laic1(3) LAPACK laic1(3)

laic1 - laic1: condition estimate, step in gelsy


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.

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.

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.

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.

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.

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