Commit 28f92c594a81eaac6ca0356e682fb4b8247e81b3 - r-cran-rspectra

Update upstream source from tag 'upstream/0.16-0' Update to upstream version '0.16-0' with Debian dir 6d695e381397edde401e8eca191e4b25eec74355 Andreas Tille 4 years ago

15 changed file(s) with 454 addition(s) and 119 deletion(s). Raw diff Collapse all Expand all

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DESCRIPTION less more

0	0	Package: RSpectra
1	1	Type: Package
2	2	Title: Solvers for Large-Scale Eigenvalue and SVD Problems
3		Version: 0.15-0
4		Date: 2019-06-10
	3	Version: 0.16-0
	4	Date: 2019-11-29
5	5	Authors@R: c(
6	6	person("Yixuan", "Qiu", , "yixuan.qiu@cos.name", c("aut", "cre")),
7	7	person("Jiali", "Mei", , "vermouthmjl@gmail.com", "aut",

29	29	Suggests: knitr, rmarkdown, prettydoc
30	30	LinkingTo: Rcpp, RcppEigen (>= 0.3.3.3.0)
31	31	VignetteBuilder: knitr, rmarkdown
32		RoxygenNote: 6.1.1
	32	RoxygenNote: 7.0.1
33	33	NeedsCompilation: yes
34		Packaged: 2019-06-10 19:19:24 UTC; qyx
	34	Packaged: 2019-11-29 21:58:51 UTC; qyx
35	35	Author: Yixuan Qiu [aut, cre],
36	36	Jiali Mei [aut] (Function interface of matrix operation),
37	37	Gael Guennebaud [ctb] (Eigenvalue solvers from the 'Eigen' library),
38	38	Jitse Niesen [ctb] (Eigenvalue solvers from the 'Eigen' library)
39	39	Maintainer: Yixuan Qiu <yixuan.qiu@cos.name>
40	40	Repository: CRAN
41		Date/Publication: 2019-06-11 04:30:26 UTC
	41	Date/Publication: 2019-12-01 20:10:20 UTC

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MD5 less more

0		64e38fcfaf0f9f0c60bbfc15b2521f5e *DESCRIPTION
1		066198dddcf0e082af7228244693e6a2 *NAMESPACE
	0	2815c93b47bd698a6cd028f5ea736316 *DESCRIPTION
	1	ceb214b33967ce46ac0a3a0bdf011361 *NAMESPACE
2	2	19bddaedad91a3ee7958d32ce829b3c5 *R/00_eigs.R
3	3	785b9b56fb917aadeb2d4278fd0ef178 *R/10_eigs_real_gen.R
4	4	215cf2f3dc1f22bf6378406894234f65 *R/20_eigs_real_sym.R
5		92fdc023d9f1771b955d2f832052d450 *R/30_svds.R
6		c6bfcc347160b5d66f0042d87dbe5a4e *R/40_svds_real_gen.R
	5	e5e0e4e8cbe410887285c0633d4f747b *R/30_svds.R
	6	185fae5c2f0a1eb558581896ce40c6f5 *R/40_svds_real_gen.R
7	7	3a80c73444a81336ec1a924838d748be *R/50_svds_real_sym.R
8	8	7047695fa5e35fafda16b83090580cc2 *R/99_is_sym.R
9		ace7ca4f756f45c342b1f6779e1f3d14 *README.md
10		9accfcb1635633f15aa0335746602873 *build/vignette.rds
11		26f15ba975889deedad42e6639db5168 *inst/NEWS.Rd
12		4bb6a5bde3f5f1ef6b1b2e3e70be08af *inst/doc/introduction.R
	9	1d77e69e9064efd92c22edb7cdc2c40a *README.md
	10	067ef54f81c2c2969984ffcb16c21175 *build/vignette.rds
	11	398e3fb8b1484a81a704cec2a1ef40e8 *inst/NEWS.Rd
	12	16e57fc15a64b61bcae2048bd961e6ab *inst/doc/introduction.R
13	13	92e06cc7be8c5be22b1638d1fd6d910e *inst/doc/introduction.Rmd
14		2659b464d372824108c72a8ec21b23c4 *inst/doc/introduction.html
	14	3482da2e37fb84faf1bd7aead038f432 *inst/doc/introduction.html
15	15	d70daa579bd3ee753cdebdac648f92d3 *inst/examples/eigs.R
16	16	a0f17fa11721d2ce0405a8672f5d7da0 *inst/examples/svds.R
	17	05d7fca713184ac5d1331cdd0a8e8e83 *inst/examples/svds_center_scale.R
17	18	b7300312c9360e7267bca8270b52f419 *inst/include/GenEigs.h
18	19	650981a1be65fc9da700bb29f81211e4 *inst/include/RMatOp.h
19	20	c1ec511ed9f2d023966fe13e279e8e3f *inst/include/RMatOp/ComplexShift.h

37	38	bfd6b63364f6fafb4ce44fa457a11f8f *inst/include/RMatOp/RealShift_sym_dgeMatrix.h
38	39	8ee0c6f14f2be97a6ab6e4016fd97b27 *inst/include/RMatOp/RealShift_sym_matrix.h
39	40	aca1678f69741150309109a7f2a9e797 *inst/include/RMatOp/RealShift_sym_sparseMatrix.h
40		a851965dd3e2722de709115b49133f5c *inst/include/RMatOp/SVDOp.h
	41	cb4bd7ec6a327393fbc38493e39fc486 *inst/include/RMatOp/SVDOp.h
41	42	79fc58de48585d5bf7d353b19ef662ef *inst/include/RMatOp/SparseMatrixMapping.h
42	43	5faefa94a2f0333086ba4de93833e9e2 *inst/include/Spectra/GenEigsBase.h
43	44	1cdccb61bb9132e29d15872f0258d2ec *inst/include/Spectra/GenEigsComplexShiftSolver.h

