At the risk of being flamed . . . What is the difference between log1p(x) and log(x+1)? The two methods appear to give the same results:> log1p(0.000001)/log(0.000001+1)[1] 1 John John David Sorkin M.D., Ph.D. Professor of Medicine Chief, Biostatistics and Informatics University of Maryland School of Medicine Division of Gerontology and Geriatric Medicine Baltimore VA Medical Center 10 North Greene Street GRECC (BT/18/GR) Baltimore, MD 21201-1524 (Phone) 410-605-7119 (Fax) 410-605-7913 (Please call phone number above prior to faxing)>>> William Dunlap via R-help <r-help at r-project.org> 12/12/16 11:38 AM >>>log1p(x), in the base package computes log(1+x) accurately for small x (and large). E.g.,> options(digits=16) > base::log1p(1e-14)[1] 9.99999999999995e-15> base::log1p(1e-14) - base::log(1+1e-14)[1] 7.992778373591124e-18> as.numeric(log(Rmpfr::mpfr(1,precBits=1000) + Rmpfr::mpfr(1e-14,precBits=1000))) - log1p(1e-14) [1] 0 Bill Dunlap TIBCO Software wdunlap tibco.com On Mon, Dec 12, 2016 at 8:23 AM, Faradj Koliev <faradj.g at gmail.com> wrote:> Hi all, > > How do I perform log(x+1) in R? > > log1p_trans() from the package ?scales" doesn?t seem to work for me. > > Best, > Faradj > ______________________________________________ > R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/ > posting-guide.html > and provide commented, minimal, self-contained, reproducible code.[[alternative HTML version deleted]] ______________________________________________ R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. Confidentiality Statement: This email message, including any attachments, is for the sole use of the intended recipient(s) and may contain confidential and privileged information. Any unauthorized use, disclosure or distribution is prohibited. If you are not the intended recipient, please contact the sender by reply email and destroy all copies of the original message.
> On Dec 12, 2016, at 8:53 AM, John Sorkin <jsorkin at grecc.umaryland.edu> wrote: > > At the risk of being flamed . . . > What is the difference between log1p(x) and log(x+1)? > The two methods appear to give the same results: >> log1p(0.000001)/log(0.000001+1) > [1] 1 > JohnRead the help page more carefully. -- David.> > > John David Sorkin M.D., Ph.D. > Professor of Medicine > Chief, Biostatistics and Informatics > University of Maryland School of Medicine Division of Gerontology and > Geriatric Medicine > Baltimore VA Medical Center > 10 North Greene Street > GRECC (BT/18/GR) > Baltimore, MD 21201-1524 > (Phone) 410-605-7119 > (Fax) 410-605-7913 (Please call phone number above prior to faxing) >>>> William Dunlap via R-help <r-help at r-project.org> 12/12/16 11:38 AM >>>> > log1p(x), in the base package computes log(1+x) accurately for small x > (and > large). > > E.g., >> options(digits=16) >> base::log1p(1e-14) > [1] 9.99999999999995e-15 >> base::log1p(1e-14) - base::log(1+1e-14) > [1] 7.992778373591124e-18 >> as.numeric(log(Rmpfr::mpfr(1,precBits=1000) + Rmpfr::mpfr(1e-14, > precBits=1000))) - log1p(1e-14) > [1] 0 > > > Bill Dunlap > TIBCO Software > wdunlap tibco.com > > On Mon, Dec 12, 2016 at 8:23 AM, Faradj Koliev <faradj.g at gmail.com> > wrote: > >> Hi all, >> >> How do I perform log(x+1) in R? >> >> log1p_trans() from the package ?scales" doesn?t seem to work for me. >> >> Best, >> Faradj >> ______________________________________________ >> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see >> https://stat.ethz.ch/mailman/listinfo/r-help >> PLEASE do read the posting guide http://www.R-project.org/ >> posting-guide.html >> and provide commented, minimal, self-contained, reproducible code. > > [[alternative HTML version deleted]] > > ______________________________________________ > R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide > http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. > Confidentiality Statement: > This email message, including any attachments, is for ...{{dropped:16}}
