Package ubic.basecode.math.linalg

Class Blas

java.lang.Object

ubic.basecode.math.linalg.Blas

public class Blas
extends Object

This class contains Java versions of a number of the LINPACK basic linear algebra subroutines (blas):

1. isamax_j
2. daxpy_j
3. ddot_j
4. dscal_j
5. dswap_j
6. dnrm2_j
7. dcopy_j
8. drotg_j

It also contains utility routines that the translator found useful while translating the FORTRAN code to Java code. "col" indicates that the routine operates on two columns of a matrix. "colv" indicates that the routine operates on a column of a matrix and a vector. The "p" at the end of dscalp, dnrm2p, and dcopyp indicates that these routines operate on a portion of a vector:

1. colisamax_j
2. colaxpy_j
3. colvaxpy_j
4. colvraxpy_j
5. coldot_j
6. colvdot_j
7. colscal_j
8. dscalp_j
9. colswap_j
10. colnrm2_j
11. dnrm2p_j
12. dcopyp_j
13. colrot_j
14. sign_j

IMPORTANT: The "_j" suffixes indicate that these routines use Java style indexing. For example, you will see for (i = 0; i < n; i++) rather than (FORTRAN style) for (i = 1; i <= n; i++) To use the "_j" routines you will have to fill elements 0 through n - 1 of vectors rather than elements 1 through n. [Also, before using the isamax and colisamax methods make sure that they are doing what you expect them to do.] Versions of these programs that use FORTRAN style indexing are also available. They end with the suffix "_f77".

This class was translated by a statistician from FORTRAN versions of the LINPACK blas. It is NOT an official translation. When public domain Java numerical analysis routines become available from the people who produce LAPACK, then THE CODE PRODUCED BY THE NUMERICAL ANALYSTS SHOULD BE USED.

Meanwhile, if you have suggestions for improving this code, please contact Steve Verrill at sverrill@fs.fed.us.

Version:

.5 --- June 3, 1997

Author:

Steve Verrill

Constructor Summary

Constructors

Constructor	Description
Blas()

Method Summary

Modifier and Type	Method	Description
static void	colaxpy_j(int nrow, double a, double[][] x, int begin, int j1, int j2)	This method multiplies a constant times a portion of a column of a matrix and adds the product to the corresponding portion of another column of the matrix --- a portion of col2 is replaced by the corresponding portion of a*col1 + col2.
static double	coldot_j(int nrow, double[][] x, int begin, int j1, int j2)	This method calculates the dot product of portions of two columns of a matrix.
static int	colisamax_j(int n, double[][] x, int incx, int begin, int j)	This method finds the index of the element of a portion of a column of a matrix that has the maximum absolute value.
static double	colnrm2_j(int nrow, double[][] x, int begin, int j)	This method calculates the Euclidean norm of a portion of a column of a matrix.
static void	colrot_j(int n, double[][] x, int j1, int j2, double c, double s)	This method "applies a plane rotation." It is a modification of the LINPACK function DROT.
static void	colscal_j(int nrow, double a, double[][] x, int begin, int j)	This method scales a portion of a column of a matrix by a constant.
static void	colswap_j(int n, double[][] x, int j1, int j2)	This method interchanges two columns of a matrix.
static void	colvaxpy_j(int nrow, double a, double[][] x, double[] y, int begin, int j)	This method multiplies a constant times a portion of a column of a matrix x[ ][ ] and adds the product to the corresponding portion of a vector y[ ] --- a portion of y[ ] is replaced by the corresponding portion of ax[ ][j] + y[ ].
static double	colvdot_j(int nrow, double[][] x, double[] y, int begin, int j)	This method calculates the dot product of a portion of a column of a matrix and the corresponding portion of a vector.
static void	colvraxpy_j(int nrow, double a, double[] y, double[][] x, int begin, int j)	This method multiplies a constant times a portion of a vector y[ ] and adds the product to the corresponding portion of a column of a matrix x[ ][ ] --- a portion of column j of x[ ][ ] is replaced by the corresponding portion of ay[ ] + x[ ][j].
static void	daxpy_j(int n, double da, double[] dx, int incx, double[] dy, int incy)	This method multiplies a constant times a vector and adds the product to another vector --- dy[ ] = da*dx[ ] + dy[ ].
static void	dcopy_j(int n, double[] dx, int incx, double[] dy, int incy)	This method copies the vector dx[ ] to the vector dy[ ].
static void	dcopyp_j(int nrow, double[] x, double[] y, int begin)	This method copies a portion of vector x[ ] to the corresponding portion of vector y[ ].
static double	ddot_j(int n, double[] dx, int incx, double[] dy, int incy)	This method calculates the dot product of two vectors.
static double	dnrm2_j(int n, double[] x, int incx)	This method calculates the Euclidean norm of the vector stored in dx[ ] with storage increment incx.
static double	dnrm2p_j(int nrow, double[] x, int begin)	This method calculates the Euclidean norm of a portion of a vector x[ ].
static void	drotg_j(double[] rotvec)	This method constructs a Givens plane rotation.
static void	dscal_j(int n, double da, double[] dx, int incx)	This method scales a vector by a constant.
static void	dscalp_j(int nrow, double a, double[] x, int begin)	This method scales a portion of a vector by a constant.
static void	dswap_j(int n, double[] dx, int incx, double[] dy, int incy)	This method interchanges two vectors.
static int	isamax_j(int n, double[] x, int incx)	This method finds the index of the element of a vector that has the maximum absolute value.
static void	matmat_j(double[][] a, double[][] b, double[][] c, int n, int p, int r)	This method multiplies an n x p matrix by a p x r matrix.
static void	mattran_j(double[][] a, double[][] at, int n, int p)	This method obtains the transpose of an n x p matrix.
static void	matvec_j(double[][] a, double[] b, double[] c, int n, int p)	This method multiplies an n x p matrix by a p x 1 vector.
static double	sign_j(double a, double b)	This method implements the FORTRAN sign (not sin) function.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

