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diff --git a/TESTING/LIN/chet01_3.f b/TESTING/LIN/chet01_3.f new file mode 100644 index 00000000..7b26c398 --- /dev/null +++ b/TESTING/LIN/chet01_3.f @@ -0,0 +1,264 @@ +*> \brief \b CHET01_3 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition: +* =========== +* +* SUBROUTINE CHET01_3( UPLO, N, A, LDA, AFAC, LDAFAC, E, IPIV, C, +* LDC, RWORK, RESID ) +* +* .. Scalar Arguments .. +* CHARACTER UPLO +* INTEGER LDA, LDAFAC, LDC, N +* REAL RESID +* .. +* .. Array Arguments .. +* INTEGER IPIV( * ) +* REAL RWORK( * ) +* COMPLEX A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ), +* E( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> CHET01_3 reconstructs a Hermitian indefinite matrix A from its +*> block L*D*L' or U*D*U' factorization computed by CHETRF_RK +*> (or CHETRF_BK) and computes the residual +*> norm( C - A ) / ( N * norm(A) * EPS ), +*> where C is the reconstructed matrix and EPS is the machine epsilon. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> Specifies whether the upper or lower triangular part of the +*> Hermitian matrix A is stored: +*> = 'U': Upper triangular +*> = 'L': Lower triangular +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of rows and columns of the matrix A. N >= 0. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is COMPLEX*16 array, dimension (LDA,N) +*> The original Hermitian matrix A. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= max(1,N) +*> \endverbatim +*> +*> \param[in] AFAC +*> \verbatim +*> AFAC is COMPLEX array, dimension (LDAFAC,N) +*> Diagonal of the block diagonal matrix D and factors U or L +*> as computed by CHETRF_RK and CHETRF_BK: +*> a) ONLY diagonal elements of the Hermitian block diagonal +*> matrix D on the diagonal of A, i.e. D(k,k) = A(k,k); +*> (superdiagonal (or subdiagonal) elements of D +*> should be provided on entry in array E), and +*> b) If UPLO = 'U': factor U in the superdiagonal part of A. +*> If UPLO = 'L': factor L in the subdiagonal part of A. +*> \endverbatim +*> +*> \param[in] LDAFAC +*> \verbatim +*> LDAFAC is INTEGER +*> The leading dimension of the array AFAC. +*> LDAFAC >= max(1,N). +*> \endverbatim +*> +*> \param[in] E +*> \verbatim +*> E is COMPLEX array, dimension (N) +*> On entry, contains the superdiagonal (or subdiagonal) +*> elements of the Hermitian block diagonal matrix D +*> with 1-by-1 or 2-by-2 diagonal blocks, where +*> If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not refernced; +*> If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced. +*> \endverbatim +*> +*> \param[in] IPIV +*> \verbatim +*> IPIV is INTEGER array, dimension (N) +*> The pivot indices from CHETRF_RK (or CHETRF_BK). +*> \endverbatim +*> +*> \param[out] C +*> \verbatim +*> C is COMPLEX array, dimension (LDC,N) +*> \endverbatim +*> +*> \param[in] LDC +*> \verbatim +*> LDC is INTEGER +*> The leading dimension of the array C. LDC >= max(1,N). +*> \endverbatim +*> +*> \param[out] RWORK +*> \verbatim +*> RWORK is REAL array, dimension (N) +*> \endverbatim +*> +*> \param[out] RESID +*> \verbatim +*> RESID is REAL +*> If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS ) +*> If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS ) +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2016 +* +*> \ingroup complex_lin +* +* ===================================================================== + SUBROUTINE CHET01_3( UPLO, N, A, LDA, AFAC, LDAFAC, E, IPIV, C, + $ LDC, RWORK, RESID ) +* +* -- LAPACK test routine (version 3.7.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2016 +* +* .. Scalar Arguments .. + CHARACTER UPLO + INTEGER LDA, LDAFAC, LDC, N + REAL RESID +* .. +* .. Array Arguments .. + INTEGER IPIV( * ) + REAL RWORK( * ) + COMPLEX A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ), + $ E( * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + REAL ZERO, ONE + PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) + COMPLEX CZERO, CONE + PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ), + $ CONE = ( 1.0E+0, 0.0E+0 ) ) +* .. +* .. Local Scalars .. + INTEGER I, INFO, J + REAL ANORM, EPS +* .. +* .. External Functions .. + LOGICAL LSAME + REAL CLANHE, SLAMCH + EXTERNAL LSAME, CLANHE, SLAMCH +* .. +* .. External Subroutines .. + EXTERNAL CLASET, CLAVHE_ROOK, CSYCONVF_ROOK +* .. +* .. Intrinsic Functions .. + INTRINSIC AIMAG, REAL +* .. +* .. Executable Statements .. +* +* Quick exit if N = 0. +* + IF( N.LE.0 ) THEN + RESID = ZERO + RETURN + END IF +* +* a) Revert to multiplyers of L +* + CALL CSYCONVF_ROOK( UPLO, 'R', N, AFAC, LDAFAC, E, IPIV, INFO ) +* +* 1) Determine EPS and the norm of A. +* + EPS = SLAMCH( 'Epsilon' ) + ANORM = CLANHE( '1', UPLO, N, A, LDA, RWORK ) +* +* Check the imaginary parts of the diagonal elements and return with +* an error code if any are nonzero. +* + DO J = 1, N + IF( AIMAG( AFAC( J, J ) ).NE.ZERO ) THEN + RESID = ONE / EPS + RETURN + END IF + END DO +* +* 2) Initialize C to the identity matrix. +* + CALL CLASET( 'Full', N, N, CZERO, CONE, C, LDC ) +* +* 3) Call CLAVHE_ROOK to form the product D * U' (or D * L' ). +* + CALL CLAVHE_ROOK( UPLO, 'Conjugate', 'Non-unit', N, N, AFAC, + $ LDAFAC, IPIV, C, LDC, INFO ) +* +* 4) Call ZLAVHE_RK again to multiply by U (or L ). +* + CALL CLAVHE_ROOK( UPLO, 'No transpose', 'Unit', N, N, AFAC, + $ LDAFAC, IPIV, C, LDC, INFO ) +* +* 5) Compute the difference C - A . +* + IF( LSAME( UPLO, 'U' ) ) THEN + DO J = 1, N + DO I = 1, J - 1 + C( I, J ) = C( I, J ) - A( I, J ) + END DO + C( J, J ) = C( J, J ) - REAL( A( J, J ) ) + END DO + ELSE + DO J = 1, N + C( J, J ) = C( J, J ) - REAL( A( J, J ) ) + DO I = J + 1, N + C( I, J ) = C( I, J ) - A( I, J ) + END DO + END DO + END IF +* +* 6) Compute norm( C - A ) / ( N * norm(A) * EPS ) +* + RESID = CLANHE( '1', UPLO, N, C, LDC, RWORK ) +* + IF( ANORM.LE.ZERO ) THEN + IF( RESID.NE.ZERO ) + $ RESID = ONE / EPS + ELSE + RESID = ( ( RESID/REAL( N ) )/ANORM ) / EPS + END IF +* +* b) Convert to factor of L (or U) +* + CALL CSYCONVF_ROOK( UPLO, 'C', N, AFAC, LDAFAC, E, IPIV, INFO ) +* + RETURN +* +* End of CHET01_3 +* + END |