SUBROUTINE SPOT03( UPLO, N, A, LDA, AINV, LDAINV, WORK, LDWORK, \$ RWORK, RCOND, RESID ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER LDA, LDAINV, LDWORK, N REAL RCOND, RESID * .. * .. Array Arguments .. REAL A( LDA, * ), AINV( LDAINV, * ), RWORK( * ), \$ WORK( LDWORK, * ) * .. * * Purpose * ======= * * SPOT03 computes the residual for a symmetric matrix times its * inverse: * norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ), * where EPS is the machine epsilon. * * Arguments * ========== * * UPLO (input) CHARACTER*1 * Specifies whether the upper or lower triangular part of the * symmetric 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) REAL array, dimension (LDA,N) * The original symmetric matrix A. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N) * * AINV (input/output) REAL array, dimension (LDAINV,N) * On entry, the inverse of the matrix A, stored as a symmetric * matrix in the same format as A. * In this version, AINV is expanded into a full matrix and * multiplied by A, so the opposing triangle of AINV will be * changed; i.e., if the upper triangular part of AINV is * stored, the lower triangular part will be used as work space. * * LDAINV (input) INTEGER * The leading dimension of the array AINV. LDAINV >= max(1,N). * * WORK (workspace) REAL array, dimension (LDWORK,N) * * LDWORK (input) INTEGER * The leading dimension of the array WORK. LDWORK >= max(1,N). * * RWORK (workspace) REAL array, dimension (N) * * RCOND (output) REAL * The reciprocal of the condition number of A, computed as * ( 1/norm(A) ) / norm(AINV). * * RESID (output) REAL * norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS ) * * ===================================================================== * * .. Parameters .. REAL ZERO, ONE PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) * .. * .. Local Scalars .. INTEGER I, J REAL AINVNM, ANORM, EPS * .. * .. External Functions .. LOGICAL LSAME REAL SLAMCH, SLANGE, SLANSY EXTERNAL LSAME, SLAMCH, SLANGE, SLANSY * .. * .. External Subroutines .. EXTERNAL SSYMM * .. * .. Intrinsic Functions .. INTRINSIC REAL * .. * .. Executable Statements .. * * Quick exit if N = 0. * IF( N.LE.0 ) THEN RCOND = ONE RESID = ZERO RETURN END IF * * Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0. * EPS = SLAMCH( 'Epsilon' ) ANORM = SLANSY( '1', UPLO, N, A, LDA, RWORK ) AINVNM = SLANSY( '1', UPLO, N, AINV, LDAINV, RWORK ) IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN RCOND = ZERO RESID = ONE / EPS RETURN END IF RCOND = ( ONE / ANORM ) / AINVNM * * Expand AINV into a full matrix and call SSYMM to multiply * AINV on the left by A. * IF( LSAME( UPLO, 'U' ) ) THEN DO 20 J = 1, N DO 10 I = 1, J - 1 AINV( J, I ) = AINV( I, J ) 10 CONTINUE 20 CONTINUE ELSE DO 40 J = 1, N DO 30 I = J + 1, N AINV( J, I ) = AINV( I, J ) 30 CONTINUE 40 CONTINUE END IF CALL SSYMM( 'Left', UPLO, N, N, -ONE, A, LDA, AINV, LDAINV, ZERO, \$ WORK, LDWORK ) * * Add the identity matrix to WORK . * DO 50 I = 1, N WORK( I, I ) = WORK( I, I ) + ONE 50 CONTINUE * * Compute norm(I - A*AINV) / (N * norm(A) * norm(AINV) * EPS) * RESID = SLANGE( '1', N, N, WORK, LDWORK, RWORK ) * RESID = ( ( RESID*RCOND ) / EPS ) / REAL( N ) * RETURN * * End of SPOT03 * END