dgesv(l) [redhat man page]

DGESV(l)								 )								  DGESV(l)

NAME

       DGESV - compute the solution to a real system of linear equations A * X = B,

SYNOPSIS

       SUBROUTINE DGESV( N, NRHS, A, LDA, IPIV, B, LDB, INFO )

	   INTEGER	 INFO, LDA, LDB, N, NRHS

	   INTEGER	 IPIV( * )

	   DOUBLE	 PRECISION A( LDA, * ), B( LDB, * )

PURPOSE

       DGESV computes the solution to a real system of linear equations A * X = B, where A is an N-by-N matrix and X and B are N-by-NRHS matrices.

       The LU decomposition with partial pivoting and row interchanges is used to factor A as
	  A = P * L * U,
       where  P  is a permutation matrix, L is unit lower triangular, and U is upper triangular.  The factored form of A is then used to solve the
       system of equations A * X = B.

ARGUMENTS

       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 N-by-N coefficient matrix A.  On exit, the factors L and U from the factorization A = P*L*U; the unit  diagonal  ele-
	       ments of L are not stored.

       LDA     (input) INTEGER
	       The leading dimension of the array A.  LDA >= max(1,N).

       IPIV    (output) INTEGER array, dimension (N)
	       The pivot indices that define the permutation matrix P; row i of the matrix was interchanged with row IPIV(i).

       B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
	       On entry, the N-by-NRHS matrix of 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, U(i,i) is exactly zero.	The factorization has been completed, but the factor U is exactly singular, so the
	       solution could not be computed.

LAPACK version 3.0						   15 June 2000 							  DGESV(l)

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DSYTRS(l)								 )								 DSYTRS(l)

NAME

       DSYTRS  -  solve  a  system of linear equations A*X = B with a real symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T
       computed by DSYTRF

SYNOPSIS

       SUBROUTINE DSYTRS( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )

	   CHARACTER	  UPLO

	   INTEGER	  INFO, LDA, LDB, N, NRHS

	   INTEGER	  IPIV( * )

	   DOUBLE	  PRECISION A( LDA, * ), B( LDB, * )

PURPOSE

       DSYTRS solves a system of linear equations A*X = B with a real symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T com-
       puted by DSYTRF.

ARGUMENTS

       UPLO    (input) CHARACTER*1
	       Specifies  whether  the	details of the factorization are stored as an upper or lower triangular matrix.  = 'U':  Upper triangular,
	       form is A = U*D*U**T;
	       = 'L':  Lower triangular, form is A = L*D*L**T.

       N       (input) INTEGER
	       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) DOUBLE PRECISION array, dimension (LDA,N)
	       The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by DSYTRF.

       LDA     (input) INTEGER
	       The leading dimension of the array A.  LDA >= max(1,N).

       IPIV    (input) INTEGER array, dimension (N)
	       Details of the interchanges and the block structure of D as determined by DSYTRF.

       B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
	       On entry, the right hand side matrix B.	On exit, the 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

LAPACK version 3.0						   15 June 2000 							 DSYTRS(l)

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