The difference increases as the value gets closer to 0:> dput(log1p(0.000001))9.99999500000333e-07> dput(log(1+0.000001))9.99999499918067e-07> dput(log1p(0.000001)/log(0.000001+1))1.00000000008227> dput(log1p(0.00000001)/log(0.00000001+1))1.00000000607747> dput(log1p(0.0000000001)/log(0.0000000001+1))0.999999917259636> dput(log1p(0.000000000001)/log(0.000000000001+1))0.99991110732027> dput(log1p(0.00000000000001)/log(0.00000000000001+1))1.00079991719344 ------------------------------------- David L Carlson Department of Anthropology Texas A&M University College Station, TX 77840-4352 -----Original Message----- From: R-help [mailto:r-help-bounces at r-project.org] On Behalf Of John Sorkin Sent: Monday, December 12, 2016 10:54 AM To: faradj.g at gmail.com; r-help at r-project.org; wdunlap at tibco.com Subject: Re: [R] Log plus one transformation in R At the risk of being flamed . . . What is the difference between log1p(x) and log(x+1)? The two methods appear to give the same results:> log1p(0.000001)/log(0.000001+1)[1] 1 John John David Sorkin M.D., Ph.D. Professor of Medicine Chief, Biostatistics and Informatics University of Maryland School of Medicine Division of Gerontology and Geriatric Medicine Baltimore VA Medical Center 10 North Greene Street GRECC (BT/18/GR) Baltimore, MD 21201-1524 (Phone) 410-605-7119 (Fax) 410-605-7913 (Please call phone number above prior to faxing)>>> William Dunlap via R-help <r-help at r-project.org> 12/12/16 11:38 AM >>>log1p(x), in the base package computes log(1+x) accurately for small x (and large). E.g.,> options(digits=16) > base::log1p(1e-14)[1] 9.99999999999995e-15> base::log1p(1e-14) - base::log(1+1e-14)[1] 7.992778373591124e-18> as.numeric(log(Rmpfr::mpfr(1,precBits=1000) + Rmpfr::mpfr(1e-14,precBits=1000))) - log1p(1e-14) [1] 0 Bill Dunlap TIBCO Software wdunlap tibco.com On Mon, Dec 12, 2016 at 8:23 AM, Faradj Koliev <faradj.g at gmail.com> wrote:> Hi all, > > How do I perform log(x+1) in R? > > log1p_trans() from the package ?scales" doesn?t seem to work for me. > > Best, > Faradj > ______________________________________________ > R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/ > posting-guide.html > and provide commented, minimal, self-contained, reproducible code.[[alternative HTML version deleted]] ______________________________________________ R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. Confidentiality Statement: This email message, including any attachments, is for the sole use of the intended recipient(s) and may contain confidential and privileged information. Any unauthorized use, disclosure or distribution is prohibited. If you are not the intended recipient, please contact the sender by reply email and destroy all copies of the original message. ______________________________________________ R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
David, I did read the help page. All it says is log1p(x) computes log(1+x) accurately also for |x| << 1 (and less accurately when x is approximately -1). This gives me pause. Does it mean that log(x) does not give accurate results? If log1p gives more accurate values than log, why is the log function not written to use the more accurate computation performed by log1p. I don't believe I can look directly at the code for log and log1p, so I need to rely on the kindness of others to explain the differences between the computations performed by the functions. I guess the test I ran, log1p(0.000001)/log(0.000001+1), did not have enough precision to demonstrate a difference between the two functions. John John David Sorkin M.D., Ph.D. Professor of Medicine Chief, Biostatistics and Informatics University of Maryland School of Medicine Division of Gerontology and Geriatric Medicine Baltimore VA Medical Center 10 North Greene Street GRECC (BT/18/GR) Baltimore, MD 21201-1524 (Phone) 410-605-7119 (Fax) 410-605-7913 (Please call phone number above prior to faxing)>>> David Winsemius <dwinsemius at comcast.net> 12/12/16 12:05 PM >>>> On Dec 12, 2016, at 8:53 AM, John Sorkin <jsorkin at grecc.umaryland.edu>wrote:> > At the risk of being flamed . . . > What is the difference between log1p(x) and log(x+1)? > The two methods appear to give the same results: >> log1p(0.000001)/log(0.000001+1) > [1] 1 > JohnRead the help page more carefully. -- David.