ssptrf.f.html

来自「famous linear algebra library (LAPACK) p」· HTML 代码 · 共 572 行 · 第 1/3 页

</span><span class="comment">*</span><span class="comment">
</span>         ABSAKK = ABS( AP( KC ) )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        IMAX is the row-index of the largest off-diagonal element in
</span><span class="comment">*</span><span class="comment">        column K, and COLMAX is its absolute value
</span><span class="comment">*</span><span class="comment">
</span>         IF( K.LT.N ) THEN
            IMAX = K + ISAMAX( N-K, AP( KC+1 ), 1 )
            COLMAX = ABS( AP( KC+IMAX-K ) )
         ELSE
            COLMAX = ZERO
         END IF
<span class="comment">*</span><span class="comment">
</span>         IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Column K is zero: set INFO and continue
</span><span class="comment">*</span><span class="comment">
</span>            IF( INFO.EQ.0 )
     $         INFO = K
            KP = K
         ELSE
            IF( ABSAKK.GE.ALPHA*COLMAX ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              no interchange, use 1-by-1 pivot block
</span><span class="comment">*</span><span class="comment">
</span>               KP = K
            ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              JMAX is the column-index of the largest off-diagonal
</span><span class="comment">*</span><span class="comment">              element in row IMAX, and ROWMAX is its absolute value
</span><span class="comment">*</span><span class="comment">
</span>               ROWMAX = ZERO
               KX = KC + IMAX - K
               DO 70 J = K, IMAX - 1
                  IF( ABS( AP( KX ) ).GT.ROWMAX ) THEN
                     ROWMAX = ABS( AP( KX ) )
                     JMAX = J
                  END IF
                  KX = KX + N - J
   70          CONTINUE
               KPC = NPP - ( N-IMAX+1 )*( N-IMAX+2 ) / 2 + 1
               IF( IMAX.LT.N ) THEN
                  JMAX = IMAX + ISAMAX( N-IMAX, AP( KPC+1 ), 1 )
                  ROWMAX = MAX( ROWMAX, ABS( AP( KPC+JMAX-IMAX ) ) )
               END IF
<span class="comment">*</span><span class="comment">
</span>               IF( ABSAKK.GE.ALPHA*COLMAX*( COLMAX / ROWMAX ) ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                 no interchange, use 1-by-1 pivot block
</span><span class="comment">*</span><span class="comment">
</span>                  KP = K
               ELSE IF( ABS( AP( KPC ) ).GE.ALPHA*ROWMAX ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                 interchange rows and columns K and IMAX, use 1-by-1
</span><span class="comment">*</span><span class="comment">                 pivot block
</span><span class="comment">*</span><span class="comment">
</span>                  KP = IMAX
               ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                 interchange rows and columns K+1 and IMAX, use 2-by-2
</span><span class="comment">*</span><span class="comment">                 pivot block
</span><span class="comment">*</span><span class="comment">
</span>                  KP = IMAX
                  KSTEP = 2
               END IF
            END IF
<span class="comment">*</span><span class="comment">
</span>            KK = K + KSTEP - 1
            IF( KSTEP.EQ.2 )
     $         KNC = KNC + N - K + 1
            IF( KP.NE.KK ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              Interchange rows and columns KK and KP in the trailing
</span><span class="comment">*</span><span class="comment">              submatrix A(k:n,k:n)
</span><span class="comment">*</span><span class="comment">
</span>               IF( KP.LT.N )
     $            CALL SSWAP( N-KP, AP( KNC+KP-KK+1 ), 1, AP( KPC+1 ),
     $                        1 )
               KX = KNC + KP - KK
               DO 80 J = KK + 1, KP - 1
                  KX = KX + N - J + 1
                  T = AP( KNC+J-KK )
                  AP( KNC+J-KK ) = AP( KX )
                  AP( KX ) = T
   80          CONTINUE
               T = AP( KNC )
               AP( KNC ) = AP( KPC )
               AP( KPC ) = T
               IF( KSTEP.EQ.2 ) THEN
                  T = AP( KC+1 )
                  AP( KC+1 ) = AP( KC+KP-K )
                  AP( KC+KP-K ) = T
               END IF
