*nix Documentation Project
·  Home
 +   man pages
·  Linux HOWTOs
·  FreeBSD Tips
·  *niX Forums

  man pages->IRIX man pages -> complib/zgbsv (3)              
Title
Content
Arch
Section
 

Contents


ZGBSV(3F)							     ZGBSV(3F)


NAME    [Toc]    [Back]

     ZGBSV - compute the solution to a complex system of linear	equations A *
     X = B, where A is a band matrix of	order N	with KL	subdiagonals and KU
     superdiagonals, and X and B are N-by-NRHS matrices

SYNOPSIS    [Toc]    [Back]

     SUBROUTINE	ZGBSV( N, KL, KU, NRHS,	AB, LDAB, IPIV,	B, LDB,	INFO )

	 INTEGER       INFO, KL, KU, LDAB, LDB,	N, NRHS

	 INTEGER       IPIV( * )

	 COMPLEX*16    AB( LDAB, * ), B( LDB, *	)

PURPOSE    [Toc]    [Back]

     ZGBSV computes the	solution to a complex system of	linear equations A * X
     = B, where	A is a band matrix of order N with KL subdiagonals and KU
     superdiagonals, 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 =	L * U, where L is a product of permutation and unit
     lower triangular matrices with KL subdiagonals, and U is upper triangular
     with KL+KU	superdiagonals.	 The factored form of A	is then	used to	solve
     the system	of equations A * X = B.

ARGUMENTS    [Toc]    [Back]

     N	     (input) INTEGER
	     The number	of linear equations, i.e., the order of	the matrix A.
	     N >= 0.

     KL	     (input) INTEGER
	     The number	of subdiagonals	within the band	of A.  KL >= 0.

     KU	     (input) INTEGER
	     The number	of superdiagonals within the band of A.	 KU >= 0.

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

     AB	     (input/output) COMPLEX*16 array, dimension	(LDAB,N)
	     On	entry, the matrix A in band storage, in	rows KL+1 to
	     2*KL+KU+1;	rows 1 to KL of	the array need not be set.  The	j-th
	     column of A is stored in the j-th column of the array AB as
	     follows:  AB(KL+KU+1+i-j,j) = A(i,j) for max(1,jKU)<=i<=min(N,j+KL)
 On exit, details of the factorization:	U is
	     stored as an upper	triangular band	matrix with KL+KU
	     superdiagonals in rows 1 to KL+KU+1, and the multipliers used
	     during the	factorization are stored in rows KL+KU+2 to 2*KL+KU+1.
	     See below for further details.




									Page 1






ZGBSV(3F)							     ZGBSV(3F)



     LDAB    (input) INTEGER
	     The leading dimension of the array	AB.  LDAB >= 2*KL+KU+1.

     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) 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).

     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, and the
	     solution has not been computed.

FURTHER	DETAILS
     The band storage scheme is	illustrated by the following example, when M =
     N = 6, KL = 2, KU = 1:

     On	entry:			     On	exit:

	 *    *	   *	+    +	  +	  *    *    *	u14  u25  u36
	 *    *	   +	+    +	  +	  *    *   u13	u24  u35  u46
	 *   a12  a23  a34  a45	 a56	  *   u12  u23	u34  u45  u56
	a11  a22  a33  a44  a55	 a66	 u11  u22  u33	u44  u55  u66
	a21  a32  a43  a54  a65	  *	 m21  m32  m43	m54  m65   *
	a31  a42  a53  a64   *	  *	 m31  m42  m53	m64   *	   *

     Array elements marked * are not used by the routine; elements marked +
     need not be set on	entry, but are required	by the routine to store
     elements of U because of fill-in resulting	from the row interchanges.
ZGBSV(3F)							     ZGBSV(3F)


NAME    [Toc]    [Back]

     ZGBSV - compute the solution to a complex system of linear	equations A *
     X = B, where A is a band matrix of	order N	with KL	subdiagonals and KU
     superdiagonals, and X and B are N-by-NRHS matrices

SYNOPSIS    [Toc]    [Back]

