LAPACK: SRC/zpotrf.f Source File

Go to the documentation of this file.
00001       SUBROUTINE ZPOTRF( UPLO, N, A, LDA, INFO )
00002 *
00003 *  -- LAPACK routine (version 3.2) --
00004 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00005 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00006 *     November 2006
00007 *
00008 *     .. Scalar Arguments ..
00009       CHARACTER          UPLO
00010       INTEGER            INFO, LDA, N
00011 *     ..
00012 *     .. Array Arguments ..
00013       COMPLEX*16         A( LDA, * )
00014 *     ..
00015 *
00016 *  Purpose
00017 *  =======
00018 *
00019 *  ZPOTRF computes the Cholesky factorization of a complex Hermitian
00020 *  positive definite matrix A.
00021 *
00022 *  The factorization has the form
00023 *     A = U**H * U,  if UPLO = 'U', or
00024 *     A = L  * L**H,  if UPLO = 'L',
00025 *  where U is an upper triangular matrix and L is lower triangular.
00026 *
00027 *  This is the block version of the algorithm, calling Level 3 BLAS.
00028 *
00029 *  Arguments
00030 *  =========
00031 *
00032 *  UPLO    (input) CHARACTER*1
00033 *          = 'U':  Upper triangle of A is stored;
00034 *          = 'L':  Lower triangle of A is stored.
00035 *
00036 *  N       (input) INTEGER
00037 *          The order of the matrix A.  N >= 0.
00038 *
00039 *  A       (input/output) COMPLEX*16 array, dimension (LDA,N)
00040 *          On entry, the Hermitian matrix A.  If UPLO = 'U', the leading
00041 *          N-by-N upper triangular part of A contains the upper
00042 *          triangular part of the matrix A, and the strictly lower
00043 *          triangular part of A is not referenced.  If UPLO = 'L', the
00044 *          leading N-by-N lower triangular part of A contains the lower
00045 *          triangular part of the matrix A, and the strictly upper
00046 *          triangular part of A is not referenced.
00047 *
00048 *          On exit, if INFO = 0, the factor U or L from the Cholesky
00049 *          factorization A = U**H*U or A = L*L**H.
00050 *
00051 *  LDA     (input) INTEGER
00052 *          The leading dimension of the array A.  LDA >= max(1,N).
00053 *
00054 *  INFO    (output) INTEGER
00055 *          = 0:  successful exit
00056 *          < 0:  if INFO = -i, the i-th argument had an illegal value
00057 *          > 0:  if INFO = i, the leading minor of order i is not
00058 *                positive definite, and the factorization could not be
00059 *                completed.
00060 *
00061 *  =====================================================================
00062 *
00063 *     .. Parameters ..
00064       DOUBLE PRECISION   ONE
00065       COMPLEX*16         CONE
00066       PARAMETER          ( ONE = 1.0D+0, CONE = ( 1.0D+0, 0.0D+0 ) )
00067 *     ..
00068 *     .. Local Scalars ..
00069       LOGICAL            UPPER
00070       INTEGER            J, JB, NB
00071 *     ..
00072 *     .. External Functions ..
00073       LOGICAL            LSAME
00074       INTEGER            ILAENV
00075       EXTERNAL           LSAME, ILAENV
00076 *     ..
00077 *     .. External Subroutines ..
00078       EXTERNAL           XERBLA, ZGEMM, ZHERK, ZPOTF2, ZTRSM
00079 *     ..
00080 *     .. Intrinsic Functions ..
00081       INTRINSIC          MAX, MIN
00082 *     ..
00083 *     .. Executable Statements ..
00084 *
00085 *     Test the input parameters.
