LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
dpotrf.f
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00001 C> \brief \b DPOTRF VARIANT: top-looking block version of the algorithm, calling Level 3 BLAS.
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *  Definition:
00009 *  ===========
00010 *
00011 *       SUBROUTINE DPOTRF ( UPLO, N, A, LDA, INFO )
00012 * 
00013 *       .. Scalar Arguments ..
00014 *       CHARACTER          UPLO
00015 *       INTEGER            INFO, LDA, N
00016 *       ..
00017 *       .. Array Arguments ..
00018 *       DOUBLE PRECISION   A( LDA, * )
00019 *       ..
00020 *  
00021 *  Purpose
00022 *  =======
00023 *
00024 C>\details \b Purpose:
00025 C>\verbatim
00026 C>
00027 C> DPOTRF computes the Cholesky factorization of a real symmetric
00028 C> positive definite matrix A.
00029 C>
00030 C> The factorization has the form
00031 C>    A = U**T * U,  if UPLO = 'U', or
00032 C>    A = L  * L**T,  if UPLO = 'L',
00033 C> where U is an upper triangular matrix and L is lower triangular.
00034 C>
00035 C> This is the top-looking block version of the algorithm, calling Level 3 BLAS.
00036 C>
00037 C>\endverbatim
00038 *
00039 *  Arguments:
00040 *  ==========
00041 *
00042 C> \param[in] UPLO
00043 C> \verbatim
00044 C>          UPLO is CHARACTER*1
00045 C>          = 'U':  Upper triangle of A is stored;
00046 C>          = 'L':  Lower triangle of A is stored.
00047 C> \endverbatim
00048 C>
00049 C> \param[in] N
00050 C> \verbatim
00051 C>          N is INTEGER
00052 C>          The order of the matrix A.  N >= 0.
00053 C> \endverbatim
00054 C>
00055 C> \param[in,out] A
00056 C> \verbatim
00057 C>          A is DOUBLE PRECISION array, dimension (LDA,N)
00058 C>          On entry, the symmetric matrix A.  If UPLO = 'U', the leading
00059 C>          N-by-N upper triangular part of A contains the upper
00060 C>          triangular part of the matrix A, and the strictly lower
00061 C>          triangular part of A is not referenced.  If UPLO = 'L', the
00062 C>          leading N-by-N lower triangular part of A contains the lower
00063 C>          triangular part of the matrix A, and the strictly upper
00064 C>          triangular part of A is not referenced.
00065 C> \endverbatim
00066 C> \verbatim
00067 C>          On exit, if INFO = 0, the factor U or L from the Cholesky
00068 C>          factorization A = U**T*U or A = L*L**T.
00069 C> \endverbatim
00070 C>
00071 C> \param[in] LDA
00072 C> \verbatim
00073 C>          LDA is INTEGER
00074 C>          The leading dimension of the array A.  LDA >= max(1,N).
00075 C> \endverbatim
00076 C>
00077 C> \param[out] INFO
00078 C> \verbatim
00079 C>          INFO is INTEGER
00080 C>          = 0:  successful exit
00081 C>          < 0:  if INFO = -i, the i-th argument had an illegal value
00082 C>          > 0:  if INFO = i, the leading minor of order i is not
00083 C>                positive definite, and the factorization could not be
00084 C>                completed.
00085 C> \endverbatim
00086 C>
00087 *
00088 *  Authors:
00089 *  ========
00090 *
00091 C> \author Univ. of Tennessee 
00092 C> \author Univ. of California Berkeley 
00093 C> \author Univ. of Colorado Denver 
00094 C> \author NAG Ltd. 
00095 *
00096 C> \date November 2011
00097 *
00098 C> \ingroup variantsPOcomputational
00099 *
00100 *  =====================================================================
00101       SUBROUTINE DPOTRF ( UPLO, N, A, LDA, INFO )
00102 *
00103 *  -- LAPACK computational routine (version 3.1) --
00104 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00105 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00106 *     November 2011
00107 *
00108 *     .. Scalar Arguments ..
00109       CHARACTER          UPLO
00110       INTEGER            INFO, LDA, N
00111 *     ..
00112 *     .. Array Arguments ..
00113       DOUBLE PRECISION   A( LDA, * )
00114 *     ..
00115 *
00116 *  =====================================================================
00117 *
00118 *     .. Parameters ..
