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Annotation of rpl/lapack/lapack/dppsv.f, revision 1.1

1.1     ! bertrand    1:       SUBROUTINE DPPSV( UPLO, N, NRHS, AP, B, LDB, INFO )
        !             2: *
        !             3: *  -- LAPACK driver routine (version 3.2) --
        !             4: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
        !             5: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
        !             6: *     November 2006
        !             7: *
        !             8: *     .. Scalar Arguments ..
        !             9:       CHARACTER          UPLO
        !            10:       INTEGER            INFO, LDB, N, NRHS
        !            11: *     ..
        !            12: *     .. Array Arguments ..
        !            13:       DOUBLE PRECISION   AP( * ), B( LDB, * )
        !            14: *     ..
        !            15: *
        !            16: *  Purpose
        !            17: *  =======
        !            18: *
        !            19: *  DPPSV computes the solution to a real system of linear equations
        !            20: *     A * X = B,
        !            21: *  where A is an N-by-N symmetric positive definite matrix stored in
        !            22: *  packed format and X and B are N-by-NRHS matrices.
        !            23: *
        !            24: *  The Cholesky decomposition is used to factor A as
        !            25: *     A = U**T* U,  if UPLO = 'U', or
        !            26: *     A = L * L**T,  if UPLO = 'L',
        !            27: *  where U is an upper triangular matrix and L is a lower triangular
        !            28: *  matrix.  The factored form of A is then used to solve the system of
        !            29: *  equations A * X = B.
        !            30: *
        !            31: *  Arguments
        !            32: *  =========
        !            33: *
        !            34: *  UPLO    (input) CHARACTER*1
        !            35: *          = 'U':  Upper triangle of A is stored;
        !            36: *          = 'L':  Lower triangle of A is stored.
        !            37: *
        !            38: *  N       (input) INTEGER
        !            39: *          The number of linear equations, i.e., the order of the
        !            40: *          matrix A.  N >= 0.
        !            41: *
        !            42: *  NRHS    (input) INTEGER
        !            43: *          The number of right hand sides, i.e., the number of columns
        !            44: *          of the matrix B.  NRHS >= 0.
        !            45: *
        !            46: *  AP      (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
        !            47: *          On entry, the upper or lower triangle of the symmetric matrix
        !            48: *          A, packed columnwise in a linear array.  The j-th column of A
        !            49: *          is stored in the array AP as follows:
        !            50: *          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
        !            51: *          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
        !            52: *          See below for further details.
        !            53: *
        !            54: *          On exit, if INFO = 0, the factor U or L from the Cholesky
        !            55: *          factorization A = U**T*U or A = L*L**T, in the same storage
        !            56: *          format as A.
        !            57: *
        !            58: *  B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
        !            59: *          On entry, the N-by-NRHS right hand side matrix B.
        !            60: *          On exit, if INFO = 0, the N-by-NRHS solution matrix X.
        !            61: *
        !            62: *  LDB     (input) INTEGER
        !            63: *          The leading dimension of the array B.  LDB >= max(1,N).
        !            64: *
        !            65: *  INFO    (output) INTEGER
        !            66: *          = 0:  successful exit
        !            67: *          < 0:  if INFO = -i, the i-th argument had an illegal value
        !            68: *          > 0:  if INFO = i, the leading minor of order i of A is not
        !            69: *                positive definite, so the factorization could not be
        !            70: *                completed, and the solution has not been computed.
        !            71: *
        !            72: *  Further Details
        !            73: *  ===============
        !            74: *
        !            75: *  The packed storage scheme is illustrated by the following example
        !            76: *  when N = 4, UPLO = 'U':
        !            77: *
        !            78: *  Two-dimensional storage of the symmetric matrix A:
        !            79: *
        !            80: *     a11 a12 a13 a14
        !            81: *         a22 a23 a24
        !            82: *             a33 a34     (aij = conjg(aji))
        !            83: *                 a44
        !            84: *
        !            85: *  Packed storage of the upper triangle of A:
        !            86: *
        !            87: *  AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
        !            88: *
        !            89: *  =====================================================================
        !            90: *
        !            91: *     .. External Functions ..
        !            92:       LOGICAL            LSAME
        !            93:       EXTERNAL           LSAME
        !            94: *     ..
        !            95: *     .. External Subroutines ..
        !            96:       EXTERNAL           DPPTRF, DPPTRS, XERBLA
        !            97: *     ..
        !            98: *     .. Intrinsic Functions ..
        !            99:       INTRINSIC          MAX
        !           100: *     ..
        !           101: *     .. Executable Statements ..
        !           102: *
        !           103: *     Test the input parameters.
        !           104: *
        !           105:       INFO = 0
        !           106:       IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
        !           107:          INFO = -1
        !           108:       ELSE IF( N.LT.0 ) THEN
        !           109:          INFO = -2
        !           110:       ELSE IF( NRHS.LT.0 ) THEN
        !           111:          INFO = -3
        !           112:       ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
        !           113:          INFO = -6
        !           114:       END IF
        !           115:       IF( INFO.NE.0 ) THEN
        !           116:          CALL XERBLA( 'DPPSV ', -INFO )
        !           117:          RETURN
        !           118:       END IF
        !           119: *
        !           120: *     Compute the Cholesky factorization A = U'*U or A = L*L'.
        !           121: *
        !           122:       CALL DPPTRF( UPLO, N, AP, INFO )
        !           123:       IF( INFO.EQ.0 ) THEN
        !           124: *
        !           125: *        Solve the system A*X = B, overwriting B with X.
        !           126: *
        !           127:          CALL DPPTRS( UPLO, N, NRHS, AP, B, LDB, INFO )
        !           128: *
        !           129:       END IF
        !           130:       RETURN
        !           131: *
        !           132: *     End of DPPSV
        !           133: *
        !           134:       END