76	77	4bc7cc8931ee9332d70c32f87e50ea1b *inst/include/Spectra/Util/TypeTraits.h
77	78	c8825d4727017d1d2c3226c768c717de *inst/include/SpectraC.h
78	79	92cf191e41211dc2b67d297f7a87be98 *inst/include/SymEigs.h
79		04268dcd682995d252a4f4bd2f8109ca *man/eigs.Rd
80		36fad5ca80c072eaddb34f4059590c97 *man/svds.Rd
	80	f0889c832fdf97754f1e03391e1c88ae *man/eigs.Rd
	81	e47b2ab616176bfc9cd03c6ef6977c02 *man/svds.Rd
81	82	2728f0d0ac13607bcc74c86edb4af036 *src/Makevars
82	83	2728f0d0ac13607bcc74c86edb4af036 *src/Makevars.win
83	84	cac08dfcd9ded333541cfd1daf55eb1f *src/eigs_gen.cpp

87	88	03b54ad755a5a36f149ed8b8eeac4616 *src/matops.h
88	89	97713c0a809dbb597ec08f5304bc5435 *src/matops_c.h
89	90	bd2524b8d6779f01c7d822ae39810d9f *src/register_routines.c
90		b3502d7569977cbb760e3371d6b7e1d0 *src/svds.cpp
	91	4701f97ce67cf7f077a68465899a4ff1 *src/svds.cpp
91	92	92e06cc7be8c5be22b1638d1fd6d910e *vignettes/introduction.Rmd

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NAMESPACE less more

0	0	import(Rcpp)
1	1	importClassesFrom(Matrix, dgeMatrix, dgCMatrix, dgRMatrix, dsyMatrix)
2		importMethodsFrom(Matrix, isSymmetric, dim, as.matrix, coerce)
	2	importMethodsFrom(Matrix, isSymmetric, dim, as.matrix, coerce, colMeans, colSums)
3	3
4	4	S3method(eigs, matrix)
5	5	S3method(eigs, dgeMatrix)

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R/30_svds.R less more

71	71	##' Default is \code{min(p, max(2*k+1, 20))}.}
72	72	##' \item{\code{tol}}{Precision parameter. Default is 1e-10.}
73	73	##' \item{\code{maxitr}}{Maximum number of iterations. Default is 1000.}
	74	##' \item{\code{center}}{Either a logical value (\code{TRUE}/\code{FALSE}), or a numeric
	75	##' vector of length \eqn{n}. If a vector \eqn{c} is supplied, then
	76	##' SVD is computed on the matrix \eqn{A - 1c'}{A - 1 * c'},
	77	##' in an implicit way without actually forming this matrix.
	78	##' \code{center = TRUE} has the same effect as
	79	##' \code{center = colMeans(A)}. Default is \code{FALSE}.}
	80	##' \item{\code{scale}}{Either a logical value (\code{TRUE}/\code{FALSE}), or a numeric
	81	##' vector of length \eqn{n}. If a vector \eqn{s} is supplied, then
	82	##' SVD is computed on the matrix \eqn{(A - 1c')S}{(A - 1 * c')S},
	83	##' where \eqn{c} is the centering vector and \eqn{S = diag(1/s)}.
	84	##' If \code{scale = TRUE}, then the vector \eqn{s} is computed as
	85	##' the column norm of \eqn{A - 1c'}{A - 1 * c'}.
	86	##' Default is \code{FALSE}.}
74	87	##' }
75	88	##'
76	89	##' @section Function Interface:

93	106	##' arguments can be passed in through the
94	107	##' \code{args} parameter. In \code{svds()}, user should also provide
95	108	##' the dimension of the implicit matrix through the argument \code{dim}.
	109	##'
	110	##' The function interface does not support the \code{center} and \code{scale} parameters
	111	##' in \code{opts}.
96	112	##'
97	113	##' @return A list with the following components:
98	114	##' \item{d}{A vector of the computed singular values.}

147	163	svds <- function(A, k, nu = k, nv = k, opts = list(), ...)
148	164	UseMethod("svds")
149	165
	166
	167
	168	## Use a symmetric solver if:
	169	## 1. A is symmetric
	170	## 2. center = FALSE, scale = FALSE (default) in opts
	171	use_sym_solver <- function(A, opts)
	172	{
	173	if(isTRUE(opts$center) \|\| is.numeric(opts$center) \|\|
	174	isTRUE(opts$scale) \|\| is.numeric(opts$scale))
	175	return(FALSE)
	176
	177	is_sym(A)
	178	}
	179
150	180	##' @rdname svds
151	181	##' @export
152	182	svds.matrix <- function(A, k, nu = k, nv = k, opts = list(), ...)
153	183	{
154		fun = if(is_sym(A)) svds_real_sym else svds_real_gen
	184	fun = if(use_sym_solver(A, opts)) svds_real_sym else svds_real_gen
155	185	fun(A, k, nu, nv, opts, mattype = "matrix")
156	186	}
157	187

159	189	##' @export
160	190	svds.dgeMatrix <- function(A, k, nu = k, nv = k, opts = list(), ...)
161	191	{
162		fun = if(is_sym(A)) svds_real_sym else svds_real_gen
	192	fun = if(use_sym_solver(A, opts)) svds_real_sym else svds_real_gen
163	193	fun(A, k, nu, nv, opts, mattype = "dgeMatrix")
164	194	}
165	195

