B(1:RANK,1:NRHS)
*
CALL CTRSM( 'Left', 'Upper', 'No transpose', 'Non-unit', RANK,
\$            NRHS, CONE, A, LDA, B, LDB )
*
DO 40 I = RANK + 1, N
DO 30 J = 1, NRHS
B( I, J ) = CZERO
30    CONTINUE
40 CONTINUE
*
*     B(1:N,1:NRHS) := Y' * B(1:N,1:NRHS)
*
IF( RANK.LT.N ) THEN
DO 50 I = 1, RANK
CALL CLATZM( 'Left', N-RANK+1, NRHS, A( I, RANK+1 ), LDA,
\$                   CONJG( WORK( MN+I ) ), B( I, 1 ),
\$                   B( RANK+1, 1 ), LDB, WORK( 2*MN+1 ) )
50    CONTINUE
END IF
*
*     workspace NRHS
*
*     B(1:N,1:NRHS) := P * B(1:N,1:NRHS)
*
DO 90 J = 1, NRHS
DO 60 I = 1, N
WORK( 2*MN+I ) = NTDONE
60    CONTINUE
DO 80 I = 1, N
IF( WORK( 2*MN+I ).EQ.NTDONE ) THEN
IF( JPVT( I ).NE.I ) THEN
K = I
T1 = B( K, J )
T2 = B( JPVT( K ), J )
70             CONTINUE
B( JPVT( K ), J ) = T1
WORK( 2*MN+K ) = DONE
T1 = T2
K = JPVT( K )
T2 = B( JPVT( K ), J )
IF( JPVT( K ).NE.I )
\$               GO TO 70
B( I, J ) = T1
WORK( 2*MN+K ) = DONE
END IF
END IF
80    CONTINUE
90 CONTINUE
*
*     Undo scaling
*
IF( IASCL.EQ.1 ) THEN
CALL CLASCL( 'G', 0, 0, ANRM, SMLNUM, N, NRHS, B, LDB, INFO )
CALL CLASCL( 'U', 0, 0, SMLNUM, ANRM, RANK, RANK, A, LDA,
\$                INFO )
ELSE IF( IASCL.EQ.2 ) THEN
CALL CLASCL( 'G', 0, 0, ANRM, BIGNUM, N, NRHS, B, LDB, INFO )
CALL CLASCL( 'U', 0, 0, BIGNUM, ANRM, RANK, RANK, A, LDA,
\$                INFO )
END IF
IF( IBSCL.EQ.1 ) THEN
CALL CLASCL( 'G', 0, 0, SMLNUM, BNRM, N, NRHS, B, LDB, INFO )
ELSE IF( IBSCL.EQ.2 ) THEN
CALL CLASCL( 'G', 0, 0, BIGNUM, BNRM, N, NRHS, B, LDB, INFO )
END IF
*
100 CONTINUE
*
RETURN
*
*     End of CGELSX
*
END

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