dgelsx.f.html

来自「famous linear algebra library (LAPACK) p」· HTML 代码 · 共 374 行 · 第 1/2 页

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</span>      SMLNUM = <a name="DLAMCH.169"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>( <span class="string">'S'</span> ) / <a name="DLAMCH.169"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>( <span class="string">'P'</span> )
      BIGNUM = ONE / SMLNUM
      CALL <a name="DLABAD.171"></a><a href="dlabad.f.html#DLABAD.1">DLABAD</a>( SMLNUM, BIGNUM )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Scale A, B if max elements outside range [SMLNUM,BIGNUM]
</span><span class="comment">*</span><span class="comment">
</span>      ANRM = <a name="DLANGE.175"></a><a href="dlange.f.html#DLANGE.1">DLANGE</a>( <span class="string">'M'</span>, M, N, A, LDA, WORK )
      IASCL = 0
      IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Scale matrix norm up to SMLNUM
</span><span class="comment">*</span><span class="comment">
</span>         CALL <a name="DLASCL.181"></a><a href="dlascl.f.html#DLASCL.1">DLASCL</a>( <span class="string">'G'</span>, 0, 0, ANRM, SMLNUM, M, N, A, LDA, INFO )
         IASCL = 1
      ELSE IF( ANRM.GT.BIGNUM ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Scale matrix norm down to BIGNUM
</span><span class="comment">*</span><span class="comment">
</span>         CALL <a name="DLASCL.187"></a><a href="dlascl.f.html#DLASCL.1">DLASCL</a>( <span class="string">'G'</span>, 0, 0, ANRM, BIGNUM, M, N, A, LDA, INFO )
         IASCL = 2
      ELSE IF( ANRM.EQ.ZERO ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Matrix all zero. Return zero solution.
</span><span class="comment">*</span><span class="comment">
</span>         CALL <a name="DLASET.193"></a><a href="dlaset.f.html#DLASET.1">DLASET</a>( <span class="string">'F'</span>, MAX( M, N ), NRHS, ZERO, ZERO, B, LDB )
         RANK = 0
         GO TO 100
      END IF
<span class="comment">*</span><span class="comment">
</span>      BNRM = <a name="DLANGE.198"></a><a href="dlange.f.html#DLANGE.1">DLANGE</a>( <span class="string">'M'</span>, M, NRHS, B, LDB, WORK )
      IBSCL = 0
      IF( BNRM.GT.ZERO .AND. BNRM.LT.SMLNUM ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Scale matrix norm up to SMLNUM
</span><span class="comment">*</span><span class="comment">
</span>         CALL <a name="DLASCL.204"></a><a href="dlascl.f.html#DLASCL.1">DLASCL</a>( <span class="string">'G'</span>, 0, 0, BNRM, SMLNUM, M, NRHS, B, LDB, INFO )
         IBSCL = 1
      ELSE IF( BNRM.GT.BIGNUM ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Scale matrix norm down to BIGNUM
</span><span class="comment">*</span><span class="comment">
</span>         CALL <a name="DLASCL.210"></a><a href="dlascl.f.html#DLASCL.1">DLASCL</a>( <span class="string">'G'</span>, 0, 0, BNRM, BIGNUM, M, NRHS, B, LDB, INFO )
         IBSCL = 2
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Compute QR factorization with column pivoting of A:
</span><span class="comment">*</span><span class="comment">        A * P = Q * R
</span><span class="comment">*</span><span class="comment">
</span>      CALL <a name="DGEQPF.217"></a><a href="dgeqpf.f.html#DGEQPF.1">DGEQPF</a>( M, N, A, LDA, JPVT, WORK( 1 ), WORK( MN+1 ), INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     workspace 3*N. Details of Householder rotations stored
</span><span class="comment">*</span><span class="comment">     in WORK(1:MN).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Determine RANK using incremental condition estimation
</span><span class="comment">*</span><span class="comment">
</span>      WORK( ISMIN ) = ONE
      WORK( ISMAX ) = ONE
      SMAX = ABS( A( 1, 1 ) )
      SMIN = SMAX
      IF( ABS( A( 1, 1 ) ).EQ.ZERO ) THEN
         RANK = 0
         CALL <a name="DLASET.230"></a><a href="dlaset.f.html#DLASET.1">DLASET</a>( <span class="string">'F'</span>, MAX( M, N ), NRHS, ZERO, ZERO, B, LDB )
         GO TO 100
      ELSE
         RANK = 1
      END IF
<span class="comment">*</span><span class="comment">
</span>   10 CONTINUE
      IF( RANK.LT.MN ) THEN
         I = RANK + 1
         CALL <a name="DLAIC1.239"></a><a href="dlaic1.f.html#DLAIC1.1">DLAIC1</a>( IMIN, RANK, WORK( ISMIN ), SMIN, A( 1, I ),
     $                A( I, I ), SMINPR, S1, C1 )
         CALL <a name="DLAIC1.241"></a><a href="dlaic1.f.html#DLAIC1.1">DLAIC1</a>( IMAX, RANK, WORK( ISMAX ), SMAX, A( 1, I ),
