sgelss.f.html

来自「famous linear algebra library (LAPACK) p」· HTML 代码 · 共 642 行 · 第 1/4 页

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</span>         CALL <a name="SBDSQR.465"></a><a href="sbdsqr.f.html#SBDSQR.1">SBDSQR</a>( <span class="string">'U'</span>, M, M, 0, NRHS, S, WORK( IE ), WORK( IL ),
     $                LDWORK, A, LDA, B, LDB, WORK( IWORK ), INFO )
         IF( INFO.NE.0 )
     $      GO TO 70
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Multiply B by reciprocals of singular values
</span><span class="comment">*</span><span class="comment">
</span>         THR = MAX( RCOND*S( 1 ), SFMIN )
         IF( RCOND.LT.ZERO )
     $      THR = MAX( EPS*S( 1 ), SFMIN )
         RANK = 0
         DO 30 I = 1, M
            IF( S( I ).GT.THR ) THEN
               CALL <a name="SRSCL.478"></a><a href="srscl.f.html#SRSCL.1">SRSCL</a>( NRHS, S( I ), B( I, 1 ), LDB )
               RANK = RANK + 1
            ELSE
               CALL <a name="SLASET.481"></a><a href="slaset.f.html#SLASET.1">SLASET</a>( <span class="string">'F'</span>, 1, NRHS, ZERO, ZERO, B( I, 1 ), LDB )
            END IF
   30    CONTINUE
         IWORK = IE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Multiply B by right singular vectors of L in WORK(IL)
</span><span class="comment">*</span><span class="comment">        (Workspace: need M*M+2*M, prefer M*M+M+M*NRHS)
</span><span class="comment">*</span><span class="comment">
</span>         IF( LWORK.GE.LDB*NRHS+IWORK-1 .AND. NRHS.GT.1 ) THEN
            CALL SGEMM( <span class="string">'T'</span>, <span class="string">'N'</span>, M, NRHS, M, ONE, WORK( IL ), LDWORK,
     $                  B, LDB, ZERO, WORK( IWORK ), LDB )
            CALL <a name="SLACPY.492"></a><a href="slacpy.f.html#SLACPY.1">SLACPY</a>( <span class="string">'G'</span>, M, NRHS, WORK( IWORK ), LDB, B, LDB )
         ELSE IF( NRHS.GT.1 ) THEN
            CHUNK = ( LWORK-IWORK+1 ) / M
            DO 40 I = 1, NRHS, CHUNK
               BL = MIN( NRHS-I+1, CHUNK )
               CALL SGEMM( <span class="string">'T'</span>, <span class="string">'N'</span>, M, BL, M, ONE, WORK( IL ), LDWORK,
     $                     B( 1, I ), LDB, ZERO, WORK( IWORK ), M )
               CALL <a name="SLACPY.499"></a><a href="slacpy.f.html#SLACPY.1">SLACPY</a>( <span class="string">'G'</span>, M, BL, WORK( IWORK ), M, B( 1, I ),
     $                      LDB )
   40       CONTINUE
         ELSE
            CALL SGEMV( <span class="string">'T'</span>, M, M, ONE, WORK( IL ), LDWORK, B( 1, 1 ),
     $                  1, ZERO, WORK( IWORK ), 1 )
            CALL SCOPY( M, WORK( IWORK ), 1, B( 1, 1 ), 1 )
         END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Zero out below first M rows of B
</span><span class="comment">*</span><span class="comment">
</span>         CALL <a name="SLASET.510"></a><a href="slaset.f.html#SLASET.1">SLASET</a>( <span class="string">'F'</span>, N-M, NRHS, ZERO, ZERO, B( M+1, 1 ), LDB )
         IWORK = ITAU + M
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Multiply transpose(Q) by B
</span><span class="comment">*</span><span class="comment">        (Workspace: need M+NRHS, prefer M+NRHS*NB)
</span><span class="comment">*</span><span class="comment">
</span>         CALL <a name="SORMLQ.516"></a><a href="sormlq.f.html#SORMLQ.1">SORMLQ</a>( <span class="string">'L'</span>, <span class="string">'T'</span>, N, NRHS, M, A, LDA, WORK( ITAU ), B,
     $                LDB, WORK( IWORK ), LWORK-IWORK+1, INFO )
<span class="comment">*</span><span class="comment">
</span>      ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Path 2 - remaining underdetermined cases
</span><span class="comment">*</span><span class="comment">
</span>         IE = 1
         ITAUQ = IE + M
         ITAUP = ITAUQ + M
         IWORK = ITAUP + M
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Bidiagonalize A
</span><span class="comment">*</span><span class="comment">        (Workspace: need 3*M+N, prefer 3*M+(M+N)*NB)
</span><span class="comment">*</span><span class="comment">
</span>         CALL <a name="SGEBRD.531"></a><a href="sgebrd.f.html#SGEBRD.1">SGEBRD</a>( M, N, A, LDA, S, WORK( IE ), WORK( ITAUQ ),
     $                WORK( ITAUP ), WORK( IWORK ), LWORK-IWORK+1,
     $                INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Multiply B by transpose of left bidiagonalizing vectors
</span><span class="comment">*</span><span class="comment">        (Workspace: need 3*M+NRHS, prefer 3*M+NRHS*NB)
</span><span class="comment">*</span><span class="comment">
</span>         CALL <a name="SORMBR.538"></a><a href="sormbr.f.html#SORMBR.1">SORMBR</a>( <span class="string">'Q'</span>, <span class="string">'L'</span>, <span class="string">'T'</span>, M, NRHS, N, A, LDA, WORK( ITAUQ ),
