1        2        3        4        5        6        7        8        9       10       11       12       13       14       15       16       17       18       19       20       21       22       23       24       25       26       27       28       29       30       31       32       33       34       35       36       37       38       39       40       41       42       43       44       45       46       47       48       49       50       51       52       53       54       55       56       57       58       59       60       61       62       63       64       65       66       67       68       69       70       71       72       73       74       75       76       77       78       79       80       81       82       83       84       85       86       87       88       89       90       91       92       93       94       95       96       97       98       99      100      101      102      103      104      105      106      107      108      109      110      111      112      113      114      115      116      117      118      119      120      121      122 SUBROUTINE DPOSV( UPLO, N, NRHS, A, LDA, B, LDB, INFO ) * *  -- LAPACK driver routine (version 3.3.1) -- *  -- LAPACK is a software package provided by Univ. of Tennessee,    -- *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- *  -- April 2011                                                      -- * *     .. Scalar Arguments ..       CHARACTER          UPLO       INTEGER            INFO, LDA, LDB, N, NRHS *     .. *     .. Array Arguments ..       DOUBLE PRECISION   A( LDA, * ), B( LDB, * ) *     .. * *  Purpose *  ======= * *  DPOSV computes the solution to a real system of linear equations *     A * X = B, *  where A is an N-by-N symmetric positive definite matrix and X and B *  are N-by-NRHS matrices. * *  The Cholesky decomposition is used to factor A as *     A = U**T* U,  if UPLO = 'U', or *     A = L * L**T,  if UPLO = 'L', *  where U is an upper triangular matrix and L is a lower triangular *  matrix.  The factored form of A is then used to solve the system of *  equations A * X = B. * *  Arguments *  ========= * *  UPLO    (input) CHARACTER*1 *          = 'U':  Upper triangle of A is stored; *          = 'L':  Lower triangle of A is stored. * *  N       (input) INTEGER *          The number of linear equations, i.e., the order of the *          matrix A.  N >= 0. * *  NRHS    (input) INTEGER *          The number of right hand sides, i.e., the number of columns *          of the matrix B.  NRHS >= 0. * *  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N) *          On entry, the symmetric matrix A.  If UPLO = 'U', the leading *          N-by-N upper triangular part of A contains the upper *          triangular part of the matrix A, and the strictly lower *          triangular part of A is not referenced.  If UPLO = 'L', the *          leading N-by-N lower triangular part of A contains the lower *          triangular part of the matrix A, and the strictly upper *          triangular part of A is not referenced. * *          On exit, if INFO = 0, the factor U or L from the Cholesky *          factorization A = U**T*U or A = L*L**T. * *  LDA     (input) INTEGER *          The leading dimension of the array A.  LDA >= max(1,N). * *  B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS) *          On entry, the N-by-NRHS right hand side matrix B. *          On exit, if INFO = 0, the N-by-NRHS solution matrix X. * *  LDB     (input) INTEGER *          The leading dimension of the array B.  LDB >= max(1,N). * *  INFO    (output) INTEGER *          = 0:  successful exit *          < 0:  if INFO = -i, the i-th argument had an illegal value *          > 0:  if INFO = i, the leading minor of order i of A is not *                positive definite, so the factorization could not be *                completed, and the solution has not been computed. * *  ===================================================================== * *     .. External Functions ..       LOGICAL            LSAME       EXTERNAL           LSAME *     .. *     .. External Subroutines ..       EXTERNAL           DPOTRF, DPOTRS, XERBLA *     .. *     .. Intrinsic Functions ..       INTRINSIC          MAX *     .. *     .. Executable Statements .. * *     Test the input parameters. *       INFO = 0       IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN          INFO = -1       ELSE IF( N.LT.0 ) THEN          INFO = -2       ELSE IF( NRHS.LT.0 ) THEN          INFO = -3       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN          INFO = -5       ELSE IF( LDB.LT.MAX( 1, N ) ) THEN          INFO = -7       END IF       IF( INFO.NE.0 ) THEN          CALL XERBLA( 'DPOSV ', -INFO )          RETURN       END IF * *     Compute the Cholesky factorization A = U**T*U or A = L*L**T. *       CALL DPOTRF( UPLO, N, A, LDA, INFO )       IF( INFO.EQ.0 ) THEN * *        Solve the system A*X = B, overwriting B with X. *          CALL DPOTRS( UPLO, N, NRHS, A, LDA, B, LDB, INFO ) *       END IF       RETURN * *     End of DPOSV *       END