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Class Jampack.Rot
java.lang.Object
|
+----Jampack.Rot
- public class Rot
- extends Object
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.
-
c
- The cosine of the rotation
-
si
- The imaginary part of the sine of the rotation
-
sr
- The real part of the sine of the rotation
-
zi
- The imaginary part of the first component of the transformed vector
-
zr
- The real part of the first component of the transformed vector
-
Rot()
-
-
ap(Zmat, Rot, int, int, int, int)
- Multiplies columns (ii1:ii2,jj1) and A(ii2:ii2,jj1)
of a Zmat (altered) by a plane rotation.
-
aph(Zmat, Rot, int, int, int, int)
- Multiplies columns (ii1:ii2,jj1) and A(ii2:ii2,jj1)
of a Zmat (altered) by the conjugate transpose of plane rotation.
-
genc(double, double)
- Given a real 2-vector, genc returns
a real plane rotation P such that
P|x| = | c s||x| = |z|
|y| |-s c||y| |0|
-
genc(double, double, double, double)
- Given the real and imaginary parts of a 2-vector, genc returns
a plane rotation P such that
P|x| = | c s||x| = |z|
|y| |-conj(s) c||y| |0|
-
genc(Rot, double, double)
- Given a real 2-vectc, genc generates
a real plane rotation P such that
P|x| = | c s||x| = |z|
|y| |-s c||y| |0|
-
genc(Rot, double, double, double, double)
- Given the real and imaginary parts of a 2-vector, genc generates
a plane rotation P such that
P|x| = | c s||x| = |z|
|y| |-conj(s) c||y| |0|
-
genc(Rot, Zmat, int, int, int)
- Given a Zmat A, genc generates a plane rotation that on
premultiplication into rows ii1 and ii2
annihilates A(ii2,jj).
-
genc(Zmat, int, int, int)
- Given a Zmat A, genc returns a plane rotation that on
premultiplication into rows ii1 and ii2
annihilates A(ii2,jj).
-
genr(double, double)
- Given a real 2-vector, genr returns
a plane rotation such that
|x y|P = |x y|| c s||x| = |z 0|
|-s c||y|
-
genr(double, double, double, double)
- Given the real and imaginary parts of a 2-vector, genr returns
a plane rotation such that
|x y|P = |x y|| c s||x| = |z 0|
|-conj(s) c||y|
-
genr(Rot, double, double)
- Given a real 2-vector, genr generates
a plane rotation such that
|x y|P = |x y|| c s||x| = |z 0|
|-s c||y|
-
genr(Rot, double, double, double, double)
- Given the real and imaginary parts of a 2-vector, genr generates
a plane rotation such that
|x y|P = |x y|| c s||x| = |z 0|
|-conj(s) c||y|
-
genr(Rot, Zmat, int, int, int)
- Given a Zmat A, genr returns a plane rotation that on
postmultiplication into column jj1 and jj2
annihilates A(ii,jj2).
-
genr(Zmat, int, int, int)
- Given a Zmat A, genr returns a plane rotation that on
postmultiplication into column jj1 and jj2
annihilates A(ii,jj2).
-
pa(Rot, Zmat, int, int, int, int)
- Multiplies rows (ii1,jj1:jj2) and (ii2,jj1:jj2)
of a Zmat (altered) by a plane rotation.
-
pha(Rot, Zmat, int, int, int, int)
- Multiplies rows (ii1,jj1:jj2) and (ii2,jj1:jj2)
of a Zmat (altered) by the conjugate transpose of a plane rotation.
c
protected double c
- The cosine of the rotation
sr
public double sr
- The real part of the sine of the rotation
si
public double si
- The imaginary part of the sine of the rotation
zr
public double zr
- The real part of the first component of the transformed vector
zi
public double zi
- The imaginary part of the first component of the transformed vector
Rot
public Rot()
genc
public 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
P|x| = | c s||x| = |z|
|y| |-conj(s) c||y| |0|
- Parameters:
- xr - The real part of the first component of the 2-vector
- xi - The imaginary part of the first component of the 2-vector
- yr - The real part of the second component of the 2-vector
- yi - The imaginary part of the second component of the 2-vector
- Returns:
- The rotation
genc
public static void genc(Rot P,
double xr,
double xi,
double yr,
double yi)
- Given the real and imaginary parts of a 2-vector, genc generates
a plane rotation P such that
P|x| = | c s||x| = |z|
|y| |-conj(s) c||y| |0|
- Parameters:
- P - The rotation (must be initialized)
- xr - The real part of the first component of the 2-vector
- xi - The imaginary part of the first component of the 2-vector
- yr - The real part of the second component of the 2-vector
- yi - The imaginary part of the second component of the 2-vector
genc
public static Rot genc(double x,
double y)
- Given a real 2-vector, genc returns
a real plane rotation P such that
P|x| = | c s||x| = |z|
|y| |-s c||y| |0|
- Parameters:
- x - The first component of the two vector
- y - The second component of the two vector
- Returns:
- The rotation
genc
public static void genc(Rot P,
double x,
double y)
- Given a real 2-vectc, genc generates
a real plane rotation P such that
P|x| = | c s||x| = |z|
|y| |-s c||y| |0|
- Parameters:
- P - The plane rotation
- x - The first component of the two vector
- y - The second component of the two vector
genc
public 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). The element A(ii2,jj) is
overwriten by zero and the element A(ii1,jj) is
overwritten by its transformed value.
