pcgbtrs(3) [debian man page]

PCGBTRS(l)						   LAPACK routine (version 1.5) 						PCGBTRS(l)

NAME

       PCGBTRS - solve a system of linear equations   A(1:N, JA:JA+N-1) * X = B(IB:IB+N-1, 1:NRHS)

SYNOPSIS

       SUBROUTINE PCGBTRS( TRANS, N, BWL, BWU, NRHS, A, JA, DESCA, IPIV, B, IB, DESCB, AF, LAF, WORK, LWORK, INFO )

	   CHARACTER	   TRANS

	   INTEGER	   BWU, BWL, IB, INFO, JA, LAF, LWORK, N, NRHS

	   INTEGER	   DESCA( * ), DESCB( * ), IPIV(*)

	   COMPLEX	   A( * ), AF( * ), B( * ), WORK( * )

PURPOSE

       PCGBTRS solves a system of linear equations
					 or
		 A(1:N, JA:JA+N-1)' * X = B(IB:IB+N-1, 1:NRHS)

       where A(1:N, JA:JA+N-1) is the matrix used to produce the factors stored in A(1:N,JA:JA+N-1) and AF by PCGBTRF.
       A(1:N, JA:JA+N-1) is an N-by-N complex
       banded distributed
       matrix with bandwidth BWL, BWU.

       Routine PCGBTRF MUST be called first.

LAPACK version 1.5						    12 May 1997 							PCGBTRS(l)

ZHESV(l)								 )								  ZHESV(l)

NAME

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

SYNOPSIS

       SUBROUTINE ZHESV( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO )

	   CHARACTER	 UPLO

	   INTEGER	 INFO, LDA, LDB, LWORK, N, NRHS

	   INTEGER	 IPIV( * )

	   COMPLEX*16	 A( LDA, * ), B( LDB, * ), WORK( * )

PURPOSE

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

       The diagonal pivoting method is used to factor A as
	  A = U * D * U**H,  if UPLO = 'U', or
	  A = L * D * L**H,  if UPLO = 'L',
       where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is Hermitian and block  diagonal  with  1-by-1
       and 2-by-2 diagonal blocks.  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) COMPLEX*16 array, dimension (LDA,N)
	       On  entry, the Hermitian 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 block diagonal matrix D and the multipliers used to obtain the factor U or L from the factorization A =
	       U*D*U**H or A = L*D*L**H as computed by ZHETRF.

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

       IPIV    (output) INTEGER array, dimension (N)
	       Details of the interchanges and the block structure of D, as determined by ZHETRF.  If IPIV(k) > 0, then rows  and  columns  k  and
	       IPIV(k) were interchanged, and D(k,k) is a 1-by-1 diagonal block.  If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and columns
	       k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) is a 2-by-2 diagonal block.  If UPLO = 'L' and IPIV(k) = IPIV(k+1) < 0,  then
	       rows and columns k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.

       B       (input/output) COMPLEX*16 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).

       WORK    (workspace/output) COMPLEX*16 array, dimension (LWORK)
	       On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

       LWORK   (input) INTEGER
	       The length of WORK.  LWORK >= 1, and for best performance LWORK >= N*NB, where NB is the optimal blocksize for ZHETRF.

	       If  LWORK  =  -1,  then	a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this
	       value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.

       INFO    (output) INTEGER
	       = 0: successful exit
	       < 0: if INFO = -i, the i-th argument had an illegal value
	       > 0: if INFO = i, D(i,i) is exactly zero.  The factorization has been completed, but the block diagonal matrix D is exactly  singu-
	       lar, so the solution could not be computed.

LAPACK version 3.0						   15 June 2000 							  ZHESV(l)