Blas

public Blas()

Method Detail

colaxpy_j

public static void colaxpy_j(int nrow,
                             double a,
                             double[][] x,
                             int begin,
                             int j1,
                             int j2)

This method multiplies a constant times a portion of a column of a matrix and adds the product to the corresponding portion of another column of the matrix --- a portion of col2 is replaced by the corresponding portion of a*col1 + col2. It uses unrolled loops. It is a modification of the LINPACK subroutine DAXPY. In the LINPACK listing DAXPY is attributed to Jack Dongarra with a date of 3/11/78. Translated and modified by Steve Verrill, February 26, 1997.

Parameters:

nrow - The number of rows involved

a - The constant

x - [ ][ ] The matrix

begin - The starting row

j1 - The id of col1

j2 - The id of col2

coldot_j

public static double coldot_j(int nrow,
                              double[][] x,
                              int begin,
                              int j1,
                              int j2)

This method calculates the dot product of portions of two columns of a matrix. It uses unrolled loops. It is a modification of the LINPACK function DDOT. In the LINPACK listing DDOT is attributed to Jack Dongarra with a date of 3/11/78. Translated and modified by Steve Verrill, February 27, 1997.

Parameters:

nrow - The number of rows involved

x - [ ][ ] The matrix

begin - The starting row

j1 - The id of the first column

j2 - The id of the second column

colisamax_j

public static int colisamax_j(int n,
                              double[][] x,
                              int incx,
                              int begin,
                              int j)

This method finds the index of the element of a portion of a column of a matrix that has the maximum absolute value. It is a modification of the LINPACK function ISAMAX. In the LINPACK listing ISAMAX is attributed to Jack Dongarra with a date of March 11, 1978. Translated by Steve Verrill, March 10, 1998.

