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SUBROUTINE ZHPT01( UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID )
* * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER LDC, N DOUBLE PRECISION RESID * .. * .. Array Arguments .. INTEGER IPIV( * ) DOUBLE PRECISION RWORK( * ) COMPLEX*16 A( * ), AFAC( * ), C( LDC, * ) * .. * * Purpose * ======= * * ZHPT01 reconstructs a Hermitian indefinite packed matrix A from its * block L*D*L' or U*D*U' factorization and computes the residual * norm( C - A ) / ( N * norm(A) * EPS ), * where C is the reconstructed matrix, EPS is the machine epsilon, * L' is the conjugate transpose of L, and U' is the conjugate transpose * of U. * * Arguments * ========== * * UPLO (input) CHARACTER*1 * Specifies whether the upper or lower triangular part of the * Hermitian matrix A is stored: * = 'U': Upper triangular * = 'L': Lower triangular * * N (input) INTEGER * The number of rows and columns of the matrix A. N >= 0. * * A (input) COMPLEX*16 array, dimension (N*(N+1)/2) * The original Hermitian matrix A, stored as a packed * triangular matrix. * * AFAC (input) COMPLEX*16 array, dimension (N*(N+1)/2) * The factored form of the matrix A, stored as a packed * triangular matrix. AFAC contains the block diagonal matrix D * and the multipliers used to obtain the factor L or U from the * block L*D*L' or U*D*U' factorization as computed by ZHPTRF. * * IPIV (input) INTEGER array, dimension (N) * The pivot indices from ZHPTRF. * * C (workspace) COMPLEX*16 array, dimension (LDC,N) * * LDC (integer) INTEGER * The leading dimension of the array C. LDC >= max(1,N). * * RWORK (workspace) DOUBLE PRECISION array, dimension (N) * * RESID (output) DOUBLE PRECISION * If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS ) * If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS ) * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) COMPLEX*16 CZERO, CONE PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ), $ CONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. INTEGER I, INFO, J, JC DOUBLE PRECISION ANORM, EPS * .. * .. External Functions .. LOGICAL LSAME DOUBLE PRECISION DLAMCH, ZLANHE, ZLANHP EXTERNAL LSAME, DLAMCH, ZLANHE, ZLANHP * .. * .. External Subroutines .. EXTERNAL ZLASET, ZLAVHP * .. * .. Intrinsic Functions .. INTRINSIC DBLE, DIMAG * .. * .. Executable Statements .. * * Quick exit if N = 0. * IF( N.LE.0 ) THEN RESID = ZERO RETURN END IF * * Determine EPS and the norm of A. * EPS = DLAMCH( 'Epsilon' ) ANORM = ZLANHP( '1', UPLO, N, A, RWORK ) * * Check the imaginary parts of the diagonal elements and return with * an error code if any are nonzero. * JC = 1 IF( LSAME( UPLO, 'U' ) ) THEN DO 10 J = 1, N IF( DIMAG( AFAC( JC ) ).NE.ZERO ) THEN RESID = ONE / EPS RETURN END IF JC = JC + J + 1 10 CONTINUE ELSE DO 20 J = 1, N IF( DIMAG( AFAC( JC ) ).NE.ZERO ) THEN RESID = ONE / EPS RETURN END IF JC = JC + N - J + 1 20 CONTINUE END IF * * Initialize C to the identity matrix. * CALL ZLASET( 'Full', N, N, CZERO, CONE, C, LDC ) * * Call ZLAVHP to form the product D * U' (or D * L' ). * CALL ZLAVHP( UPLO, 'Conjugate', 'Non-unit', N, N, AFAC, IPIV, C, $ LDC, INFO ) * * Call ZLAVHP again to multiply by U ( or L ). * CALL ZLAVHP( UPLO, 'No transpose', 'Unit', N, N, AFAC, IPIV, C, $ LDC, INFO ) * * Compute the difference C - A . * IF( LSAME( UPLO, 'U' ) ) THEN JC = 0 DO 40 J = 1, N DO 30 I = 1, J - 1 C( I, J ) = C( I, J ) - A( JC+I ) 30 CONTINUE C( J, J ) = C( J, J ) - DBLE( A( JC+J ) ) JC = JC + J 40 CONTINUE ELSE JC = 1 DO 60 J = 1, N C( J, J ) = C( J, J ) - DBLE( A( JC ) ) DO 50 I = J + 1, N C( I, J ) = C( I, J ) - A( JC+I-J ) 50 CONTINUE JC = JC + N - J + 1 60 CONTINUE END IF * * Compute norm( C - A ) / ( N * norm(A) * EPS ) * RESID = ZLANHE( '1', UPLO, N, C, LDC, RWORK ) * IF( ANORM.LE.ZERO ) THEN IF( RESID.NE.ZERO ) $ RESID = ONE / EPS ELSE RESID = ( ( RESID / DBLE( N ) ) / ANORM ) / EPS END IF * RETURN * * End of ZHPT01 * END |