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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b CPOTF2 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download CPOTF2 + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cpotf2.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cpotf2.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cpotf2.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE CPOTF2( UPLO, N, A, LDA, INFO ) 00022 * 00023 * .. Scalar Arguments .. 00024 * CHARACTER UPLO 00025 * INTEGER INFO, LDA, N 00026 * .. 00027 * .. Array Arguments .. 00028 * COMPLEX A( LDA, * ) 00029 * .. 00030 * 00031 * 00032 *> \par Purpose: 00033 * ============= 00034 *> 00035 *> \verbatim 00036 *> 00037 *> CPOTF2 computes the Cholesky factorization of a complex Hermitian 00038 *> positive definite 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 and L is lower triangular. 00044 *> 00045 *> This is the unblocked version of the algorithm, calling Level 2 BLAS. 00046 *> \endverbatim 00047 * 00048 * Arguments: 00049 * ========== 00050 * 00051 *> \param[in] UPLO 00052 *> \verbatim 00053 *> UPLO is CHARACTER*1 00054 *> Specifies whether the upper or lower triangular part of the 00055 *> Hermitian matrix A is stored. 00056 *> = 'U': Upper triangular 00057 *> = 'L': Lower triangular 00058 *> \endverbatim 00059 *> 00060 *> \param[in] N 00061 *> \verbatim 00062 *> N is INTEGER 00063 *> The order of the matrix A. N >= 0. 00064 *> \endverbatim 00065 *> 00066 *> \param[in,out] A 00067 *> \verbatim 00068 *> A is COMPLEX array, dimension (LDA,N) 00069 *> On entry, the Hermitian matrix A. If UPLO = 'U', the leading 00070 *> n by n upper triangular part of A contains the upper 00071 *> triangular part of the matrix A, and the strictly lower 00072 *> triangular part of A is not referenced. If UPLO = 'L', the 00073 *> leading n by n lower triangular part of A contains the lower 00074 *> triangular part of the matrix A, and the strictly upper 00075 *> triangular part of A is not referenced. 00076 *> 00077 *> On exit, if INFO = 0, the factor U or L from the Cholesky 00078 *> factorization A = U**H *U or A = L*L**H. 00079 *> \endverbatim 00080 *> 00081 *> \param[in] LDA 00082 *> \verbatim 00083 *> LDA is INTEGER 00084 *> The leading dimension of the array A. LDA >= max(1,N). 00085 *> \endverbatim 00086 *> 00087 *> \param[out] INFO 00088 *> \verbatim 00089 *> INFO is INTEGER 00090 *> = 0: successful exit 00091 *> < 0: if INFO = -k, the k-th argument had an illegal value 00092 *> > 0: if INFO = k, the leading minor of order k is not 00093 *> positive definite, and the factorization could not be 00094 *> completed. 00095 *> \endverbatim 00096 * 00097 * Authors: 00098 * ======== 00099 * 00100 *> \author Univ. of Tennessee 00101 *> \author Univ. of California Berkeley 00102 *> \author Univ. of Colorado Denver 00103 *> \author NAG Ltd. 00104 * 00105 *> \date November 2011 00106 * 00107 *> \ingroup complexPOcomputational 00108 * 00109 * ===================================================================== 00110 SUBROUTINE CPOTF2( UPLO, N, A, LDA, INFO ) 00111 * 00112 * -- LAPACK computational routine (version 3.4.0) -- 00113 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00114 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00115 * November 2011 00116 * 00117 * .. Scalar Arguments .. 