     $                A( I, I ), SMAXPR, S2, C2 )
<span class="comment">*</span><span class="comment">
</span>         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
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Logically partition R = [ R11 R12 ]
</span><span class="comment">*</span><span class="comment">                             [  0  R22 ]
</span><span class="comment">*</span><span class="comment">     where R11 = R(1:RANK,1:RANK)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     [R11,R12] = [ T11, 0 ] * Y
</span><span class="comment">*</span><span class="comment">
</span>      IF( RANK.LT.N )
     $   CALL <a name="DTZRQF.265"></a><a href="dtzrqf.f.html#DTZRQF.1">DTZRQF</a>( RANK, N, A, LDA, WORK( MN+1 ), INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Details of Householder rotations stored in WORK(MN+1:2*MN)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     B(1:M,1:NRHS) := Q' * B(1:M,1:NRHS)
</span><span class="comment">*</span><span class="comment">
</span>      CALL <a name="DORM2R.271"></a><a href="dorm2r.f.html#DORM2R.1">DORM2R</a>( <span class="string">'Left'</span>, <span class="string">'Transpose'</span>, M, NRHS, MN, A, LDA, WORK( 1 ),
     $             B, LDB, WORK( 2*MN+1 ), INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     workspace NRHS
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     B(1:RANK,1:NRHS) := inv(T11) * B(1:RANK,1:NRHS)
</span><span class="comment">*</span><span class="comment">
</span>      CALL DTRSM( <span class="string">'Left'</span>, <span class="string">'Upper'</span>, <span class="string">'No transpose'</span>, <span class="string">'Non-unit'</span>, RANK,
     $            NRHS, ONE, A, LDA, B, LDB )
<span class="comment">*</span><span class="comment">
</span>      DO 40 I = RANK + 1, N
         DO 30 J = 1, NRHS
            B( I, J ) = ZERO
   30    CONTINUE
   40 CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     B(1:N,1:NRHS) := Y' * B(1:N,1:NRHS)
</span><span class="comment">*</span><span class="comment">
</span>      IF( RANK.LT.N ) THEN
         DO 50 I = 1, RANK
            CALL <a name="DLATZM.291"></a><a href="dlatzm.f.html#DLATZM.1">DLATZM</a>( <span class="string">'Left'</span>, N-RANK+1, NRHS, A( I, RANK+1 ), LDA,
     $                   WORK( MN+I ), B( I, 1 ), B( RANK+1, 1 ), LDB,
     $                   WORK( 2*MN+1 ) )
   50    CONTINUE
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     workspace NRHS
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     B(1:N,1:NRHS) := P * B(1:N,1:NRHS)
</span><span class="comment">*</span><span class="comment">
</span>      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
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Undo scaling
</span><span class="comment">*</span><span class="comment">
</span>      IF( IASCL.EQ.1 ) THEN
         CALL <a name="DLASCL.329"></a><a href="dlascl.f.html#DLASCL.1">DLASCL</a>( <span class="string">'G'</span>, 0, 0, ANRM, SMLNUM, N, NRHS, B, LDB, INFO )
         CALL <a name="DLASCL.330"></a><a href="dlascl.f.html#DLASCL.1">DLASCL</a>( <span class="string">'U'</span>, 0, 0, SMLNUM, ANRM, RANK, RANK, A, LDA,
     $                INFO )
      ELSE IF( IASCL.EQ.2 ) THEN
         CALL <a name="DLASCL.333"></a><a href="dlascl.f.html#DLASCL.1">DLASCL</a>( <span class="string">'G'</span>, 0, 0, ANRM, BIGNUM, N, NRHS, B, LDB, INFO )
         CALL <a name="DLASCL.334"></a><a href="dlascl.f.html#DLASCL.1">DLASCL</a>( <span class="string">'U'</span>, 0, 0, BIGNUM, ANRM, RANK, RANK, A, LDA,
     $                INFO )
      END IF
      IF( IBSCL.EQ.1 ) THEN
         CALL <a name="DLASCL.338"></a><a href="dlascl.f.html#DLASCL.1">DLASCL</a>( <span class="string">'G'</span>, 0, 0, SMLNUM, BNRM, N, NRHS, B, LDB, INFO )
      ELSE IF( IBSCL.EQ.2 ) THEN
         CALL <a name="DLASCL.340"></a><a href="dlascl.f.html#DLASCL.1">DLASCL</a>( <span class="string">'G'</span>, 0, 0, BIGNUM, BNRM, N, NRHS, B, LDB, INFO )
      END IF
<span class="comment">*</span><span class="comment">
</span>  100 CONTINUE
<span class="comment">*</span><span class="comment">
</span>      RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     End of <a name="DGELSX.347"></a><a href="dgelsx.f.html#DGELSX.1">DGELSX</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

</pre>

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