00001 SUBROUTINE ZTBT03( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, 00002 $ SCALE, CNORM, TSCAL, X, LDX, B, LDB, WORK, 00003 $ RESID ) 00004 * 00005 * -- LAPACK test routine (version 3.1) -- 00006 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. 00007 * November 2006 00008 * 00009 * .. Scalar Arguments .. 00010 CHARACTER DIAG, TRANS, UPLO 00011 INTEGER KD, LDAB, LDB, LDX, N, NRHS 00012 DOUBLE PRECISION RESID, SCALE, TSCAL 00013 * .. 00014 * .. Array Arguments .. 00015 DOUBLE PRECISION CNORM( * ) 00016 COMPLEX*16 AB( LDAB, * ), B( LDB, * ), WORK( * ), 00017 $ X( LDX, * ) 00018 * .. 00019 * 00020 * Purpose 00021 * ======= 00022 * 00023 * ZTBT03 computes the residual for the solution to a scaled triangular 00024 * system of equations A*x = s*b, A**T *x = s*b, or A**H *x = s*b 00025 * when A is a triangular band matrix. Here A**T denotes the transpose 00026 * of A, A**H denotes the conjugate transpose of A, s is a scalar, and 00027 * x and b are N by NRHS matrices. The test ratio is the maximum over 00028 * the number of right hand sides of 00029 * norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ), 00030 * where op(A) denotes A, A**T, or A**H, and EPS is the machine epsilon. 00031 * 00032 * Arguments 00033 * ========= 00034 * 00035 * UPLO (input) CHARACTER*1 00036 * Specifies whether the matrix A is upper or lower triangular. 00037 * = 'U': Upper triangular 00038 * = 'L': Lower triangular 00039 * 00040 * TRANS (input) CHARACTER*1 00041 * Specifies the operation applied to A. 00042 * = 'N': A *x = s*b (No transpose) 00043 * = 'T': A**T *x = s*b (Transpose) 00044 * = 'C': A**H *x = s*b (Conjugate transpose) 00045 * 00046 * DIAG (input) CHARACTER*1 00047 * Specifies whether or not the matrix A is unit triangular. 00048 * = 'N': Non-unit triangular 00049 * = 'U': Unit triangular 00050 * 00051 * N (input) INTEGER 00052 * The order of the matrix A. N >= 0. 00053 * 00054 * KD (input) INTEGER 00055 * The number of superdiagonals or subdiagonals of the 00056 * triangular band matrix A. KD >= 0. 00057 * 00058 * NRHS (input) INTEGER 00059 * The number of right hand sides, i.e., the number of columns 00060 * of the matrices X and B. NRHS >= 0. 00061 * 00062 * AB (input) COMPLEX*16 array, dimension (LDAB,N) 00063 * The upper or lower triangular band matrix A, stored in the 00064 * first kd+1 rows of the array. The j-th column of A is stored 00065 * in the j-th column of the array AB as follows: 00066 * if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; 00067 * if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). 00068 * 00069 * LDAB (input) INTEGER 00070 * The leading dimension of the array AB. LDAB >= KD+1. 00071 * 00072 * SCALE (input) DOUBLE PRECISION 00073 * The scaling factor s used in solving the triangular system. 00074 * 00075 * CNORM (input) DOUBLE PRECISION array, dimension (N) 00076 * The 1-norms of the columns of A, not counting the diagonal. 00077 * 00078 * TSCAL (input) DOUBLE PRECISION 00079 * The scaling factor used in computing the 1-norms in CNORM. 00080 * CNORM actually contains the column norms of TSCAL*A. 00081 * 00082 * X (input) COMPLEX*16 array, dimension (LDX,NRHS) 00083 * The computed solution vectors for the system of linear 00084 * equations. 