167	197	##' @export
168	198	svds.dgCMatrix <- function(A, k, nu = k, nv = k, opts = list(), ...)
169	199	{
170		fun = if(is_sym(A)) svds_real_sym else svds_real_gen
	200	fun = if(use_sym_solver(A, opts)) svds_real_sym else svds_real_gen
171	201	fun(A, k, nu, nv, opts, mattype = "dgCMatrix")
172	202	}
173	203

175	205	##' @export
176	206	svds.dgRMatrix <- function(A, k, nu = k, nv = k, opts = list(), ...)
177	207	{
178		fun = if(is_sym(A)) svds_real_sym else svds_real_gen
	208	fun = if(use_sym_solver(A, opts)) svds_real_sym else svds_real_gen
179	209	fun(A, k, nu, nv, opts, mattype = "dgRMatrix")
180	210	}
181	211
182	212	##' @rdname svds
183	213	##' @export
184	214	svds.dsyMatrix <- function(A, k, nu = k, nv = k, opts = list(), ...)
185		svds_real_sym(A, k, nu, nv, opts, mattype = "dsyMatrix",
186		extra_args = list(use_lower = (A@uplo == "L")))
	215	{
	216	fun = if(use_sym_solver(A, opts)) svds_real_sym else svds_real_gen
	217	fun(A, k, nu, nv, opts, mattype = "dsyMatrix",
	218	extra_args = list(use_lower = (A@uplo == "L")))
	219	}
	220
187	221
188	222	##' @rdname svds
189	223	##' @export
190	224	svds.dsCMatrix <- function(A, k, nu = k, nv = k, opts = list(), ...)
191		svds_real_sym(A, k, nu, nv, opts, mattype = "sym_dgCMatrix",
192		extra_args = list(use_lower = (A@uplo == "L")))
	225	{
	226	fun = if(use_sym_solver(A, opts)) svds_real_sym else svds_real_gen
	227	fun(A, k, nu, nv, opts, mattype = "sym_dgCMatrix",
	228	extra_args = list(use_lower = (A@uplo == "L")))
	229	}
193	230
194	231	##' @rdname svds
195	232	##' @export
196	233	svds.dsRMatrix <- function(A, k, nu = k, nv = k, opts = list(), ...)
197		svds_real_sym(A, k, nu, nv, opts, mattype = "sym_dgRMatrix",
198		extra_args = list(use_lower = (A@uplo == "L")))
	234	{
	235	fun = if(use_sym_solver(A, opts)) svds_real_sym else svds_real_gen
	236	fun(A, k, nu, nv, opts, mattype = "sym_dgRMatrix",
	237	extra_args = list(use_lower = (A@uplo == "L")))
	238	}
199	239
200	240	##' @rdname svds
201	241	##' @export
202	242	svds.function <- function(A, k, nu = k, nv = k, opts = list(), ...,
203	243	Atrans, dim, args = NULL)
	244	{
	245	if(isTRUE(opts$center))
	246	stop("opts$center must be FALSE or a vector when A is a function")
	247	if(isTRUE(opts$scale))
	248	stop("opts$scale must be FALSE or a vector when A is a function")
	249
204	250	svds_real_gen(A, k, nu, nv, opts, mattype = "function",
205	251	extra_args = list(Atrans = Atrans,
206	252	dim = dim,
207	253	fun_args = args))
	254	}

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R/40_svds_real_gen.R less more

43	43	# Arguments to be passed to Spectra
44	44	spectra.param = list(ncv = min(wd, max(2 * k + 1, 20)),
45	45	tol = 1e-10,
46		maxitr = 1000)
	46	maxitr = 1000,
	47	center = FALSE,
	48	scale = FALSE)
	49	# By default center = FALSE and scale = FALSE
	50	ctr = rep(0, n)
	51	scl = rep(1, n)
	52
	53	# Update ctr and scl from opts
	54	# 1. If `center == TRUE`, then the centering vector is the column mean of A
	55	# 2. If `center` is a vector, then use this vector to center A
	56	# 3. In other cases, do not center A
	57	if (isTRUE(opts$center))
	58	{
	59	ctr = colMeans(A)
	60	} else if (is.numeric(opts$center)) {
	61	if (length(opts$center) != n)
	62	stop("opts$center must be TRUE/FALSE or a vector of length n")
	63
	64	ctr = as.numeric(opts$center)
	65	opts$center = TRUE
	66	} else {
	67	opts$center = FALSE
	68	}
	69	# Scaling is always applied to vectors after centering
	70	# 4. If `scale == TRUE`, then the scaling vector consists of the norms of column
	71	# vectors of A after centering
	72	# 5. If `scale` is a vector, then use this vector to scale A
	73	# 6. In other cases, do not scale A
	74	if (isTRUE(opts$scale))
	75	{
	76	sumx = colSums(A)
	77	sumxx = colSums(A^2)
	78	scl = sqrt(sumxx - 2 * sumx * ctr + m * ctr^2)
	79	} else if (is.numeric(opts$scale)) {
	80	if (length(opts$scale) != n)
	81	stop("opts$scale must be TRUE/FALSE or a vector of length n")
	82
	83	scl = as.numeric(opts$scale)
	84	opts$scale = TRUE
	85	} else {
	86	opts$scale = FALSE
	87	}
47	88
48	89	# Update parameters from 'opts' argument
49	90	spectra.param[names(opts)] = opts
50	91
51	92	# Any other arguments passed to C++ code
52		spectra.param = c(spectra.param, as.list(extra_args))
	93	spectra.param = c(spectra.param, as.list(extra_args),
	94	list(ctr_vec = ctr, scl_vec = scl))
53	95
54	96	# Check the value of 'ncv'
55	97	if (spectra.param$ncv <= k \| spectra.param$ncv > wd)

