CPBCO man page on IRIX

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CPBCO(3F)							     CPBCO(3F)

NAME
     CPBCO   - CPBCO factors a complex Hermitian positive definite matrix
     stored in band form and estimates the condition of the matrix.

     If	 RCOND	is not needed, CPBFA is slightly faster.  To solve  A*X = B ,
     follow CPBCO by CPBSL.  To compute	 INVERSE(A)*C , follow CPBCO by CPBSL.
     To compute	 DETERMINANT(A) , follow CPBCO by CPBDI.

SYNOPSYS
      SUBROUTINE CPBCO(ABD,LDA,N,M,RCOND,Z,INFO)

DESCRIPTION
     On Entry

     ABD COMPLEX(LDA, N)
	the matrix to be factored.  The columns of the upper
	triangle are stored in the columns of ABD and the
	diagonals of the upper triangle are stored in the
	rows of ABD .  See the comments below for details.

     LDA INTEGER
	the leading dimension of the array  ABD .
	LDA must be .GE. M + 1 .

     N INTEGER
	the order of the matrix	 A .

     M INTEGER
	the number of diagonals above the main diagonal.
	0 .LE. M .LT. N .  On Return

     ABD an upper triangular matrix  R , stored in band
	form, so that  A = CTRANS(R)*R .
	If  INFO .NE. 0 , the factorization is not complete.

     RCOND REAL
	an estimate of the reciprocal condition of  A .
	For the system	A*X = B , relative perturbations
	in  A  and  B  of size	EPSILON	 may cause
	relative perturbations in  X  of size  EPSILON/RCOND .
	If  RCOND  is so small that the logical expression
	1.0 + RCOND .EQ. 1.0
	is true, then  A  may be singular to working
	precision.  In particular,  RCOND  is zero  if
	exact singularity is detected or the estimate
	underflows.  If INFO .NE. 0 , RCOND is unchanged.

     Z COMPLEX(N)
	a work vector whose contents are usually unimportant.
	If  A  is singular to working precision, then  Z  is
	an approximate null vector in the sense that

									Page 1

CPBCO(3F)							     CPBCO(3F)

	NORM(A*Z) = RCOND*NORM(A)*NORM(Z) .
	If  INFO .NE. 0 , Z  is unchanged.

     INFO INTEGER
	= 0  for normal return.
	= K  signals an error condition.  The leading minor
	of order  K  is not positive definite.	Band Storage
	If  A  is a Hermitian positive definite band matrix,
	the following program segment will set up the input.
	M = (band width above diagonal)
	DO 20 J = 1, N
	I1 = MAX0(1, J-M)
	DO 10 I = I1, J
	K = I-J+M+1
	ABD(K,J) = A(I,J)
	10    CONTINUE
	20 CONTINUE
	This uses  M + 1  rows of  A , except for the  M by M
	upper left triangle, which is ignored.	Example:  If the original
     matrix is
	11 12 13  0  0	0
	12 22 23 24  0	0
	13 23 33 34 35	0
	0 24 34 44 45 46
	0  0 35 45 55 56
	0  0  0 46 56 66 then  N = 6 , M = 2  and  ABD	should contain
	*  * 13 24 35 46
	* 12 23 34 45 56
	11 22 33 44 55 66 LINPACK.  This version dated 08/14/78 .  Cleve
     Moler, University of New Mexico, Argonne National Lab.  Subroutines and
     Functions LINPACK CPBFA BLAS CAXPY,CDOTC,CSSCAL,SCASUM Fortran
     ABS,AIMAG,AMAX1,CMPLX,CONJG,MAX0,MIN0,REAL

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