·  Home
+   man pages
 -> Linux -> FreeBSD -> OpenBSD -> NetBSD -> Tru64 Unix -> HP-UX 11i -> IRIX
·  Linux HOWTOs
·  FreeBSD Tips
·  *niX Forums

man pages->IRIX man pages -> complib/cpteqr (3)
 Title
 Content
 Arch
 Section All Sections 1 - General Commands 2 - System Calls 3 - Subroutines 4 - Special Files 5 - File Formats 6 - Games 7 - Macros and Conventions 8 - Maintenance Commands 9 - Kernel Interface n - New Commands

### Contents

```
CPTEQR(3F)							    CPTEQR(3F)

```

### NAME[Toc][Back]

```     CPTEQR - compute all eigenvalues and, optionally, eigenvectors of a
symmetric positive	definite tridiagonal matrix by first factoring the
matrix using SPTTRF and then calling CBDSQR to compute the	singular
values of the bidiagonal factor
```

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	CPTEQR(	COMPZ, N, D, E,	Z, LDZ,	WORK, INFO )

CHARACTER	COMPZ

INTEGER	INFO, LDZ, N

REAL		D( * ),	E( * ),	WORK( *	)

COMPLEX	Z( LDZ,	* )
```

### PURPOSE[Toc][Back]

```     CPTEQR computes all eigenvalues and, optionally, eigenvectors of a
symmetric positive	definite tridiagonal matrix by first factoring the
matrix using SPTTRF and then calling CBDSQR to compute the	singular
values of the bidiagonal factor.

This routine computes the eigenvalues of the positive definite
tridiagonal matrix	to high	relative accuracy.  This means that if the
eigenvalues range over many orders	of magnitude in	size, then the small
eigenvalues and corresponding eigenvectors	will be	computed more
accurately	than, for example, with	the standard QR	method.

The eigenvectors of a full	or band	positive definite Hermitian matrix can
also be found if CHETRD, CHPTRD, or CHBTRD	has been used to reduce	this
matrix to tridiagonal form.  (The reduction to tridiagonal	form, however,
may preclude the possibility of obtaining high relative accuracy in the
small eigenvalues of the original matrix, if these	eigenvalues range over
many orders of magnitude.)

```

### ARGUMENTS[Toc][Back]

```     COMPZ   (input) CHARACTER*1
= 'N':  Compute eigenvalues only.
= 'V':  Compute eigenvectors of original Hermitian	matrix also.
Array Z contains the unitary matrix used to reduce	the original
matrix to tridiagonal form.  = 'I':  Compute eigenvectors of
tridiagonal matrix	also.

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

D	     (input/output) REAL array,	dimension (N)
On	entry, the n diagonal elements of the tridiagonal matrix.  On
normal exit, D contains the eigenvalues, in descending order.

Page 1

CPTEQR(3F)							    CPTEQR(3F)

E	     (input/output) REAL array,	dimension (N-1)
On	entry, the (n-1) subdiagonal elements of the tridiagonal
matrix.  On exit, E has been destroyed.

Z	     (input/output) COMPLEX array, dimension (LDZ, N)
On	entry, if COMPZ	= 'V', the unitary matrix used in the
reduction to tridiagonal form.  On	exit, if COMPZ = 'V', the
orthonormal eigenvectors of the original Hermitian	matrix;	if
COMPZ = 'I', the orthonormal eigenvectors of the tridiagonal
matrix.  If INFO >	0 on exit, Z contains the eigenvectors
associated	with only the stored eigenvalues.  If  COMPZ = 'N',
then Z is not referenced.

LDZ     (input) INTEGER
The leading dimension of the array	Z.  LDZ	>= 1, and if COMPZ =
'V' or 'I', LDZ >=	max(1,N).

