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Why Vector processors Basic Vector Architecture Vector Execution time Vector load - store units and Vector memory systems Vector length - VLR Vector stride Enhancing Vector performance Measuring Vector performance SSE Instruction set and Applications A case study - Intel Larrabee vector processor

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12 VECTOR GEOMETRY 12.1 VectorsinthePlane Preliminary Questions 1. Answer true or false. Every nonzero vector is: (a) equivalent to a vector based at the origin. (b) equivalent to a unit vector based at the origin. (c) parallel to a vector based at the origin. (d) parallel to a unit vector based at the origin. solution (a) This statement is true. Translating the vector so that it is based on .

Vector Length (MVL) VEC-1 Typical MVL 64 (Cray) Add vector Typical MVL 64-128 Range 64-4996 (Vector-vector instruction shown) Vector processing exploits data parallelism by performing the same computation on linear arrays of numbers "vectors" using one instruction. The maximum number of elements in a vector supported by a vector ISA is

Unit vectors A unit vector is any vector with unit length. When we want to indicate that a vector is a unit vector we put a hat (circum ex) above it, e.g., u. The special vectors i, j and k are unit vectors. Since vectors can be scaled, any vector can be rescaled b to be a unit vector. Example: Find a unit vector that is parallel to h3;4i. 1 3 4

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Components of Vector Processors Vector Registers o Typically 8-32 vector registers with 64 - 128 64-bit elements o Each contains a vector of double-precision numbers o Register size determines the maximum vector length o Each includes at least 2 read and 1 write ports Vector Functional Units (FUs) o Fully pipelin

Vector Calculus 16.1 Vector Fields This chapter is concerned with applying calculus in the context of vector fields. A two-dimensional vector field is a function f that maps each point (x,y) in R2 to a two-dimensional vector hu,vi, and similarly a three-dimensional vector field maps (x,y,z) to hu,v,wi.

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Acceleration vector, m/s 2 c. Kinetic energy scalar, J d. 2Momentum vector, kg0m/s e. Velocity vector, m/s f. Displacement vector, m g. Force vector, N h. Torque vector, Nm i. Distance scalar, m 2.) From the top of a cliff, a person uses a slingshot to fire a pebble straight

2. Subtraction of Vectors: If a vector . is to be subtracted from a vector , the difference vector . can be obtained by adding vectors and . The vector . is a vector which is equal and parallel to that of vector but its arrow-head points in opposite direction. Now the vectors . and . can be added by the head-to-tail rule. Thus the line . AC

5. The negative of a vector. 6. Subtraction of vectors. 7. Algebraic properties of vector addition. F. Properties of a vector space. G. Metric spaces and the scalar product. 1. The scalar product. 2. Definition of a metric space. H. The vector product. I. Dimensionality of a vector space and linear independence. J. Components in a rotated .

vector y. A linear solver computes the state-space vector and output vector from Equation 4. An internal signal generator and external analog and digital input ports provide the input vector u to the state-space solver. The state-space vector x and the output vector y are accessible in real-time through low-latency analog output ports.

6.2 Vector Glyphs Draw arrow or line segment in the direction of the vector with length equal to the vector magnitude. Advantages: Good perception of visualized data (use illuminated volumetric icons for 3D vector field visualization). Disadvantages: Not clear which data point vector represents Leads to visual cluttering

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Fig.4.1 Step response using P controller Fig.4.2 Fig.4.3 Fig.4.4 Fig.4.5 Step response using PID controller Fig.4.6 Comparison of bode plot for smith predictor and PI . Step response of IMC PDF control structure Step response of PDF controller Step response using PI controller Step response using PID controller Step response using PI controller

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ORDINARY DIFFERENTIAL EQUATIONS: SYSTEMS OF EQUATIONS 5 25.4 Vector Fields A vector field on Rm is a mapping F: Rm Rm that assigns a vector in Rm to any point in Rm. If A is an m mmatrix, we can define a vector field on Rm by F(x) Ax. Many other vector fields are possible, such as F(x) x2

3.2 Vectors expressed in terms of Unit Vectors in Rectangular coordinate Systems - A simple and convenient way to express vector quantities Let: i unit vector along the x-axis j unit vector along the y-axis k unit vector along the z-axis in a rectangular coordinate system (x,y,z), or a cylindrical polar coordinate system (r, θ,z).