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README.md less more

0		## Solvers for Large Scale Eigenvalue and SVD Problems
	0	## Solvers for Large Scale Eigenvalue and SVD Problems <img src="https://statr.me/images/sticker-rspectra.png" alt="RSpectra" height="150px" align="right" />
1	1
2	2	### Introduction
3	3

build/vignette.rds less more

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inst/NEWS.Rd less more

0	0	\name{NEWS}
1	1	\title{News for Package "RSpectra"}
	2
	3	\section{Changes in RSpectra version 0.16-0}{
	4	\subsection{NEW FEATURES}{
	5	\itemize{
	6	\item \code{svds()} now supports implicit centering and scaling of the matrix
	7	via the \code{center} and \code{scale} parameters in the \code{opts}
	8	argument, suggested by \href{https://github.com/robmaz}{@robmaz}
	9	(\href{https://github.com/yixuan/spectra/issues/73}{#73} of Spectra).
	10	}
	11	}
	12	}
2	13
3	14	\section{Changes in RSpectra version 0.15-0}{
4	15	\subsection{NEW FEATURES}{

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inst/doc/introduction.R less more

0		## ------------------------------------------------------------------------
	0	## -----------------------------------------------------------------------------
1	1	set.seed(123)
2	2	n = 100 # matrix size
3	3	k = 5 # number of eigenvalues to calculate

9	9	head(eigen(A)$values, 5)
10	10	head(eigen(A)$vectors[, 1:5])
11	11
12		## ------------------------------------------------------------------------
	12	## -----------------------------------------------------------------------------
13	13	library(RSpectra)
14	14	res = eigs_sym(A, k, which = "LM") # "LM" is the default
15	15	res$values
16	16	head(res$vectors)
17	17
18		## ------------------------------------------------------------------------
	18	## -----------------------------------------------------------------------------
19	19	eigs_sym(A, k, opts = list(retvec = FALSE))
20	20
21		## ------------------------------------------------------------------------
	21	## -----------------------------------------------------------------------------
22	22	library(Matrix)
23	23	Msp = as(M, "dgCMatrix")
24	24	Asp = as(A, "dgRMatrix")

26	26	eigs(Msp, k, which = "LR", opts = list(retvec = FALSE))$values # largest real part
27	27	eigs_sym(Asp, k, opts = list(retvec = FALSE))$values
28	28
29		## ------------------------------------------------------------------------
	29	## -----------------------------------------------------------------------------
30	30	# Implicitly define the matrix by a function that calculates A %*% x
31	31	# Below represents a diagonal matrix whose elements are stored in the `args` parameter
32	32	f = function(x, args)

36	36	}
37	37	eigs_sym(f, k = 3, n = 10, args = 1:10)
38	38
39		## ------------------------------------------------------------------------
	39	## -----------------------------------------------------------------------------
40	40	eigs_sym(A, k, which = "LM", sigma = 0)$values # recommended way
41	41	eigs_sym(A, k, which = "SM")$values # not recommended
42	42
43		## ------------------------------------------------------------------------
	43	## -----------------------------------------------------------------------------
44	44	set.seed(123)
45	45	m = 100
46	46	n = 20

49	49
50	50	str(svds(A, k, nu = k, nv = k))
51	51
52		## ------------------------------------------------------------------------
	52	## -----------------------------------------------------------------------------
53	53	Asp = as(A, "dgCMatrix")
54	54	svds(Asp, k, nu = 0, nv = 0)
55	55
56		## ------------------------------------------------------------------------
	56	## -----------------------------------------------------------------------------
57	57	Af = function(x, args) as.numeric(args %*% x)
58	58	Atransf = function(x, args) as.numeric(crossprod(args, x))
59	59	str(svds(Af, k, Atrans = Atransf, dim = c(m, n), args = Asp))

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inst/doc/introduction.html less more

3	3
4	4	<head>
5	5
6		<meta charset="utf-8">
	6	<meta charset="utf-8" />
7	7	<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
8	8	<meta name="generator" content="pandoc" />
	9	<meta http-equiv="X-UA-Compatible" content="IE=EDGE" />
9	10
10	11	<meta name="viewport" content="width=device-width, initial-scale=1">
11	12
12	13	<meta name="author" content="Yixuan Qiu" />
13	14
14		<meta name="date" content="2019-06-10" />
	15	<meta name="date" content="2019-11-29" />
15	16
16	17	<title>Large-Scale Eigenvalue Decomposition and SVD with RSpectra</title>
17	18
18	19
19	20
20	21	<style type="text/css">code{white-space: pre;}</style>
21		<style type="text/css">
	22	<style type="text/css" data-origin="pandoc">
22	23	a.sourceLine { display: inline-block; line-height: 1.25; }
23	24	a.sourceLine { pointer-events: none; color: inherit; text-decoration: inherit; }
24	25	a.sourceLine:empty { height: 1.2em; }

80	81	code span.va { color: #19177c; } /* Variable */
81	82	code span.vs { color: #4070a0; } /* VerbatimString */
82	83	code span.wa { color: #60a0b0; font-weight: bold; font-style: italic; } /* Warning */
	84
	85	/* A workaround for https://github.com/jgm/pandoc/issues/4278 */
	86	a.sourceLine {
	87	pointer-events: auto;
	88	}
	89
83	90	</style>
	91	<script>
	92	// apply pandoc div.sourceCode style to pre.sourceCode instead
	93	(function() {
	94	var sheets = document.styleSheets;
	95	for (var i = 0; i < sheets.length; i++) {
	96	if (sheets[i].ownerNode.dataset["origin"] !== "pandoc") continue;
	97	try { var rules = sheets[i].cssRules; } catch (e) { continue; }
	98	for (var j = 0; j < rules.length; j++) {
	99	var rule = rules[j];
	100	// check if there is a div.sourceCode rule
	101	if (rule.type !== rule.STYLE_RULE \|\| rule.selectorText !== "div.sourceCode") continue;
	102	var style = rule.style.cssText;
	103	// check if color or background-color is set
	104	if (rule.style.color === '' && rule.style.backgroundColor === '') continue;
	105	// replace div.sourceCode by a pre.sourceCode rule
	106	sheets[i].deleteRule(j);
	107	sheets[i].insertRule('pre.sourceCode{' + style + '}', j);
	108	}
	109	}
	110	})();
	111	</script>
84	112
85	113
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99	131	</head>
100	132

