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LAPACK 3.3.1
Linear Algebra PACKage
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LAPACK 3.3.1
Linear Algebra PACKage
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00001 SUBROUTINE ZTBCON( NORM, UPLO, DIAG, N, KD, AB, LDAB, RCOND, WORK, 00002 $ RWORK, INFO ) 00003 * 00004 * -- LAPACK routine (version 3.2) -- 00005 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00006 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00007 * November 2006 00008 * 00009 * Modified to call ZLACN2 in place of ZLACON, 10 Feb 03, SJH. 00010 * 00011 * .. Scalar Arguments .. 00012 CHARACTER DIAG, NORM, UPLO 00013 INTEGER INFO, KD, LDAB, N 00014 DOUBLE PRECISION RCOND 00015 * .. 00016 * .. Array Arguments .. 00017 DOUBLE PRECISION RWORK( * ) 00018 COMPLEX*16 AB( LDAB, * ), WORK( * ) 00019 * .. 00020 * 00021 * Purpose 00022 * ======= 00023 * 00024 * ZTBCON estimates the reciprocal of the condition number of a 00025 * triangular band matrix A, in either the 1-norm or the infinity-norm. 00026 * 00027 * The norm of A is computed and an estimate is obtained for 00028 * norm(inv(A)), then the reciprocal of the condition number is 00029 * computed as 00030 * RCOND = 1 / ( norm(A) * norm(inv(A)) ). 00031 * 00032 * Arguments 00033 * ========= 00034 * 00035 * NORM (input) CHARACTER*1 00036 * Specifies whether the 1-norm condition number or the 00037 * infinity-norm condition number is required: 00038 * = '1' or 'O': 1-norm; 00039 * = 'I': Infinity-norm. 00040 * 00041 * UPLO (input) CHARACTER*1 00042 * = 'U': A is upper triangular; 00043 * = 'L': A is lower triangular. 00044 * 00045 * DIAG (input) CHARACTER*1 00046 * = 'N': A is non-unit triangular; 00047 * = 'U': A is unit triangular. 00048 * 00049 * N (input) INTEGER 00050 * The order of the matrix A. N >= 0. 00051 * 00052 * KD (input) INTEGER 00053 * The number of superdiagonals or subdiagonals of the 00054 * triangular band matrix A. KD >= 0. 00055 * 00056 * AB (input) COMPLEX*16 array, dimension (LDAB,N) 00057 * The upper or lower triangular band matrix A, stored in the 00058 * first kd+1 rows of the array. The j-th column of A is stored 00059 * in the j-th column of the array AB as follows: 00060 * if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; 00061 * if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). 00062 * If DIAG = 'U', the diagonal elements of A are not referenced 00063 * and are assumed to be 1. 00064 * 00065 * LDAB (input) INTEGER 00066 * The leading dimension of the array AB. LDAB >= KD+1. 00067 * 00068 * RCOND (output) DOUBLE PRECISION 00069 * The reciprocal of the condition number of the matrix A, 00070 * computed as RCOND = 1/(norm(A) * norm(inv(A))). 00071 * 00072 * WORK (workspace) COMPLEX*16 array, dimension (2*N) 00073 * 00074 * RWORK (workspace) DOUBLE PRECISION array, dimension (N) 00075 * 00076 * INFO (output) INTEGER 00077 * = 0: successful exit 00078 * < 0: if INFO = -i, the i-th argument had an illegal value 00079 * 00080 * ===================================================================== 00081 * 00082 * .. Parameters .. 00083 DOUBLE PRECISION ONE, ZERO 00084 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) 00085 * .. 