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---
:name: claic1
:md5sum: 22926ad0c8db95eafc17cf2632e11865
:category: :subroutine
:arguments:
- job:
:type: integer
:intent: input
- j:
:type: integer
:intent: input
- x:
:type: complex
:intent: input
:dims:
- j
- sest:
:type: real
:intent: input
- w:
:type: complex
:intent: input
:dims:
- j
- gamma:
:type: complex
:intent: input
- sestpr:
:type: real
:intent: output
- s:
:type: complex
:intent: output
- c:
:type: complex
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE CLAIC1( JOB, J, X, SEST, W, GAMMA, SESTPR, S, C )\n\n\
* Purpose\n\
* =======\n\
*\n\
* CLAIC1 applies one step of incremental condition estimation in\n\
* its simplest version:\n\
*\n\
* Let x, twonorm(x) = 1, be an approximate singular vector of an j-by-j\n\
* lower triangular matrix L, such that\n\
* twonorm(L*x) = sest\n\
* Then CLAIC1 computes sestpr, s, c such that\n\
* the vector\n\
* [ s*x ]\n\
* xhat = [ c ]\n\
* is an approximate singular vector of\n\
* [ L 0 ]\n\
* Lhat = [ w' gamma ]\n\
* in the sense that\n\
* twonorm(Lhat*xhat) = sestpr.\n\
*\n\
* Depending on JOB, an estimate for the largest or smallest singular\n\
* value is computed.\n\
*\n\
* Note that [s c]' and sestpr**2 is an eigenpair of the system\n\
*\n\
* diag(sest*sest, 0) + [alpha gamma] * [ conjg(alpha) ]\n\
* [ conjg(gamma) ]\n\
*\n\
* where alpha = conjg(x)'*w.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* JOB (input) INTEGER\n\
* = 1: an estimate for the largest singular value is computed.\n\
* = 2: an estimate for the smallest singular value is computed.\n\
*\n\
* J (input) INTEGER\n\
* Length of X and W\n\
*\n\
* X (input) COMPLEX array, dimension (J)\n\
* The j-vector x.\n\
*\n\
* SEST (input) REAL\n\
* Estimated singular value of j by j matrix L\n\
*\n\
* W (input) COMPLEX array, dimension (J)\n\
* The j-vector w.\n\
*\n\
* GAMMA (input) COMPLEX\n\
* The diagonal element gamma.\n\
*\n\
* SESTPR (output) REAL\n\
* Estimated singular value of (j+1) by (j+1) matrix Lhat.\n\
*\n\
* S (output) COMPLEX\n\
* Sine needed in forming xhat.\n\
*\n\
* C (output) COMPLEX\n\
* Cosine needed in forming xhat.\n\
*\n\n\
* =====================================================================\n\
*\n"
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