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man pages->IRIX man pages -> complib/zlaic1 (3)
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### Contents

```
ZLAIC1(3F)							    ZLAIC1(3F)

```

### NAME[Toc][Back]

```     ZLAIC1 - applie one step of incremental condition estimation in its
simplest version
```

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	ZLAIC1(	JOB, J,	X, SEST, W, GAMMA, SESTPR, S, C	)

INTEGER	J, JOB

DOUBLE		PRECISION SEST,	SESTPR

COMPLEX*16	C, GAMMA, S

COMPLEX*16	W( J ),	X( J )
```

### PURPOSE[Toc][Back]

```     ZLAIC1 applies one	step of	incremental condition estimation in its
simplest version:

Let x, twonorm(x) = 1, be an approximate singular vector of an j-by-j
lower triangular matrix L,	such that
twonorm(L*x) = sest
Then ZLAIC1 computes sestpr, s, c such that
the vector
[ s*x ]
xhat = [	c  ]
is	an approximate singular	vector of
[ L     0	]
Lhat = [ w' gamma	]
in	the sense that
twonorm(Lhat*xhat) = sestpr.

Depending on JOB, an estimate for the largest or smallest singular	value
is	computed.

Note that [s c]' and sestpr**2 is an eigenpair of the system

diag(sest*sest, 0) + [alpha  gamma] * [ conjg(alpha) ]
[ conjg(gamma) ]

where  alpha =  conjg(x)'*w.

```

### ARGUMENTS[Toc][Back]

```     JOB     (input) INTEGER
= 1: an estimate for the largest singular value is	computed.
= 2: an estimate for the smallest singular	value is computed.

J	     (input) INTEGER
Length of X and W

Page 1

ZLAIC1(3F)							    ZLAIC1(3F)

X	     (input) COMPLEX*16	array, dimension (J)
The j-vector x.

SEST    (input) DOUBLE PRECISION
Estimated singular	value of j by j	matrix L

W	     (input) COMPLEX*16	array, dimension (J)
The j-vector w.

GAMMA   (input) COMPLEX*16
The diagonal element gamma.

SEDTPR  (output) DOUBLE PRECISION
Estimated singular	value of (j+1) by (j+1)	matrix Lhat.

S	     (output) COMPLEX*16
Sine needed in forming xhat.

C	     (output) COMPLEX*16
Cosine needed in forming xhat.
ZLAIC1(3F)							    ZLAIC1(3F)

```

### NAME[Toc][Back]

```     ZLAIC1 - applie one step of incremental condition estimation in its
simplest version
```

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	ZLAIC1(	JOB, J,	X, SEST, W, GAMMA, SESTPR, S, C	)

INTEGER	J, JOB

DOUBLE		PRECISION SEST,	SESTPR

COMPLEX*16	C, GAMMA, S

COMPLEX*16	W( J ),	X( J )
```

### PURPOSE[Toc][Back]

```     ZLAIC1 applies one	step of	incremental condition estimation in its
simplest version:

Let x, twonorm(x) = 1, be an approximate singular vector of an j-by-j
lower triangular matrix L,	such that
twonorm(L*x) = sest
Then ZLAIC1 computes sestpr, s, c such that
the vector
[ s*x ]
xhat = [	c  ]
is	an approximate singular	vector of
[ L     0	]
Lhat = [ w' gamma	]
in	the sense that
twonorm(Lhat*xhat) = sestpr.

Depending on JOB, an estimate for the largest or smallest singular	value
is	computed.

Note that [s c]' and sestpr**2 is an eigenpair of the system

diag(sest*sest, 0) + [alpha  gamma] * [ conjg(alpha) ]
[ conjg(gamma) ]

where  alpha =  conjg(x)'*w.

```

### ARGUMENTS[Toc][Back]

```     JOB     (input) INTEGER
= 1: an estimate for the largest singular value is	computed.
= 2: an estimate for the smallest singular	value is computed.

J	     (input) INTEGER
Length of X and W

Page 1

ZLAIC1(3F)							    ZLAIC1(3F)

X	     (input) COMPLEX*16	array, dimension (J)
The j-vector x.

SEST    (input) DOUBLE PRECISION
Estimated singular	value of j by j	matrix L

W	     (input) COMPLEX*16	array, dimension (J)
The j-vector w.

GAMMA   (input) COMPLEX*16
The diagonal element gamma.

SEDTPR  (output) DOUBLE PRECISION
Estimated singular	value of (j+1) by (j+1)	matrix Lhat.

S	     (output) COMPLEX*16
Sine needed in forming xhat.

C	     (output) COMPLEX*16
Cosine needed in forming xhat.

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