106	138	<section class="page-header">
107	139	<h1 class="title toc-ignore project-name">Large-Scale Eigenvalue Decomposition and SVD with RSpectra</h1>
108	140	<h4 class="author project-author">Yixuan Qiu</h4>
109		<h4 class="date project-date">2019-06-10</h4>
	141	<h4 class="date project-date">2019-11-29</h4>
110	142	</section>
111	143
112	144

183	215	<a class="sourceLine" id="cb11-3" data-line-number="3">Asp =<span class="st"> </span><span class="kw">as</span>(A, <span class="st">"dgRMatrix"</span>)</a>
184	216	<a class="sourceLine" id="cb11-4" data-line-number="4"></a>
185	217	<a class="sourceLine" id="cb11-5" data-line-number="5"><span class="kw">eigs</span>(Msp, k, <span class="dt">which =</span> <span class="st">"LR"</span>, <span class="dt">opts =</span> <span class="kw">list</span>(<span class="dt">retvec =</span> <span class="ot">FALSE</span>))<span class="op">$</span>values <span class="co"># largest real part</span></a></code></pre></div>
186		<pre><code>## [1] 9.685399-1.964917i 9.685399+1.964917i 9.696766+0.000000i
187		## [4] 8.270271+1.751652i 8.270271-1.751652i</code></pre>
	218	<pre><code>## [1] 9.685399-1.964917i 9.685399+1.964917i 9.696766+0.000000i 8.270271+1.751652i
	219	## [5] 8.270271-1.751652i</code></pre>
188	220	<div class="sourceCode" id="cb13"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb13-1" data-line-number="1"><span class="kw">eigs_sym</span>(Asp, k, <span class="dt">opts =</span> <span class="kw">list</span>(<span class="dt">retvec =</span> <span class="ot">FALSE</span>))<span class="op">$</span>values</a></code></pre></div>
189	221	<pre><code>## [1] 391.3649 367.1143 353.5425 322.6301 315.4341</code></pre>
190	222	<p>An even more general way to specify the matrix <code>A</code> is to define a function that calculates <code>A %*% x</code> for any vector <code>x</code>. This representation is called the <strong>Function Interface</strong>, which can also be regarded as a sparse format, since users do not need to store the matrix <code>A</code>, but only the operator <code>x -> Ax</code>. For example, to represent a diagonal matrix <span class="math inline">$diag(1, 2, \ldots, 10)$</span> and calculate its eigenvalues, we can define the function <code>f</code> and call the <code>eigs_sym()</code> function:</p>

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inst/examples/svds_center_scale.R less more

	0	library(RSpectra)
	1	library(Matrix)
	2	n = 100
	3	p = 50
	4	k = 5
	5
	6	## Set up the test matrix
	7	set.seed(123)
	8	x = matrix(rnorm(n * p), n)
	9	x[sample(n * p, floor(n * p / 2))] = 0
	10
	11	## Test whether the calculated (d, u, v) are consistent with svd()
	12	## Return the largest residual
	13	svd_resid = function(res, svd0)
	14	{
	15	d_resid = svd0$d[1:length(res$d)] - res$d
	16	u_resid = v_resid = 0
	17	if(!is.null(res$u))
	18	u_resid = abs(svd0$u[, 1:ncol(res$u)]) - abs(res$u)
	19	if(!is.null(res$v))
	20	v_resid = abs(svd0$v[, 1:ncol(res$v)]) - abs(res$v)
	21	mabs = function(x) max(abs(x))
	22	maxerr = max(mabs(d_resid), mabs(u_resid), mabs(v_resid))
	23	return(paste("residual <", format(maxerr, digits = 5)))
	24	}
	25
	26	## Different matrix types
	27	x1 = x
	28	x2 = as(x, "dgeMatrix")
	29	x3 = as(x, "dgCMatrix")
	30	x4 = as(x, "dgRMatrix")
	31
	32	## Regular mode
	33	svd0 = svd(x)
	34	res1 = svds(x1, k)
	35	res2 = svds(x2, k)
	36	res3 = svds(x3, k)
	37	res4 = svds(x4, k)
	38	svd_resid(res1, svd0)
	39	svd_resid(res2, svd0)
	40	svd_resid(res3, svd0)
	41	svd_resid(res4, svd0)
	42
	43	## Center x
	44	xc = sweep(x, 2, colMeans(x), "-")
	45	svd0 = svd(xc)
	46	res1 = svds(x1, k, opts = list(center = TRUE))
	47	res2 = svds(x2, k, opts = list(center = TRUE))
	48	res3 = svds(x3, k, opts = list(center = TRUE))
	49	res4 = svds(x4, k, opts = list(center = TRUE))
	50	svd_resid(res1, svd0)
	51	svd_resid(res2, svd0)
	52	svd_resid(res3, svd0)
	53	svd_resid(res4, svd0)
	54
	55	## Scale x
	56	xs = sweep(x, 2, sqrt(colSums(x^2)), "/")
	57	svd0 = svd(xs)
	58	res1 = svds(x1, k, opts = list(scale = TRUE))
	59	res2 = svds(x2, k, opts = list(scale = TRUE))
	60	res3 = svds(x3, k, opts = list(scale = TRUE))
	61	res4 = svds(x4, k, opts = list(scale = TRUE))
	62	svd_resid(res1, svd0)
	63	svd_resid(res2, svd0)
	64	svd_resid(res3, svd0)
	65	svd_resid(res4, svd0)
	66
	67	## Center and scale x
	68	xcs = sweep(xc, 2, sqrt(colSums(xc^2)), "/")
	69	svd0 = svd(xcs)
	70	res1 = svds(x1, k, opts = list(center = TRUE, scale = TRUE))
	71	res2 = svds(x2, k, opts = list(center = TRUE, scale = TRUE))
	72	res3 = svds(x3, k, opts = list(center = TRUE, scale = TRUE))
	73	res4 = svds(x4, k, opts = list(center = TRUE, scale = TRUE))
	74	svd_resid(res1, svd0)
	75	svd_resid(res2, svd0)
	76	svd_resid(res3, svd0)
	77	svd_resid(res4, svd0)
	78
	79	## Center and scale with given vectors
	80	ctr = rnorm(p)
	81	scl = abs(rnorm(p))
	82	y = sweep(x, 2, ctr, "-")
	83	y = sweep(y, 2, scl, "/")
	84	svd0 = svd(y)
	85	res1 = svds(x1, k, opts = list(center = ctr, scale = scl))
	86	res2 = svds(x2, k, opts = list(center = ctr, scale = scl))
	87	res3 = svds(x3, k, opts = list(center = ctr, scale = scl))
	88	res4 = svds(x4, k, opts = list(center = ctr, scale = scl))
	89	svd_resid(res1, svd0)
	90	svd_resid(res2, svd0)
	91	svd_resid(res3, svd0)
	92	svd_resid(res4, svd0)

