1SPOSV(1)              LAPACK driver routine (version 3.1)             SPOSV(1)
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NAME

6       SPOSV - the solution to a real system of linear equations  A * X = B,
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SYNOPSIS

9       SUBROUTINE SPOSV( UPLO, N, NRHS, A, LDA, B, LDB, INFO )
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11           CHARACTER     UPLO
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13           INTEGER       INFO, LDA, LDB, N, NRHS
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15           REAL          A( LDA, * ), B( LDB, * )
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PURPOSE

18       SPOSV computes the solution to a real system of linear equations
19          A  *  X = B, where A is an N-by-N symmetric positive definite matrix
20       and X and B are N-by-NRHS matrices.
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22       The Cholesky decomposition is used to factor A as
23          A = U**T* U,  if UPLO = 'U', or
24          A = L * L**T,  if UPLO = 'L',
25       where U is an upper triangular matrix  and  L  is  a  lower  triangular
26       matrix.   The  factored  form  of A is then used to solve the system of
27       equations A * X = B.
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ARGUMENTS

31       UPLO    (input) CHARACTER*1
32               = 'U':  Upper triangle of A is stored;
33               = 'L':  Lower triangle of A is stored.
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35       N       (input) INTEGER
36               The number of linear equations, i.e., the order of  the  matrix
37               A.  N >= 0.
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39       NRHS    (input) INTEGER
40               The  number of right hand sides, i.e., the number of columns of
41               the matrix B.  NRHS >= 0.
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43       A       (input/output) REAL array, dimension (LDA,N)
44               On entry, the symmetric matrix A.  If UPLO = 'U',  the  leading
45               N-by-N upper triangular part of A contains the upper triangular
46               part of the matrix A, and the strictly lower triangular part of
47               A  is  not referenced.  If UPLO = 'L', the leading N-by-N lower
48               triangular part of A contains the lower triangular part of  the
49               matrix  A,  and  the strictly upper triangular part of A is not
50               referenced.
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52               On exit, if INFO = 0, the factor U or L from the Cholesky  fac‐
53               torization A = U**T*U or A = L*L**T.
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55       LDA     (input) INTEGER
56               The leading dimension of the array A.  LDA >= max(1,N).
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58       B       (input/output) REAL array, dimension (LDB,NRHS)
59               On  entry, the N-by-NRHS right hand side matrix B.  On exit, if
60               INFO = 0, the N-by-NRHS solution matrix X.
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62       LDB     (input) INTEGER
63               The leading dimension of the array B.  LDB >= max(1,N).
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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 completed,
70               and the solution has not been computed.
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74 LAPACK driver routine (version 3.N1o)vember 2006                        SPOSV(1)