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cpbsv(3P)		    Sun Performance Library		     cpbsv(3P)

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

SYNOPSIS
       SUBROUTINE CPBSV(UPLO, N, KD, NRHS, A, LDA, B, LDB, INFO)

       CHARACTER * 1 UPLO
       COMPLEX A(LDA,*), B(LDB,*)
       INTEGER N, KD, NRHS, LDA, LDB, INFO

       SUBROUTINE CPBSV_64(UPLO, N, KD, NRHS, A, LDA, B, LDB, INFO)

       CHARACTER * 1 UPLO
       COMPLEX A(LDA,*), B(LDB,*)
       INTEGER*8 N, KD, NRHS, LDA, LDB, INFO

   F95 INTERFACE
       SUBROUTINE PBSV(UPLO, [N], KD, [NRHS], A, [LDA], B, [LDB], [INFO])

       CHARACTER(LEN=1) :: UPLO
       COMPLEX, DIMENSION(:,:) :: A, B
       INTEGER :: N, KD, NRHS, LDA, LDB, INFO

       SUBROUTINE PBSV_64(UPLO, [N], KD, [NRHS], A, [LDA], B, [LDB],
	      [INFO])

       CHARACTER(LEN=1) :: UPLO
       COMPLEX, DIMENSION(:,:) :: A, B
       INTEGER(8) :: N, KD, NRHS, LDA, LDB, INFO

   C INTERFACE
       #include <sunperf.h>

       void cpbsv(char uplo, int n, int kd, int nrhs,  complex	*a,  int  lda,
		 complex *b, int ldb, int *info);

       void  cpbsv_64(char  uplo, long n, long kd, long nrhs, complex *a, long
		 lda, complex *b, long ldb, long *info);

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

       The Cholesky decomposition is used to factor A as
	  A = U**H * U,	 if UPLO = 'U', or
	  A = L * L**H,	 if UPLO = 'L',
       where U is an upper triangular band matrix, and L is a lower triangular
       band matrix, with the same number of superdiagonals or subdiagonals  as
       A.   The	 factored  form of A is then used to solve the system of equa‐
       tions A * X = B.

ARGUMENTS
       UPLO (input)
		 = 'U':	 Upper triangle of A is stored;
		 = 'L':	 Lower triangle of A is stored.

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

       KD (input)
		 The  number  of superdiagonals of the matrix A if UPLO = 'U',
		 or the number of subdiagonals if UPLO = 'L'.  KD >= 0.

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

       A (input/output)
		 On  entry,  the upper or lower triangle of the Hermitian band
		 matrix A, stored in the first KD+1 rows of the array.	The j-
		 th column of A is stored in the j-th column of the array A as
		 follows: if UPLO = 'U', A(KD+1+i-j,j) = A(i,j)	 for  max(1,j-
		 KD)<=i<=j;   if  UPLO	=  'L',	 A(1+i-j,j)	=  A(i,j)  for
		 j<=i<=min(N,j+KD).  See below for further details.

		 On exit, if INFO = 0, the triangular factor U or L  from  the
		 Cholesky  factorization  A = U**H*U or A = L*L**H of the band
		 matrix A, in the same storage format as A.

       LDA (input)
		 The leading dimension of the array A.	LDA >= KD+1.

       B (input/output)
		 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)
		 The leading dimension of the array B.	LDB >= max(1,N).

       INFO (output)
		 = 0:  successful exit
		 < 0:  if INFO = -i, the i-th argument had an illegal value
		 >  0:	 if INFO = i, the leading minor of order i of A is not
		 positive definite, so the factorization  could	 not  be  com‐
		 pleted, and the solution has not been computed.

FURTHER DETAILS
       The band storage scheme is illustrated by the following example, when N
       = 6, KD = 2, and UPLO = 'U':

       On entry:		       On exit:

	   *	*   a13	 a24  a35  a46	    *	 *   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

       Similarly, if UPLO = 'L' the format of A is as follows:

       On entry:		       On exit:

	  a11  a22  a33	 a44  a55  a66	   l11	l22  l33  l44  l55  l66
	  a21  a32  a43	 a54  a65   *	   l21	l32  l43  l54  l65   *
	  a31  a42  a53	 a64   *    *	   l31	l42  l53  l64	*    *

       Array elements marked * are not used by the routine.

				  6 Mar 2009			     cpbsv(3P)
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