SUBROUTINE ZTPT02( UPLO, TRANS, DIAG, N, NRHS, AP, X, LDX, B, LDB, \$ WORK, RWORK, RESID ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. CHARACTER DIAG, TRANS, UPLO INTEGER LDB, LDX, N, NRHS DOUBLE PRECISION RESID * .. * .. Array Arguments .. DOUBLE PRECISION RWORK( * ) COMPLEX*16 AP( * ), B( LDB, * ), WORK( * ), X( LDX, * ) * .. * * Purpose * ======= * * ZTPT02 computes the residual for the computed solution to a * triangular system of linear equations A*x = b, A**T *x = b, or * A**H *x = b, when the triangular matrix A is stored in packed format. * Here A**T denotes the transpose of A, A**H denotes the conjugate * transpose of A, and x and b are N by NRHS matrices. The test ratio * is the maximum over the number of right hand sides of * the maximum over the number of right hand sides of * norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ), * where op(A) denotes A, A**T, or A**H, and 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 * * TRANS (input) CHARACTER*1 * Specifies the operation applied to A. * = 'N': A *x = b (No transpose) * = 'T': A**T *x = b (Transpose) * = 'C': A**H *x = b (Conjugate transpose) * * 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. * * NRHS (input) INTEGER * The number of right hand sides, i.e., the number of columns * of the matrices X and B. NRHS >= 0. * * AP (input) COMPLEX*16 array, dimension (N*(N+1)/2) * The 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. * * X (input) COMPLEX*16 array, dimension (LDX,NRHS) * The computed solution vectors for the system of linear * equations. * * LDX (input) INTEGER * The leading dimension of the array X. LDX >= max(1,N). * * B (input) COMPLEX*16 array, dimension (LDB,NRHS) * The right hand side vectors for the system of linear * equations. * * LDB (input) INTEGER * The leading dimension of the array B. LDB >= max(1,N). * * WORK (workspace) COMPLEX*16 array, dimension (N) * * RWORK (workspace) DOUBLE PRECISION array, dimension (N) * * RESID (output) DOUBLE PRECISION * The maximum over the number of right hand sides of * norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ). * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) * .. * .. Local Scalars .. INTEGER J DOUBLE PRECISION ANORM, BNORM, EPS, XNORM * .. * .. External Functions .. LOGICAL LSAME DOUBLE PRECISION DLAMCH, DZASUM, ZLANTP EXTERNAL LSAME, DLAMCH, DZASUM, ZLANTP * .. * .. External Subroutines .. EXTERNAL ZAXPY, ZCOPY, ZTPMV * .. * .. Intrinsic Functions .. INTRINSIC DCMPLX, MAX * .. * .. Executable Statements .. * * Quick exit if N = 0 or NRHS = 0 * IF( N.LE.0 .OR. NRHS.LE.0 ) THEN RESID = ZERO RETURN END IF * * Compute the 1-norm of A or A**H. * IF( LSAME( TRANS, 'N' ) ) THEN ANORM = ZLANTP( '1', UPLO, DIAG, N, AP, RWORK ) ELSE ANORM = ZLANTP( 'I', UPLO, DIAG, N, AP, RWORK ) END IF * * Exit with RESID = 1/EPS if ANORM = 0. * EPS = DLAMCH( 'Epsilon' ) IF( ANORM.LE.ZERO ) THEN RESID = ONE / EPS RETURN END IF * * Compute the maximum over the number of right hand sides of * norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ). * RESID = ZERO DO 10 J = 1, NRHS CALL ZCOPY( N, X( 1, J ), 1, WORK, 1 ) CALL ZTPMV( UPLO, TRANS, DIAG, N, AP, WORK, 1 ) CALL ZAXPY( N, DCMPLX( -ONE ), B( 1, J ), 1, WORK, 1 ) BNORM = DZASUM( N, WORK, 1 ) XNORM = DZASUM( N, X( 1, J ), 1 ) IF( XNORM.LE.ZERO ) THEN RESID = ONE / EPS ELSE RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS ) END IF 10 CONTINUE * RETURN * * End of ZTPT02 * END