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inst/include/RMatOp/SVDOp.h less more

0	0	#ifndef SVDOP_H
1	1	#define SVDOP_H
2	2
	3	#include <RcppEigen.h>
3	4	#include <algorithm>
4	5	#include "MatProd.h"
5	6
6	7	class SVDTallOp: public MatProd
7	8	{
8	9	private:
9		MatProd* op;
10		const int dim;
11		double* work;
	10	typedef Eigen::VectorXd Vector;
	11	typedef Eigen::Map<const Vector> MapConstVec;
	12	typedef Eigen::Map<Vector> MapVec;
	13
	14	MatProd* op;
	15	const int nrow;
	16	const int ncol;
	17	const int dim;
	18
	19	const bool center;
	20	const bool scale;
	21	MapConstVec ctr_vec;
	22	MapConstVec scl_vec;
	23
	24	Vector workm;
	25	Vector workn;
12	26	public:
13		SVDTallOp(MatProd* op_) :
14		op(op_),
15		dim(std::min(op->rows(), op->cols())),
16		work(new double[op->rows()])
	27	SVDTallOp(MatProd* op_, bool center_, bool scale_,
	28	const MapConstVec& ctr_vec_, const MapConstVec& scl_vec_) :
	29	op(op_), nrow(op->rows()), ncol(op->cols()), dim(ncol),
	30	center(center_), scale(scale_),
	31	ctr_vec(ctr_vec_.data(), ctr_vec_.size()),
	32	scl_vec(scl_vec_.data(), scl_vec_.size()),
	33	workm(nrow), workn(ncol)
17	34	{}
18	35
19		~SVDTallOp()
20		{
21		delete [] work;
22		}
23
	36	// Number of rows and columns of the operator B'B, not of B itself
24	37	int rows() const { return dim; }
25	38	int cols() const { return dim; }
26	39
27		// y_out = A'A * x_in
	40	// y_out = B'B * x_in
	41	// B = (A - 1c')S, c = ctr_vec, S = diag(1 / scl_vec)
	42	// Bv = A * (Sv) - (c'Sv) * 1
	43	// B'v = S(A'v) - S((1'v)c)
28	44	void perform_op(const double* x_in, double* y_out)
29	45	{
30		op->perform_op (x_in, work);
31		op->perform_tprod(work, y_out);
	46	// No centering or scaling
	47	if(!(center \|\| scale))
	48	{
	49	op->perform_op (x_in, workm.data());
	50	op->perform_tprod(workm.data(), y_out);
	51	} else {
	52	// Sv = v / s
	53	workn.noalias() = MapConstVec(x_in, ncol).cwiseQuotient(scl_vec);
	54	// A * (Sv)
	55	op->perform_op(workn.data(), workm.data());
	56	// A * (Sv) - (c'Sv) * 1
	57	workm.array() -= ctr_vec.dot(workn);
	58
	59	// A'v
	60	op->perform_tprod(workm.data(), workn.data());
	61	// A'v - (1'v)c
	62	workn.noalias() -= workm.sum() * ctr_vec;
	63	// S(A'v) - S((1'v)c)
	64	MapVec(y_out, ncol).array() = workn.array() / scl_vec.array();
	65	}
32	66	}
33	67
34	68	void perform_tprod(const double* x_in, double* y_out)

