LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
spotrf.f
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00001 *> \brief \b SPOTRF
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download SPOTRF + dependencies 
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00011 *> [TGZ]</a> 
00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/spotrf.f"> 
00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/spotrf.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE SPOTRF( UPLO, N, A, LDA, INFO )
00022 * 
00023 *       .. Scalar Arguments ..
00024 *       CHARACTER          UPLO
00025 *       INTEGER            INFO, LDA, N
00026 *       ..
00027 *       .. Array Arguments ..
00028 *       REAL               A( LDA, * )
00029 *       ..
00030 *  
00031 *
00032 *> \par Purpose:
00033 *  =============
00034 *>
00035 *> \verbatim
00036 *>
00037 *> SPOTRF computes the Cholesky factorization of a real symmetric
00038 *> positive definite matrix A.
00039 *>
00040 *> The factorization has the form
00041 *>    A = U**T * U,  if UPLO = 'U', or
00042 *>    A = L  * L**T,  if UPLO = 'L',
00043 *> where U is an upper triangular matrix and L is lower triangular.
00044 *>
00045 *> This is the block version of the algorithm, calling Level 3 BLAS.
00046 *> \endverbatim
00047 *
00048 *  Arguments:
00049 *  ==========
00050 *
00051 *> \param[in] UPLO
00052 *> \verbatim
00053 *>          UPLO is CHARACTER*1
00054 *>          = 'U':  Upper triangle of A is stored;
00055 *>          = 'L':  Lower triangle of A is stored.
00056 *> \endverbatim
00057 *>
00058 *> \param[in] N
00059 *> \verbatim
00060 *>          N is INTEGER
00061 *>          The order of the matrix A.  N >= 0.
00062 *> \endverbatim
00063 *>
00064 *> \param[in,out] A
00065 *> \verbatim
00066 *>          A is REAL array, dimension (LDA,N)
00067 *>          On entry, the symmetric matrix A.  If UPLO = 'U', the leading
00068 *>          N-by-N upper triangular part of A contains the upper
00069 *>          triangular part of the matrix A, and the strictly lower
00070 *>          triangular part of A is not referenced.  If UPLO = 'L', the
00071 *>          leading N-by-N lower triangular part of A contains the lower
00072 *>          triangular part of the matrix A, and the strictly upper
00073 *>          triangular part of A is not referenced.
00074 *>
00075 *>          On exit, if INFO = 0, the factor U or L from the Cholesky
00076 *>          factorization A = U**T*U or A = L*L**T.
00077 *> \endverbatim
00078 *>
00079 *> \param[in] LDA
00080 *> \verbatim
00081 *>          LDA is INTEGER
00082 *>          The leading dimension of the array A.  LDA >= max(1,N).
00083 *> \endverbatim
00084 *>
00085 *> \param[out] INFO
00086 *> \verbatim
00087 *>          INFO is INTEGER
00088 *>          = 0:  successful exit
00089 *>          < 0:  if INFO = -i, the i-th argument had an illegal value
00090 *>          > 0:  if INFO = i, the leading minor of order i is not
00091 *>                positive definite, and the factorization could not be
00092 *>                completed.
00093 *> \endverbatim
00094 *
00095 *  Authors:
00096 *  ========
00097 *
00098 *> \author Univ. of Tennessee 
00099 *> \author Univ. of California Berkeley 
00100 *> \author Univ. of Colorado Denver 
00101 *> \author NAG Ltd. 
00102 *
00103 *> \date November 2011
00104 *
00105 *> \ingroup realPOcomputational
00106 *
00107 *  =====================================================================
00108       SUBROUTINE SPOTRF( UPLO, N, A, LDA, INFO )
00109 *
00110 *  -- LAPACK computational routine (version 3.4.0) --
00111 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00112 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00113 *     November 2011
00114 *
00115 *     .. Scalar Arguments ..
00116       CHARACTER          UPLO
00117       INTEGER            INFO, LDA, N
00118 *     ..
00119 *     .. Array Arguments ..
00120       REAL               A( LDA, * )
00121 *     ..
00122 *
00123 *  =====================================================================
00124 *
00125 *     .. Parameters ..
00126       REAL               ONE
00127       PARAMETER          ( ONE = 1.0E+0 )
00128 *     ..
00129 *     .. Local Scalars ..
00130       LOGICAL            UPPER
00131       INTEGER            J, JB, NB
00132 *     ..
00133 *     .. External Functions ..
