zhptri.f

          SUBROUTINE ZHPTRI( UPLO, N, AP, IPIV, WORK, INFO )
    *
    *  -- LAPACK routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          UPLO
          INTEGER            INFO, N
    *     ..
    *     .. Array Arguments ..
          INTEGER            IPIV( * )
          COMPLEX*16         AP( * ), WORK( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  ZHPTRI computes the inverse of a complex Hermitian indefinite matrix
    *  A in packed storage using the factorization A = U*D*U**H or
    *  A = L*D*L**H computed by ZHPTRF.
    *
    *  Arguments
    *  =========
    *
    *  UPLO    (input) CHARACTER*1
    *          Specifies whether the details of the factorization are stored
    *          as an upper or lower triangular matrix.
    *          = 'U':  Upper triangular, form is A = U*D*U**H;
    *          = 'L':  Lower triangular, form is A = L*D*L**H.
    *
    *  N       (input) INTEGER
    *          The order of the matrix A.  N >= 0.
    *
    *  AP      (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
    *          On entry, the block diagonal matrix D and the multipliers
    *          used to obtain the factor U or L as computed by ZHPTRF,
    *          stored as a packed triangular matrix.
    *
    *          On exit, if INFO = 0, the (Hermitian) inverse of the original
    *          matrix, stored as a packed triangular matrix. The j-th column
    *          of inv(A) is stored in the array AP as follows:
    *          if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j;
    *          if UPLO = 'L',
    *             AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n.
    *
    *  IPIV    (input) INTEGER array, dimension (N)
    *          Details of the interchanges and the block structure of D
    *          as determined by ZHPTRF.
    *
    *  WORK    (workspace) COMPLEX*16 array, dimension (N)
    *
    *  INFO    (output) INTEGER
    *          = 0: successful exit
    *          < 0: if INFO = -i, the i-th argument had an illegal value
    *          > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
    *               inverse could not be computed.
    *
    *  =====================================================================
    *
    *     .. Parameters ..
          DOUBLE PRECISION   ONE
          COMPLEX*16         CONE, ZERO
          PARAMETER          ( ONE = 1.0D+0, CONE = ( 1.0D+0, 0.0D+0 ),
         $                   ZERO = ( 0.0D+0, 0.0D+0 ) )
    *     ..
    *     .. Local Scalars ..
          LOGICAL            UPPER
          INTEGER            J, K, KC, KCNEXT, KP, KPC, KSTEP, KX, NPP
          DOUBLE PRECISION   AK, AKP1, D, T
          COMPLEX*16         AKKP1, TEMP
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          COMPLEX*16         ZDOTC
          EXTERNAL           LSAME, ZDOTC
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           XERBLA, ZCOPY, ZHPMV, ZSWAP
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          ABS, DBLE, DCONJG
    *     ..
    *     .. Executable Statements ..
    *
    *     Test the input parameters.
    *
          INFO = 0
          UPPER = LSAME( UPLO, 'U' )
          IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
             INFO = -1
          ELSE IF( N.LT.0 ) THEN
             INFO = -2
          END IF
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'ZHPTRI', -INFO )
             RETURN
          END IF
    *
    *     Quick return if possible
    *
          IF( N.EQ.0 )
         $   RETURN
    *
    *     Check that the diagonal matrix D is nonsingular.
    *
          IF( UPPER ) THEN
    *
    *        Upper triangular storage: examine D from bottom to top
    *
             KP = N*( N+1 ) / 2
             DO 10 INFO = N, 1, -1
                IF( IPIV( INFO ).GT.0 .AND. AP( KP ).EQ.ZERO )
         $         RETURN
                KP = KP - INFO
       10    CONTINUE
          ELSE
    *
    *        Lower triangular storage: examine D from top to bottom.
    *
             KP = 1
             DO 20 INFO = 1, N
                IF( IPIV( INFO ).GT.0 .AND. AP( KP ).EQ.ZERO )
         $         RETURN
                KP = KP + N - INFO + 1
       20    CONTINUE
          END IF
          INFO = 0
    *
          IF( UPPER ) THEN
    *
    *        Compute inv(A) from the factorization A = U*D*U'.
    *
    *        K is the main loop index, increasing from 1 to N in steps of
    *        1 or 2, depending on the size of the diagonal blocks.
    *
             K = 1
             KC = 1
       30    CONTINUE
    *
    *        If K > N, exit from loop.
    *
             IF( K.GT.N )
         $      GO TO 50
    *
             KCNEXT = KC + K
             IF( IPIV( K ).GT.0 ) THEN
    *
    *           1 x 1 diagonal block
    *
    *           Invert the diagonal block.
    *
                AP( KC+K-1 ) = ONE / DBLE( AP( KC+K-1 ) )
    *
    *           Compute column K of the inverse.
    *
                IF( K.GT.1 ) THEN
                   CALL ZCOPY( K-1, AP( KC ), 1, WORK, 1 )
                   CALL ZHPMV( UPLO, K-1, -CONE, AP, WORK, 1, ZERO,
         $                     AP( KC ), 1 )
                   AP( KC+K-1 ) = AP( KC+K-1 ) -
         $                        DBLE( ZDOTC( K-1, WORK, 1, AP( KC ), 1 ) )
                END IF
                KSTEP = 1
             ELSE
    *
    *           2 x 2 diagonal block
    *
    *           Invert the diagonal block.
    *
                T = ABS( AP( KCNEXT+K-1 ) )
                AK = DBLE( AP( KC+K-1 ) ) / T
                AKP1 = DBLE( 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
    *
    *           Compute columns K and K+1 of the inverse.
