?laic1

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

?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

slaic1 dlaic1 claic1 zlaic1

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

is an approximate singular vector of

(for complex flavors), or

(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 sestpr^{2} is an eigenpair of the system

where alpha = x^{T}*w .

For complex flavors, [sc]^{H} and sestpr^{2} 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 .

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?laic1

Syntax

Include Files

Description

Input Parameters

Output Parameters