chptri.f.html

来自「famous linear algebra library (LAPACK) p」· HTML 代码 · 共 368 行 · 第 1/2 页

<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           2 x 2 diagonal block
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Invert the diagonal block.
</span><span class="comment">*</span><span class="comment">
</span>            T = ABS( AP( KCNEXT+K-1 ) )
            AK = REAL( AP( KC+K-1 ) ) / T
            AKP1 = REAL( AP( KCNEXT+K ) ) / T
            AKKP1 = AP( KCNEXT+K-1 ) / T
            D = T*( AK*AKP1-ONE )
            AP( KC+K-1 ) = AKP1 / D
            AP( KCNEXT+K ) = AK / D
            AP( KCNEXT+K-1 ) = -AKKP1 / D
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Compute columns K and K+1 of the inverse.
</span><span class="comment">*</span><span class="comment">
</span>            IF( K.GT.1 ) THEN
               CALL CCOPY( K-1, AP( KC ), 1, WORK, 1 )
               CALL CHPMV( UPLO, K-1, -CONE, AP, WORK, 1, ZERO,
     $                     AP( KC ), 1 )
               AP( KC+K-1 ) = AP( KC+K-1 ) -
     $                        REAL( CDOTC( K-1, WORK, 1, AP( KC ), 1 ) )
               AP( KCNEXT+K-1 ) = AP( KCNEXT+K-1 ) -
     $                            CDOTC( K-1, AP( KC ), 1, AP( KCNEXT ),
     $                            1 )
               CALL CCOPY( K-1, AP( KCNEXT ), 1, WORK, 1 )
               CALL CHPMV( UPLO, K-1, -CONE, AP, WORK, 1, ZERO,
     $                     AP( KCNEXT ), 1 )
               AP( KCNEXT+K ) = AP( KCNEXT+K ) -
     $                          REAL( CDOTC( K-1, WORK, 1, AP( KCNEXT ),
     $                          1 ) )
            END IF
            KSTEP = 2
            KCNEXT = KCNEXT + K + 1
         END IF
<span class="comment">*</span><span class="comment">
</span>         KP = ABS( IPIV( K ) )
         IF( KP.NE.K ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Interchange rows and columns K and KP in the leading
</span><span class="comment">*</span><span class="comment">           submatrix A(1:k+1,1:k+1)
</span><span class="comment">*</span><span class="comment">
</span>            KPC = ( KP-1 )*KP / 2 + 1
            CALL CSWAP( KP-1, AP( KC ), 1, AP( KPC ), 1 )
            KX = KPC + KP - 1
            DO 40 J = KP + 1, K - 1
               KX = KX + J - 1
               TEMP = CONJG( AP( KC+J-1 ) )
               AP( KC+J-1 ) = CONJG( AP( KX ) )
               AP( KX ) = TEMP
   40       CONTINUE
            AP( KC+KP-1 ) = CONJG( AP( KC+KP-1 ) )
            TEMP = AP( KC+K-1 )
            AP( KC+K-1 ) = AP( KPC+KP-1 )
            AP( KPC+KP-1 ) = TEMP
            IF( KSTEP.EQ.2 ) THEN
               TEMP = AP( KC+K+K-1 )
               AP( KC+K+K-1 ) = AP( KC+K+KP-1 )
               AP( KC+K+KP-1 ) = TEMP
            END IF
         END IF
<span class="comment">*</span><span class="comment">
</span>         K = K + KSTEP
         KC = KCNEXT
         GO TO 30
   50    CONTINUE
<span class="comment">*</span><span class="comment">
</span>      ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Compute inv(A) from the factorization A = L*D*L'.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        K is the main loop index, increasing from 1 to N in steps of
</span><span class="comment">*</span><span class="comment">        1 or 2, depending on the size of the diagonal blocks.
</span><span class="comment">*</span><span class="comment">
</span>         NPP = N*( N+1 ) / 2
         K = N
         KC = NPP
   60    CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        If K &lt; 1, exit from loop.
</span><span class="comment">*</span><span class="comment">
</span>         IF( K.LT.1 )
     $      GO TO 80
<span class="comment">*</span><span class="comment">
</span>         KCNEXT = KC - ( N-K+2 )
         IF( IPIV( K ).GT.0 ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           1 x 1 diagonal block
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Invert the diagonal block.