Parameters:

n - The number of elements to be checked

x - [ ][ ] The matrix

incx - The subscript increment for x[ ][ ]

begin - The starting row

j - The id of the column

colnrm2_j

public static double colnrm2_j(int nrow,
                               double[][] x,
                               int begin,
                               int j)

This method calculates the Euclidean norm of a portion of a column of a matrix. It is a modification of the LINPACK function dnrm2. In the LINPACK listing dnrm2 is attributed to C.L. Lawson with a date of January 8, 1978. The routine below is based on a more recent dnrm2 version that is attributed in LAPACK documentation to Sven Hammarling. Translated and modified by Steve Verrill, February 26, 1997.

Parameters:

nrow - The number of rows involved

x - [ ][ ] The matrix

begin - The starting row

j - The id of the column

colrot_j

public static void colrot_j(int n,
                            double[][] x,
                            int j1,
                            int j2,
                            double c,
                            double s)

This method "applies a plane rotation." It is a modification of the LINPACK function DROT. In the LINPACK listing DROT is attributed to Jack Dongarra with a date of 3/11/78. Translated and modified by Steve Verrill, March 4, 1997.

Parameters:

n - The order of x[ ][ ]

x - [ ][ ] The matrix

j1 - The id of the first column

j2 - The id of the second column

c - "cos"

s - "sin"

colscal_j

public static void colscal_j(int nrow,
                             double a,
                             double[][] x,
                             int begin,
                             int j)

This method scales a portion of a column of a matrix by a constant. It uses unrolled loops. It is a modification of the LINPACK subroutine DSCAL. In the LINPACK listing DSCAL is attributed to Jack Dongarra with a date of 3/11/78. Translated and modified by Steve Verrill, February 27, 1997.

Parameters:

nrow - The number of rows involved

a - The constant

x - [ ][ ] The matrix

begin - The starting row

j - The id of the column

colswap_j

public static void colswap_j(int n,
                             double[][] x,
                             int j1,
                             int j2)

This method interchanges two columns of a matrix. It uses unrolled loops. It is a modification of the LINPACK function DSWAP. In the LINPACK listing DSWAP is attributed to Jack Dongarra with a date of 3/11/78. Translated and modified by Steve Verrill, February 26, 1997.

Parameters:

n - The number of rows of the matrix

x - [ ][ ] The matrix

j1 - The id of the first column

j2 - The id of the second column

colvaxpy_j

public static void colvaxpy_j(int nrow,
                              double a,
                              double[][] x,
                              double[] y,
                              int begin,
                              int j)

This method multiplies a constant times a portion of a column of a matrix x[ ][ ] and adds the product to the corresponding portion of a vector y[ ] --- a portion of y[ ] is replaced by the corresponding portion of ax[ ][j] + y[ ]. It uses unrolled loops. It is a modification of the LINPACK subroutine DAXPY. In the LINPACK listing DAXPY is attributed to Jack Dongarra with a date of 3/11/78. Translated and modified by Steve Verrill, March 1, 1997.

Parameters:

nrow - The number of rows involved

a - The constant

x - [ ][ ] The matrix

y - [ ] The vector

begin - The starting row

j - The id of the column of the x matrix

colvdot_j

public static double colvdot_j(int nrow,
                               double[][] x,
                               double[] y,
                               int begin,
                               int j)

This method calculates the dot product of a portion of a column of a matrix and the corresponding portion of a vector. It uses unrolled loops. It is a modification of the LINPACK function DDOT. In the LINPACK listing DDOT is attributed to Jack Dongarra with a date of 3/11/78. Translated and modified by Steve Verrill, March 1, 1997.

Parameters:

nrow - The number of rows involved

x - [ ][ ] The matrix

y - [ ] The vector

begin - The starting row

j - The id of the column of the matrix

colvraxpy_j

public static void colvraxpy_j(int nrow,
                               double a,
                               double[] y,
                               double[][] x,
                               int begin,
                               int j)

This method multiplies a constant times a portion of a vector y[ ] and adds the product to the corresponding portion of a column of a matrix x[ ][ ] --- a portion of column j of x[ ][ ] is replaced by the corresponding portion of ay[ ] + x[ ][j]. It uses unrolled loops. It is a modification of the LINPACK subroutine DAXPY. In the LINPACK listing DAXPY is attributed to Jack Dongarra with a date of 3/11/78. Translated and modified by Steve Verrill, March 3, 1997.

