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SUBROUTINE ZTPT01( UPLO, DIAG, N, AP, AINVP, RCOND, RWORK, RESID )
* * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. CHARACTER DIAG, UPLO INTEGER N DOUBLE PRECISION RCOND, RESID * .. * .. Array Arguments .. DOUBLE PRECISION RWORK( * ) COMPLEX*16 AINVP( * ), AP( * ) * .. * * Purpose * ======= * * ZTPT01 computes the residual for a triangular matrix A times its * inverse when A is stored in packed format: * RESID = norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS ), * where EPS is the machine epsilon. * * Arguments * ========== * * UPLO (input) CHARACTER*1 * Specifies whether the matrix A is upper or lower triangular. * = 'U': Upper triangular * = 'L': Lower triangular * * DIAG (input) CHARACTER*1 * Specifies whether or not the matrix A is unit triangular. * = 'N': Non-unit triangular * = 'U': Unit triangular * * N (input) INTEGER * The order of the matrix A. N >= 0. * * AP (input) COMPLEX*16 array, dimension (N*(N+1)/2) * The original upper or lower triangular matrix A, packed * columnwise in a linear array. The j-th column of A is stored * in the array AP as follows: * if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j; * if UPLO = 'L', * AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n. * * AINVP (input) COMPLEX*16 array, dimension (N*(N+1)/2) * On entry, the (triangular) inverse of the matrix A, packed * columnwise in a linear array as in AP. * On exit, the contents of AINVP are destroyed. * * RCOND (output) DOUBLE PRECISION * The reciprocal condition number of A, computed as * 1/(norm(A) * norm(AINV)). * * RWORK (workspace) DOUBLE PRECISION array, dimension (N) * * RESID (output) DOUBLE PRECISION * norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS ) * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) * .. * .. Local Scalars .. LOGICAL UNITD INTEGER J, JC DOUBLE PRECISION AINVNM, ANORM, EPS * .. * .. External Functions .. LOGICAL LSAME DOUBLE PRECISION DLAMCH, ZLANTP EXTERNAL LSAME, DLAMCH, ZLANTP * .. * .. External Subroutines .. EXTERNAL ZTPMV * .. * .. Intrinsic Functions .. INTRINSIC DBLE * .. * .. 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 = DLAMCH( 'Epsilon' ) ANORM = ZLANTP( '1', UPLO, DIAG, N, AP, RWORK ) AINVNM = ZLANTP( '1', UPLO, DIAG, N, AINVP, RWORK ) IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN RCOND = ZERO RESID = ONE / EPS RETURN END IF RCOND = ( ONE / ANORM ) / AINVNM * * Compute A * AINV, overwriting AINV. * UNITD = LSAME( DIAG, 'U' ) IF( LSAME( UPLO, 'U' ) ) THEN JC = 1 DO 10 J = 1, N IF( UNITD ) $ AINVP( JC+J-1 ) = ONE * * Form the j-th column of A*AINV. * CALL ZTPMV( 'Upper', 'No transpose', DIAG, J, AP, $ AINVP( JC ), 1 ) * * Subtract 1 from the diagonal to form A*AINV - I. * AINVP( JC+J-1 ) = AINVP( JC+J-1 ) - ONE JC = JC + J 10 CONTINUE ELSE JC = 1 DO 20 J = 1, N IF( UNITD ) $ AINVP( JC ) = ONE * * Form the j-th column of A*AINV. * CALL ZTPMV( 'Lower', 'No transpose', DIAG, N-J+1, AP( JC ), $ AINVP( JC ), 1 ) * * Subtract 1 from the diagonal to form A*AINV - I. * AINVP( JC ) = AINVP( JC ) - ONE JC = JC + N - J + 1 20 CONTINUE END IF * * Compute norm(A*AINV - I) / (N * norm(A) * norm(AINV) * EPS) * RESID = ZLANTP( '1', UPLO, 'Non-unit', N, AINVP, RWORK ) * RESID = ( ( RESID*RCOND ) / DBLE( N ) ) / EPS * RETURN * * End of ZTPT01 * END |