LAPACK 3.3.1 Linear Algebra PACKage

# dppsv.f

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```00001       SUBROUTINE DPPSV( UPLO, N, NRHS, AP, B, LDB, INFO )
00002 *
00003 *  -- LAPACK driver routine (version 3.3.1) --
00004 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00005 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00006 *  -- April 2011                                                      --
00007 *
00008 *     .. Scalar Arguments ..
00009       CHARACTER          UPLO
00010       INTEGER            INFO, LDB, N, NRHS
00011 *     ..
00012 *     .. Array Arguments ..
00013       DOUBLE PRECISION   AP( * ), B( LDB, * )
00014 *     ..
00015 *
00016 *  Purpose
00017 *  =======
00018 *
00019 *  DPPSV computes the solution to a real system of linear equations
00020 *     A * X = B,
00021 *  where A is an N-by-N symmetric positive definite matrix stored in
00022 *  packed format and X and B are N-by-NRHS matrices.
00023 *
00024 *  The Cholesky decomposition is used to factor A as
00025 *     A = U**T* U,  if UPLO = 'U', or
00026 *     A = L * L**T,  if UPLO = 'L',
00027 *  where U is an upper triangular matrix and L is a lower triangular
00028 *  matrix.  The factored form of A is then used to solve the system of
00029 *  equations A * X = B.
00030 *
00031 *  Arguments
00032 *  =========
00033 *
00034 *  UPLO    (input) CHARACTER*1
00035 *          = 'U':  Upper triangle of A is stored;
00036 *          = 'L':  Lower triangle of A is stored.
00037 *
00038 *  N       (input) INTEGER
00039 *          The number of linear equations, i.e., the order of the
00040 *          matrix A.  N >= 0.
00041 *
00042 *  NRHS    (input) INTEGER
00043 *          The number of right hand sides, i.e., the number of columns
00044 *          of the matrix B.  NRHS >= 0.
00045 *
00046 *  AP      (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
00047 *          On entry, the upper or lower triangle of the symmetric matrix
00048 *          A, packed columnwise in a linear array.  The j-th column of A
00049 *          is stored in the array AP as follows:
00050 *          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
00051 *          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
00052 *          See below for further details.
00053 *
00054 *          On exit, if INFO = 0, the factor U or L from the Cholesky
00055 *          factorization A = U**T*U or A = L*L**T, in the same storage
00056 *          format as A.
00057 *
00058 *  B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
00059 *          On entry, the N-by-NRHS right hand side matrix B.
00060 *          On exit, if INFO = 0, the N-by-NRHS solution matrix X.
00061 *
00062 *  LDB     (input) INTEGER
00063 *          The leading dimension of the array B.  LDB >= max(1,N).
00064 *
00065 *  INFO    (output) INTEGER
00066 *          = 0:  successful exit
00067 *          < 0:  if INFO = -i, the i-th argument had an illegal value
00068 *          > 0:  if INFO = i, the leading minor of order i of A is not
00069 *                positive definite, so the factorization could not be
00070 *                completed, and the solution has not been computed.
00071 *
00072 *  Further Details
00073 *  ===============
00074 *
00075 *  The packed storage scheme is illustrated by the following example
00076 *  when N = 4, UPLO = 'U':
00077 *
00078 *  Two-dimensional storage of the symmetric matrix A:
00079 *
00080 *     a11 a12 a13 a14
00081 *         a22 a23 a24
00082 *             a33 a34     (aij = conjg(aji))
00083 *                 a44
00084 *
00085 *  Packed storage of the upper triangle of A:
00086 *
00087 *  AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
00088 *
00089 *  =====================================================================
00090 *
00091 *     .. External Functions ..
00092       LOGICAL            LSAME
00093       EXTERNAL           LSAME
00094 *     ..
00095 *     .. External Subroutines ..
00096       EXTERNAL           DPPTRF, DPPTRS, XERBLA
00097 *     ..
00098 *     .. Intrinsic Functions ..
00099       INTRINSIC          MAX
00100 *     ..
00101 *     .. Executable Statements ..
00102 *
00103 *     Test the input parameters.
00104 *
00105       INFO = 0
00106       IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
00107          INFO = -1
00108       ELSE IF( N.LT.0 ) THEN
00109          INFO = -2
00110       ELSE IF( NRHS.LT.0 ) THEN
00111          INFO = -3
00112       ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
00113          INFO = -6
00114       END IF
00115       IF( INFO.NE.0 ) THEN
00116          CALL XERBLA( 'DPPSV ', -INFO )
00117          RETURN
00118       END IF
00119 *
00120 *     Compute the Cholesky factorization A = U**T*U or A = L*L**T.
00121 *
00122       CALL DPPTRF( UPLO, N, AP, INFO )
00123       IF( INFO.EQ.0 ) THEN
00124 *
00125 *        Solve the system A*X = B, overwriting B with X.
00126 *
00127          CALL DPPTRS( UPLO, N, NRHS, AP, B, LDB, INFO )
00128 *
00129       END IF
00130       RETURN
00131 *
00132 *     End of DPPSV
00133 *
00134       END
```