    *
                IF( K.GT.1 ) THEN
                   CALL ZCOPY( K-1, AP( KC ), 1, WORK, 1 )
                   CALL ZHPMV( UPLO, K-1, -CONE, AP, WORK, 1, ZERO,
         $                     AP( KC ), 1 )
                   AP( KC+K-1 ) = AP( KC+K-1 ) -
         $                        DBLE( ZDOTC( K-1, WORK, 1, AP( KC ), 1 ) )
                   AP( KCNEXT+K-1 ) = AP( KCNEXT+K-1 ) -
         $                            ZDOTC( K-1, AP( KC ), 1, AP( KCNEXT ),
         $                            1 )
                   CALL ZCOPY( K-1, AP( KCNEXT ), 1, WORK, 1 )
                   CALL ZHPMV( UPLO, K-1, -CONE, AP, WORK, 1, ZERO,
         $                     AP( KCNEXT ), 1 )
                   AP( KCNEXT+K ) = AP( KCNEXT+K ) -
         $                          DBLE( ZDOTC( K-1, WORK, 1, AP( KCNEXT ),
         $                          1 ) )
                END IF
                KSTEP = 2
                KCNEXT = KCNEXT + K + 1
             END IF
    *
             KP = ABS( IPIV( K ) )
             IF( KP.NE.K ) THEN
    *
    *           Interchange rows and columns K and KP in the leading
    *           submatrix A(1:k+1,1:k+1)
    *
                KPC = ( KP-1 )*KP / 2 + 1
                CALL ZSWAP( KP-1, AP( KC ), 1, AP( KPC ), 1 )
                KX = KPC + KP - 1
                DO 40 J = KP + 1, K - 1
                   KX = KX + J - 1
                   TEMP = DCONJG( AP( KC+J-1 ) )
                   AP( KC+J-1 ) = DCONJG( AP( KX ) )
                   AP( KX ) = TEMP
       40       CONTINUE
                AP( KC+KP-1 ) = DCONJG( 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
    *
             K = K + KSTEP
             KC = KCNEXT
             GO TO 30
       50    CONTINUE
    *
          ELSE
    *
    *        Compute inv(A) from the factorization A = L*D*L'.
    *
    *        K is the main loop index, increasing from 1 to N in steps of
    *        1 or 2, depending on the size of the diagonal blocks.
    *
             NPP = N*( N+1 ) / 2
             K = N
             KC = NPP
       60    CONTINUE
    *
    *        If K < 1, exit from loop.
    *
             IF( K.LT.1 )
         $      GO TO 80
    *
             KCNEXT = KC - ( N-K+2 )
             IF( IPIV( K ).GT.0 ) THEN
    *
    *           1 x 1 diagonal block
    *
    *           Invert the diagonal block.
    *
                AP( KC ) = ONE / DBLE( AP( KC ) )
    *
    *           Compute column K of the inverse.
    *
                IF( K.LT.N ) THEN
                   CALL ZCOPY( N-K, AP( KC+1 ), 1, WORK, 1 )
                   CALL ZHPMV( UPLO, N-K, -CONE, AP( KC+N-K+1 ), WORK, 1,
         $                     ZERO, AP( KC+1 ), 1 )
                   AP( KC ) = AP( KC ) - DBLE( ZDOTC( N-K, WORK, 1,
         $                    AP( KC+1 ), 1 ) )
                END IF
                KSTEP = 1
             ELSE
    *
    *           2 x 2 diagonal block
    *
    *           Invert the diagonal block.
    *
                T = ABS( AP( KCNEXT+1 ) )
                AK = DBLE( AP( KCNEXT ) ) / T
                AKP1 = DBLE( 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
    *
    *           Compute columns K-1 and K of the inverse.
    *
                IF( K.LT.N ) THEN
                   CALL ZCOPY( N-K, AP( KC+1 ), 1, WORK, 1 )
                   CALL ZHPMV( UPLO, N-K, -CONE, AP( KC+( N-K+1 ) ), WORK,
         $                     1, ZERO, AP( KC+1 ), 1 )
                   AP( KC ) = AP( KC ) - DBLE( ZDOTC( N-K, WORK, 1,
         $                    AP( KC+1 ), 1 ) )
                   AP( KCNEXT+1 ) = AP( KCNEXT+1 ) -
         $                          ZDOTC( N-K, AP( KC+1 ), 1,
         $                          AP( KCNEXT+2 ), 1 )
                   CALL ZCOPY( N-K, AP( KCNEXT+2 ), 1, WORK, 1 )
                   CALL ZHPMV( UPLO, N-K, -CONE, AP( KC+( N-K+1 ) ), WORK,
         $                     1, ZERO, AP( KCNEXT+2 ), 1 )
                   AP( KCNEXT ) = AP( KCNEXT ) -
         $                        DBLE( ZDOTC( N-K, WORK, 1, AP( KCNEXT+2 ),
         $                        1 ) )
                END IF
                KSTEP = 2
                KCNEXT = KCNEXT - ( N-K+3 )
             END IF
    *
             KP = ABS( IPIV( K ) )
             IF( KP.NE.K ) THEN
    *
    *           Interchange rows and columns K and KP in the trailing
    *           submatrix A(k-1:n,k-1:n)
    *
                KPC = NPP - ( N-KP+1 )*( N-KP+2 ) / 2 + 1
                IF( KP.LT.N )
         $         CALL ZSWAP( 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 = DCONJG( AP( KC+J-K ) )
                   AP( KC+J-K ) = DCONJG( AP( KX ) )
                   AP( KX ) = TEMP
       70       CONTINUE
                AP( KC+KP-K ) = DCONJG( 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
    *
             K = K - KSTEP
             KC = KCNEXT
             GO TO 60
       80    CONTINUE
          END IF
    *
          RETURN
    *
    *     End of ZHPTRI
    *
          END