     SUBROUTINE	ZGBSV( N, KL, KU, NRHS,	AB, LDAB, IPIV,	B, LDB,	INFO )

	 INTEGER       INFO, KL, KU, LDAB, LDB,	N, NRHS

	 INTEGER       IPIV( * )

	 COMPLEX*16    AB( LDAB, * ), B( LDB, *	)

PURPOSE    [Toc]    [Back]

     ZGBSV computes the	solution to a complex system of	linear equations A * X
     = B, where	A is a band matrix of order N with KL subdiagonals and KU
     superdiagonals, 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 =	L * U, where L is a product of permutation and unit
     lower triangular matrices with KL subdiagonals, and U is upper triangular
     with KL+KU	superdiagonals.	 The factored form of A	is then	used to	solve
     the system	of equations A * X = B.

ARGUMENTS    [Toc]    [Back]

     N	     (input) INTEGER
	     The number	of linear equations, i.e., the order of	the matrix A.
	     N >= 0.

     KL	     (input) INTEGER
	     The number	of subdiagonals	within the band	of A.  KL >= 0.

     KU	     (input) INTEGER
	     The number	of superdiagonals within the band of A.	 KU >= 0.

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

     AB	     (input/output) COMPLEX*16 array, dimension	(LDAB,N)
	     On	entry, the matrix A in band storage, in	rows KL+1 to
	     2*KL+KU+1;	rows 1 to KL of	the array need not be set.  The	j-th
	     column of A is stored in the j-th column of the array AB as
	     follows:  AB(KL+KU+1+i-j,j) = A(i,j) for max(1,jKU)<=i<=min(N,j+KL)
 On exit, details of the factorization:	U is
	     stored as an upper	triangular band	matrix with KL+KU
	     superdiagonals in rows 1 to KL+KU+1, and the multipliers used
	     during the	factorization are stored in rows KL+KU+2 to 2*KL+KU+1.
	     See below for further details.




									Page 1






ZGBSV(3F)							     ZGBSV(3F)



     LDAB    (input) INTEGER
	     The leading dimension of the array	AB.  LDAB >= 2*KL+KU+1.

     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) 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).

     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, and the
	     solution has not been computed.

FURTHER	DETAILS
     The band storage scheme is	illustrated by the following example, when M =
     N = 6, KL = 2, KU = 1:

     On	entry:			     On	exit:

	 *    *	   *	+    +	  +	  *    *    *	u14  u25  u36
	 *    *	   +	+    +	  +	  *    *   u13	u24  u35  u46
	 *   a12  a23  a34  a45	 a56	  *   u12  u23	u34  u45  u56
	a11  a22  a33  a44  a55	 a66	 u11  u22  u33	u44  u55  u66
	a21  a32  a43  a54  a65	  *	 m21  m32  m43	m54  m65   *
	a31  a42  a53  a64   *	  *	 m31  m42  m53	m64   *	   *

     Array elements marked * are not used by the routine; elements marked +
     need not be set on	entry, but are required	by the routine to store
     elements of U because of fill-in resulting	from the row interchanges.


									PPPPaaaaggggeeee 2222
[ Back ]
 Similar pages
Name OS Title
dgbsv IRIX compute the solution to a real system of linear equations A * X = B, where A is a band matrix of order N with
sgbsv IRIX compute the solution to a real system of linear equations A * X = B, where A is a band matrix of order N with
cppsvx IRIX compute the solution to a complex system of linear equations A * X = B,
zposvx IRIX compute the solution to a complex system of linear equations A * X = B,
zppsvx IRIX compute the solution to a complex system of linear equations A * X = B,
cposvx IRIX compute the solution to a complex system of linear equations A * X = B,
zpbsvx IRIX compute the solution to a complex system of linear equations A * X = B,
cpbsvx IRIX compute the solution to a complex system of linear equations A * X = B,
dposvx IRIX compute the solution to a real system of linear equations A * X = B,
spbsvx IRIX compute the solution to a real system of linear equations A * X = B,
Copyright © 2004-2005 DeniX Solutions SRL
newsletter delivery service