     $                B, LDB, WORK( IWORK ), LWORK-IWORK+1, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Generate right bidiagonalizing vectors in A
</span><span class="comment">*</span><span class="comment">        (Workspace: need 4*M, prefer 3*M+M*NB)
</span><span class="comment">*</span><span class="comment">
</span>         CALL <a name="SORGBR.544"></a><a href="sorgbr.f.html#SORGBR.1">SORGBR</a>( <span class="string">'P'</span>, M, N, M, A, LDA, WORK( ITAUP ),
     $                WORK( IWORK ), LWORK-IWORK+1, INFO )
         IWORK = IE + M
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Perform bidiagonal QR iteration,
</span><span class="comment">*</span><span class="comment">           computing right singular vectors of A in A and
</span><span class="comment">*</span><span class="comment">           multiplying B by transpose of left singular vectors
</span><span class="comment">*</span><span class="comment">        (Workspace: need BDSPAC)
</span><span class="comment">*</span><span class="comment">
</span>         CALL <a name="SBDSQR.553"></a><a href="sbdsqr.f.html#SBDSQR.1">SBDSQR</a>( <span class="string">'L'</span>, M, N, 0, NRHS, S, WORK( IE ), A, LDA, VDUM,
     $                1, B, LDB, WORK( IWORK ), INFO )
         IF( INFO.NE.0 )
     $      GO TO 70
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Multiply B by reciprocals of singular values
</span><span class="comment">*</span><span class="comment">
</span>         THR = MAX( RCOND*S( 1 ), SFMIN )
         IF( RCOND.LT.ZERO )
     $      THR = MAX( EPS*S( 1 ), SFMIN )
         RANK = 0
         DO 50 I = 1, M
            IF( S( I ).GT.THR ) THEN
               CALL <a name="SRSCL.566"></a><a href="srscl.f.html#SRSCL.1">SRSCL</a>( NRHS, S( I ), B( I, 1 ), LDB )
               RANK = RANK + 1
            ELSE
               CALL <a name="SLASET.569"></a><a href="slaset.f.html#SLASET.1">SLASET</a>( <span class="string">'F'</span>, 1, NRHS, ZERO, ZERO, B( I, 1 ), LDB )
            END IF
   50    CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Multiply B by right singular vectors of A
</span><span class="comment">*</span><span class="comment">        (Workspace: need N, prefer N*NRHS)
</span><span class="comment">*</span><span class="comment">
</span>         IF( LWORK.GE.LDB*NRHS .AND. NRHS.GT.1 ) THEN
            CALL SGEMM( <span class="string">'T'</span>, <span class="string">'N'</span>, N, NRHS, M, ONE, A, LDA, B, LDB, ZERO,
     $                  WORK, LDB )
            CALL <a name="SLACPY.579"></a><a href="slacpy.f.html#SLACPY.1">SLACPY</a>( <span class="string">'F'</span>, N, NRHS, WORK, LDB, B, LDB )
         ELSE IF( NRHS.GT.1 ) THEN
            CHUNK = LWORK / N
            DO 60 I = 1, NRHS, CHUNK
               BL = MIN( NRHS-I+1, CHUNK )
               CALL SGEMM( <span class="string">'T'</span>, <span class="string">'N'</span>, N, BL, M, ONE, A, LDA, B( 1, I ),
     $                     LDB, ZERO, WORK, N )
               CALL <a name="SLACPY.586"></a><a href="slacpy.f.html#SLACPY.1">SLACPY</a>( <span class="string">'F'</span>, N, BL, WORK, N, B( 1, I ), LDB )
   60       CONTINUE
         ELSE
            CALL SGEMV( <span class="string">'T'</span>, M, N, ONE, A, LDA, B, 1, ZERO, WORK, 1 )
            CALL SCOPY( N, WORK, 1, B, 1 )
         END IF
      END IF
<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="SLASCL.597"></a><a href="slascl.f.html#SLASCL.1">SLASCL</a>( <span class="string">'G'</span>, 0, 0, ANRM, SMLNUM, N, NRHS, B, LDB, INFO )
         CALL <a name="SLASCL.598"></a><a href="slascl.f.html#SLASCL.1">SLASCL</a>( <span class="string">'G'</span>, 0, 0, SMLNUM, ANRM, MINMN, 1, S, MINMN,
     $                INFO )
      ELSE IF( IASCL.EQ.2 ) THEN
         CALL <a name="SLASCL.601"></a><a href="slascl.f.html#SLASCL.1">SLASCL</a>( <span class="string">'G'</span>, 0, 0, ANRM, BIGNUM, N, NRHS, B, LDB, INFO )
         CALL <a name="SLASCL.602"></a><a href="slascl.f.html#SLASCL.1">SLASCL</a>( <span class="string">'G'</span>, 0, 0, BIGNUM, ANRM, MINMN, 1, S, MINMN,
     $                INFO )
      END IF
      IF( IBSCL.EQ.1 ) THEN
         CALL <a name="SLASCL.606"></a><a href="slascl.f.html#SLASCL.1">SLASCL</a>( <span class="string">'G'</span>, 0, 0, SMLNUM, BNRM, N, NRHS, B, LDB, INFO )
      ELSE IF( IBSCL.EQ.2 ) THEN
         CALL <a name="SLASCL.608"></a><a href="slascl.f.html#SLASCL.1">SLASCL</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>   70 CONTINUE
      WORK( 1 ) = MAXWRK
      RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     End of <a name="SGELSS.615"></a><a href="sgelss.f.html#SGELSS.1">SGELSS</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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