?laic1

Applies one step of incremental condition estimation.

Syntax

call slaic1( job, j, x, sest, w, gamma, sestpr, s, c )

call dlaic1( job, j, x, sest, w, gamma, sestpr, s, c )

call claic1( job, j, x, sest, w, gamma, sestpr, s, c )

call zlaic1( job, j, x, sest, w, gamma, sestpr, s, c )

Include Files

  • Fortran: mkl.fi
  • C: mkl.h

Description

The routine ?laic1 applies one step of incremental condition estimation in its simplest version.

Let x, ||x||2 = 1 (where ||a||2 denotes the 2-norm of a), be an approximate singular vector of an j-by-j lower triangular matrix L, such that

||L*x||2 = sest

Then ?laic1 computes sestpr, s, c such that the vector

Equation

is an approximate singular vector of

Equation (for complex flavors), or

Equation (for real flavors), in the sense that

||Lhat*xhat||2 = sestpr.

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

For real flavors, [s c]T and sestpr2 is an eigenpair of the system


Equation

where alpha = xT*w .

For complex flavors, [s c]H and sestpr2 is an eigenpair of the system


Equation

where alpha = xH*w.

Input Parameters

job

INTEGER.

If job =1, an estimate for the largest singular value is computed;

If job =2, an estimate for the smallest singular value is computed;

j

INTEGER. Length of x and w.

x, w

REAL for slaic1

DOUBLE PRECISION for dlaic1

COMPLEX for claic1

DOUBLE COMPLEX for zlaic1.

Arrays, dimension (j) each. Contain vectors x and w, respectively.

sest

REAL for slaic1/claic1;

DOUBLE PRECISION for dlaic1/zlaic1.

Estimated singular value of j-by-j matrix L.

gamma

REAL for slaic1

DOUBLE PRECISION for dlaic1

COMPLEX for claic1

DOUBLE COMPLEX for zlaic1.

The diagonal element gamma.

Output Parameters

sestpr

REAL for slaic1/claic1;

DOUBLE PRECISION for dlaic1/zlaic1.

Estimated singular value of (j+1)-by-(j+1) matrix Lhat.

s, c

REAL for slaic1

DOUBLE PRECISION for dlaic1

COMPLEX for claic1

DOUBLE COMPLEX for zlaic1.

Sine and cosine needed in forming xhat.

For more complete information about compiler optimizations, see our Optimization Notice.