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LAPACK 3.3.0
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LAPACK 3.3.0
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00001 SUBROUTINE CTRCON( NORM, UPLO, DIAG, N, A, LDA, 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 CLACN2 in place of CLACON, 10 Feb 03, SJH. 00010 * 00011 * .. Scalar Arguments .. 00012 CHARACTER DIAG, NORM, UPLO 00013 INTEGER INFO, LDA, N 00014 REAL RCOND 00015 * .. 00016 * .. Array Arguments .. 00017 REAL RWORK( * ) 00018 COMPLEX A( LDA, * ), WORK( * ) 00019 * .. 00020 * 00021 * Purpose 00022 * ======= 00023 * 00024 * CTRCON estimates the reciprocal of the condition number of a 00025 * triangular 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 * A (input) COMPLEX array, dimension (LDA,N) 00053 * The triangular matrix A. If UPLO = 'U', the leading N-by-N 00054 * upper triangular part of the array A contains the upper 00055 * triangular matrix, and the strictly lower triangular part of 00056 * A is not referenced. If UPLO = 'L', the leading N-by-N lower 00057 * triangular part of the array A contains the lower triangular 00058 * matrix, and the strictly upper triangular part of A is not 00059 * referenced. If DIAG = 'U', the diagonal elements of A are 00060 * also not referenced and are assumed to be 1. 00061 * 00062 * LDA (input) INTEGER 00063 * The leading dimension of the array A. LDA >= max(1,N). 00064 * 00065 * RCOND (output) REAL 00066 * The reciprocal of the condition number of the matrix A, 00067 * computed as RCOND = 1/(norm(A) * norm(inv(A))). 00068 * 00069 * WORK (workspace) COMPLEX array, dimension (2*N) 00070 * 00071 * RWORK (workspace) REAL array, dimension (N) 00072 * 00073 * INFO (output) INTEGER 00074 * = 0: successful exit 00075 * < 0: if INFO = -i, the i-th argument had an illegal value 00076 * 00077 * ===================================================================== 00078 * 00079 * .. Parameters .. 00080 REAL ONE, ZERO 00081 PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) 00082 * .. 00083 * .. Local Scalars .. 00084 LOGICAL NOUNIT, ONENRM, UPPER 00085 CHARACTER NORMIN 00086 INTEGER IX, KASE, KASE1 00087 REAL AINVNM, ANORM, SCALE, SMLNUM, XNORM 00088 COMPLEX ZDUM 00089 * .. 00090 * .. Local Arrays .. 00091 INTEGER ISAVE( 3 ) 00092 * .. 00093 * .. External Functions .. 00094 LOGICAL LSAME 00095 INTEGER ICAMAX 00096 REAL CLANTR, SLAMCH 00097 EXTERNAL LSAME, ICAMAX, CLANTR, SLAMCH 00098 * .. 00099 * .. External Subroutines .. 00100 EXTERNAL CLACN2, CLATRS, CSRSCL, XERBLA 00101 * .. 00102 * .. Intrinsic Functions .. 00103 INTRINSIC ABS, AIMAG, MAX, REAL 00104 * .. 00105 * .. Statement Functions .. 00106 REAL CABS1 00107 * .. 00108 * .. Statement Function definitions .. 00109 CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) ) 00110 * .. 00111 * .. Executable Statements .. 00112 * 00113 * Test the input parameters. 00114 * 00115 INFO = 0 00116 UPPER = LSAME( UPLO, 'U' ) 00117 ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' ) 00118 NOUNIT = LSAME( DIAG, 'N' ) 00119 * 00120 IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN 00121 INFO = -1 00122 ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 00123 INFO = -2 00124 ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN 00125 INFO = -3 00126 ELSE IF( N.LT.0 ) THEN 00127 INFO = -4 00128 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 00129 INFO = -6 00130 END IF 00131 IF( INFO.NE.0 ) THEN 00132 CALL XERBLA( 'CTRCON', -INFO ) 00133 RETURN 00134 END IF 00135 * 00136 * Quick return if possible 00137 * 00138 IF( N.EQ.0 ) THEN 00139 RCOND = ONE 00140 RETURN 00141 END IF 00142 * 00143 RCOND = ZERO 00144 SMLNUM = SLAMCH( 'Safe minimum' )*REAL( MAX( 1, N ) ) 00145 * 00146 * Compute the norm of the triangular matrix A. 00147 * 00148 ANORM = CLANTR( NORM, UPLO, DIAG, N, N, A, LDA, RWORK ) 00149 * 00150 * Continue only if ANORM > 0. 00151 * 00152 IF( ANORM.GT.ZERO ) THEN 00153 * 00154 * Estimate the norm of the inverse of A. 00155 * 00156 AINVNM = ZERO 00157 NORMIN = 'N' 00158 IF( ONENRM ) THEN 00159 KASE1 = 1 00160 ELSE 00161 KASE1 = 2 00162 END IF 00163 KASE = 0 00164 10 CONTINUE 00165 CALL CLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE ) 00166 IF( KASE.NE.0 ) THEN 00167 IF( KASE.EQ.KASE1 ) THEN 00168 * 00169 * Multiply by inv(A). 00170 * 00171 CALL CLATRS( UPLO, 'No transpose', DIAG, NORMIN, N, A, 00172 $ LDA, WORK, SCALE, RWORK, INFO ) 00173 ELSE 00174 * 00175 * Multiply by inv(A'). 00176 * 00177 CALL CLATRS( UPLO, 'Conjugate transpose', DIAG, NORMIN, 00178 $ N, A, LDA, WORK, SCALE, RWORK, INFO ) 00179 END IF 00180 NORMIN = 'Y' 00181 * 00182 * Multiply by 1/SCALE if doing so will not cause overflow. 00183 * 00184 IF( SCALE.NE.ONE ) THEN 00185 IX = ICAMAX( N, WORK, 1 ) 00186 XNORM = CABS1( WORK( IX ) ) 00187 IF( SCALE.LT.XNORM*SMLNUM .OR. SCALE.EQ.ZERO ) 00188 $ GO TO 20 00189 CALL CSRSCL( N, SCALE, WORK, 1 ) 00190 END IF 00191 GO TO 10 00192 END IF 00193 * 00194 * Compute the estimate of the reciprocal condition number. 00195 * 00196 IF( AINVNM.NE.ZERO ) 00197 $ RCOND = ( ONE / ANORM ) / AINVNM 00198 END IF 00199 * 00200 20 CONTINUE 00201 RETURN 00202 * 00203 * End of CTRCON 00204 * 00205 END
1.7.3 
