laic1 - laic1: condition estimate, step in gelsy

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subroutineclaic1(integerjob,integerj,complex,dimension(j)x,realsest,complex,dimension(j)w,complexgamma,realsestpr,complexs,complexc)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. ParametersJOB 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. subroutinedlaic1(integerjob,integerj,doubleprecision,dimension(j)x,doubleprecisionsest,doubleprecision,dimension(j)w,doubleprecisiongamma,doubleprecisionsestpr,doubleprecisions,doubleprecisionc)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. ParametersJOB 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. subroutineslaic1(integerjob,integerj,real,dimension(j)x,realsest,real,dimension(j)w,realgamma,realsestpr,reals,realc)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. ParametersJOB 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. subroutinezlaic1(integerjob,integerj,complex*16,dimension(j)x,doubleprecisionsest,complex*16,dimension(j)w,complex*16gamma,doubleprecisionsestpr,complex*16s,complex*16c)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. ParametersJOB 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.

laic1 - laic1: condition estimate, step in gelsy

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.