Algorithm 539: Basic Linear Algebra Subprograms for Fortran Usage [F1]

Lawson, Charles L.; Hanson, Richard J.; Krogh, Fred T.; Kincaid, David R.

doi:10.1145/355841.355848

Cited by 76 publications

(32 citation statements)

References 1 publication

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“…This generic algorithm is implemented in the TRIQS det_manip class, using BLAS Level 2 [19,20] internally. The class provides a simple API, in order to make these manipulations as straightforward and efficient as possible.…”

Section: Determinant Manipulations (C++)mentioning

confidence: 99%

TRIQS: A toolbox for research on interacting quantum systems

Parcollet

Ferrero

Ayral

et al. 2015

Computer Physics Communications

402

291

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International audienceWe present the TRIQS library, a Toolbox for Research on Interacting Quantum Systems. It is an open-source, computational physics library providing a framework for the quick development of applications in the field of many-body quantum physics, and in particular, strongly-correlated electronic systems. It supplies components to develop codes in a modern, concise and efficient way: e.g. Green's function containers, a generic Monte Carlo class, and simple interfaces to HDF5. TRIQS is a C++/Python library that can be used from either language. It is distributed under the GNU General Public License (GPLv3). State-of-the-art applications based on the library, such as modern quantum many-body solvers and interfaces between density-functional-theory codes and dynamical mean-field theory (DMFT) codes are distributed along with it

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Section: Determinant Manipulations (C++)mentioning

confidence: 99%

TRIQS: A toolbox for research on interacting quantum systems

Parcollet

Ferrero

Ayral

et al. 2015

Computer Physics Communications

402

291

View full text Add to dashboard Cite

show abstract

“…We implemented the 1-norm formulation (6) in HOPDM [14; 1] which was modified to perform matrix multiplications in dense mode using the BLAS library [21]. The experiments were performed using an Intel Pentium 4 PC running at 3GHz, with 1GB RAM and 1024KB cache.…”

Section: Numerical Experiments and Resultsmentioning

confidence: 99%

Exploiting separability in large-scale linear support vector machine training

Woodsend

Gondzio

2009

Comput Optim Appl

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Linear support vector machine training can be represented as a large quadratic program. We present an efficient and numerically stable algorithm for this problem using interior point methods, which requires only O(n) operations per iteration. Through exploiting the separability of the Hessian, we provide a unified approach, from an optimization perspective, to 1-norm classification, 2-norm classification, universum classification, ordinal regression and -insensitive regression. Our approach has the added advantage of obtaining the hyperplane weights and bias directly from the solver. Numerical experiments indicate that, in contrast to existing methods, the algorithm is largely unaffected by noisy data, and they show training times for our implementation are consistent and highly competitive. We discuss the effect of using multiple correctors, and monitoring the angle of the normal to the hyperplane to determine termination.

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“…Gaussian functions are frequently used to approximate error correlations (Daley, 1991;Gaspari and Cohn, 1999). The algorithm used for the fitting is the bounded and constrained least square (Lawson et al, 1979). Once σ 2 f is determined, Eq.…”

Section: Error Covariance Matricesmentioning

confidence: 99%

A variational regularization of Abel transform for GPS radio occultation

Wee

2018

Atmos. Meas. Tech.

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Abstract. In the Global Positioning System (GPS) radio occultation (RO) technique, the inverse Abel transform of measured bending angle (Abel inversion, hereafter AI) is the standard means of deriving the refractivity. While concise and straightforward to apply, the AI accumulates and propagates the measurement error downward. The measurement error propagation is detrimental to the refractivity in lower altitudes. In particular, it builds up negative refractivity bias in the tropical lower troposphere. An alternative to AI is the numerical inversion of the forward Abel transform, which does not incur the integration of error-possessing measurement and thus precludes the error propagation. The variational regularization (VR) proposed in this study approximates the inversion of the forward Abel transform by an optimization problem in which the regularized solution describes the measurement as closely as possible within the measurement's considered accuracy. The optimization problem is then solved iteratively by means of the adjoint technique. VR is formulated with error covariance matrices, which permit a rigorous incorporation of prior information on measurement error characteristics and the solution's desired behavior into the regularization. VR holds the control variable in the measurement space to take advantage of the posterior height determination and to negate the measurement error due to the mismodeling of the refractional radius. The advantages of having the solution and the measurement in the same space are elaborated using a purposely corrupted synthetic sounding with a known true solution. The competency of VR relative to AI is validated with a large number of actual RO soundings. The comparison to nearby radiosonde observations shows that VR attains considerably smaller random and systematic errors compared to AI. A noteworthy finding is that in the heights and areas that the measurement bias is supposedly small, VR follows AI very closely in the mean refractivity deserting the first guess. In the lowest few kilometers that AI produces large negative refractivity bias, VR reduces the refractivity bias substantially with the aid of the background, which in this study is the operational forecasts of the European Centre for Medium-Range Weather Forecasts (ECMWF). It is concluded based on the results presented in this study that VR offers a definite advantage over AI in the quality of refractivity.

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Algorithm 539: Basic Linear Algebra Subprograms for Fortran Usage [F1]

Cited by 76 publications

References 1 publication

TRIQS: A toolbox for research on interacting quantum systems

TRIQS: A toolbox for research on interacting quantum systems

Exploiting separability in large-scale linear support vector machine training

A variational regularization of Abel transform for GPS radio occultation

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