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.

Definition at line 134 of file claic1.f.

  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.

Definition at line 133 of file dlaic1.f.

  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.

Definition at line 133 of file slaic1.f.

  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.

Definition at line 134 of file zlaic1.f.

Author

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