dtrtrs(l) [redhat man page]

DTRTRS(l)								 )								 DTRTRS(l)

NAME

       DTRTRS - solve a triangular system of the form  A * X = B or A**T * X = B,

SYNOPSIS

       SUBROUTINE DTRTRS( UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, INFO )

	   CHARACTER	  DIAG, TRANS, UPLO

	   INTEGER	  INFO, LDA, LDB, N, NRHS

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

PURPOSE

       DTRTRS  solves  a triangular system of the form A * X = B or A**T * X = B, where A is a triangular matrix of order N, and B is an N-by-NRHS
       matrix.	A check is made to verify that A is nonsingular.

ARGUMENTS

       UPLO    (input) CHARACTER*1
	       = 'U':  A is upper triangular;
	       = 'L':  A is lower triangular.

       TRANS   (input) CHARACTER*1
	       Specifies the form of the system of equations:
	       = 'N':  A * X = B  (No transpose)
	       = 'T':  A**T * X = B  (Transpose)
	       = 'C':  A**H * X = B  (Conjugate transpose = Transpose)

       DIAG    (input) CHARACTER*1
	       = 'N':  A is non-unit triangular;
	       = 'U':  A is unit triangular.

       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 triangular matrix A.  If UPLO = 'U', the leading N-by-N upper triangular part of the array  A  contains  the  upper	triangular
	       matrix,	and the strictly lower triangular part of A is not referenced.	If UPLO = 'L', the leading N-by-N lower triangular part of
	       the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced.  If  DIAG  =  'U',
	       the diagonal elements of A are also not referenced and are assumed to be 1.

       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 right hand side matrix B.	On exit, if INFO = 0, 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
	       >  0: if INFO = i, the i-th diagonal element of A is zero, indicating that the matrix is singular and the solutions X have not been
	       computed.

LAPACK version 3.0						   15 June 2000 							 DTRTRS(l)

DTBTRS(l)								 )								 DTBTRS(l)

NAME

       DTBTRS - solve a triangular system of the form  A * X = B or A**T * X = B,

SYNOPSIS

       SUBROUTINE DTBTRS( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B, LDB, INFO )

	   CHARACTER	  DIAG, TRANS, UPLO

	   INTEGER	  INFO, KD, LDAB, LDB, N, NRHS

	   DOUBLE	  PRECISION AB( LDAB, * ), B( LDB, * )

PURPOSE

       DTBTRS  solves  a triangular system of the form A * X = B or A**T * X = B, where A is a triangular band matrix of order N, and B is an N-by
       NRHS matrix.  A check is made to verify that A is nonsingular.

ARGUMENTS

       UPLO    (input) CHARACTER*1
	       = 'U':  A is upper triangular;
	       = 'L':  A is lower triangular.

       TRANS   (input) CHARACTER*1
	       Specifies the form the system of equations:
	       = 'N':  A * X = B  (No transpose)
	       = 'T':  A**T * X = B  (Transpose)
	       = 'C':  A**H * X = B  (Conjugate transpose = Transpose)

       DIAG    (input) CHARACTER*1
	       = 'N':  A is non-unit triangular;
	       = 'U':  A is unit triangular.

       N       (input) INTEGER
	       The order of the matrix A.  N >= 0.

       KD      (input) INTEGER
	       The number of superdiagonals or subdiagonals of the triangular band matrix A.  KD >= 0.

       NRHS    (input) INTEGER
	       The number of right hand sides, i.e., the number of columns of the matrix B.  NRHS >= 0.

       AB      (input) DOUBLE PRECISION array, dimension (LDAB,N)
	       The upper or lower triangular band matrix A, stored in the first kd+1 rows of AB.  The j-th column of A is stored in the j-th  col-
	       umn  of	the  array  AB	as  follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j)	 =
	       A(i,j) for j<=i<=min(n,j+kd).  If DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be 1.

       LDAB    (input) INTEGER
	       The leading dimension of the array AB.  LDAB >= KD+1.

       B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
	       On entry, the right hand side matrix B.	On exit, if INFO = 0, 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
	       > 0:  if INFO = i, the i-th diagonal element of A is zero, indicating that the matrix is singular and the solutions X have not been
	       computed.

LAPACK version 3.0						   15 June 2000 							 DTBTRS(l)