            END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Update the trailing submatrix
</span><span class="comment">*</span><span class="comment">
</span>            IF( KSTEP.EQ.1 ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              1-by-1 pivot block D(k): column k now holds
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              W(k) = L(k)*D(k)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              where L(k) is the k-th column of L
</span><span class="comment">*</span><span class="comment">
</span>               IF( K.LT.N ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                 Perform a rank-1 update of A(k+1:n,k+1:n) as
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                 A := A - L(k)*D(k)*L(k)' = A - W(k)*(1/D(k))*W(k)'
</span><span class="comment">*</span><span class="comment">
</span>                  R1 = ONE / AP( KC )
                  CALL SSPR( UPLO, N-K, -R1, AP( KC+1 ), 1,
     $                       AP( KC+N-K+1 ) )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                 Store L(k) in column K
</span><span class="comment">*</span><span class="comment">
</span>                  CALL SSCAL( N-K, R1, AP( KC+1 ), 1 )
               END IF
            ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              2-by-2 pivot block D(k): columns K and K+1 now hold
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              ( W(k) W(k+1) ) = ( L(k) L(k+1) )*D(k)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              where L(k) and L(k+1) are the k-th and (k+1)-th columns
</span><span class="comment">*</span><span class="comment">              of L
</span><span class="comment">*</span><span class="comment">
</span>               IF( K.LT.N-1 ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                 Perform a rank-2 update of A(k+2:n,k+2:n) as
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                 A := A - ( L(k) L(k+1) )*D(k)*( L(k) L(k+1) )'
</span><span class="comment">*</span><span class="comment">                    = A - ( W(k) W(k+1) )*inv(D(k))*( W(k) W(k+1) )'
</span><span class="comment">*</span><span class="comment">
</span>                  D21 = AP( K+1+( K-1 )*( 2*N-K ) / 2 )
                  D11 = AP( K+1+K*( 2*N-K-1 ) / 2 ) / D21
                  D22 = AP( K+( K-1 )*( 2*N-K ) / 2 ) / D21
                  T = ONE / ( D11*D22-ONE )
                  D21 = T / D21
<span class="comment">*</span><span class="comment">
</span>                  DO 100 J = K + 2, N
                     WK = D21*( D11*AP( J+( K-1 )*( 2*N-K ) / 2 )-
     $                    AP( J+K*( 2*N-K-1 ) / 2 ) )
                     WKP1 = D21*( D22*AP( J+K*( 2*N-K-1 ) / 2 )-
     $                      AP( J+( K-1 )*( 2*N-K ) / 2 ) )
<span class="comment">*</span><span class="comment">
</span>                     DO 90 I = J, N
                        AP( I+( J-1 )*( 2*N-J ) / 2 ) = AP( I+( J-1 )*
     $                     ( 2*N-J ) / 2 ) - AP( I+( K-1 )*( 2*N-K ) /
     $                     2 )*WK - AP( I+K*( 2*N-K-1 ) / 2 )*WKP1
   90                CONTINUE
<span class="comment">*</span><span class="comment">
</span>                     AP( J+( K-1 )*( 2*N-K ) / 2 ) = WK
                     AP( J+K*( 2*N-K-1 ) / 2 ) = WKP1
<span class="comment">*</span><span class="comment">
</span>  100             CONTINUE
               END IF
            END IF
         END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Store details of the interchanges in IPIV
</span><span class="comment">*</span><span class="comment">
</span>         IF( KSTEP.EQ.1 ) THEN
            IPIV( K ) = KP
         ELSE
            IPIV( K ) = -KP
            IPIV( K+1 ) = -KP
         END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Increase K and return to the start of the main loop
</span><span class="comment">*</span><span class="comment">
</span>         K = K + KSTEP
         KC = KNC + N - K + 2
         GO TO 60
<span class="comment">*</span><span class="comment">
</span>      END IF
<span class="comment">*</span><span class="comment">
</span>  110 CONTINUE
      RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     End of <a name="SSPTRF.545"></a><a href="ssptrf.f.html#SSPTRF.1">SSPTRF</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

</pre>

 </body>
</html>