- Parameters:
- A - The Zmat (altered)
- ii1 - The row index of the first element
- ii2 - The row index of the second element (the
one that is annihilated
- jj - The column index of the elements
- Returns:
- The plane rotation
genc
public static void genc(Rot P,
Zmat A,
int ii1,
int ii2,
int jj)
- Given a Zmat A, genc generates a plane rotation that on
premultiplication into rows ii1 and ii2
annihilates A(ii2,jj). The element A(ii2,jj) is
overwriten by zero and the element A(ii1,jj) is
overwritten by its transformed value.
- Parameters:
- P - The plane rotation (must be initialized)
- A - The Zmat (altered)
- ii1 - The row index of the first element
- ii2 - The row index of the second element (the
one that is annihilated
- jj - The column index of the elements
genr
public 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
|x y|P = |x y|| c s||x| = |z 0|
|-conj(s) c||y|
- Parameters:
- xr - The real part of the first component of the 2-vector
- xi - The imaginary part of the first component of the 2-vector
- yr - The real part of the second component of the 2-vector
- yi - The imaginary part of the second component of the 2-vector
- Returns:
- The rotation
genr
public static void genr(Rot P,
double xr,
double xi,
double yr,
double yi)
- Given the real and imaginary parts of a 2-vector, genr generates
a plane rotation such that
|x y|P = |x y|| c s||x| = |z 0|
|-conj(s) c||y|
- Parameters:
- P - The plane rotation (must be initialized)
- xr - The real part of the first component of the 2-vector
- xi - The imaginary part of the first component of the 2-vector
- yr - The real part of the second component of the 2-vector
- yi - The imaginary part of the second component of the 2-vector
- Returns:
- The rotation
genr
public 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). The element A(ii,jj2) is
overwirten by zero and the element A(ii,jj1) is
overwritten by its transformed value.
- Parameters:
- A - The Zmat (altered)
- ii - The index of the row containing the elements
- jj1 - The column index of the first element
- jj2 - The column index of the second element (the
one that is annihilated)
- Returns:
- The rotation
genr
public static void genr(Rot P,
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). The element A(ii,jj2) is
overwirten by zero and the element A(ii,jj1) is
overwritten by its transformed value.
- Parameters:
- P - The rotation
- A - The Zmat (altered)
- ii - The index of the row containing the elements
- jj1 - The column index of the first element
- jj2 - The column index of the second element (the
one that is annihilated)
genr
public static Rot genr(double x,
double y)
- Given a real 2-vector, genr returns
a plane rotation such that
|x y|P = |x y|| c s||x| = |z 0|
|-s c||y|
- Parameters:
- x - The first component of the 2-vector
- y - The second component of the 2-vector
- Returns:
- The rotation
genr
public static void genr(Rot P,
double x,
double y)
- Given a real 2-vector, genr generates
a plane rotation such that
|x y|P = |x y|| c s||x| = |z 0|
|-s c||y|
- Parameters:
- P - The rotation
- x - The first component of the 2-vector
- y - The second component of the 2-vector
pa
public 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.
- Parameters:
- P - The plane rotation
- A - 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 rows
- jj2 - The second index of the range of the rows
pha
public 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.
- Parameters:
- P - The plane rotation
- A - 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 rows
- jj2 - The second index of the range of the rows
ap
public 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.
- Parameters:
- A - The Zmat (altered)
- P - The rotation
- ii1 - The first index of the column range
- ii2 - The second index of the column range
- jj1 - The index of the first column
- jj2 - The index of the second column
aph
public 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.
- Parameters:
- A - The Zmat (altered)
- P - The rotation
- ii1 - The first index of the column range
- ii2 - The second index of the column range
- jj1 - The index of the first column
- jj2 - The index of the second column
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