00134       LOGICAL            LSAME
00135       INTEGER            ILAENV
00136       EXTERNAL           LSAME, ILAENV
00137 *     ..
00138 *     .. External Subroutines ..
00139       EXTERNAL           SGEMM, SPOTF2, SSYRK, STRSM, XERBLA
00140 *     ..
00141 *     .. Intrinsic Functions ..
00142       INTRINSIC          MAX, MIN
00143 *     ..
00144 *     .. Executable Statements ..
00145 *
00146 *     Test the input parameters.
00147 *
00148       INFO = 0
00149       UPPER = LSAME( UPLO, 'U' )
00150       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
00151          INFO = -1
00152       ELSE IF( N.LT.0 ) THEN
00153          INFO = -2
00154       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
00155          INFO = -4
00156       END IF
00157       IF( INFO.NE.0 ) THEN
00158          CALL XERBLA( 'SPOTRF', -INFO )
00159          RETURN
00160       END IF
00161 *
00162 *     Quick return if possible
00163 *
00164       IF( N.EQ.0 )
00165      $   RETURN
00166 *
00167 *     Determine the block size for this environment.
00168 *
00169       NB = ILAENV( 1, 'SPOTRF', UPLO, N, -1, -1, -1 )
00170       IF( NB.LE.1 .OR. NB.GE.N ) THEN
00171 *
00172 *        Use unblocked code.
00173 *
00174          CALL SPOTF2( UPLO, N, A, LDA, INFO )
00175       ELSE
00176 *
00177 *        Use blocked code.
00178 *
00179          IF( UPPER ) THEN
00180 *
00181 *           Compute the Cholesky factorization A = U**T*U.
00182 *
00183             DO 10 J = 1, N, NB
00184 *
00185 *              Update and factorize the current diagonal block and test
00186 *              for non-positive-definiteness.
00187 *
00188                JB = MIN( NB, N-J+1 )
00189                CALL SSYRK( 'Upper', 'Transpose', JB, J-1, -ONE,
00190      $                     A( 1, J ), LDA, ONE, A( J, J ), LDA )
00191                CALL SPOTF2( 'Upper', JB, A( J, J ), LDA, INFO )
00192                IF( INFO.NE.0 )
00193      $            GO TO 30
00194                IF( J+JB.LE.N ) THEN
00195 *
00196 *                 Compute the current block row.
00197 *
00198                   CALL SGEMM( 'Transpose', 'No transpose', JB, N-J-JB+1,
00199      $                        J-1, -ONE, A( 1, J ), LDA, A( 1, J+JB ),
00200      $                        LDA, ONE, A( J, J+JB ), LDA )
00201                   CALL STRSM( 'Left', 'Upper', 'Transpose', 'Non-unit',
00202      $                        JB, N-J-JB+1, ONE, A( J, J ), LDA,
00203      $                        A( J, J+JB ), LDA )
00204                END IF
00205    10       CONTINUE
00206 *
00207          ELSE
00208 *
00209 *           Compute the Cholesky factorization A = L*L**T.
00210 *
00211             DO 20 J = 1, N, NB
00212 *
00213 *              Update and factorize the current diagonal block and test
00214 *              for non-positive-definiteness.
00215 *
00216                JB = MIN( NB, N-J+1 )
00217                CALL SSYRK( 'Lower', 'No transpose', JB, J-1, -ONE,
00218      $                     A( J, 1 ), LDA, ONE, A( J, J ), LDA )
00219                CALL SPOTF2( 'Lower', JB, A( J, J ), LDA, INFO )
00220                IF( INFO.NE.0 )
00221      $            GO TO 30
00222                IF( J+JB.LE.N ) THEN
00223 *
00224 *                 Compute the current block column.
00225 *
00226                   CALL SGEMM( 'No transpose', 'Transpose', N-J-JB+1, JB,
00227      $                        J-1, -ONE, A( J+JB, 1 ), LDA, A( J, 1 ),
00228      $                        LDA, ONE, A( J+JB, J ), LDA )
00229                   CALL STRSM( 'Right', 'Lower', 'Transpose', 'Non-unit',
00230      $                        N-J-JB+1, JB, ONE, A( J, J ), LDA,
00231      $                        A( J+JB, J ), LDA )
00232                END IF
00233    20       CONTINUE
00234          END IF
00235       END IF
00236       GO TO 40
00237 *
00238    30 CONTINUE
00239       INFO = INFO + J - 1
00240 *
00241    40 CONTINUE
00242       RETURN
00243 *
00244 *     End of SPOTRF
00245 *
00246       END
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