00119       DOUBLE PRECISION   ONE
00120       PARAMETER          ( ONE = 1.0D+0 )
00121 *     ..
00122 *     .. Local Scalars ..
00123       LOGICAL            UPPER
00124       INTEGER            J, JB, NB
00125 *     ..
00126 *     .. External Functions ..
00127       LOGICAL            LSAME
00128       INTEGER            ILAENV
00129       EXTERNAL           LSAME, ILAENV
00130 *     ..
00131 *     .. External Subroutines ..
00132       EXTERNAL           DGEMM, DPOTF2, DSYRK, DTRSM, XERBLA
00133 *     ..
00134 *     .. Intrinsic Functions ..
00135       INTRINSIC          MAX, MIN
00136 *     ..
00137 *     .. Executable Statements ..
00138 *
00139 *     Test the input parameters.
00140 *
00141       INFO = 0
00142       UPPER = LSAME( UPLO, 'U' )
00143       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
00144          INFO = -1
00145       ELSE IF( N.LT.0 ) THEN
00146          INFO = -2
00147       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
00148          INFO = -4
00149       END IF
00150       IF( INFO.NE.0 ) THEN
00151          CALL XERBLA( 'DPOTRF', -INFO )
00152          RETURN
00153       END IF
00154 *
00155 *     Quick return if possible
00156 *
00157       IF( N.EQ.0 )
00158      $   RETURN
00159 *
00160 *     Determine the block size for this environment.
00161 *
00162       NB = ILAENV( 1, 'DPOTRF', UPLO, N, -1, -1, -1 )
00163       IF( NB.LE.1 .OR. NB.GE.N ) THEN
00164 *
00165 *        Use unblocked code.
00166 *
00167          CALL DPOTF2( UPLO, N, A, LDA, INFO )
00168       ELSE
00169 *
00170 *        Use blocked code.
00171 *
00172          IF( UPPER ) THEN
00173 *
00174 *           Compute the Cholesky factorization A = U'*U.
00175 *
00176             DO 10 J = 1, N, NB
00177 
00178                JB = MIN( NB, N-J+1 )
00179 *
00180 *              Compute the current block.
00181 *
00182                CALL DTRSM( 'Left', 'Upper', 'Transpose', 'Non-unit',
00183      $                      J-1, JB, ONE, A( 1, 1 ), LDA,
00184      $                      A( 1, J ), LDA )
00185 
00186                CALL DSYRK( 'Upper', 'Transpose', JB, J-1, -ONE,
00187      $                      A( 1, J ), LDA, 
00188      $                      ONE, A( J, J ), LDA )
00189 *
00190 *              Update and factorize the current diagonal block and test
00191 *              for non-positive-definiteness.
00192 *
00193                CALL DPOTF2( 'Upper', JB, A( J, J ), LDA, INFO )
00194                IF( INFO.NE.0 )
00195      $            GO TO 30
00196 
00197    10       CONTINUE
00198 *
00199          ELSE
00200 *
00201 *           Compute the Cholesky factorization A = L*L'.
00202 *
00203             DO 20 J = 1, N, NB
00204 
00205                JB = MIN( NB, N-J+1 )
00206 *
00207 *              Compute the current block.
00208 *
00209                CALL DTRSM( 'Right', 'Lower', 'Transpose', 'Non-unit',
00210      $                     JB, J-1, ONE, A( 1, 1 ), LDA,
00211      $                     A( J, 1 ), LDA )
00212 
00213                CALL DSYRK( 'Lower', 'No Transpose', JB, J-1, 
00214      $                     -ONE, A( J, 1 ), LDA, 
00215      $                     ONE, A( J, J ), LDA )
00216                
00217 *
00218 *              Update and factorize the current diagonal block and test
00219 *              for non-positive-definiteness.
00220 *
00221                CALL DPOTF2( 'Lower', JB, A( J, J ), LDA, INFO )
00222                IF( INFO.NE.0 )
00223      $            GO TO 30
00224 
00225    20       CONTINUE
00226          END IF
00227       END IF
00228       GO TO 40
00229 *
00230    30 CONTINUE
00231       INFO = INFO + J - 1
00232 *
00233    40 CONTINUE
00234       RETURN
00235 *
00236 *     End of DPOTRF
00237 *
00238       END
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