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java.lang.ObjectJampack.Rot
public class Rot
Rot generates and manipulates plane rotations. Given a 2-vector compontents are x and y, there is a unitary matrix P such that
P|x| = | c s||x| = |z| |y| |-conj(s) c||y| |0|The number c, which is always real, is the cosine of the rotation. The number s, which may be complex is the sine of the rotation.
Comments: This suite will eventually contain methods for real rotations (two are already in place). The only difference between real and complex rotations is that si and zi are zero for the former. The final routines will do the efficient thing.
Field Summary | |
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double |
si
The imaginary part of the sine of the rotation |
double |
sr
The real part of the sine of the rotation |
double |
zi
The imaginary part of the first component of the transformed vector |
double |
zr
The real part of the first component of the transformed vector |
Constructor Summary | |
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Rot()
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Method Summary | |
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static void |
ap(Zmat A,
Rot P,
int ii1,
int ii2,
int jj1,
int jj2)
Multiplies columns (ii1:ii2,jj1) and A(ii2:ii2,jj1) of a Zmat (altered) by a plane rotation. |
static void |
aph(Zmat A,
Rot P,
int ii1,
int ii2,
int jj1,
int jj2)
Multiplies columns (ii1:ii2,jj1) and A(ii2:ii2,jj1) of a Zmat (altered) by the conjugate transpose of plane rotation. |
static Rot |
genc(double x,
double y)
Given a real 2-vector, genc returns a real plane rotation P such that |
static Rot |
genc(double xr,
double xi,
double yr,
double yi)
Given the real and imaginary parts of a 2-vector, genc returns a plane rotation P such that |
static void |
genc(double xr,
double xi,
double yr,
double yi,
Rot P)
Given the real and imaginary parts of a 2-vector, genc generates a plane rotation P such that |
static void |
genc(double x,
double y,
Rot P)
Given a real 2-vectc, genc generates a real plane rotation P such that |
static Rot |
genc(Zmat A,
int ii1,
int ii2,
int jj)
Given a Zmat A, genc returns a plane rotation that on premultiplication into rows ii1 and ii2 annihilates A(ii2,jj). |
static void |
genc(Zmat A,
int ii1,
int ii2,
int jj,
Rot P)
Given a Zmat A, genc generates a plane rotation that on premultiplication into rows ii1 and ii2 annihilates A(ii2,jj). |
static Rot |
genr(double x,
double y)
Given a real 2-vector, genr returns a plane rotation such that |
static Rot |
genr(double xr,
double xi,
double yr,
double yi)
Given the real and imaginary parts of a 2-vector, genr returns a plane rotation such that |
static void |
genr(double xr,
double xi,
double yr,
double yi,
Rot P)
Given the real and imaginary parts of a 2-vector, genr generates a plane rotation such that |
static void |
genr(double x,
double y,
Rot P)
Given a real 2-vector, genr generates a plane rotation such that |
static Rot |
genr(Zmat A,
int ii,
int jj1,
int jj2)
Given a Zmat A, genr returns a plane rotation that on postmultiplication into column jj1 and jj2 annihilates A(ii,jj2). |
static void |
genr(Zmat A,
int ii,
int jj1,
int jj2,
Rot P)
Given a Zmat A, genr generates a plane rotation that on postmultiplication into column jj1 and jj2 annihilates A(ii,jj2). |
static void |
pa(Rot P,
Zmat A,
int ii1,
int ii2,
int jj1,
int jj2)
Multiplies rows (ii1,jj1:jj2) and (ii2,jj1:jj2) of a Zmat (altered) by a plane rotation. |
static void |
pha(Rot P,
Zmat A,
int ii1,
int ii2,
int jj1,
int jj2)
Multiplies rows (ii1,jj1:jj2) and (ii2,jj1:jj2) of a Zmat (altered) by the conjugate transpose of a plane rotation. |
Methods inherited from class java.lang.Object |
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equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
Field Detail |
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public double sr
public double si
public double zr
public double zi
Constructor Detail |
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public Rot()
Method Detail |
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public static Rot genc(double xr, double xi, double yr, double yi)
P|x| = | c s||x| = |z| |y| |-conj(s) c||y| |0|
xr
