dgesvd.f.html

来自「famous linear algebra library (LAPACK) p」· HTML 代码 · 共 674 行 · 第 1/5 页

</span><span class="comment">*</span><span class="comment">          LWORK &gt;= MAX(1,3*MIN(M,N)+MAX(M,N),5*MIN(M,N)).
</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.123"></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">  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:  if <a name="DBDSQR.128"></a><a href="dbdsqr.f.html#DBDSQR.1">DBDSQR</a> did not converge, INFO specifies how many
</span><span class="comment">*</span><span class="comment">                superdiagonals of an intermediate bidiagonal form B
</span><span class="comment">*</span><span class="comment">                did not converge to zero. See the description of WORK
</span><span class="comment">*</span><span class="comment">                above for details.
</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 = 0.0D0, ONE = 1.0D0 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      LOGICAL            LQUERY, WNTUA, WNTUAS, WNTUN, WNTUO, WNTUS,
     $                   WNTVA, WNTVAS, WNTVN, WNTVO, WNTVS
      INTEGER            BDSPAC, BLK, CHUNK, I, IE, IERR, IR, ISCL,
     $                   ITAU, ITAUP, ITAUQ, IU, IWORK, LDWRKR, LDWRKU,
     $                   MAXWRK, MINMN, MINWRK, MNTHR, NCU, NCVT, NRU,
     $                   NRVT, WRKBL
      DOUBLE PRECISION   ANRM, BIGNUM, EPS, SMLNUM
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Arrays ..
</span>      DOUBLE PRECISION   DUM( 1 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           <a name="DBDSQR.152"></a><a href="dbdsqr.f.html#DBDSQR.1">DBDSQR</a>, <a name="DGEBRD.152"></a><a href="dgebrd.f.html#DGEBRD.1">DGEBRD</a>, <a name="DGELQF.152"></a><a href="dgelqf.f.html#DGELQF.1">DGELQF</a>, DGEMM, <a name="DGEQRF.152"></a><a href="dgeqrf.f.html#DGEQRF.1">DGEQRF</a>, <a name="DLACPY.152"></a><a href="dlacpy.f.html#DLACPY.1">DLACPY</a>,
     $                   <a name="DLASCL.153"></a><a href="dlascl.f.html#DLASCL.1">DLASCL</a>, <a name="DLASET.153"></a><a href="dlaset.f.html#DLASET.1">DLASET</a>, <a name="DORGBR.153"></a><a href="dorgbr.f.html#DORGBR.1">DORGBR</a>, <a name="DORGLQ.153"></a><a href="dorglq.f.html#DORGLQ.1">DORGLQ</a>, <a name="DORGQR.153"></a><a href="dorgqr.f.html#DORGQR.1">DORGQR</a>, <a name="DORMBR.153"></a><a href="dormbr.f.html#DORMBR.1">DORMBR</a>,
     $                   <a name="XERBLA.154"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.157"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      INTEGER            <a name="ILAENV.158"></a><a href="hfy-index.html#ILAENV">ILAENV</a>
      DOUBLE PRECISION   <a name="DLAMCH.159"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>, <a name="DLANGE.159"></a><a href="dlange.f.html#DLANGE.1">DLANGE</a>
      EXTERNAL           <a name="LSAME.160"></a><a href="lsame.f.html#LSAME.1">LSAME</a>, <a name="ILAENV.160"></a><a href="hfy-index.html#ILAENV">ILAENV</a>, <a name="DLAMCH.160"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>, <a name="DLANGE.160"></a><a href="dlange.f.html#DLANGE.1">DLANGE</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Intrinsic Functions ..
</span>      INTRINSIC          MAX, MIN, SQRT
<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 )
      WNTUA = <a name="LSAME.171"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBU, <span class="string">'A'</span> )
      WNTUS = <a name="LSAME.172"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBU, <span class="string">'S'</span> )
      WNTUAS = WNTUA .OR. WNTUS
      WNTUO = <a name="LSAME.174"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBU, <span class="string">'O'</span> )
      WNTUN = <a name="LSAME.175"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBU, <span class="string">'N'</span> )
      WNTVA = <a name="LSAME.176"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBVT, <span class="string">'A'</span> )
      WNTVS = <a name="LSAME.177"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBVT, <span class="string">'S'</span> )
      WNTVAS = WNTVA .OR. WNTVS
      WNTVO = <a name="LSAME.179"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBVT, <span class="string">'O'</span> )
      WNTVN = <a name="LSAME.180"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBVT, <span class="string">'N'</span> )
      LQUERY = ( LWORK.EQ.-1 )
<span class="comment">*</span><span class="comment">
</span>      IF( .NOT.( WNTUA .OR. WNTUS .OR. WNTUO .OR. WNTUN ) ) THEN
         INFO = -1
      ELSE IF( .NOT.( WNTVA .OR. WNTVS .OR. WNTVO .OR. WNTVN ) .OR.
     $         ( WNTVO .AND. WNTUO ) ) THEN
         INFO = -2
      ELSE IF( M.LT.0 ) THEN
         INFO = -3
      ELSE IF( N.LT.0 ) THEN
         INFO = -4
      ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
         INFO = -6
      ELSE IF( LDU.LT.1 .OR. ( WNTUAS .AND. LDU.LT.M ) ) THEN
         INFO = -9
      ELSE IF( LDVT.LT.1 .OR. ( WNTVA .AND. LDVT.LT.N ) .OR.
