·  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/ssptrd (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

```
SSPTRD(3F)							    SSPTRD(3F)

```

### NAME[Toc][Back]

```     SSPTRD - reduce a real symmetric matrix A stored in packed	form to
symmetric tridiagonal form	T by an	orthogonal similarity transformation
```

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	SSPTRD(	UPLO, N, AP, D,	E, TAU,	INFO )

CHARACTER	UPLO

INTEGER	INFO, N

REAL		AP( * ), D( * ), E( * ), TAU( *	)
```

### PURPOSE[Toc][Back]

```     SSPTRD reduces a real symmetric matrix A stored in	packed form to
symmetric tridiagonal form	T by an	orthogonal similarity transformation:
Q**T * A *	Q = T.

```

### ARGUMENTS[Toc][Back]

```     UPLO    (input) CHARACTER*1
= 'U':  Upper triangle of A is stored;
= 'L':  Lower triangle of A is stored.

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

AP	     (input/output) REAL array,	dimension (N*(N+1)/2)
On	entry, the upper or lower triangle of the symmetric matrix A,
packed columnwise in a linear array.  The j-th column of A	is
stored in the array AP as follows:	 if UPLO = 'U',	AP(i + (j1)*j/2)
= A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2*nj)/2)
= A(i,j) for	j<=i<=n.  On exit, if UPLO = 'U', the diagonal
and first superdiagonal of	A are overwritten by the corresponding
elements of the tridiagonal matrix	T, and the elements above the
first superdiagonal, with the array TAU, represent	the orthogonal
matrix Q as a product of elementary reflectors; if	UPLO = 'L',
the diagonal and first subdiagonal	of A are over- written by the
corresponding elements of the tridiagonal matrix T, and the
elements below the	first subdiagonal, with	the array TAU,
represent the orthogonal matrix Q as a product of elementary
reflectors. See Further Details.  D       (output)	REAL array,
dimension (N) The diagonal	elements of the	tridiagonal matrix T:
D(i) = A(i,i).

E	     (output) REAL array, dimension (N-1)
The off-diagonal elements of the tridiagonal matrix T:  E(i) =
A(i,i+1) if UPLO =	'U', E(i) = A(i+1,i) if	UPLO = 'L'.

TAU     (output) REAL array, dimension (N-1)
The scalar	factors	of the elementary reflectors (see Further
Details).

Page 1

SSPTRD(3F)							    SSPTRD(3F)

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value

FURTHER	DETAILS
If	UPLO = 'U', the	matrix Q is represented	as a product of	elementary
reflectors

Q = H(n-1) . . . H(2) H(1).

Each H(i) has the form

H(i) = I - tau * v * v'

where tau is a real scalar, and v is a real vector	with
v(i+1:n) =	0 and v(i) = 1;	v(1:i-1) is stored on exit in AP, overwriting
A(1:i-1,i+1), and tau is stored in	TAU(i).

If	UPLO = 'L', the	matrix Q is represented	as a product of	elementary
reflectors

Q = H(1) H(2) .	. . H(n-1).

Each H(i) has the form

H(i) = I - tau * v * v'

where tau is a real scalar, and v is a real vector	with
v(1:i) = 0	and v(i+1) = 1;	v(i+2:n) is stored on exit in AP, overwriting
A(i+2:n,i), and tau is stored in TAU(i).
SSPTRD(3F)							    SSPTRD(3F)

```

### NAME[Toc][Back]

```     SSPTRD - reduce a real symmetric matrix A stored in packed	form to
symmetric tridiagonal form	T by an	orthogonal similarity transformation
```

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	SSPTRD(	UPLO, N, AP, D,	E, TAU,	INFO )

CHARACTER	UPLO

INTEGER	INFO, N

REAL		AP( * ), D( * ), E( * ), TAU( *	)
```

### PURPOSE[Toc][Back]

```     SSPTRD reduces a real symmetric matrix A stored in	packed form to
symmetric tridiagonal form	T by an	orthogonal similarity transformation:
Q**T * A *	Q = T.

```

### ARGUMENTS[Toc][Back]

```     UPLO    (input) CHARACTER*1
= 'U':  Upper triangle of A is stored;
= 'L':  Lower triangle of A is stored.

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

AP	     (input/output) REAL array,	dimension (N*(N+1)/2)
On	entry, the upper or lower triangle of the symmetric matrix A,
packed columnwise in a linear array.  The j-th column of A	is
stored in the array AP as follows:	 if UPLO = 'U',	AP(i + (j1)*j/2)
= A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2*nj)/2)
= A(i,j) for	j<=i<=n.  On exit, if UPLO = 'U', the diagonal
and first superdiagonal of	A are overwritten by the corresponding
elements of the tridiagonal matrix	T, and the elements above the
first superdiagonal, with the array TAU, represent	the orthogonal
matrix Q as a product of elementary reflectors; if	UPLO = 'L',
the diagonal and first subdiagonal	of A are over- written by the
corresponding elements of the tridiagonal matrix T, and the
elements below the	first subdiagonal, with	the array TAU,
represent the orthogonal matrix Q as a product of elementary
reflectors. See Further Details.  D       (output)	REAL array,
dimension (N) The diagonal	elements of the	tridiagonal matrix T:
D(i) = A(i,i).

E	     (output) REAL array, dimension (N-1)
The off-diagonal elements of the tridiagonal matrix T:  E(i) =
A(i,i+1) if UPLO =	'U', E(i) = A(i+1,i) if	UPLO = 'L'.

TAU     (output) REAL array, dimension (N-1)
The scalar	factors	of the elementary reflectors (see Further
Details).

Page 1

SSPTRD(3F)							    SSPTRD(3F)

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value

FURTHER	DETAILS
If	UPLO = 'U', the	matrix Q is represented	as a product of	elementary
reflectors

Q = H(n-1) . . . H(2) H(1).

Each H(i) has the form

H(i) = I - tau * v * v'

where tau is a real scalar, and v is a real vector	with
v(i+1:n) =	0 and v(i) = 1;	v(1:i-1) is stored on exit in AP, overwriting
A(1:i-1,i+1), and tau is stored in	TAU(i).

If	UPLO = 'L', the	matrix Q is represented	as a product of	elementary
reflectors

Q = H(1) H(2) .	. . H(n-1).

Each H(i) has the form

H(i) = I - tau * v * v'

where tau is a real scalar, and v is a real vector	with
v(1:i) = 0	and v(i+1) = 1;	v(i+2:n) is stored on exit in AP, overwriting
A(i+2:n,i), and tau is stored in TAU(i).

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