00085 * 00086 * LDX (input) INTEGER 00087 * The leading dimension of the array X. LDX >= max(1,N). 00088 * 00089 * B (input) COMPLEX*16 array, dimension (LDB,NRHS) 00090 * The right hand side vectors for the system of linear 00091 * equations. 00092 * 00093 * LDB (input) INTEGER 00094 * The leading dimension of the array B. LDB >= max(1,N). 00095 * 00096 * WORK (workspace) COMPLEX*16 array, dimension (N) 00097 * 00098 * RESID (output) DOUBLE PRECISION 00099 * The maximum over the number of right hand sides of 00100 * norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ). 00101 * 00102 * ===================================================================== 00103 * 00104 * 00105 * .. Parameters .. 00106 DOUBLE PRECISION ONE, ZERO 00107 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) 00108 * .. 00109 * .. Local Scalars .. 00110 INTEGER IX, J 00111 DOUBLE PRECISION EPS, ERR, SMLNUM, TNORM, XNORM, XSCAL 00112 * .. 00113 * .. External Functions .. 00114 LOGICAL LSAME 00115 INTEGER IZAMAX 00116 DOUBLE PRECISION DLAMCH 00117 EXTERNAL LSAME, IZAMAX, DLAMCH 00118 * .. 00119 * .. External Subroutines .. 00120 EXTERNAL ZAXPY, ZCOPY, ZDSCAL, ZTBMV 00121 * .. 00122 * .. Intrinsic Functions .. 00123 INTRINSIC ABS, DBLE, DCMPLX, MAX 00124 * .. 00125 * .. Executable Statements .. 00126 * 00127 * Quick exit if N = 0 00128 * 00129 IF( N.LE.0 .OR. NRHS.LE.0 ) THEN 00130 RESID = ZERO 00131 RETURN 00132 END IF 00133 EPS = DLAMCH( 'Epsilon' ) 00134 SMLNUM = DLAMCH( 'Safe minimum' ) 00135 * 00136 * Compute the norm of the triangular matrix A using the column 00137 * norms already computed by ZLATBS. 00138 * 00139 TNORM = ZERO 00140 IF( LSAME( DIAG, 'N' ) ) THEN 00141 IF( LSAME( UPLO, 'U' ) ) THEN 00142 DO 10 J = 1, N 00143 TNORM = MAX( TNORM, TSCAL*ABS( AB( KD+1, J ) )+ 00144 $ CNORM( J ) ) 00145 10 CONTINUE 00146 ELSE 00147 DO 20 J = 1, N 00148 TNORM = MAX( TNORM, TSCAL*ABS( AB( 1, J ) )+CNORM( J ) ) 00149 20 CONTINUE 00150 END IF 00151 ELSE 00152 DO 30 J = 1, N 00153 TNORM = MAX( TNORM, TSCAL+CNORM( J ) ) 00154 30 CONTINUE 00155 END IF 00156 * 00157 * Compute the maximum over the number of right hand sides of 00158 * norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ). 00159 * 00160 RESID = ZERO 00161 DO 40 J = 1, NRHS 00162 CALL ZCOPY( N, X( 1, J ), 1, WORK, 1 ) 00163 IX = IZAMAX( N, WORK, 1 ) 00164 XNORM = MAX( ONE, ABS( X( IX, J ) ) ) 00165 XSCAL = ( ONE / XNORM ) / DBLE( KD+1 ) 00166 CALL ZDSCAL( N, XSCAL, WORK, 1 ) 00167 CALL ZTBMV( UPLO, TRANS, DIAG, N, KD, AB, LDAB, WORK, 1 ) 00168 CALL ZAXPY( N, DCMPLX( -SCALE*XSCAL ), B( 1, J ), 1, WORK, 1 ) 00169 IX = IZAMAX( N, WORK, 1 ) 00170 ERR = TSCAL*ABS( WORK( IX ) ) 00171 IX = IZAMAX( N, X( 1, J ), 1 ) 00172 XNORM = ABS( X( IX, J ) ) 00173 IF( ERR*SMLNUM.LE.XNORM ) THEN 00174 IF( XNORM.GT.ZERO ) 00175 $ ERR = ERR / XNORM 00176 ELSE 00177 IF( ERR.GT.ZERO ) 00178 $ ERR = ONE / EPS 00179 END IF 00180 IF( ERR*SMLNUM.LE.TNORM ) THEN 00181 IF( TNORM.GT.ZERO ) 00182 $ ERR = ERR / TNORM 00183 ELSE 00184 IF( ERR.GT.ZERO ) 00185 $ ERR = ONE / EPS 00186 END IF 00187 RESID = MAX( RESID, ERR ) 00188 40 CONTINUE 00189 * 00190 RETURN 00191 * 00192 * End of ZTBT03 00193 * 00194 END
1.7.2