LAPACK 3.3.1
Linear Algebra PACKage
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00001 SUBROUTINE CTPCON( NORM, UPLO, DIAG, N, AP, RCOND, WORK, RWORK, 00002 $ 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, N 00014 REAL RCOND 00015 * .. 00016 * .. Array Arguments .. 00017 REAL RWORK( * ) 00018 COMPLEX AP( * ), WORK( * ) 00019 * .. 00020 * 00021 * Purpose 00022 * ======= 00023 * 00024 * CTPCON estimates the reciprocal of the condition number of a packed 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 * AP (input) COMPLEX array, dimension (N*(N+1)/2) 00053 * The upper or lower triangular matrix A, packed columnwise in 00054 * a linear array. The j-th column of A is stored in the array 00055 * AP as follows: 00056 * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; 00057 * if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. 00058 * If DIAG = 'U', the diagonal elements of A are not referenced 00059 * and are assumed to be 1. 00060 * 00061 * RCOND (output) REAL 00062 * The reciprocal of the condition number of the matrix A, 00063 * computed as RCOND = 1/(norm(A) * norm(inv(A))). 00064 * 00065 * WORK (workspace) COMPLEX array, dimension (2*N) 00066 * 00067 * RWORK (workspace) REAL array, dimension (N) 00068 * 00069 * INFO (output) INTEGER 00070 * = 0: successful exit 00071 * < 0: if INFO = -i, the i-th argument had an illegal value 00072 * 00073 * ===================================================================== 00074 * 00075 * .. Parameters .. 00076 REAL ONE, ZERO 00077 PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) 00078 * .. 00079 * .. Local Scalars .. 00080 LOGICAL NOUNIT, ONENRM, UPPER 00081 CHARACTER NORMIN 00082 INTEGER IX, KASE, KASE1 00083 REAL AINVNM, ANORM, SCALE, SMLNUM, XNORM 00084 COMPLEX ZDUM 00085 * .. 00086 * .. Local Arrays .. 00087 INTEGER ISAVE( 3 ) 00088 * .. 00089 * .. External Functions .. 00090 LOGICAL LSAME 00091 INTEGER ICAMAX 00092 REAL CLANTP, SLAMCH 00093 EXTERNAL LSAME, ICAMAX, CLANTP, SLAMCH 00094 * .. 00095 * .. External Subroutines .. 00096 EXTERNAL CLACN2, CLATPS, CSRSCL, XERBLA 00097 * .. 00098 * .. Intrinsic Functions .. 00099 INTRINSIC ABS, AIMAG, MAX, REAL 00100 * .. 00101 * .. Statement Functions .. 00102 REAL CABS1 00103 * .. 00104 * .. Statement Function definitions .. 00105 CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) ) 00106 * .. 00107 * .. Executable Statements .. 00108 * 00109 * Test the input parameters. 00110 * 00111 INFO = 0 00112 UPPER = LSAME( UPLO, 'U' ) 00113 ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' ) 00114 NOUNIT = LSAME( DIAG, 'N' ) 00115 * 00116 IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN 00117 INFO = -1 00118 ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 00119 INFO = -2 00120 ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN 00121 INFO = -3 00122 ELSE IF( N.LT.0 ) THEN 00123 INFO = -4 00124 END IF 00125 IF( INFO.NE.0 ) THEN 00126 CALL XERBLA( 'CTPCON', -INFO ) 00127 RETURN 00128 END IF 00129 * 00130 * Quick return if possible 00131 * 00132 IF( N.EQ.0 ) THEN 00133 RCOND = ONE 00134 RETURN 00135 END IF 00136 * 00137 RCOND = ZERO 00138 SMLNUM = SLAMCH( 'Safe minimum' )*REAL( MAX( 1, N ) ) 00139 * 00140 * Compute the norm of the triangular matrix A. 00141 * 00142 ANORM = CLANTP( NORM, UPLO, DIAG, N, AP, RWORK ) 00143 * 00144 * Continue only if ANORM > 0. 00145 * 00146 IF( ANORM.GT.ZERO ) THEN 00147 * 00148 * Estimate the norm of the inverse of A. 00149 * 00150 AINVNM = ZERO 00151 NORMIN = 'N' 00152 IF( ONENRM ) THEN 00153 KASE1 = 1 00154 ELSE 00155 KASE1 = 2 00156 END IF 00157 KASE = 0 00158 10 CONTINUE 00159 CALL CLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE ) 00160 IF( KASE.NE.0 ) THEN 00161 IF( KASE.EQ.KASE1 ) THEN 00162 * 00163 * Multiply by inv(A). 00164 * 00165 CALL CLATPS( UPLO, 'No transpose', DIAG, NORMIN, N, AP, 00166 $ WORK, SCALE, RWORK, INFO ) 00167 ELSE 00168 * 00169 * Multiply by inv(A**H). 00170 * 00171 CALL CLATPS( UPLO, 'Conjugate transpose', DIAG, NORMIN, 00172 $ N, AP, WORK, SCALE, RWORK, INFO ) 00173 END IF 00174 NORMIN = 'Y' 00175 * 00176 * Multiply by 1/SCALE if doing so will not cause overflow. 00177 * 00178 IF( SCALE.NE.ONE ) THEN 00179 IX = ICAMAX( N, WORK, 1 ) 00180 XNORM = CABS1( WORK( IX ) ) 00181 IF( SCALE.LT.XNORM*SMLNUM .OR. SCALE.EQ.ZERO ) 00182 $ GO TO 20 00183 CALL CSRSCL( N, SCALE, WORK, 1 ) 00184 END IF 00185 GO TO 10 00186 END IF 00187 * 00188 * Compute the estimate of the reciprocal condition number. 00189 * 00190 IF( AINVNM.NE.ZERO ) 00191 $ RCOND = ( ONE / ANORM ) / AINVNM 00192 END IF 00193 * 00194 20 CONTINUE 00195 RETURN 00196 * 00197 * End of CTPCON 00198 * 00199 END