zgelss.f.html

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      SUBROUTINE <a name="ZGELSS.1"></a><a href="zgelss.f.html#ZGELSS.1">ZGELSS</a>( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK,
     $                   WORK, LWORK, RWORK, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- LAPACK driver routine (version 3.1) --
</span><span class="comment">*</span><span class="comment">     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment">     November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Scalar Arguments ..
</span>      INTEGER            INFO, LDA, LDB, LWORK, M, N, NRHS, RANK
      DOUBLE PRECISION   RCOND
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      DOUBLE PRECISION   RWORK( * ), S( * )
      COMPLEX*16         A( LDA, * ), B( LDB, * ), WORK( * )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Purpose
</span><span class="comment">*</span><span class="comment">  =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  <a name="ZGELSS.20"></a><a href="zgelss.f.html#ZGELSS.1">ZGELSS</a> computes the minimum norm solution to a complex linear
</span><span class="comment">*</span><span class="comment">  least squares problem:
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Minimize 2-norm(| b - A*x |).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  using the singular value decomposition (SVD) of A. A is an M-by-N
</span><span class="comment">*</span><span class="comment">  matrix which may be rank-deficient.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Several right hand side vectors b and solution vectors x can be
</span><span class="comment">*</span><span class="comment">  handled in a single call; they are stored as the columns of the
</span><span class="comment">*</span><span class="comment">  M-by-NRHS right hand side matrix B and the N-by-NRHS solution matrix
</span><span class="comment">*</span><span class="comment">  X.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  The effective rank of A is determined by treating as zero those
</span><span class="comment">*</span><span class="comment">  singular values which are less than RCOND times the largest singular
</span><span class="comment">*</span><span class="comment">  value.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Arguments
</span><span class="comment">*</span><span class="comment">  =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  M       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of rows of the matrix A. M &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  N       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of columns of the matrix A. N &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  NRHS    (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of right hand sides, i.e., the number of columns
</span><span class="comment">*</span><span class="comment">          of the matrices B and X. NRHS &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  A       (input/output) COMPLEX*16 array, dimension (LDA,N)
</span><span class="comment">*</span><span class="comment">          On entry, the M-by-N matrix A.
</span><span class="comment">*</span><span class="comment">          On exit, the first min(m,n) rows of A are overwritten with
</span><span class="comment">*</span><span class="comment">          its right singular vectors, stored rowwise.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDA     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array A. LDA &gt;= max(1,M).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  B       (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
</span><span class="comment">*</span><span class="comment">          On entry, the M-by-NRHS right hand side matrix B.
</span><span class="comment">*</span><span class="comment">          On exit, B is overwritten by the N-by-NRHS solution matrix X.
</span><span class="comment">*</span><span class="comment">          If m &gt;= n and RANK = n, the residual sum-of-squares for
</span><span class="comment">*</span><span class="comment">          the solution in the i-th column is given by the sum of
</span><span class="comment">*</span><span class="comment">          squares of the modulus of elements n+1:m in that column.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDB     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array B.  LDB &gt;= max(1,M,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  S       (output) DOUBLE PRECISION array, dimension (min(M,N))
</span><span class="comment">*</span><span class="comment">          The singular values of A in decreasing order.
</span><span class="comment">*</span><span class="comment">          The condition number of A in the 2-norm = S(1)/S(min(m,n)).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  RCOND   (input) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment">          RCOND is used to determine the effective rank of A.
</span><span class="comment">*</span><span class="comment">          Singular values S(i) &lt;= RCOND*S(1) are treated as zero.
</span><span class="comment">*</span><span class="comment">          If RCOND &lt; 0, machine precision is used instead.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  RANK    (output) INTEGER
</span><span class="comment">*</span><span class="comment">          The effective rank of A, i.e., the number of singular values
</span><span class="comment">*</span><span class="comment">          which are greater than RCOND*S(1).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  WORK    (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
</span><span class="comment">*</span><span class="comment">          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LWORK   (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The dimension of the array WORK. LWORK &gt;= 1, and also:
</span><span class="comment">*</span><span class="comment">          LWORK &gt;=  2*min(M,N) + max(M,N,NRHS)
</span><span class="comment">*</span><span class="comment">          For good performance, LWORK should generally be larger.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">          If LWORK = -1, then a workspace query is assumed; the routine
</span><span class="comment">*</span><span class="comment">          only calculates the optimal size of the WORK array, returns
</span><span class="comment">*</span><span class="comment">          this value as the first entry of the WORK array, and no error
</span><span class="comment">*</span><span class="comment">          message related to LWORK is issued by <a name="XERBLA.92"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  RWORK   (workspace) DOUBLE PRECISION array, dimension (5*min(M,N))
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  INFO    (output) INTEGER
</span><span class="comment">*</span><span class="comment">          = 0:  successful exit
</span><span class="comment">*</span><span class="comment">          &lt; 0:  if INFO = -i, the i-th argument had an illegal value.
