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man pages->IRIX man pages -> complib/CPPCO (3)
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### Contents

```
CPPCO(3F)							     CPPCO(3F)

```

### NAME[Toc][Back]

```     CPPCO   - CPPCO factors a complex Hermitian positive definite matrix
stored in packed form and estimates the condition of the matrix.

If	 RCOND	is not needed, CPPFA is	slightly faster.  To solve  A*X	= B ,
follow CPPCO by CPPSL.  To	compute	 INVERSE(A)*C ,	follow CPPCO by	CPPSL.
To	compute	 DETERMINANT(A)	, follow CPPCO by CPPDI.  To compute
INVERSE(A)	, follow CPPCO by CPPDI.

```

### SYNOPSYS[Toc][Back]

```      SUBROUTINE CPPCO(AP,N,RCOND,Z,INFO)
```

### DESCRIPTION[Toc][Back]

```     On	Entry

AP	COMPLEX	(N*(N+1)/2)
the packed form	of a Hermitian matrix  A .  The
columns	of the upper triangle are stored sequentially
in a one-dimensional array of length  N*(N+1)/2	.

N INTEGER
the order of the matrix	 A .  On Return

AP	an upper triangular matrix  R ,	stored in packed
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
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.	Packed Storage The following

Page 1

CPPCO(3F)							     CPPCO(3F)

program segment will pack the upper triangle of a Hermitian matrix.
K = 0
DO 20 J	= 1, N
DO 10 I	= 1, J
K = K +	1
AP(K) =	A(I,J)
10    CONTINUE
20 CONTINUE LINPACK.  This version dated 08/14/78 .  Cleve Moler,
University	of New Mexico, Argonne National	Lab.  Subroutines and
Functions LINPACK CPPFA BLAS CAXPY,CDOTC,CSSCAL,SCASUM Fortran
ABS,AIMAG,AMAX1,CMPLX,CONJG,REAL

PPPPaaaaggggeeee 2222```
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