*> \brief \b ZHPTRI * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZHPTRI + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZHPTRI( UPLO, N, AP, IPIV, WORK, INFO ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER INFO, N * .. * .. Array Arguments .. * INTEGER IPIV( * ) * COMPLEX*16 AP( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> 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. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is 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. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in,out] AP *> \verbatim *> AP is 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. *> \endverbatim *> *> \param[in] IPIV *> \verbatim *> IPIV is INTEGER array, dimension (N) *> Details of the interchanges and the block structure of D *> as determined by ZHPTRF. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (N) *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is 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. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup complex16OTHERcomputational * * ===================================================================== SUBROUTINE ZHPTRI( UPLO, N, AP, IPIV, WORK, INFO ) * * -- LAPACK computational routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. CHARACTER UPLO INTEGER INFO, N * .. * .. Array Arguments .. INTEGER IPIV( * ) COMPLEX*16 AP( * ), WORK( * ) * .. * * ===================================================================== * * .. 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**H. * * 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**H. * * 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