- The real part of the first component of the 2-vectorxi
- The imaginary part of the first component of the 2-vectoryr
- The real part of the second component of the 2-vectoryi
- The imaginary part of the second component of the 2-vector
public static void genc(double xr, double xi, double yr, double yi, Rot P)
P|x| = | c s||x| = |z| |y| |-conj(s) c||y| |0|
xr
- The real part of the first component of the 2-vectorxi
- The imaginary part of the first component of the 2-vectoryr
- The real part of the second component of the 2-vectoryi
- The imaginary part of the second component of the 2-vectorP
- The rotation (must be initialized)public static Rot genc(double x, double y)
P|x| = | c s||x| = |z| |y| |-s c||y| |0|
x
- The first component of the two vectory
- The second component of the two vector
public static void genc(double x, double y, Rot P)
P|x| = | c s||x| = |z| |y| |-s c||y| |0|
x
- The first component of the two vectory
- The second component of the two vectorP
- The plane rotationpublic static Rot genc(Zmat A, int ii1, int ii2, int jj)
A
- The Zmat (altered)ii1
- The row index of the first elementii2
- The row index of the second element (the
one that is annihilatedjj
- The column index of the elements
public static void genc(Zmat A, int ii1, int ii2, int jj, Rot P)
A
- The Zmat (altered)ii1
- The row index of the first elementii2
- The row index of the second element (the
one that is annihilatedjj
- The column index of the elementsP
- The plane rotation (must be initialized)public static Rot genr(double xr, double xi, double yr, double yi)
|x y|P = |x y|| c s||x| = |z 0| |-conj(s) c||y|
xr
- The real part of the first component of the 2-vectorxi
- The imaginary part of the first component of the 2-vectoryr
- The real part of the second component of the 2-vectoryi
- The imaginary part of the second component of the 2-vector
public static void genr(double xr, double xi, double yr, double yi, Rot P)
|x y|P = |x y|| c s||x| = |z 0| |-conj(s) c||y|
xr
- The real part of the first component of the 2-vectorxi
- The imaginary part of the first component of the 2-vectoryr
- The real part of the second component of the 2-vectoryi
- The imaginary part of the second component of the 2-vectorP
- The plane rotation (must be initialized)public static Rot genr(Zmat A, int ii, int jj1, int jj2)
A
- The Zmat (altered)ii
- The index of the row containing the elementsjj1
- The column index of the first elementjj2
- The column index of the second element (the
one that is annihilated)
public static void genr(Zmat A, int ii, int jj1, int jj2, Rot P)
A
- The Zmat (altered)ii
- The index of the row containing the elementsjj1
- The column index of the first elementjj2
- The column index of the second element (the
one that is annihilated)P
- The rotationpublic static Rot genr(double x, double y)
|x y|P = |x y|| c s||x| = |z 0| |-s c||y|
x
- The first component of the 2-vectory
- The second component of the 2-vector
public static void genr(double x, double y, Rot P)
|x y|P = |x y|| c s||x| = |z 0| |-s c||y|
x
- The first component of the 2-vectory
- The second component of the 2-vectorP
- The rotationpublic static void pa(Rot P, Zmat A, int ii1, int ii2, int jj1, int jj2)
P
- The plane rotationA
- The Zmat (altered)ii1
- The row index of the first row.ii2
- The row index of the second row.jj1
- The first index of the range of the rowsjj2
- The second index of the range of the rowspublic static void pha(Rot P, Zmat A, int ii1, int ii2, int jj1, int jj2)
P
- The plane rotationA
- The Zmat (altered)ii1
- The row index of the first row.ii2
- The row index of the second row.jj1
- The first index of the range of the rowsjj2
- The second index of the range of the rowspublic static void ap(Zmat A, Rot P, int ii1, int ii2, int jj1, int jj2)
A
- The Zmat (altered)P
- The rotationii1
- The first index of the column rangeii2
- The second index of the column rangejj1
- The index of the first columnjj2
- The index of the second columnpublic static void aph(Zmat A, Rot P, int ii1, int ii2, int jj1, int jj2)
A
- The Zmat (altered)P
- The rotationii1
- The first index of the column rangeii2
- The second index of the column rangejj1
- The index of the first columnjj2
- The index of the second column
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