40	74	class SVDWideOp: public MatProd
41	75	{
42	76	private:
43		MatProd* op;
44		const int dim;
45		double* work;
	77	typedef Eigen::VectorXd Vector;
	78	typedef Eigen::Map<const Vector> MapConstVec;
	79	typedef Eigen::Map<Vector> MapVec;
	80
	81	MatProd* op;
	82	const int nrow;
	83	const int ncol;
	84	const int dim;
	85
	86	const bool center;
	87	const bool scale;
	88	MapConstVec ctr_vec;
	89	MapConstVec scl_vec;
	90
	91	Vector workm;
	92	Vector workn;
46	93	public:
47		SVDWideOp(MatProd* op_) :
48		op(op_),
49		dim(std::min(op->rows(), op->cols())),
50		work(new double[op->cols()])
	94	SVDWideOp(MatProd* op_, bool center_, bool scale_,
	95	const MapConstVec& ctr_vec_, const MapConstVec& scl_vec_) :
	96	op(op_), nrow(op->rows()), ncol(op->cols()), dim(nrow),
	97	center(center_), scale(scale_),
	98	ctr_vec(ctr_vec_.data(), ctr_vec_.size()),
	99	scl_vec(scl_vec_.data(), scl_vec_.size()),
	100	workm(nrow), workn(ncol)
51	101	{}
52	102
53		~SVDWideOp()
54		{
55		delete [] work;
56		}
57
	103	// Number of rows and columns of the operator BB', not of B itself
58	104	int rows() const { return dim; }
59	105	int cols() const { return dim; }
60	106
61		// y_out = AA' * x_in
	107	// y_out = BB' * x_in
	108	// B = (A - 1c')S, c = ctr_vec, S = diag(1 / scl_vec)
	109	// B'v = S(A'v) - S((1'v)c)
	110	// Bv = A * (Sv) - (c'Sv) * 1
62	111	void perform_op(const double* x_in, double* y_out)
63	112	{
64		op->perform_tprod(x_in, work);
65		op->perform_op (work, y_out);
	113	if(!(center \|\| scale))
	114	{
	115	op->perform_tprod(x_in, workn.data());
	116	op->perform_op(workn.data(), y_out);
	117	} else {
	118	// A'v
	119	op->perform_tprod(x_in, workn.data());
	120	// A'v - (1'v)c
	121	workn.noalias() -= MapConstVec(x_in, nrow).sum() * ctr_vec;
	122	// S( S(A'v) - S((1'v)c) ) = S^2(A'v - (1'v)c)
	123	workn.array() /= scl_vec.array().square();
	124
	125	// A * (Sv)
	126	op->perform_op(workn.data(), y_out);
	127	// A * (Sv) - (c'Sv) * 1
	128	MapVec(y_out, nrow).array() -= ctr_vec.dot(workn);
	129	}
66	130	}
67	131
68	132	void perform_tprod(const double* x_in, double* y_out)

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man/eigs.Rd less more

15	15	\usage{
16	16	eigs(A, k, which = "LM", sigma = NULL, opts = list(), ...)
17	17
18		\method{eigs}{matrix}(A, k, which = "LM", sigma = NULL,
19		opts = list(), ...)
20
21		\method{eigs}{dgeMatrix}(A, k, which = "LM", sigma = NULL,
22		opts = list(), ...)
23
24		\method{eigs}{dsyMatrix}(A, k, which = "LM", sigma = NULL,
25		opts = list(), ...)
26
27		\method{eigs}{dgCMatrix}(A, k, which = "LM", sigma = NULL,
28		opts = list(), ...)
29
30		\method{eigs}{dsCMatrix}(A, k, which = "LM", sigma = NULL,
31		opts = list(), ...)
32
33		\method{eigs}{dgRMatrix}(A, k, which = "LM", sigma = NULL,
34		opts = list(), ...)
35
36		\method{eigs}{dsRMatrix}(A, k, which = "LM", sigma = NULL,
37		opts = list(), ...)
38
39		\method{eigs}{function}(A, k, which = "LM", sigma = NULL,
40		opts = list(), ..., n = NULL, args = NULL)
	18	\method{eigs}{matrix}(A, k, which = "LM", sigma = NULL, opts = list(), ...)
	19
	20	\method{eigs}{dgeMatrix}(A, k, which = "LM", sigma = NULL, opts = list(), ...)
	21
	22	\method{eigs}{dsyMatrix}(A, k, which = "LM", sigma = NULL, opts = list(), ...)
	23
	24	\method{eigs}{dgCMatrix}(A, k, which = "LM", sigma = NULL, opts = list(), ...)
	25
	26	\method{eigs}{dsCMatrix}(A, k, which = "LM", sigma = NULL, opts = list(), ...)
	27
	28	\method{eigs}{dgRMatrix}(A, k, which = "LM", sigma = NULL, opts = list(), ...)
	29
	30	\method{eigs}{dsRMatrix}(A, k, which = "LM", sigma = NULL, opts = list(), ...)
	31
	32	\method{eigs}{`function`}(
	33	A,
	34	k,
	35	which = "LM",
	36	sigma = NULL,
	37	opts = list(),
	38	...,
	39	n = NULL,
	40	args = NULL
	41	)
41	42
42	43	eigs_sym(A, k, which = "LM", sigma = NULL, opts = list(),
43	44	lower = TRUE, ...)
44	45
45		\method{eigs_sym}{function}(A, k, which = "LM", sigma = NULL,
46		opts = list(), lower = TRUE, ..., n = NULL, args = NULL)
	46	\method{eigs_sym}{`function`}(
	47	A,
	48	k,
	49	which = "LM",
	50	sigma = NULL,
	51	opts = list(),
	52	lower = TRUE,
	53	...,
	54	n = NULL,
	55	args = NULL
	56	)
47	57	}
48	58	\arguments{
49	59	\item{A}{The matrix whose eigenvalues/vectors are to be computed.