The ‗Vector approach‘ provides better insight into the various as ects of Electromagnetic phenomenon. Vector analysis is therefore an essential tool for the study of . The ‗Vector Analysis‘ comprises of ‗Vector Algebra‘ and ‗Vect r Calculus‘. Any physical quantity may be ‗Scalar quantity‘ or ‗Vector quantity‘.

g acceleration due to gravity h average height offluid in the lank gravity unit dire :tional vector unit vector in thex-direction unit vector in they.direction c.onvection-diffusionflux vector J component ofthe convection-diffusionflu" vector ix. length oftank. measured in x-direction

Technische Universiteit Eindhoven University of Technology 3 Vector Linearization 1 Vector Linearization through PCR Estimated bench time: 45 minutes Estimated total time: 5-7 hours (depends on the vector) Purpose: Preparing a linear vector which can be used in the Gibson Assembly react

Section 4.5 De nition 1. The dimension of a vector space V, denoted dim(V), is the number of vectors in a basis for V.We define the dimension of the vector space containing only the zero vector 0 to be 0. In a sense, the dimension of a vector space tells us how many vectors are needed to “build” the

vector quantities are involved, the process is more complex since the direction of the vector must be taken into account. In this experiment, three methods for vector addition, graphical, analytical, and experimental, will be examined. THEORY A vector quantity can be represented graphically by a straight line with an arrowhead at its end.

Fig. 2 illustrates the graphical method of vector addition of vectors F1 and F2 from Fig. 1. Starting at point P, draw the first vector F1 in its own direction with its length proportional to its magnitude. Then draw the second vector F2 beginning at the ending of the first vector, in its own direction, with its length proportional to its .

15.1 Vector Fields (page 554) CHAPTER 15 VECTOR CALCULUS 15.1 Vector Fields (page 554) A vector field assigns avector to each point (x, y) or (x, y, 2).In two dimensions F(x, y) M(x, )i N(x, y)j. An example is the position field R x i y j( x k).Its magnitude is lRl r and its direction is out &om the origin. It is the gradient field for f 12z(x y2).

Optimal Voltage Vector Selection Method for Torque Ripple Reduction in 1205 of phase A is turned on, Sa becomes 1. The voltage vector magnitudes are divided into three categories: 0.6472 VDC (the value of the large voltage vector), 0.4 VDC (the value of the medium voltage vector), and

8/23/2005 The Position Vector.doc 3/7 Jim Stiles The Univ. of Kansas Dept. of EECS The magnitude of r Note the magnitude of any and all position vectors is: rrr xyzr 222 The magnitude of the position vector is equal to the coordinate value r of the point the position vector is pointing to! A: That’s right! The magnitude of a directed distance vector is

Adding Vectors. Find the magnitude of a vector : If ! G vab, , the magnitude of a vector is the _ or _ of a directed line segment. The magnitude is defined to be: 22v ab If P 1 (3,2) and P 2 (6,5), find the magnitude of JJJJG P 12 P Find a unit vector in the direction of a given vector: A unit vector is a

Chapter 1 Electromagnetic Introduction and Vector Analysis You Kok Yeow SEE 2523 Theory Electromagnetic. Brief Flow Chart for Electromagnetic Study 2. Revision on Vector 1. Introduction the Electromagnetic Study Basic Law of Vector Vector Multiplication 3. Orthogonal Coordinate Systems . Electromagnetics (EM) is a branch of physics or .

The basic objects to be considered here are vector spaces of linear trans- formations, that is, a pair of vector spaces V and W and a linear subspace . The description of vector spaces of transformations of rank 1 is classical, . note will be concerned. Given any (abstract) vector space M, of dimension m, say, we may use the multiplication .

We will return to the concept of a physical vector in another section. At that time, the properties required to qualify an entity as a physical vector will be discussed. An Abstract Linear Vector Space: By definition, a vector space is any collection of physical or mathematical entities (elements) with defined binary addition and scalar

a vector space over C and Qn is a vector space over Q with similar de nitions of the addition and the scalar multiplication. In general Fnis a vector space over F. Whenever we have a vector space V over a eld F, we can look for subsets W V that are vector spaces with respect to the addition and scalar multiplication restricted from V to W.

1.2 Normed spaces 1.2.1 Vector spaces In this subsection, we recall the definition of a vector space. Roughly speaking it is a set of elements, called "vectors". Any two vectors can be "added", resulting in a new vector, and any vector can be multiplied by an element from R, so as to give a new vector. The precise definition is given .

Vector: Let i be a unit vector pointing east, j be a unit vector pointing north, and k be a unit vector pointing up. (N.B.: Unit vectors are non-denominate, have a magnitude of unity, and are used only to specify a direction.) Then the total vector, in terms of its scalar components and the unit vectors, can be written as V ai bj ck.

§ Vector operations have the letters "VV/VS" appended. - E.g. ADDVV.D is an addition of two double-precision vectors. § Vector instructions input: - 1) a pair of vector registers (ADDVV.D) or - 2) a vector register and a scalar register (ADDVS.D). » all operations use the same value in the scalar register as one input.