00086 *
00087       INFO = 0
00088       UPPER = LSAME( UPLO, 'U' )
00089       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
00090          INFO = -1
00091       ELSE IF( N.LT.0 ) THEN
00092          INFO = -2
00093       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
00094          INFO = -4
00095       END IF
00096       IF( INFO.NE.0 ) THEN
00097          CALL XERBLA( 'ZPOTRF', -INFO )
00098          RETURN
00099       END IF
00100 *
00101 *     Quick return if possible
00102 *
00103       IF( N.EQ.0 )
00104      $   RETURN
00105 *
00106 *     Determine the block size for this environment.
00107 *
00108       NB = ILAENV( 1, 'ZPOTRF', UPLO, N, -1, -1, -1 )
00109       IF( NB.LE.1 .OR. NB.GE.N ) THEN
00110 *
00111 *        Use unblocked code.
00112 *
00113          CALL ZPOTF2( UPLO, N, A, LDA, INFO )
00114       ELSE
00115 *
00116 *        Use blocked code.
00117 *
00118          IF( UPPER ) THEN
00119 *
00120 *           Compute the Cholesky factorization A = U'*U.
00121 *
00122             DO 10 J = 1, N, NB
00123 *
00124 *              Update and factorize the current diagonal block and test
00125 *              for non-positive-definiteness.
00126 *
00127                JB = MIN( NB, N-J+1 )
00128                CALL ZHERK( 'Upper', 'Conjugate transpose', JB, J-1,
00129      $                     -ONE, A( 1, J ), LDA, ONE, A( J, J ), LDA )
00130                CALL ZPOTF2( 'Upper', JB, A( J, J ), LDA, INFO )
00131                IF( INFO.NE.0 )
00132      $            GO TO 30
00133                IF( J+JB.LE.N ) THEN
00134 *
00135 *                 Compute the current block row.
00136 *
00137                   CALL ZGEMM( 'Conjugate transpose', 'No transpose', JB,
00138      $                        N-J-JB+1, J-1, -CONE, A( 1, J ), LDA,
00139      $                        A( 1, J+JB ), LDA, CONE, A( J, J+JB ),
00140      $                        LDA )
00141                   CALL ZTRSM( 'Left', 'Upper', 'Conjugate transpose',
00142      $                        'Non-unit', JB, N-J-JB+1, CONE, A( J, J ),
00143      $                        LDA, A( J, J+JB ), LDA )
00144                END IF
00145    10       CONTINUE
00146 *
00147          ELSE
00148 *
00149 *           Compute the Cholesky factorization A = L*L'.
00150 *
00151             DO 20 J = 1, N, NB
00152 *
00153 *              Update and factorize the current diagonal block and test
00154 *              for non-positive-definiteness.
00155 *
00156                JB = MIN( NB, N-J+1 )
00157                CALL ZHERK( 'Lower', 'No transpose', JB, J-1, -ONE,
00158      $                     A( J, 1 ), LDA, ONE, A( J, J ), LDA )
00159                CALL ZPOTF2( 'Lower', JB, A( J, J ), LDA, INFO )
00160                IF( INFO.NE.0 )
00161      $            GO TO 30
00162                IF( J+JB.LE.N ) THEN
00163 *
00164 *                 Compute the current block column.
00165 *
00166                   CALL ZGEMM( 'No transpose', 'Conjugate transpose',
00167      $                        N-J-JB+1, JB, J-1, -CONE, A( J+JB, 1 ),
00168      $                        LDA, A( J, 1 ), LDA, CONE, A( J+JB, J ),
00169      $                        LDA )
00170                   CALL ZTRSM( 'Right', 'Lower', 'Conjugate transpose',
00171      $                        'Non-unit', N-J-JB+1, JB, CONE, A( J, J ),
00172      $                        LDA, A( J+JB, J ), LDA )
00173                END IF
00174    20       CONTINUE
00175          END IF
00176       END IF
00177       GO TO 40
00178 *
00179    30 CONTINUE
00180       INFO = INFO + J - 1
00181 *
00182    40 CONTINUE
00183       RETURN
00184 *
00185 *     End of ZPOTRF
00186 *
00187       END