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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b ZPBTF2 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download ZPBTF2 + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zpbtf2.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zpbtf2.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zpbtf2.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE ZPBTF2( UPLO, N, KD, AB, LDAB, INFO ) 00022 * 00023 * .. Scalar Arguments .. 00024 * CHARACTER UPLO 00025 * INTEGER INFO, KD, LDAB, N 00026 * .. 00027 * .. Array Arguments .. 00028 * COMPLEX*16 AB( LDAB, * ) 00029 * .. 00030 * 00031 * 00032 *> \par Purpose: 00033 * ============= 00034 *> 00035 *> \verbatim 00036 *> 00037 *> ZPBTF2 computes the Cholesky factorization of a complex Hermitian 00038 *> positive definite band matrix A. 00039 *> 00040 *> The factorization has the form 00041 *> A = U**H * U , if UPLO = 'U', or 00042 *> A = L * L**H, if UPLO = 'L', 00043 *> where U is an upper triangular matrix, U**H is the conjugate transpose 00044 *> of U, and L is lower triangular. 00045 *> 00046 *> This is the unblocked version of the algorithm, calling Level 2 BLAS. 00047 *> \endverbatim 00048 * 00049 * Arguments: 00050 * ========== 00051 * 00052 *> \param[in] UPLO 00053 *> \verbatim 00054 *> UPLO is CHARACTER*1 00055 *> Specifies whether the upper or lower triangular part of the 00056 *> Hermitian matrix A is stored: 00057 *> = 'U': Upper triangular 00058 *> = 'L': Lower triangular 00059 *> \endverbatim 00060 *> 00061 *> \param[in] N 00062 *> \verbatim 00063 *> N is INTEGER 00064 *> The order of the matrix A. N >= 0. 00065 *> \endverbatim 00066 *> 00067 *> \param[in] KD 00068 *> \verbatim 00069 *> KD is INTEGER 00070 *> The number of super-diagonals of the matrix A if UPLO = 'U', 00071 *> or the number of sub-diagonals if UPLO = 'L'. KD >= 0. 00072 *> \endverbatim 00073 *> 00074 *> \param[in,out] AB 00075 *> \verbatim 00076 *> AB is COMPLEX*16 array, dimension (LDAB,N) 00077 *> On entry, the upper or lower triangle of the Hermitian band 00078 *> matrix A, stored in the first KD+1 rows of the array. The 00079 *> j-th column of A is stored in the j-th column of the array AB 00080 *> as follows: 00081 *> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; 00082 *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). 00083 *> 00084 *> On exit, if INFO = 0, the triangular factor U or L from the 00085 *> Cholesky factorization A = U**H *U or A = L*L**H of the band 00086 *> matrix A, in the same storage format as A. 00087 *> \endverbatim 00088 *> 00089 *> \param[in] LDAB 00090 *> \verbatim 00091 *> LDAB is INTEGER 00092 *> The leading dimension of the array AB. LDAB >= KD+1. 00093 *> \endverbatim 00094 *> 00095 *> \param[out] INFO 00096 *> \verbatim 00097 *> INFO is INTEGER 00098 *> = 0: successful exit 00099 *> < 0: if INFO = -k, the k-th argument had an illegal value 00100 *> > 0: if INFO = k, the leading minor of order k is not 00101 *> positive definite, and the factorization could not be 00102 *> completed. 00103 *> \endverbatim 00104 * 00105 * Authors: 00106 * ======== 00107 * 00108 *> \author Univ. of Tennessee 00109 *> \author Univ. of California Berkeley 00110 *> \author Univ. of Colorado Denver 00111 *> \author NAG Ltd. 00112 * 00113 *> \date November 2011 00114 * 00115 *> \ingroup complex16OTHERcomputational 00116 * 00117 *> \par Further Details: 00118 * ===================== 00119 *> 00120 *> \verbatim 00121 *> 00122 *> The band storage scheme is illustrated by the following example, when 00123 *> N = 6, KD = 2, and UPLO = 'U': 00124 *> 00125 *> On entry: On exit: 00126 *> 00127 *> * * a13 a24 a35 a46 * * u13 u24 u35 u46 00128 *> * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56 00129 *> a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66 00130 *> 00131 *> Similarly, if UPLO = 'L' the format of A is as follows: 00132 *> 00133 *> On entry: On exit: 00134 *> 00135 *> a11 a22 a33 a44 a55 a66 l11 l22 l33 l44 l55 l66 00136 *> a21 a32 a43 a54 a65 * l21 l32 l43 l54 l65 * 00137 *> a31 a42 a53 a64 * * l31 l42 l53 l64 * * 00138 *> 00139 *> Array elements marked * are not used by the routine. 