00086 * .. Local Scalars .. 00087 LOGICAL NOUNIT, ONENRM, UPPER 00088 CHARACTER NORMIN 00089 INTEGER IX, KASE, KASE1 00090 DOUBLE PRECISION AINVNM, ANORM, SCALE, SMLNUM, XNORM 00091 COMPLEX*16 ZDUM 00092 * .. 00093 * .. Local Arrays .. 00094 INTEGER ISAVE( 3 ) 00095 * .. 00096 * .. External Functions .. 00097 LOGICAL LSAME 00098 INTEGER IZAMAX 00099 DOUBLE PRECISION DLAMCH, ZLANTB 00100 EXTERNAL LSAME, IZAMAX, DLAMCH, ZLANTB 00101 * .. 00102 * .. External Subroutines .. 00103 EXTERNAL XERBLA, ZDRSCL, ZLACN2, ZLATBS 00104 * .. 00105 * .. Intrinsic Functions .. 00106 INTRINSIC ABS, DBLE, DIMAG, MAX 00107 * .. 00108 * .. Statement Functions .. 00109 DOUBLE PRECISION CABS1 00110 * .. 00111 * .. Statement Function definitions .. 00112 CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) ) 00113 * .. 00114 * .. Executable Statements .. 00115 * 00116 * Test the input parameters. 00117 * 00118 INFO = 0 00119 UPPER = LSAME( UPLO, 'U' ) 00120 ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' ) 00121 NOUNIT = LSAME( DIAG, 'N' ) 00122 * 00123 IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN 00124 INFO = -1 00125 ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 00126 INFO = -2 00127 ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN 00128 INFO = -3 00129 ELSE IF( N.LT.0 ) THEN 00130 INFO = -4 00131 ELSE IF( KD.LT.0 ) THEN 00132 INFO = -5 00133 ELSE IF( LDAB.LT.KD+1 ) THEN 00134 INFO = -7 00135 END IF 00136 IF( INFO.NE.0 ) THEN 00137 CALL XERBLA( 'ZTBCON', -INFO ) 00138 RETURN 00139 END IF 00140 * 00141 * Quick return if possible 00142 * 00143 IF( N.EQ.0 ) THEN 00144 RCOND = ONE 00145 RETURN 00146 END IF 00147 * 00148 RCOND = ZERO 00149 SMLNUM = DLAMCH( 'Safe minimum' )*DBLE( MAX( N, 1 ) ) 00150 * 00151 * Compute the 1-norm of the triangular matrix A or A**H. 00152 * 00153 ANORM = ZLANTB( NORM, UPLO, DIAG, N, KD, AB, LDAB, RWORK ) 00154 * 00155 * Continue only if ANORM > 0. 00156 * 00157 IF( ANORM.GT.ZERO ) THEN 00158 * 00159 * Estimate the 1-norm of the inverse of A. 00160 * 00161 AINVNM = ZERO 00162 NORMIN = 'N' 00163 IF( ONENRM ) THEN 00164 KASE1 = 1 00165 ELSE 00166 KASE1 = 2 00167 END IF 00168 KASE = 0 00169 10 CONTINUE 00170 CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE ) 00171 IF( KASE.NE.0 ) THEN 00172 IF( KASE.EQ.KASE1 ) THEN 00173 * 00174 * Multiply by inv(A). 00175 * 00176 CALL ZLATBS( UPLO, 'No transpose', DIAG, NORMIN, N, KD, 00177 $ AB, LDAB, WORK, SCALE, RWORK, INFO ) 00178 ELSE 00179 * 00180 * Multiply by inv(A**H). 00181 * 00182 CALL ZLATBS( UPLO, 'Conjugate transpose', DIAG, NORMIN, 00183 $ N, KD, AB, LDAB, WORK, SCALE, RWORK, INFO ) 00184 END IF 00185 NORMIN = 'Y' 00186 * 00187 * Multiply by 1/SCALE if doing so will not cause overflow. 00188 * 00189 IF( SCALE.NE.ONE ) THEN 00190 IX = IZAMAX( N, WORK, 1 ) 00191 XNORM = CABS1( WORK( IX ) ) 00192 IF( SCALE.LT.XNORM*SMLNUM .OR. SCALE.EQ.ZERO ) 00193 $ GO TO 20 00194 CALL ZDRSCL( N, SCALE, WORK, 1 ) 00195 END IF 00196 GO TO 10 00197 END IF 00198 * 00199 * Compute the estimate of the reciprocal condition number. 00200 * 00201 IF( AINVNM.NE.ZERO ) 00202 $ RCOND = ( ONE / ANORM ) / AINVNM 00203 END IF 00204 * 00205 20 CONTINUE 00206 RETURN 00207 * 00208 * End of ZTBCON 00209 * 00210 END
1.7.3 