WORK    (workspace) REAL array, dimension (LWORK)
If	 COMPZ = 'N', then LWORK = 2*N If  COMPZ = 'V' or 'I', then
LWORK = MAX(1,4*N-4)

INFO    (output) INTEGER
= 0:  successful exit.
< 0:  if INFO = -i, the i-th argument had an illegal value.
> 0:  if INFO = i,	and i is:  <= N	 the Cholesky factorization of
the matrix	could not be performed because the i-th	principal
minor was not positive definite.  > N   the SVD algorithm failed
to	converge; if INFO = N+i, i off-diagonal	elements of the
bidiagonal	factor did not converge	to zero.
CPTEQR(3F)							    CPTEQR(3F)

```

### NAME[Toc][Back]

```     CPTEQR - compute all eigenvalues and, optionally, eigenvectors of a
symmetric positive	definite tridiagonal matrix by first factoring the
matrix using SPTTRF and then calling CBDSQR to compute the	singular
values of the bidiagonal factor
```

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	CPTEQR(	COMPZ, N, D, E,	Z, LDZ,	WORK, INFO )

CHARACTER	COMPZ

INTEGER	INFO, LDZ, N

REAL		D( * ),	E( * ),	WORK( *	)

COMPLEX	Z( LDZ,	* )
```

### PURPOSE[Toc][Back]

```     CPTEQR computes all eigenvalues and, optionally, eigenvectors of a
symmetric positive	definite tridiagonal matrix by first factoring the
matrix using SPTTRF and then calling CBDSQR to compute the	singular
values of the bidiagonal factor.

This routine computes the eigenvalues of the positive definite
tridiagonal matrix	to high	relative accuracy.  This means that if the
eigenvalues range over many orders	of magnitude in	size, then the small
eigenvalues and corresponding eigenvectors	will be	computed more
accurately	than, for example, with	the standard QR	method.

The eigenvectors of a full	or band	positive definite Hermitian matrix can
also be found if CHETRD, CHPTRD, or CHBTRD	has been used to reduce	this
matrix to tridiagonal form.  (The reduction to tridiagonal	form, however,
may preclude the possibility of obtaining high relative accuracy in the
small eigenvalues of the original matrix, if these	eigenvalues range over
many orders of magnitude.)

```

### ARGUMENTS[Toc][Back]

```     COMPZ   (input) CHARACTER*1
= 'N':  Compute eigenvalues only.
= 'V':  Compute eigenvectors of original Hermitian	matrix also.
Array Z contains the unitary matrix used to reduce	the original
matrix to tridiagonal form.  = 'I':  Compute eigenvectors of
tridiagonal matrix	also.

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

D	     (input/output) REAL array,	dimension (N)
On	entry, the n diagonal elements of the tridiagonal matrix.  On
normal exit, D contains the eigenvalues, in descending order.

Page 1

CPTEQR(3F)							    CPTEQR(3F)

E	     (input/output) REAL array,	dimension (N-1)
On	entry, the (n-1) subdiagonal elements of the tridiagonal
matrix.  On exit, E has been destroyed.

Z	     (input/output) COMPLEX array, dimension (LDZ, N)
On	entry, if COMPZ	= 'V', the unitary matrix used in the
reduction to tridiagonal form.  On	exit, if COMPZ = 'V', the
orthonormal eigenvectors of the original Hermitian	matrix;	if
COMPZ = 'I', the orthonormal eigenvectors of the tridiagonal
matrix.  If INFO >	0 on exit, Z contains the eigenvectors
associated	with only the stored eigenvalues.  If  COMPZ = 'N',
then Z is not referenced.

LDZ     (input) INTEGER
The leading dimension of the array	Z.  LDZ	>= 1, and if COMPZ =
'V' or 'I', LDZ >=	max(1,N).

WORK    (workspace) REAL array, dimension (LWORK)
If	 COMPZ = 'N', then LWORK = 2*N If  COMPZ = 'V' or 'I', then
LWORK = MAX(1,4*N-4)

INFO    (output) INTEGER
= 0:  successful exit.
< 0:  if INFO = -i, the i-th argument had an illegal value.
> 0:  if INFO = i,	and i is:  <= N	 the Cholesky factorization of
the matrix	could not be performed because the i-th	principal
minor was not positive definite.  > N   the SVD algorithm failed
to	converge; if INFO = N+i, i off-diagonal	elements of the
bidiagonal	factor did not converge	to zero.

PPPPaaaaggggeeee 2222```
[ Back ]
Similar pages