SUBROUTINE CSPT03( UPLO, N, A, AINV, WORK, LDW, 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 LDW, N REAL RCOND, RESID * .. * .. Array Arguments .. REAL RWORK( * ) COMPLEX A( * ), AINV( * ), WORK( LDW, * ) * .. * * Purpose * ======= * * CSPT03 computes the residual for a complex symmetric packed 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 * complex 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) COMPLEX array, dimension (N*(N+1)/2) * The original complex symmetric matrix A, stored as a packed * triangular matrix. * * AINV (input) COMPLEX array, dimension (N*(N+1)/2) * The (symmetric) inverse of the matrix A, stored as a packed * triangular matrix. * * WORK (workspace) COMPLEX 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, ICOL, J, JCOL, K, KCOL, NALL REAL AINVNM, ANORM, EPS COMPLEX T * .. * .. External Functions .. LOGICAL LSAME REAL CLANGE, CLANSP, SLAMCH COMPLEX CDOTU EXTERNAL LSAME, CLANGE, CLANSP, SLAMCH, CDOTU * .. * .. 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 = CLANSP( '1', UPLO, N, A, RWORK ) AINVNM = CLANSP( '1', UPLO, N, AINV, RWORK ) IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN RCOND = ZERO RESID = ONE / EPS RETURN END IF RCOND = ( ONE/ANORM ) / AINVNM * * Case where both A and AINV are upper triangular: * Each element of - A * AINV is computed by taking the dot product * of a row of A with a column of AINV. * IF( LSAME( UPLO, 'U' ) ) THEN DO 70 I = 1, N ICOL = ( ( I-1 )*I ) / 2 + 1 * * Code when J <= I * DO 30 J = 1, I JCOL = ( ( J-1 )*J ) / 2 + 1 T = CDOTU( J, A( ICOL ), 1, AINV( JCOL ), 1 ) JCOL = JCOL + 2*J - 1 KCOL = ICOL - 1 DO 10 K = J + 1, I T = T + A( KCOL+K )*AINV( JCOL ) JCOL = JCOL + K 10 CONTINUE KCOL = KCOL + 2*I DO 20 K = I + 1, N T = T + A( KCOL )*AINV( JCOL ) KCOL = KCOL + K JCOL = JCOL + K 20 CONTINUE WORK( I, J ) = -T 30 CONTINUE * * Code when J > I * DO 60 J = I + 1, N JCOL = ( ( J-1 )*J ) / 2 + 1 T = CDOTU( I, A( ICOL ), 1, AINV( JCOL ), 1 ) JCOL = JCOL - 1 KCOL = ICOL + 2*I - 1 DO 40 K = I + 1, J T = T + A( KCOL )*AINV( JCOL+K ) KCOL = KCOL + K 40 CONTINUE JCOL = JCOL + 2*J DO 50 K = J + 1, N T = T + A( KCOL )*AINV( JCOL ) KCOL = KCOL + K JCOL = JCOL + K 50 CONTINUE WORK( I, J ) = -T 60 CONTINUE 70 CONTINUE ELSE * * Case where both A and AINV are lower triangular * NALL = ( N*( N+1 ) ) / 2 DO 140 I = 1, N * * Code when J <= I * ICOL = NALL - ( ( N-I+1 )*( N-I+2 ) ) / 2 + 1 DO 100 J = 1, I JCOL = NALL - ( ( N-J )*( N-J+1 ) ) / 2 - ( N-I ) T = CDOTU( N-I+1, A( ICOL ), 1, AINV( JCOL ), 1 ) KCOL = I JCOL = J DO 80 K = 1, J - 1 T = T + A( KCOL )*AINV( JCOL ) JCOL = JCOL + N - K KCOL = KCOL + N - K 80 CONTINUE JCOL = JCOL - J DO 90 K = J, I - 1 T = T + A( KCOL )*AINV( JCOL+K ) KCOL = KCOL + N - K 90 CONTINUE WORK( I, J ) = -T 100 CONTINUE * * Code when J > I * ICOL = NALL - ( ( N-I )*( N-I+1 ) ) / 2 DO 130 J = I + 1, N JCOL = NALL - ( ( N-J+1 )*( N-J+2 ) ) / 2 + 1 T = CDOTU( N-J+1, A( ICOL-N+J ), 1, AINV( JCOL ), 1 ) KCOL = I JCOL = J DO 110 K = 1, I - 1 T = T + A( KCOL )*AINV( JCOL ) JCOL = JCOL + N - K KCOL = KCOL + N - K 110 CONTINUE KCOL = KCOL - I DO 120 K = I, J - 1 T = T + A( KCOL+K )*AINV( JCOL ) JCOL = JCOL + N - K 120 CONTINUE WORK( I, J ) = -T 130 CONTINUE 140 CONTINUE END IF * * Add the identity matrix to WORK . * DO 150 I = 1, N WORK( I, I ) = WORK( I, I ) + ONE 150 CONTINUE * * Compute norm(I - A*AINV) / (N * norm(A) * norm(AINV) * EPS) * RESID = CLANGE( '1', N, N, WORK, LDW, RWORK ) * RESID = ( ( RESID*RCOND )/EPS ) / REAL( N ) * RETURN * * End of CSPT03 * END