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Annotation of rpl/lapack/lapack/dppsv.f, revision 1.4

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