</span><span class="comment">*</span><span class="comment">          &gt; 0:  the algorithm for computing the SVD failed to converge;
</span><span class="comment">*</span><span class="comment">                if INFO = i, i off-diagonal elements of an intermediate
</span><span class="comment">*</span><span class="comment">                bidiagonal form did not converge to zero.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Parameters ..
</span>      DOUBLE PRECISION   ZERO, ONE
      PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
      COMPLEX*16         CZERO, CONE
      PARAMETER          ( CZERO = ( 0.0D+0, 0.0D+0 ),
     $                   CONE = ( 1.0D+0, 0.0D+0 ) )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      LOGICAL            LQUERY
      INTEGER            BL, CHUNK, I, IASCL, IBSCL, IE, IL, IRWORK,
     $                   ITAU, ITAUP, ITAUQ, IWORK, LDWORK, MAXMN,
     $                   MAXWRK, MINMN, MINWRK, MM, MNTHR
      DOUBLE PRECISION   ANRM, BIGNUM, BNRM, EPS, SFMIN, SMLNUM, THR
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Arrays ..
</span>      COMPLEX*16         VDUM( 1 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           <a name="DLABAD.123"></a><a href="dlabad.f.html#DLABAD.1">DLABAD</a>, <a name="DLASCL.123"></a><a href="dlascl.f.html#DLASCL.1">DLASCL</a>, <a name="DLASET.123"></a><a href="dlaset.f.html#DLASET.1">DLASET</a>, <a name="XERBLA.123"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>, <a name="ZBDSQR.123"></a><a href="zbdsqr.f.html#ZBDSQR.1">ZBDSQR</a>, ZCOPY,
     $                   <a name="ZDRSCL.124"></a><a href="zdrscl.f.html#ZDRSCL.1">ZDRSCL</a>, <a name="ZGEBRD.124"></a><a href="zgebrd.f.html#ZGEBRD.1">ZGEBRD</a>, <a name="ZGELQF.124"></a><a href="zgelqf.f.html#ZGELQF.1">ZGELQF</a>, ZGEMM, ZGEMV, <a name="ZGEQRF.124"></a><a href="zgeqrf.f.html#ZGEQRF.1">ZGEQRF</a>,
     $                   <a name="ZLACPY.125"></a><a href="zlacpy.f.html#ZLACPY.1">ZLACPY</a>, <a name="ZLASCL.125"></a><a href="zlascl.f.html#ZLASCL.1">ZLASCL</a>, <a name="ZLASET.125"></a><a href="zlaset.f.html#ZLASET.1">ZLASET</a>, <a name="ZUNGBR.125"></a><a href="zungbr.f.html#ZUNGBR.1">ZUNGBR</a>, <a name="ZUNMBR.125"></a><a href="zunmbr.f.html#ZUNMBR.1">ZUNMBR</a>, <a name="ZUNMLQ.125"></a><a href="zunmlq.f.html#ZUNMLQ.1">ZUNMLQ</a>,
     $                   <a name="ZUNMQR.126"></a><a href="zunmqr.f.html#ZUNMQR.1">ZUNMQR</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      INTEGER            <a name="ILAENV.129"></a><a href="hfy-index.html#ILAENV">ILAENV</a>
      DOUBLE PRECISION   <a name="DLAMCH.130"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>, <a name="ZLANGE.130"></a><a href="zlange.f.html#ZLANGE.1">ZLANGE</a>
      EXTERNAL           <a name="ILAENV.131"></a><a href="hfy-index.html#ILAENV">ILAENV</a>, <a name="DLAMCH.131"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>, <a name="ZLANGE.131"></a><a href="zlange.f.html#ZLANGE.1">ZLANGE</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Intrinsic Functions ..
</span>      INTRINSIC          MAX, MIN
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Test the input arguments
</span><span class="comment">*</span><span class="comment">
</span>      INFO = 0
      MINMN = MIN( M, N )
      MAXMN = MAX( M, N )
      LQUERY = ( LWORK.EQ.-1 )
      IF( M.LT.0 ) THEN
         INFO = -1
      ELSE IF( N.LT.0 ) THEN
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