> > > John David Sorkin M.D., Ph.D. > Professor of Medicine > Chief, Biostatistics and Informatics > University of Maryland School of Medicine Division of Gerontology and > Geriatric Medicine > Baltimore VA Medical Center > 10 North Greene Street > GRECC (BT/18/GR) > Baltimore, MD 21201-1524 > (Phone) 410-605-7119 > (Fax) 410-605-7913 (Please call phone number above prior to faxing) >>>> William Dunlap via R-help <r-help at r-project.org> 12/12/16 11:38 AM >>>> > log1p(x), in the base package computes log(1+x) accurately for small x > (and > large). > > E.g., >> options(digits=16) >> base::log1p(1e-14) > [1] 9.99999999999995e-15 >> base::log1p(1e-14) - base::log(1+1e-14) > [1] 7.992778373591124e-18 >> as.numeric(log(Rmpfr::mpfr(1,precBits=1000) + Rmpfr::mpfr(1e-14, > precBits=1000))) - log1p(1e-14) > [1] 0 > > > Bill Dunlap > TIBCO Software > wdunlap tibco.com > > On Mon, Dec 12, 2016 at 8:23 AM, Faradj Koliev <faradj.g at gmail.com> > wrote: > >> Hi all, >> >> How do I perform log(x+1) in R? >> >> log1p_trans() from the package ?scales" doesn?t seem to work for me. >> >> Best, >> Faradj >> ______________________________________________ >> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see >> https://stat.ethz.ch/mailman/listinfo/r-help >> PLEASE do read the posting guide http://www.R-project.org/ >> posting-guide.html >> and provide commented, minimal, self-contained, reproducible code. > > [[alternative HTML version deleted]] > > ______________________________________________ > R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide > http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. > Confidentiality Statement: > This email message, including any attachments, is for the sole use of > the intended recipient(s) and may contain confidential and privileged > information. Any unauthorized use, disclosure or distribution is > prohibited. If you are not the intended recipient, please contact the > sender by reply email and destroy all copies of the original message. > ______________________________________________ > R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guidehttp://www.R-project.org/posting-guide.html> and provide commented, minimal, self-contained, reproducible code.David Winsemius the intended recipient(s) and may contain confidential and privileged information. Any unauthorized use, disclosure or distribution is prohibited. If you are not the intended recipient, please contact the sender by reply email and destroy all copies of the original message.
Print more digits of the quotient or subtract one from it and you will see the difference:> log1p(0.000001)/log(0.000001+1) - 1[1] 8.22666379463044e-11 Bill Dunlap TIBCO Software wdunlap tibco.com On Mon, Dec 12, 2016 at 8:53 AM, John Sorkin <jsorkin at grecc.umaryland.edu> wrote:> At the risk of being flamed . . . > What is the difference between log1p(x) and log(x+1)? > The two methods appear to give the same results: > > log1p(0.000001)/log(0.000001+1) > [1] 1 > John > > > John David Sorkin M.D., Ph.D. > Professor of Medicine > Chief, Biostatistics and Informatics > University of Maryland School of Medicine Division of Gerontology and > Geriatric Medicine > Baltimore VA Medical Center > 10 North Greene Street > GRECC (BT/18/GR) > Baltimore, MD 21201-1524 > (Phone) 410-605-7119 > (Fax) 410-605-7913 (Please call phone number above prior to faxing) > > >>> William Dunlap via R-help <r-help at r-project.org> 12/12/16 11:38 AM >>> > log1p(x), in the base package computes log(1+x) accurately for small x (and > large). > > E.g., > > options(digits=16) > > base::log1p(1e-14) > [1] 9.99999999999995e-15 > > base::log1p(1e-14) - base::log(1+1e-14) > [1] 7.992778373591124e-18 > > as.numeric(log(Rmpfr::mpfr(1,precBits=1000) + Rmpfr::mpfr(1e-14, > precBits=1000))) - log1p(1e-14) > [1] 0 > > > Bill Dunlap > TIBCO Software > wdunlap tibco.com > > On Mon, Dec 12, 2016 at 8:23 AM, Faradj Koliev <faradj.g at gmail.com> wrote: > > > Hi all, > > > > How do I perform log(x+1) in R? > > > > log1p_trans() from the package ?scales" doesn?t seem to work for me. > > > > Best, > > Faradj > > ______________________________________________ > > R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see > > https://stat.ethz.ch/mailman/listinfo/r-help > > PLEASE do read the posting guide http://www.R-project.org/ > > posting-guide.html > > and provide commented, minimal, self-contained, reproducible code. > > [[alternative HTML version deleted]] > > ______________________________________________ > R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/ > posting-guide.html > and provide commented, minimal, self-contained, reproducible code. > > *Confidentiality Statement:* > > This email message, including any attachments, is for ...{{dropped:10}}
And, for crying out loud... just try it with x = 1.234e-16 or so. One would think that the hint |x| << 1 was obvious enough. -pd> On 12 Dec 2016, at 18:26 , William Dunlap via R-help <r-help at r-project.org> wrote: > > Print more digits of the quotient or subtract one from it and you will see > the difference: > >> log1p(0.000001)/log(0.000001+1) - 1 > [1] 8.22666379463044e-11 > > > Bill Dunlap > TIBCO Software > wdunlap tibco.com > > On Mon, Dec 12, 2016 at 8:53 AM, John Sorkin <jsorkin at grecc.umaryland.edu> > wrote: > >> At the risk of being flamed . . . >> What is the difference between log1p(x) and log(x+1)? >> The two methods appear to give the same results: >>> log1p(0.000001)/log(0.000001+1) >> [1] 1 >> John >> >> >> John David Sorkin M.D., Ph.D. >> Professor of Medicine >> Chief, Biostatistics and Informatics >> University of Maryland School of Medicine Division of Gerontology and >> Geriatric Medicine >> Baltimore VA Medical Center >> 10 North Greene Street >> GRECC (BT/18/GR) >> Baltimore, MD 21201-1524 >> (Phone) 410-605-7119 >> (Fax) 410-605-7913 (Please call phone number above prior to faxing) >> >>>>> William Dunlap via R-help <r-help at r-project.org> 12/12/16 11:38 AM >>> >> log1p(x), in the base package computes log(1+x) accurately for small x (and >> large). >> >> E.g., >>> options(digits=16) >>> base::log1p(1e-14) >> [1] 9.99999999999995e-15 >>> base::log1p(1e-14) - base::log(1+1e-14) >> [1] 7.992778373591124e-18 >>> as.numeric(log(Rmpfr::mpfr(1,precBits=1000) + Rmpfr::mpfr(1e-14, >> precBits=1000))) - log1p(1e-14) >> [1] 0 >> >> >> Bill Dunlap >> TIBCO Software >> wdunlap tibco.com >> >> On Mon, Dec 12, 2016 at 8:23 AM, Faradj Koliev <faradj.g at gmail.com> wrote: >> >>> Hi all, >>> >>> How do I perform log(x+1) in R? >>> >>> log1p_trans() from the package ?scales" doesn?t seem to work for me. >>> >>> Best, >>> Faradj >>> ______________________________________________ >>> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see >>> https://stat.ethz.ch/mailman/listinfo/r-help >>> PLEASE do read the posting guide http://www.R-project.org/ >>> posting-guide.html >>> and provide commented, minimal, self-contained, reproducible code. >> >> [[alternative HTML version deleted]] >> >> ______________________________________________ >> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see >> https://stat.ethz.ch/mailman/listinfo/r-help >> PLEASE do read the posting guide http://www.R-project.org/ >> posting-guide.html >> and provide commented, minimal, self-contained, reproducible code. >> >> *Confidentiality Statement:* >> >> This email message, including any attachments, is for ...{{dropped:10}} > > ______________________________________________ > R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code.-- Peter Dalgaard, Professor, Center for Statistics, Copenhagen Business School Solbjerg Plads 3, 2000 Frederiksberg, Denmark Phone: (+45)38153501 Office: A 4.23 Email: pd.mes at cbs.dk Priv: PDalgd at gmail.com