</span><span class="comment">*</span><span class="comment">
</span>            AP( KC ) = ONE / REAL( AP( KC ) )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Compute column K of the inverse.
</span><span class="comment">*</span><span class="comment">
</span>            IF( K.LT.N ) THEN
               CALL CCOPY( N-K, AP( KC+1 ), 1, WORK, 1 )
               CALL CHPMV( UPLO, N-K, -CONE, AP( KC+N-K+1 ), WORK, 1,
     $                     ZERO, AP( KC+1 ), 1 )
               AP( KC ) = AP( KC ) - REAL( CDOTC( N-K, WORK, 1,
     $                    AP( KC+1 ), 1 ) )
            END IF
            KSTEP = 1
         ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           2 x 2 diagonal block
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Invert the diagonal block.
</span><span class="comment">*</span><span class="comment">
</span>            T = ABS( AP( KCNEXT+1 ) )
            AK = REAL( AP( KCNEXT ) ) / T
            AKP1 = REAL( AP( KC ) ) / T
            AKKP1 = AP( KCNEXT+1 ) / T
            D = T*( AK*AKP1-ONE )
            AP( KCNEXT ) = AKP1 / D
            AP( KC ) = AK / D
            AP( KCNEXT+1 ) = -AKKP1 / D
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Compute columns K-1 and K of the inverse.
</span><span class="comment">*</span><span class="comment">
</span>            IF( K.LT.N ) THEN
               CALL CCOPY( N-K, AP( KC+1 ), 1, WORK, 1 )
               CALL CHPMV( UPLO, N-K, -CONE, AP( KC+( N-K+1 ) ), WORK,
     $                     1, ZERO, AP( KC+1 ), 1 )
               AP( KC ) = AP( KC ) - REAL( CDOTC( N-K, WORK, 1,
     $                    AP( KC+1 ), 1 ) )
               AP( KCNEXT+1 ) = AP( KCNEXT+1 ) -
     $                          CDOTC( N-K, AP( KC+1 ), 1,
     $                          AP( KCNEXT+2 ), 1 )
               CALL CCOPY( N-K, AP( KCNEXT+2 ), 1, WORK, 1 )
               CALL CHPMV( UPLO, N-K, -CONE, AP( KC+( N-K+1 ) ), WORK,
     $                     1, ZERO, AP( KCNEXT+2 ), 1 )
               AP( KCNEXT ) = AP( KCNEXT ) -
     $                        REAL( CDOTC( N-K, WORK, 1, AP( KCNEXT+2 ),
     $                        1 ) )
            END IF
            KSTEP = 2
            KCNEXT = KCNEXT - ( N-K+3 )
         END IF
<span class="comment">*</span><span class="comment">
</span>         KP = ABS( IPIV( K ) )
         IF( KP.NE.K ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Interchange rows and columns K and KP in the trailing
</span><span class="comment">*</span><span class="comment">           submatrix A(k-1:n,k-1:n)
</span><span class="comment">*</span><span class="comment">
</span>            KPC = NPP - ( N-KP+1 )*( N-KP+2 ) / 2 + 1
            IF( KP.LT.N )
     $         CALL CSWAP( N-KP, AP( KC+KP-K+1 ), 1, AP( KPC+1 ), 1 )
            KX = KC + KP - K
            DO 70 J = K + 1, KP - 1
               KX = KX + N - J + 1
               TEMP = CONJG( AP( KC+J-K ) )
               AP( KC+J-K ) = CONJG( AP( KX ) )
               AP( KX ) = TEMP
   70       CONTINUE
            AP( KC+KP-K ) = CONJG( AP( KC+KP-K ) )
            TEMP = AP( KC )
            AP( KC ) = AP( KPC )
            AP( KPC ) = TEMP
            IF( KSTEP.EQ.2 ) THEN
               TEMP = AP( KC-N+K-1 )
               AP( KC-N+K-1 ) = AP( KC-N+KP-1 )
               AP( KC-N+KP-1 ) = TEMP
            END IF
         END IF
<span class="comment">*</span><span class="comment">
</span>         K = K - KSTEP
         KC = KCNEXT
         GO TO 60
   80    CONTINUE
      END IF
<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="CHPTRI.341"></a><a href="chptri.f.html#CHPTRI.1">CHPTRI</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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