Annotation of rpl/lapack/lapack/dpptrf.f, revision 1.9

1.9     ! bertrand    1: *> \brief \b DPPTRF
        !             2: *
        !             3: *  =========== DOCUMENTATION ===========
        !             4: *
        !             5: * Online html documentation available at 
        !             6: *            http://www.netlib.org/lapack/explore-html/ 
        !             7: *
        !             8: *> \htmlonly
        !             9: *> Download DPPTRF + dependencies 
        !            10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dpptrf.f"> 
        !            11: *> [TGZ]</a> 
        !            12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dpptrf.f"> 
        !            13: *> [ZIP]</a> 
        !            14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dpptrf.f"> 
        !            15: *> [TXT]</a>
        !            16: *> \endhtmlonly 
        !            17: *
        !            18: *  Definition:
        !            19: *  ===========
        !            20: *
        !            21: *       SUBROUTINE DPPTRF( UPLO, N, AP, INFO )
        !            22: * 
        !            23: *       .. Scalar Arguments ..
        !            24: *       CHARACTER          UPLO
        !            25: *       INTEGER            INFO, N
        !            26: *       ..
        !            27: *       .. Array Arguments ..
        !            28: *       DOUBLE PRECISION   AP( * )
        !            29: *       ..
        !            30: *  
        !            31: *
        !            32: *> \par Purpose:
        !            33: *  =============
        !            34: *>
        !            35: *> \verbatim
        !            36: *>
        !            37: *> DPPTRF computes the Cholesky factorization of a real symmetric
        !            38: *> positive definite matrix A stored in packed format.
        !            39: *>
        !            40: *> The factorization has the form
        !            41: *>    A = U**T * U,  if UPLO = 'U', or
        !            42: *>    A = L  * L**T,  if UPLO = 'L',
        !            43: *> where U is an upper triangular matrix and L is lower triangular.
        !            44: *> \endverbatim
        !            45: *
        !            46: *  Arguments:
        !            47: *  ==========
        !            48: *
        !            49: *> \param[in] UPLO
        !            50: *> \verbatim
        !            51: *>          UPLO is CHARACTER*1
        !            52: *>          = 'U':  Upper triangle of A is stored;
        !            53: *>          = 'L':  Lower triangle of A is stored.
        !            54: *> \endverbatim
        !            55: *>
        !            56: *> \param[in] N
        !            57: *> \verbatim
        !            58: *>          N is INTEGER
        !            59: *>          The order of the matrix A.  N >= 0.
        !            60: *> \endverbatim
        !            61: *>
        !            62: *> \param[in,out] AP
        !            63: *> \verbatim
        !            64: *>          AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
        !            65: *>          On entry, the upper or lower triangle of the symmetric matrix
        !            66: *>          A, packed columnwise in a linear array.  The j-th column of A
        !            67: *>          is stored in the array AP as follows:
        !            68: *>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
        !            69: *>          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
        !            70: *>          See below for further details.
        !            71: *>
        !            72: *>          On exit, if INFO = 0, the triangular factor U or L from the
        !            73: *>          Cholesky factorization A = U**T*U or A = L*L**T, in the same
        !            74: *>          storage format as A.
        !            75: *> \endverbatim
        !            76: *>
        !            77: *> \param[out] INFO
        !            78: *> \verbatim
        !            79: *>          INFO is INTEGER
        !            80: *>          = 0:  successful exit
        !            81: *>          < 0:  if INFO = -i, the i-th argument had an illegal value
        !            82: *>          > 0:  if INFO = i, the leading minor of order i is not
        !            83: *>                positive definite, and the factorization could not be
        !            84: *>                completed.
        !            85: *> \endverbatim
        !            86: *
        !            87: *  Authors:
        !            88: *  ========
        !            89: *
        !            90: *> \author Univ. of Tennessee 
        !            91: *> \author Univ. of California Berkeley 
        !            92: *> \author Univ. of Colorado Denver 
        !            93: *> \author NAG Ltd. 
        !            94: *
        !            95: *> \date November 2011
        !            96: *
        !            97: *> \ingroup doubleOTHERcomputational
        !            98: *
        !            99: *> \par Further Details:
        !           100: *  =====================
        !           101: *>
        !           102: *> \verbatim
        !           103: *>
        !           104: *>  The packed storage scheme is illustrated by the following example
        !           105: *>  when N = 4, UPLO = 'U':
        !           106: *>
        !           107: *>  Two-dimensional storage of the symmetric matrix A:
        !           108: *>
        !           109: *>     a11 a12 a13 a14
        !           110: *>         a22 a23 a24
        !           111: *>             a33 a34     (aij = aji)
        !           112: *>                 a44
        !           113: *>
        !           114: *>  Packed storage of the upper triangle of A:
        !           115: *>
        !           116: *>  AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
        !           117: *> \endverbatim
        !           118: *>
        !           119: *  =====================================================================
1.1       bertrand  120:       SUBROUTINE DPPTRF( UPLO, N, AP, INFO )
                    121: *
1.9     ! bertrand  122: *  -- LAPACK computational routine (version 3.4.0) --
1.1       bertrand  123: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
                    124: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9     ! bertrand  125: *     November 2011
1.1       bertrand  126: *
                    127: *     .. Scalar Arguments ..
