Modified givens rotation for matrices with complex numbers
First Claim
1. A method for nulling a cell of a complex matrix, comprising:
- obtaining the complex matrix as input to a processing unit;
obtaining a modified Givens rotation matrix as input to the processing unit;
multiplying the complex matrix with the modified Givens rotation matrix by the processing unit for the nulling of the cell of the complex matrix to provide a modified form thereof, the modified form comprising real numbers; and
outputting the modified form by the processing unit;
the modified Givens rotation matrix including complex numbers c*, c, −
s, and s*, wherein the complex number s* is the complex conjugate of the complex number s, and wherein the complex number c* is the complex conjugate of the complex number c; and
the complex numbers c and s being associated with complex numbers of the complex matrix including the cell to be nulled.
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Abstract
Nulling a cell of a complex matrix is described. A complex matrix and a modified Givens rotation matrix are obtained for multiplication by a processing unit, such as a systolic array or a CPU, for example, for the nulling of the cell to provide a modified form of the complex matrix. The modified Givens rotation matrix includes complex numbers c*, c, −s, and s*, wherein the complex number s* is the complex conjugate of the complex number s, and wherein the complex number c* is the complex conjugate of the complex number c. The complex numbers c and s are associated with complex numbers of the complex matrix including the cell to be nulled. The modified form is then output by the processing unit. The modified Givens rotation matrix may be implemented as a systolic array or otherwise used for processing complex numbers or matrices.
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Citations
18 Claims
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1. A method for nulling a cell of a complex matrix, comprising:
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obtaining the complex matrix as input to a processing unit; obtaining a modified Givens rotation matrix as input to the processing unit; multiplying the complex matrix with the modified Givens rotation matrix by the processing unit for the nulling of the cell of the complex matrix to provide a modified form thereof, the modified form comprising real numbers; and outputting the modified form by the processing unit; the modified Givens rotation matrix including complex numbers c*, c, −
s, and s*, wherein the complex number s* is the complex conjugate of the complex number s, and wherein the complex number c* is the complex conjugate of the complex number c; andthe complex numbers c and s being associated with complex numbers of the complex matrix including the cell to be nulled. - View Dependent Claims (2, 3, 4)
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5. A non-transitory machine-readable medium having stored thereon information representing instructions that, when executed by processor means, causes the processor means to perform operations for nulling a cell of a complex matrix, the operations when executed comprising:
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obtaining the complex matrix; multiplying the complex matrix with a modified Givens rotation matrix using the processor means to generate a modified form of the complex matrix, the modified form comprising real numbers; and outputting the modified form; the modified Givens rotation matrix including complex numbers c*, c, −
s, and s*, wherein the complex number s* is the complex conjugate of the complex number s, and wherein the complex number c* is the complex conjugate of the complex number c;the complex numbers c*, c, −
s, and s* being calculated with the processor means; andthe complex numbers c and s being associated with complex numbers of the complex matrix including the cell to be nulled. - View Dependent Claims (6, 7, 8, 9, 10, 11)
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12. An apparatus configured to perform operations for nulling a cell of a complex matrix, comprising:
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a processing unit configured for; obtaining the complex matrix; multiplying the complex matrix with a modified Givens rotation matrix to generate a modified form of the complex matrix, the modified form comprising real numbers; and outputting the modified form; wherein the modified Givens rotation matrix includes complex numbers c*, c, −
s, and s*, wherein the complex number s* is the complex conjugate of the complex number s, and wherein the complex number c* is the complex conjugate of the complex number c; andwherein the complex numbers c and s are associated with complex numbers of the complex matrix including the cell to be nulled. - View Dependent Claims (13, 14, 15, 16, 17, 18)
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Specification