Parameters:

nrow - The number of rows involved

a - The constant

y - [ ] The vector

x - [ ][ ] The matrix

begin - The starting row

j - The id of the column of the x matrix

daxpy_j

public static void daxpy_j(int n,
                           double da,
                           double[] dx,
                           int incx,
                           double[] dy,
                           int incy)

This method multiplies a constant times a vector and adds the product to another vector --- dy[ ] = da*dx[ ] + dy[ ]. It uses unrolled loops for increments equal to one. It is a translation from FORTRAN to Java of the LINPACK subroutine DAXPY. In the LINPACK listing DAXPY is attributed to Jack Dongarra with a date of 3/11/78. Translated by Steve Verrill, June 3, 1997.

Parameters:

n - The order of the vectors dy[ ] and dx[ ]

da - The constant

dx - [ ] This vector will be multiplied by the constant da

incx - The subscript increment for dx[ ]

dy - [ ] This vector will be added to da*dx[ ]

incy - The subscript increment for dy[ ]

dcopy_j

public static void dcopy_j(int n,
                           double[] dx,
                           int incx,
                           double[] dy,
                           int incy)

This method copies the vector dx[ ] to the vector dy[ ]. It uses unrolled loops for increments equal to one. It is a translation from FORTRAN to Java of the LINPACK subroutine DCOPY. In the LINPACK listing DCOPY is attributed to Jack Dongarra with a date of 3/11/78. Translated by Steve Verrill, March 1, 1997.

Parameters:

n - The order of dx[ ] and dy[ ]

dx - [ ] vector

incx - The subscript increment for dx[ ]

dy - [ ] vector

incy - The subscript increment for dy[ ]

dcopyp_j

public static void dcopyp_j(int nrow,
                            double[] x,
                            double[] y,
                            int begin)

This method copies a portion of vector x[ ] to the corresponding portion of vector y[ ]. It uses unrolled loops. It is a modification of the LINPACK subroutine dcopy. In the LINPACK listing dcopy is attributed to Jack Dongarra with a date of 3/11/78. Translated by Steve Verrill, March 1, 1997.

Parameters:

nrow - The number of rows involved

x - [ ] vector

y - [ ] vector

begin - The starting row

ddot_j

public static double ddot_j(int n,
                            double[] dx,
                            int incx,
                            double[] dy,
                            int incy)

This method calculates the dot product of two vectors. It uses unrolled loops for increments equal to one. It is a translation from FORTRAN to Java of the LINPACK function DDOT. In the LINPACK listing DDOT is attributed to Jack Dongarra with a date of 3/11/78. Translated by Steve Verrill, June 3, 1997.

Parameters:

n - The order of the vectors dx[ ] and dy[ ]

dx - [ ] vector

incx - The subscript increment for dx[ ]

dy - [ ] vector

incy - The subscript increment for dy[ ]

dnrm2_j

public static double dnrm2_j(int n,
                             double[] x,
                             int incx)

This method calculates the Euclidean norm of the vector stored in dx[ ] with storage increment incx. It is a translation from FORTRAN to Java of the LINPACK function DNRM2. In the LINPACK listing DNRM2 is attributed to C.L. Lawson with a date of January 8, 1978. The routine below is based on a more recent DNRM2 version that is attributed in LAPACK documentation to Sven Hammarling. Translated by Steve Verrill, June 3, 1997.

Parameters:

n - The order of the vector x[ ]

x - [ ] vector

incx - The subscript increment for x[ ]

dnrm2p_j

public static double dnrm2p_j(int nrow,
                              double[] x,
                              int begin)

This method calculates the Euclidean norm of a portion of a vector x[ ]. It is a modification of the LINPACK function dnrm2. In the LINPACK listing dnrm2 is attributed to C.L. Lawson with a date of January 8, 1978. The routine below is based on a more recent dnrm2 version that is attributed in LAPACK documentation to Sven Hammarling. Translated by Steve Verrill, March 3, 1997.