                    128:       CHARACTER          UPLO
                    129:       INTEGER            INFO, N
                    130: *     ..
                    131: *     .. Array Arguments ..
                    132:       DOUBLE PRECISION   AP( * )
                    133: *     ..
                    134: *
                    135: *  =====================================================================
                    136: *
                    137: *     .. Parameters ..
                    138:       DOUBLE PRECISION   ONE, ZERO
                    139:       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
                    140: *     ..
                    141: *     .. Local Scalars ..
                    142:       LOGICAL            UPPER
                    143:       INTEGER            J, JC, JJ
                    144:       DOUBLE PRECISION   AJJ
                    145: *     ..
                    146: *     .. External Functions ..
                    147:       LOGICAL            LSAME
                    148:       DOUBLE PRECISION   DDOT
                    149:       EXTERNAL           LSAME, DDOT
                    150: *     ..
                    151: *     .. External Subroutines ..
                    152:       EXTERNAL           DSCAL, DSPR, DTPSV, XERBLA
                    153: *     ..
                    154: *     .. Intrinsic Functions ..
                    155:       INTRINSIC          SQRT
                    156: *     ..
                    157: *     .. Executable Statements ..
                    158: *
                    159: *     Test the input parameters.
                    160: *
                    161:       INFO = 0
                    162:       UPPER = LSAME( UPLO, 'U' )
                    163:       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
                    164:          INFO = -1
                    165:       ELSE IF( N.LT.0 ) THEN
                    166:          INFO = -2
                    167:       END IF
                    168:       IF( INFO.NE.0 ) THEN
                    169:          CALL XERBLA( 'DPPTRF', -INFO )
                    170:          RETURN
                    171:       END IF
                    172: *
                    173: *     Quick return if possible
                    174: *
                    175:       IF( N.EQ.0 )
                    176:      $   RETURN
                    177: *
                    178:       IF( UPPER ) THEN
                    179: *
1.8       bertrand  180: *        Compute the Cholesky factorization A = U**T*U.
1.1       bertrand  181: *
                    182:          JJ = 0
                    183:          DO 10 J = 1, N
                    184:             JC = JJ + 1
                    185:             JJ = JJ + J
                    186: *
                    187: *           Compute elements 1:J-1 of column J.
                    188: *
                    189:             IF( J.GT.1 )
                    190:      $         CALL DTPSV( 'Upper', 'Transpose', 'Non-unit', J-1, AP,
                    191:      $                     AP( JC ), 1 )
                    192: *
                    193: *           Compute U(J,J) and test for non-positive-definiteness.
                    194: *
                    195:             AJJ = AP( JJ ) - DDOT( J-1, AP( JC ), 1, AP( JC ), 1 )
                    196:             IF( AJJ.LE.ZERO ) THEN
                    197:                AP( JJ ) = AJJ
                    198:                GO TO 30
                    199:             END IF
                    200:             AP( JJ ) = SQRT( AJJ )
                    201:    10    CONTINUE
                    202:       ELSE
                    203: *
1.8       bertrand  204: *        Compute the Cholesky factorization A = L*L**T.
1.1       bertrand  205: *
                    206:          JJ = 1
                    207:          DO 20 J = 1, N
                    208: *
                    209: *           Compute L(J,J) and test for non-positive-definiteness.
                    210: *
                    211:             AJJ = AP( JJ )
                    212:             IF( AJJ.LE.ZERO ) THEN
                    213:                AP( JJ ) = AJJ
                    214:                GO TO 30
                    215:             END IF
                    216:             AJJ = SQRT( AJJ )
                    217:             AP( JJ ) = AJJ
                    218: *
                    219: *           Compute elements J+1:N of column J and update the trailing
                    220: *           submatrix.
                    221: *
                    222:             IF( J.LT.N ) THEN
                    223:                CALL DSCAL( N-J, ONE / AJJ, AP( JJ+1 ), 1 )
                    224:                CALL DSPR( 'Lower', N-J, -ONE, AP( JJ+1 ), 1,
                    225:      $                    AP( JJ+N-J+1 ) )
                    226:                JJ = JJ + N - J + 1
                    227:             END IF
                    228:    20    CONTINUE
                    229:       END IF
                    230:       GO TO 40
                    231: *
                    232:    30 CONTINUE
                    233:       INFO = J
                    234: *
                    235:    40 CONTINUE
                    236:       RETURN
                    237: *
                    238: *     End of DPPTRF
                    239: *
                    240:       END

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