?laic1

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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?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

mkl.fi

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, [sc]^T and sestpr² is an eigenpair of the system

where alpha = x^T*w .

For complex flavors, [sc]^H and sestpr² is an eigenpair of the system

where alpha = x^H*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.

Parent topic: LAPACK Auxiliary Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?laic1