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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 ZPBCON( UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK, 00002 $ RWORK, INFO ) 00003 * 00004 * -- LAPACK routine (version 3.3.1) -- 00005 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00006 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00007 * -- April 2011 -- 00008 * 00009 * Modified to call ZLACN2 in place of ZLACON, 10 Feb 03, SJH. 00010 * 00011 * .. Scalar Arguments .. 00012 CHARACTER UPLO 00013 INTEGER INFO, KD, LDAB, N 00014 DOUBLE PRECISION ANORM, RCOND 00015 * .. 00016 * .. Array Arguments .. 00017 DOUBLE PRECISION RWORK( * ) 00018 COMPLEX*16 AB( LDAB, * ), WORK( * ) 00019 * .. 00020 * 00021 * Purpose 00022 * ======= 00023 * 00024 * ZPBCON estimates the reciprocal of the condition number (in the 00025 * 1-norm) of a complex Hermitian positive definite band matrix using 00026 * the Cholesky factorization A = U**H*U or A = L*L**H computed by 00027 * ZPBTRF. 00028 * 00029 * An estimate is obtained for norm(inv(A)), and the reciprocal of the 00030 * condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). 00031 * 00032 * Arguments 00033 * ========= 00034 * 00035 * UPLO (input) CHARACTER*1 00036 * = 'U': Upper triangular factor stored in AB; 00037 * = 'L': Lower triangular factor stored in AB. 00038 * 00039 * N (input) INTEGER 00040 * The order of the matrix A. N >= 0. 00041 * 00042 * KD (input) INTEGER 00043 * The number of superdiagonals of the matrix A if UPLO = 'U', 00044 * or the number of sub-diagonals if UPLO = 'L'. KD >= 0. 00045 * 00046 * AB (input) COMPLEX*16 array, dimension (LDAB,N) 00047 * The triangular factor U or L from the Cholesky factorization 00048 * A = U**H*U or A = L*L**H of the band matrix A, stored in the 00049 * first KD+1 rows of the array. The j-th column of U or L is 00050 * stored in the j-th column of the array AB as follows: 00051 * if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j; 00052 * if UPLO ='L', AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd). 00053 * 00054 * LDAB (input) INTEGER 00055 * The leading dimension of the array AB. LDAB >= KD+1. 00056 * 00057 * ANORM (input) DOUBLE PRECISION 00058 * The 1-norm (or infinity-norm) of the Hermitian band matrix A. 00059 * 00060 * RCOND (output) DOUBLE PRECISION 00061 * The reciprocal of the condition number of the matrix A, 00062 * computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an 00063 * estimate of the 1-norm of inv(A) computed in this routine. 00064 * 00065 * WORK (workspace) COMPLEX*16 array, dimension (2*N) 00066 * 00067 * RWORK (workspace) DOUBLE PRECISION 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 DOUBLE PRECISION ONE, ZERO 00077 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) 00078 * .. 00079 * .. Local Scalars .. 00080 LOGICAL UPPER 00081 CHARACTER NORMIN 00082 INTEGER IX, KASE 00083 DOUBLE PRECISION AINVNM, SCALE, SCALEL, SCALEU, SMLNUM 00084 COMPLEX*16 ZDUM 00085 * .. 00086 * .. Local Arrays .. 00087 INTEGER ISAVE( 3 ) 00088 * .. 00089 * .. External Functions .. 00090 LOGICAL LSAME 00091 INTEGER IZAMAX 00092 DOUBLE PRECISION DLAMCH 00093 EXTERNAL LSAME, IZAMAX, DLAMCH 00094 * .. 00095 * .. External Subroutines .. 00096 EXTERNAL XERBLA, ZDRSCL, ZLACN2, ZLATBS 00097 * .. 00098 * .. Intrinsic Functions .. 00099 INTRINSIC ABS, DBLE, DIMAG 00100 * .. 00101 * .. Statement Functions .. 00102 DOUBLE PRECISION CABS1 00103 * .. 00104 * .. Statement Function definitions .. 00105 CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) ) 00106 * .. 00107 * .. Executable Statements .. 00108 * 00109 * Test the input parameters. 00110 * 00111 INFO = 0 00112 UPPER = LSAME( UPLO, 'U' ) 00113 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 00114 INFO = -1 00115 ELSE IF( N.LT.0 ) THEN 00116 INFO = -2 00117 ELSE IF( KD.LT.0 ) THEN 00118 INFO = -3 00119 ELSE IF( LDAB.LT.KD+1 ) THEN 00120 INFO = -5 00121 ELSE IF( ANORM.LT.ZERO ) THEN 00122 INFO = -6 00123 END IF 00124 IF( INFO.NE.0 ) THEN 00125 CALL XERBLA( 'ZPBCON', -INFO ) 00126 RETURN 00127 END IF 00128 * 00129 * Quick return if possible 00130 * 00131 RCOND = ZERO 00132 IF( N.EQ.0 ) THEN 00133 RCOND = ONE 00134 RETURN 00135 ELSE IF( ANORM.EQ.ZERO ) THEN 00136 RETURN 00137 END IF 00138 * 00139 SMLNUM = DLAMCH( 'Safe minimum' ) 00140 * 00141 * Estimate the 1-norm of the inverse. 00142 * 00143 KASE = 0 00144 NORMIN = 'N' 00145 10 CONTINUE 00146 CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE ) 00147 IF( KASE.NE.0 ) THEN 00148 IF( UPPER ) THEN 00149 * 00150 * Multiply by inv(U**H). 00151 * 00152 CALL ZLATBS( 'Upper', 'Conjugate transpose', 'Non-unit', 00153 $ NORMIN, N, KD, AB, LDAB, WORK, SCALEL, RWORK, 00154 $ INFO ) 00155 NORMIN = 'Y' 00156 * 00157 * Multiply by inv(U). 00158 * 00159 CALL ZLATBS( 'Upper', 'No transpose', 'Non-unit', NORMIN, N, 00160 $ KD, AB, LDAB, WORK, SCALEU, RWORK, INFO ) 00161 ELSE 00162 * 00163 * Multiply by inv(L). 00164 * 00165 CALL ZLATBS( 'Lower', 'No transpose', 'Non-unit', NORMIN, N, 00166 $ KD, AB, LDAB, WORK, SCALEL, RWORK, INFO ) 00167 NORMIN = 'Y' 00168 * 00169 * Multiply by inv(L**H). 00170 * 00171 CALL ZLATBS( 'Lower', 'Conjugate transpose', 'Non-unit', 00172 $ NORMIN, N, KD, AB, LDAB, WORK, SCALEU, RWORK, 00173 $ INFO ) 00174 END IF 00175 * 00176 * Multiply by 1/SCALE if doing so will not cause overflow. 00177 * 00178 SCALE = SCALEL*SCALEU 00179 IF( SCALE.NE.ONE ) THEN 00180 IX = IZAMAX( N, WORK, 1 ) 00181 IF( SCALE.LT.CABS1( WORK( IX ) )*SMLNUM .OR. SCALE.EQ.ZERO ) 00182 $ GO TO 20 00183 CALL ZDRSCL( 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 / AINVNM ) / ANORM 00192 * 00193 20 CONTINUE 00194 * 00195 RETURN 00196 * 00197 * End of ZPBCON 00198 * 00199 END
1.7.3 