Parameters:

nrow - The number of rows involved

x - [ ] vector

begin - The starting row

drotg_j

public static void drotg_j(double[] rotvec)

This method constructs a Givens plane rotation. It is a translation from FORTRAN to Java of the LINPACK subroutine DROTG. In the LINPACK listing DROTG is attributed to Jack Dongarra with a date of 3/11/78. Translated by Steve Verrill, March 3, 1997.

Parameters:

rotvec - [] Contains the a,b,c,s values. In Java they cannot be passed as primitive types (e.g., double or int or ...) if we want their return values to be altered.

dscal_j

public static void dscal_j(int n,
                           double da,
                           double[] dx,
                           int incx)

This method scales a vector by a constant. It uses unrolled loops for an increment equal to one. It is a translation from FORTRAN to Java of the LINPACK subroutine DSCAL. In the LINPACK listing DSCAL is attributed to Jack Dongarra with a date of 3/11/78. Translated by Steve Verrill, June 3, 1997.

Parameters:

n - The order of the vector dx[ ]

da - The constant

dx - [ ] This vector will be multiplied by the constant da

incx - The subscript increment for dx[ ]

dscalp_j

public static void dscalp_j(int nrow,
                            double a,
                            double[] x,
                            int begin)

This method scales a portion of a vector by a constant. It uses unrolled loops. It is a modification of the LINPACK subroutine DSCAL. In the LINPACK listing DSCAL is attributed to Jack Dongarra with a date of 3/11/78. Translated and modified by Steve Verrill, March 3, 1997.

Parameters:

nrow - The number of rows involved

a - The constant

x - [ ] The vector

begin - The starting row

dswap_j

public static void dswap_j(int n,
                           double[] dx,
                           int incx,
                           double[] dy,
                           int incy)

This method interchanges two vectors. It uses unrolled loops for increments equal to one. It is a translation from FORTRAN to Java of the LINPACK function DSWAP. In the LINPACK listing DSWAP is attributed to Jack Dongarra with a date of 3/11/78. Translated by Steve Verrill, June 3, 1997.

Parameters:

n - The order of the vectors dx[ ] and dy[ ]

dx - [ ] vector

incx - The subscript increment for dx[ ]

dy - [ ] vector

incy - The subscript increment for dy[ ]

isamax_j

public static int isamax_j(int n,
                           double[] x,
                           int incx)

This method finds the index of the element of a vector that has the maximum absolute value. It is a translation from FORTRAN to Java of the LINPACK function ISAMAX. In the LINPACK listing ISAMAX is attributed to Jack Dongarra with a date of March 11, 1978. Before you use this version of isamax, make certain that it is doing what you expect it to do. Translated by Steve Verrill, March 10, 1998.

Parameters:

n - The number of elements to be checked

x - [ ] vector

incx - The subscript increment for x[ ]

matmat_j

public static void matmat_j(double[][] a,
                            double[][] b,
                            double[][] c,
                            int n,
                            int p,
                            int r)

This method multiplies an n x p matrix by a p x r matrix. Created by Steve Verrill, March 1997.

Parameters:

a - [ ][ ] The left matrix

b - [ ][ ] The right matrix

c - [ ][ ] The product

n - n

p - p

r - r

mattran_j

public static void mattran_j(double[][] a,
                             double[][] at,
                             int n,
                             int p)

This method obtains the transpose of an n x p matrix. Created by Steve Verrill, March 1997.

Parameters:

a - [ ][ ] matrix

at - [ ][ ] transpose of the matrix

n - n

p - p

matvec_j

public static void matvec_j(double[][] a,
                            double[] b,
                            double[] c,
                            int n,
                            int p)

This method multiplies an n x p matrix by a p x 1 vector. Created by Steve Verrill, March 1997.

Parameters:

a - [ ][ ] The matrix

b - [ ] The vector

c - [ ] The product

n - n

p - p

sign_j

public static double sign_j(double a,
                            double b)

This method implements the FORTRAN sign (not sin) function. See the code for details. Created by Steve Verrill, March 1997.

Parameters:

a - a

b - b