LAPACK 3.3.1
Linear Algebra PACKage
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00001 SUBROUTINE STBCON( NORM, UPLO, DIAG, N, KD, AB, LDAB, RCOND, WORK, 00002 $ IWORK, 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 SLACN2 in place of SLACON, 7 Feb 03, SJH. 00010 * 00011 * .. Scalar Arguments .. 00012 CHARACTER DIAG, NORM, UPLO 00013 INTEGER INFO, KD, LDAB, N 00014 REAL RCOND 00015 * .. 00016 * .. Array Arguments .. 00017 INTEGER IWORK( * ) 00018 REAL AB( LDAB, * ), WORK( * ) 00019 * .. 00020 * 00021 * Purpose 00022 * ======= 00023 * 00024 * STBCON 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) REAL 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) REAL 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) REAL array, dimension (3*N) 00073 * 00074 * IWORK (workspace) INTEGER 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 REAL ONE, ZERO 00084 PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) 00085 * .. 00086 * .. Local Scalars .. 00087 LOGICAL NOUNIT, ONENRM, UPPER 00088 CHARACTER NORMIN 00089 INTEGER IX, KASE, KASE1 00090 REAL AINVNM, ANORM, SCALE, SMLNUM, XNORM 00091 * .. 00092 * .. Local Arrays .. 00093 INTEGER ISAVE( 3 ) 00094 * .. 00095 * .. External Functions .. 00096 LOGICAL LSAME 00097 INTEGER ISAMAX 00098 REAL SLAMCH, SLANTB 00099 EXTERNAL LSAME, ISAMAX, SLAMCH, SLANTB 00100 * .. 00101 * .. External Subroutines .. 00102 EXTERNAL SLACN2, SLATBS, SRSCL, XERBLA 00103 * .. 00104 * .. Intrinsic Functions .. 00105 INTRINSIC ABS, MAX, REAL 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 ELSE IF( KD.LT.0 ) THEN 00125 INFO = -5 00126 ELSE IF( LDAB.LT.KD+1 ) THEN 00127 INFO = -7 00128 END IF 00129 IF( INFO.NE.0 ) THEN 00130 CALL XERBLA( 'STBCON', -INFO ) 00131 RETURN 00132 END IF 00133 * 00134 * Quick return if possible 00135 * 00136 IF( N.EQ.0 ) THEN 00137 RCOND = ONE 00138 RETURN 00139 END IF 00140 * 00141 RCOND = ZERO 00142 SMLNUM = SLAMCH( 'Safe minimum' )*REAL( MAX( 1, N ) ) 00143 * 00144 * Compute the norm of the triangular matrix A. 00145 * 00146 ANORM = SLANTB( NORM, UPLO, DIAG, N, KD, AB, LDAB, WORK ) 00147 * 00148 * Continue only if ANORM > 0. 00149 * 00150 IF( ANORM.GT.ZERO ) THEN 00151 * 00152 * Estimate the norm of the inverse of A. 00153 * 00154 AINVNM = ZERO 00155 NORMIN = 'N' 00156 IF( ONENRM ) THEN 00157 KASE1 = 1 00158 ELSE 00159 KASE1 = 2 00160 END IF 00161 KASE = 0 00162 10 CONTINUE 00163 CALL SLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE ) 00164 IF( KASE.NE.0 ) THEN 00165 IF( KASE.EQ.KASE1 ) THEN 00166 * 00167 * Multiply by inv(A). 00168 * 00169 CALL SLATBS( UPLO, 'No transpose', DIAG, NORMIN, N, KD, 00170 $ AB, LDAB, WORK, SCALE, WORK( 2*N+1 ), INFO ) 00171 ELSE 00172 * 00173 * Multiply by inv(A**T). 00174 * 00175 CALL SLATBS( UPLO, 'Transpose', DIAG, NORMIN, N, KD, AB, 00176 $ LDAB, WORK, SCALE, WORK( 2*N+1 ), INFO ) 00177 END IF 00178 NORMIN = 'Y' 00179 * 00180 * Multiply by 1/SCALE if doing so will not cause overflow. 00181 * 00182 IF( SCALE.NE.ONE ) THEN 00183 IX = ISAMAX( N, WORK, 1 ) 00184 XNORM = ABS( WORK( IX ) ) 00185 IF( SCALE.LT.XNORM*SMLNUM .OR. SCALE.EQ.ZERO ) 00186 $ GO TO 20 00187 CALL SRSCL( N, SCALE, WORK, 1 ) 00188 END IF 00189 GO TO 10 00190 END IF 00191 * 00192 * Compute the estimate of the reciprocal condition number. 00193 * 00194 IF( AINVNM.NE.ZERO ) 00195 $ RCOND = ( ONE / ANORM ) / AINVNM 00196 END IF 00197 * 00198 20 CONTINUE 00199 RETURN 00200 * 00201 * End of STBCON 00202 * 00203 END