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SUBROUTINE ZPPT01( UPLO, N, A, AFAC, 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 N DOUBLE PRECISION RESID * .. * .. Array Arguments .. DOUBLE PRECISION RWORK( * ) COMPLEX*16 A( * ), AFAC( * ) * .. * * Purpose * ======= * * ZPPT01 reconstructs a Hermitian positive definite packed matrix A * from its L*L' or U'*U factorization and computes the residual * norm( L*L' - A ) / ( N * norm(A) * EPS ) or * norm( U'*U - A ) / ( N * norm(A) * EPS ), * where 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/output) COMPLEX*16 array, dimension (N*(N+1)/2) * On entry, the factor L or U from the L*L' or U'*U * factorization of A, stored as a packed triangular matrix. * Overwritten with the reconstructed matrix, and then with the * difference L*L' - A (or U'*U - A). * * RWORK (workspace) DOUBLE PRECISION array, dimension (N) * * RESID (output) DOUBLE PRECISION * If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS ) * If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS ) * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) * .. * .. Local Scalars .. INTEGER I, K, KC DOUBLE PRECISION ANORM, EPS, TR COMPLEX*16 TC * .. * .. External Functions .. LOGICAL LSAME DOUBLE PRECISION DLAMCH, ZLANHP COMPLEX*16 ZDOTC EXTERNAL LSAME, DLAMCH, ZLANHP, ZDOTC * .. * .. External Subroutines .. EXTERNAL ZHPR, ZSCAL, ZTPMV * .. * .. Intrinsic Functions .. INTRINSIC DBLE, DIMAG * .. * .. Executable Statements .. * * Quick exit if N = 0 * IF( N.LE.0 ) THEN RESID = ZERO RETURN END IF * * Exit with RESID = 1/EPS if ANORM = 0. * EPS = DLAMCH( 'Epsilon' ) ANORM = ZLANHP( '1', UPLO, N, A, RWORK ) IF( ANORM.LE.ZERO ) THEN RESID = ONE / EPS RETURN END IF * * Check the imaginary parts of the diagonal elements and return with * an error code if any are nonzero. * KC = 1 IF( LSAME( UPLO, 'U' ) ) THEN DO 10 K = 1, N IF( DIMAG( AFAC( KC ) ).NE.ZERO ) THEN RESID = ONE / EPS RETURN END IF KC = KC + K + 1 10 CONTINUE ELSE DO 20 K = 1, N IF( DIMAG( AFAC( KC ) ).NE.ZERO ) THEN RESID = ONE / EPS RETURN END IF KC = KC + N - K + 1 20 CONTINUE END IF * * Compute the product U'*U, overwriting U. * IF( LSAME( UPLO, 'U' ) ) THEN KC = ( N*( N-1 ) ) / 2 + 1 DO 30 K = N, 1, -1 * * Compute the (K,K) element of the result. * TR = ZDOTC( K, AFAC( KC ), 1, AFAC( KC ), 1 ) AFAC( KC+K-1 ) = TR * * Compute the rest of column K. * IF( K.GT.1 ) THEN CALL ZTPMV( 'Upper', 'Conjugate', 'Non-unit', K-1, AFAC, $ AFAC( KC ), 1 ) KC = KC - ( K-1 ) END IF 30 CONTINUE * * Compute the difference L*L' - A * KC = 1 DO 50 K = 1, N DO 40 I = 1, K - 1 AFAC( KC+I-1 ) = AFAC( KC+I-1 ) - A( KC+I-1 ) 40 CONTINUE AFAC( KC+K-1 ) = AFAC( KC+K-1 ) - DBLE( A( KC+K-1 ) ) KC = KC + K 50 CONTINUE * * Compute the product L*L', overwriting L. * ELSE KC = ( N*( N+1 ) ) / 2 DO 60 K = N, 1, -1 * * Add a multiple of column K of the factor L to each of * columns K+1 through N. * IF( K.LT.N ) $ CALL ZHPR( 'Lower', N-K, ONE, AFAC( KC+1 ), 1, $ AFAC( KC+N-K+1 ) ) * * Scale column K by the diagonal element. * TC = AFAC( KC ) CALL ZSCAL( N-K+1, TC, AFAC( KC ), 1 ) * KC = KC - ( N-K+2 ) 60 CONTINUE * * Compute the difference U'*U - A * KC = 1 DO 80 K = 1, N AFAC( KC ) = AFAC( KC ) - DBLE( A( KC ) ) DO 70 I = K + 1, N AFAC( KC+I-K ) = AFAC( KC+I-K ) - A( KC+I-K ) 70 CONTINUE KC = KC + N - K + 1 80 CONTINUE END IF * * Compute norm( L*U - A ) / ( N * norm(A) * EPS ) * RESID = ZLANHP( '1', UPLO, N, AFAC, RWORK ) * RESID = ( ( RESID / DBLE( N ) ) / ANORM ) / EPS * RETURN * * End of ZPPT01 * END |