00140 *> \endverbatim 00141 *> 00142 * ===================================================================== 00143 SUBROUTINE ZPBTF2( UPLO, N, KD, AB, LDAB, INFO ) 00144 * 00145 * -- LAPACK computational routine (version 3.4.0) -- 00146 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00147 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00148 * November 2011 00149 * 00150 * .. Scalar Arguments .. 00151 CHARACTER UPLO 00152 INTEGER INFO, KD, LDAB, N 00153 * .. 00154 * .. Array Arguments .. 00155 COMPLEX*16 AB( LDAB, * ) 00156 * .. 00157 * 00158 * ===================================================================== 00159 * 00160 * .. Parameters .. 00161 DOUBLE PRECISION ONE, ZERO 00162 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) 00163 * .. 00164 * .. Local Scalars .. 00165 LOGICAL UPPER 00166 INTEGER J, KLD, KN 00167 DOUBLE PRECISION AJJ 00168 * .. 00169 * .. External Functions .. 00170 LOGICAL LSAME 00171 EXTERNAL LSAME 00172 * .. 00173 * .. External Subroutines .. 00174 EXTERNAL XERBLA, ZDSCAL, ZHER, ZLACGV 00175 * .. 00176 * .. Intrinsic Functions .. 00177 INTRINSIC DBLE, MAX, MIN, SQRT 00178 * .. 00179 * .. Executable Statements .. 00180 * 00181 * Test the input parameters. 00182 * 00183 INFO = 0 00184 UPPER = LSAME( UPLO, 'U' ) 00185 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 00186 INFO = -1 00187 ELSE IF( N.LT.0 ) THEN 00188 INFO = -2 00189 ELSE IF( KD.LT.0 ) THEN 00190 INFO = -3 00191 ELSE IF( LDAB.LT.KD+1 ) THEN 00192 INFO = -5 00193 END IF 00194 IF( INFO.NE.0 ) THEN 00195 CALL XERBLA( 'ZPBTF2', -INFO ) 00196 RETURN 00197 END IF 00198 * 00199 * Quick return if possible 00200 * 00201 IF( N.EQ.0 ) 00202 $ RETURN 00203 * 00204 KLD = MAX( 1, LDAB-1 ) 00205 * 00206 IF( UPPER ) THEN 00207 * 00208 * Compute the Cholesky factorization A = U**H * U. 00209 * 00210 DO 10 J = 1, N 00211 * 00212 * Compute U(J,J) and test for non-positive-definiteness. 00213 * 00214 AJJ = DBLE( AB( KD+1, J ) ) 00215 IF( AJJ.LE.ZERO ) THEN 00216 AB( KD+1, J ) = AJJ 00217 GO TO 30 00218 END IF 00219 AJJ = SQRT( AJJ ) 00220 AB( KD+1, J ) = AJJ 00221 * 00222 * Compute elements J+1:J+KN of row J and update the 00223 * trailing submatrix within the band. 00224 * 00225 KN = MIN( KD, N-J ) 00226 IF( KN.GT.0 ) THEN 00227 CALL ZDSCAL( KN, ONE / AJJ, AB( KD, J+1 ), KLD ) 00228 CALL ZLACGV( KN, AB( KD, J+1 ), KLD ) 00229 CALL ZHER( 'Upper', KN, -ONE, AB( KD, J+1 ), KLD, 00230 $ AB( KD+1, J+1 ), KLD ) 00231 CALL ZLACGV( KN, AB( KD, J+1 ), KLD ) 00232 END IF 00233 10 CONTINUE 00234 ELSE 00235 * 00236 * Compute the Cholesky factorization A = L*L**H. 00237 * 00238 DO 20 J = 1, N 00239 * 00240 * Compute L(J,J) and test for non-positive-definiteness. 00241 * 00242 AJJ = DBLE( AB( 1, J ) ) 00243 IF( AJJ.LE.ZERO ) THEN 00244 AB( 1, J ) = AJJ 00245 GO TO 30 00246 END IF 00247 AJJ = SQRT( AJJ ) 00248 AB( 1, J ) = AJJ 00249 * 00250 * Compute elements J+1:J+KN of column J and update the 00251 * trailing submatrix within the band. 00252 * 00253 KN = MIN( KD, N-J ) 00254 IF( KN.GT.0 ) THEN 00255 CALL ZDSCAL( KN, ONE / AJJ, AB( 2, J ), 1 ) 00256 CALL ZHER( 'Lower', KN, -ONE, AB( 2, J ), 1, 00257 $ AB( 1, J+1 ), KLD ) 00258 END IF 00259 20 CONTINUE 00260 END IF 00261 RETURN 00262 * 00263 30 CONTINUE 00264 INFO = J 00265 RETURN 00266 * 00267 * End of ZPBTF2 00268 * 00269 END