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laic1(3) LAPACK laic1(3)

NAME

laic1 - laic1: condition estimate, step in gelsy

SYNOPSIS

Functions


subroutine claic1 (job, j, x, sest, w, gamma, sestpr, s, c)
CLAIC1 applies one step of incremental condition estimation. subroutine dlaic1 (job, j, x, sest, w, gamma, sestpr, s, c)
DLAIC1 applies one step of incremental condition estimation. subroutine slaic1 (job, j, x, sest, w, gamma, sestpr, s, c)
SLAIC1 applies one step of incremental condition estimation. subroutine zlaic1 (job, j, x, sest, w, gamma, sestpr, s, c)
ZLAIC1 applies one step of incremental condition estimation.

Detailed Description

Function Documentation

subroutine claic1 (integer job, integer j, complex, dimension( j ) x, real sest, complex, dimension( j ) w, complex gamma, real sestpr, complex s, complex c)

CLAIC1 applies one step of incremental condition estimation.

Purpose:



 CLAIC1 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 CLAIC1 computes sestpr, s, c such that


 the vector


                 [ s*x ]


          xhat = [  c  ]


 is an approximate singular vector of


                 [ L      0  ]


          Lhat = [ w**H 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]**H and sestpr**2 is an eigenpair of the system


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


                                           [ conjg(gamma) ]


 where  alpha =  x**H*w.

Parameters

JOB 



          JOB is INTEGER


          = 1: an estimate for the largest singular value is computed.


          = 2: an estimate for the smallest singular value is computed.

J



          J is INTEGER


          Length of X and W

X



          X is COMPLEX array, dimension (J)


          The j-vector x.

SEST



          SEST is REAL


          Estimated singular value of j by j matrix L

W



          W is COMPLEX array, dimension (J)


          The j-vector w.

GAMMA



          GAMMA is COMPLEX


          The diagonal element gamma.

SESTPR



          SESTPR is REAL


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

S



          S is COMPLEX


          Sine needed in forming xhat.

C



          C is COMPLEX


          Cosine needed in forming xhat.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine dlaic1 (integer job, integer j, double precision, dimension( j ) x, double precision sest, double precision, dimension( j ) w, double precision gamma, double precision sestpr, double precision s, double precision c)

DLAIC1 applies one step of incremental condition estimation.

Purpose:



 DLAIC1 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 DLAIC1 computes sestpr, s, c such that


 the vector


                 [ s*x ]


          xhat = [  c  ]


 is an approximate singular vector of


                 [ L       0  ]


          Lhat = [ w**T 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]**T and sestpr**2 is an eigenpair of the system


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


                                           [ gamma ]


 where  alpha =  x**T*w.

Parameters

JOB 



          JOB is INTEGER


          = 1: an estimate for the largest singular value is computed.


          = 2: an estimate for the smallest singular value is computed.

J



          J is INTEGER


          Length of X and W

X



          X is DOUBLE PRECISION array, dimension (J)


          The j-vector x.

SEST



          SEST is DOUBLE PRECISION


          Estimated singular value of j by j matrix L

W



          W is DOUBLE PRECISION array, dimension (J)


          The j-vector w.

GAMMA



          GAMMA is DOUBLE PRECISION


          The diagonal element gamma.

SESTPR



          SESTPR is DOUBLE PRECISION


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

S



          S is DOUBLE PRECISION


          Sine needed in forming xhat.

C



          C is DOUBLE PRECISION


          Cosine needed in forming xhat.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine slaic1 (integer job, integer j, real, dimension( j ) x, real sest, real, dimension( j ) w, real gamma, real sestpr, real s, real c)

SLAIC1 applies one step of incremental condition estimation.

Purpose:



 SLAIC1 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 SLAIC1 computes sestpr, s, c such that


 the vector


                 [ s*x ]


          xhat = [  c  ]


 is an approximate singular vector of


                 [ L      0  ]


          Lhat = [ w**T 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]**T and sestpr**2 is an eigenpair of the system


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


                                           [ gamma ]


 where  alpha =  x**T*w.

Parameters

JOB 



          JOB is INTEGER


          = 1: an estimate for the largest singular value is computed.


          = 2: an estimate for the smallest singular value is computed.

J



          J is INTEGER


          Length of X and W

X



          X is REAL array, dimension (J)


          The j-vector x.

SEST



          SEST is REAL


          Estimated singular value of j by j matrix L

W



          W is REAL array, dimension (J)


          The j-vector w.

GAMMA



          GAMMA is REAL


          The diagonal element gamma.

SESTPR



          SESTPR is REAL


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

S



          S is REAL


          Sine needed in forming xhat.

C



          C is REAL


          Cosine needed in forming xhat.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine zlaic1 (integer job, integer j, complex*16, dimension( j ) x, double precision sest, complex*16, dimension( j ) w, complex*16 gamma, double precision sestpr, complex*16 s, complex*16 c)

ZLAIC1 applies one step of incremental condition estimation.

Purpose:



 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**H 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]**H and sestpr**2 is an eigenpair of the system


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


                                           [ conjg(gamma) ]


 where  alpha =  x**H * w.

Parameters

JOB 



          JOB is INTEGER


          = 1: an estimate for the largest singular value is computed.


          = 2: an estimate for the smallest singular value is computed.

J



          J is INTEGER


          Length of X and W

X



          X is COMPLEX*16 array, dimension (J)


          The j-vector x.

SEST



          SEST is DOUBLE PRECISION


          Estimated singular value of j by j matrix L

W



          W is COMPLEX*16 array, dimension (J)


          The j-vector w.

GAMMA



          GAMMA is COMPLEX*16


          The diagonal element gamma.

SESTPR



          SESTPR is DOUBLE PRECISION


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

S



          S is COMPLEX*16


          Sine needed in forming xhat.

C



          C is COMPLEX*16


          Cosine needed in forming xhat.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Author

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