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man/svds.Rd less more

27	27
28	28	\method{svds}{dsRMatrix}(A, k, nu = k, nv = k, opts = list(), ...)
29	29
30		\method{svds}{function}(A, k, nu = k, nv = k, opts = list(), ...,
31		Atrans, dim, args = NULL)
	30	\method{svds}{`function`}(A, k, nu = k, nv = k, opts = list(), ..., Atrans, dim, args = NULL)
32	31	}
33	32	\arguments{
34	33	\item{A}{The matrix whose truncated SVD is to be computed.}

125	124	Default is \code{min(p, max(2*k+1, 20))}.}
126	125	\item{\code{tol}}{Precision parameter. Default is 1e-10.}
127	126	\item{\code{maxitr}}{Maximum number of iterations. Default is 1000.}
	127	\item{\code{center}}{Either a logical value (\code{TRUE}/\code{FALSE}), or a numeric
	128	vector of length \eqn{n}. If a vector \eqn{c} is supplied, then
	129	SVD is computed on the matrix \eqn{A - 1c'}{A - 1 * c'},
	130	in an implicit way without actually forming this matrix.
	131	\code{center = TRUE} has the same effect as
	132	\code{center = colMeans(A)}. Default is \code{FALSE}.}
	133	\item{\code{scale}}{Either a logical value (\code{TRUE}/\code{FALSE}), or a numeric
	134	vector of length \eqn{n}. If a vector \eqn{s} is supplied, then
	135	SVD is computed on the matrix \eqn{(A - 1c')S}{(A - 1 * c')S},
	136	where \eqn{c} is the centering vector and \eqn{S = diag(1/s)}.
	137	If \code{scale = TRUE}, then the vector \eqn{s} is computed as
	138	the column norm of \eqn{A - 1c'}{A - 1 * c'}.
	139	Default is \code{FALSE}.}
128	140	}
129	141	}
130	142	\section{Function Interface}{

148	160	arguments can be passed in through the
149	161	\code{args} parameter. In \code{svds()}, user should also provide
150	162	the dimension of the implicit matrix through the argument \code{dim}.
	163
	164	The function interface does not support the \code{center} and \code{scale} parameters
	165	in \code{opts}.
151	166	}
152	167
153	168	\examples{

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src/svds.cpp less more

91	91	{
92	92	BEGIN_RCPP
93	93
	94	typedef Eigen::Map<const Eigen::VectorXd> MapConstVec;
	95	typedef Eigen::Map<Eigen::MatrixXd> MapMat;
	96
94	97	Rcpp::List params_svds(params_list_r);
95	98
96	99	int m = as<int>(m_scalar_r);

101	104	int ncv = as<int>(params_svds["ncv"]);
102	105	double tol = as<double>(params_svds["tol"]);
103	106	int maxitr = as<int>(params_svds["maxitr"]);
	107	bool center = as<bool>(params_svds["center"]);
	108	bool scale = as<bool>(params_svds["scale"]);
104	109	int mattype = as<int>(mattype_scalar_r);
	110
	111	Rcpp::NumericVector ctr_vec = params_svds["ctr_vec"];
	112	Rcpp::NumericVector scl_vec = params_svds["scl_vec"];
	113	MapConstVec ctr_map(ctr_vec.begin(), n);
	114	MapConstVec scl_map(scl_vec.begin(), n);
105	115
106	116	// Operation for original matrix
107	117	MatProd* op_orig = get_mat_prod_op(A_mat_r, m, n, params_list_r, mattype);
108	118	// Operation for SVD
109	119	MatProd* op;
110	120	if(m > n)
111		op = new SVDTallOp(op_orig);
	121	op = new SVDTallOp(op_orig, center, scale, ctr_map, scl_map);
112	122	else
113		op = new SVDWideOp(op_orig);
	123	op = new SVDWideOp(op_orig, center, scale, ctr_map, scl_map);
114	124
115	125	SymEigsSolver<double, LARGEST_ALGE, MatProd> eigs(op, k, ncv);
116	126	eigs.init();

126	136
127	137	Rcpp::NumericVector d(nconv);
128	138	Rcpp::NumericMatrix u(m, nu), v(n, nv);
	139	MapMat umap = as<MapMat>(u);
	140	MapMat vmap = as<MapMat>(v);
129	141	int nops = 0;
130	142
131	143	// Copy evals to d and take the square root

142	154	// Calculate the other one
143	155	if(m > n)
144	156	{
145		// A = UDV', A'A = VD^2V', AV = UD, ui = A * vi / di
	157	// B = (A - 1c')S, S = diag(1 / s)
	158	// B = UDV', B'B = VD^2V', BV = UD, ui = B * vi / di
	159	// B * x = A * (Sx) - (c'Sx) * 1
	160	// B * vi / di = A * (vi / s / di) - c'(vi / s / di) * 1
146	161	// evecs has already been copied to v, so we can overwrite evecs
147	162	for(int i = 0; i < nu; i++)
148	163	{
149		evecs.col(i) /= d[i];
	164	evecs.col(i).array() /= (d[i] * scl_map).array();
150	165	op_orig->perform_op(&evecs(0, i), &u(0, i));
	166	umap.col(i).array() -= ctr_map.dot(evecs.col(i));
151	167	nops++;
152	168	}
153	169	} else {
154		// A = UDV', AA' = UD^2U', A'U = VD, vi = A' * ui / di
	170	// B = (A - 1c')S, S = diag(1 / s)
	171	// B = UDV', BB' = UD^2U', B'U = VD, vi = B' * ui / di
	172	// B' * x = S(A' * x) - S(c(1'x))
	173	// B' * ui / di = (A' * (ui / di)) / s - 1'(ui / di) * c / s
155	174	// evecs has already been copied to u, so we can overwrite evecs
156	175	for(int i = 0; i < nv; i++)
157	176	{
158		evecs.col(i) /= d[i];
159	177	op_orig->perform_tprod(&evecs(0, i), &v(0, i));
	178	vmap.col(i).array() -= evecs.col(i).sum() * ctr_map.array();
	179	vmap.col(i).array() /= (d[i] * scl_map.array());
160	180	nops++;
161	181	}
162	182	}