00118 CHARACTER UPLO 00119 INTEGER INFO, LDA, N 00120 * .. 00121 * .. Array Arguments .. 00122 COMPLEX A( LDA, * ) 00123 * .. 00124 * 00125 * ===================================================================== 00126 * 00127 * .. Parameters .. 00128 REAL ONE, ZERO 00129 PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) 00130 COMPLEX CONE 00131 PARAMETER ( CONE = ( 1.0E+0, 0.0E+0 ) ) 00132 * .. 00133 * .. Local Scalars .. 00134 LOGICAL UPPER 00135 INTEGER J 00136 REAL AJJ 00137 * .. 00138 * .. External Functions .. 00139 LOGICAL LSAME, SISNAN 00140 COMPLEX CDOTC 00141 EXTERNAL LSAME, CDOTC, SISNAN 00142 * .. 00143 * .. External Subroutines .. 00144 EXTERNAL CGEMV, CLACGV, CSSCAL, XERBLA 00145 * .. 00146 * .. Intrinsic Functions .. 00147 INTRINSIC MAX, REAL, SQRT 00148 * .. 00149 * .. Executable Statements .. 00150 * 00151 * Test the input parameters. 00152 * 00153 INFO = 0 00154 UPPER = LSAME( UPLO, 'U' ) 00155 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 00156 INFO = -1 00157 ELSE IF( N.LT.0 ) THEN 00158 INFO = -2 00159 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 00160 INFO = -4 00161 END IF 00162 IF( INFO.NE.0 ) THEN 00163 CALL XERBLA( 'CPOTF2', -INFO ) 00164 RETURN 00165 END IF 00166 * 00167 * Quick return if possible 00168 * 00169 IF( N.EQ.0 ) 00170 $ RETURN 00171 * 00172 IF( UPPER ) THEN 00173 * 00174 * Compute the Cholesky factorization A = U**H *U. 00175 * 00176 DO 10 J = 1, N 00177 * 00178 * Compute U(J,J) and test for non-positive-definiteness. 00179 * 00180 AJJ = REAL( A( J, J ) ) - CDOTC( J-1, A( 1, J ), 1, 00181 $ A( 1, J ), 1 ) 00182 IF( AJJ.LE.ZERO.OR.SISNAN( AJJ ) ) THEN 00183 A( J, J ) = AJJ 00184 GO TO 30 00185 END IF 00186 AJJ = SQRT( AJJ ) 00187 A( J, J ) = AJJ 00188 * 00189 * Compute elements J+1:N of row J. 00190 * 00191 IF( J.LT.N ) THEN 00192 CALL CLACGV( J-1, A( 1, J ), 1 ) 00193 CALL CGEMV( 'Transpose', J-1, N-J, -CONE, A( 1, J+1 ), 00194 $ LDA, A( 1, J ), 1, CONE, A( J, J+1 ), LDA ) 00195 CALL CLACGV( J-1, A( 1, J ), 1 ) 00196 CALL CSSCAL( N-J, ONE / AJJ, A( J, J+1 ), LDA ) 00197 END IF 00198 10 CONTINUE 00199 ELSE 00200 * 00201 * Compute the Cholesky factorization A = L*L**H. 00202 * 00203 DO 20 J = 1, N 00204 * 00205 * Compute L(J,J) and test for non-positive-definiteness. 00206 * 00207 AJJ = REAL( A( J, J ) ) - CDOTC( J-1, A( J, 1 ), LDA, 00208 $ A( J, 1 ), LDA ) 00209 IF( AJJ.LE.ZERO.OR.SISNAN( AJJ ) ) THEN 00210 A( J, J ) = AJJ 00211 GO TO 30 00212 END IF 00213 AJJ = SQRT( AJJ ) 00214 A( J, J ) = AJJ 00215 * 00216 * Compute elements J+1:N of column J. 00217 * 00218 IF( J.LT.N ) THEN 00219 CALL CLACGV( J-1, A( J, 1 ), LDA ) 00220 CALL CGEMV( 'No transpose', N-J, J-1, -CONE, A( J+1, 1 ), 00221 $ LDA, A( J, 1 ), LDA, CONE, A( J+1, J ), 1 ) 00222 CALL CLACGV( J-1, A( J, 1 ), LDA ) 00223 CALL CSSCAL( N-J, ONE / AJJ, A( J+1, J ), 1 ) 00224 END IF 00225 20 CONTINUE 00226 END IF 00227 GO TO 40 00228 * 00229 30 CONTINUE 00230 INFO = J 00231 * 00232 40 CONTINUE 00233 RETURN 00234 * 00235 * End of CPOTF2 00236 * 00237 END