     $         ( WNTVS .AND. LDVT.LT.MINMN ) ) THEN
         INFO = -11
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Compute workspace
</span><span class="comment">*</span><span class="comment">      (Note: Comments in the code beginning &quot;Workspace:&quot; describe the
</span><span class="comment">*</span><span class="comment">       minimal amount of workspace needed at that point in the code,
</span><span class="comment">*</span><span class="comment">       as well as the preferred amount for good performance.
</span><span class="comment">*</span><span class="comment">       NB refers to the optimal block size for the immediately
</span><span class="comment">*</span><span class="comment">       following subroutine, as returned by <a name="ILAENV.206"></a><a href="hfy-index.html#ILAENV">ILAENV</a>.)
</span><span class="comment">*</span><span class="comment">
</span>      IF( INFO.EQ.0 ) THEN
         MINWRK = 1
         MAXWRK = 1
         IF( M.GE.N .AND. MINMN.GT.0 ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Compute space needed for <a name="DBDSQR.213"></a><a href="dbdsqr.f.html#DBDSQR.1">DBDSQR</a>
</span><span class="comment">*</span><span class="comment">
</span>            MNTHR = <a name="ILAENV.215"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 6, <span class="string">'<a name="DGESVD.215"></a><a href="dgesvd.f.html#DGESVD.1">DGESVD</a>'</span>, JOBU // JOBVT, M, N, 0, 0 )
            BDSPAC = 5*N
            IF( M.GE.MNTHR ) THEN
               IF( WNTUN ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                 Path 1 (M much larger than N, JOBU='N')
</span><span class="comment">*</span><span class="comment">
</span>                  MAXWRK = N + N*<a name="ILAENV.222"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="DGEQRF.222"></a><a href="dgeqrf.f.html#DGEQRF.1">DGEQRF</a>'</span>, <span class="string">' '</span>, M, N, -1,
     $                     -1 )
                  MAXWRK = MAX( MAXWRK, 3*N+2*N*
     $                     <a name="ILAENV.225"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="DGEBRD.225"></a><a href="dgebrd.f.html#DGEBRD.1">DGEBRD</a>'</span>, <span class="string">' '</span>, N, N, -1, -1 ) )
                  IF( WNTVO .OR. WNTVAS )
     $               MAXWRK = MAX( MAXWRK, 3*N+( N-1 )*
     $                        <a name="ILAENV.228"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="DORGBR.228"></a><a href="dorgbr.f.html#DORGBR.1">DORGBR</a>'</span>, <span class="string">'P'</span>, N, N, N, -1 ) )
                  MAXWRK = MAX( MAXWRK, BDSPAC )
                  MINWRK = MAX( 4*N, BDSPAC )
               ELSE IF( WNTUO .AND. WNTVN ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                 Path 2 (M much larger than N, JOBU='O', JOBVT='N')
</span><span class="comment">*</span><span class="comment">
</span>                  WRKBL = N + N*<a name="ILAENV.235"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="DGEQRF.235"></a><a href="dgeqrf.f.html#DGEQRF.1">DGEQRF</a>'</span>, <span class="string">' '</span>, M, N, -1, -1 )
                  WRKBL = MAX( WRKBL, N+N*<a name="ILAENV.236"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="DORGQR.236"></a><a href="dorgqr.f.html#DORGQR.1">DORGQR</a>'</span>, <span class="string">' '</span>, M,
     $                    N, N, -1 ) )
                  WRKBL = MAX( WRKBL, 3*N+2*N*
     $                    <a name="ILAENV.239"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="DGEBRD.239"></a><a href="dgebrd.f.html#DGEBRD.1">DGEBRD</a>'</span>, <span class="string">' '</span>, N, N, -1, -1 ) )
                  WRKBL = MAX( WRKBL, 3*N+N*
     $                    <a name="ILAENV.241"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="DORGBR.241"></a><a href="dorgbr.f.html#DORGBR.1">DORGBR</a>'</span>, <span class="string">'Q'</span>, N, N, N, -1 ) )
                  WRKBL = MAX( WRKBL, BDSPAC )
                  MAXWRK = MAX( N*N+WRKBL, N*N+M*N+N )
                  MINWRK = MAX( 3*N+M, BDSPAC )
               ELSE IF( WNTUO .AND. WNTVAS ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                 Path 3 (M much larger than N, JOBU='O', JOBVT='S' or
</span><span class="comment">*</span><span class="comment">                 'A')
</span><span class="comment">*</span><span class="comment">
</span>                  WRKBL = N + N*<a name="ILAENV.250"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="DGEQRF.250"></a><a href="dgeqrf.f.html#DGEQRF.1">DGEQRF</a>'</span>, <span class="string">' '</span>, M, N, -1, -1 )
                  WRKBL = MAX( WRKBL, N+N*<a name="ILAENV.251"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="DORGQR.251"></a><a href="dorgqr.f.html#DORGQR.1">DORGQR</a>'</span>, <span class="string">' '</span>, M,