linear_algebra
Class Blas_f77

java.lang.Object
  |
  +--linear_algebra.Blas_f77

public class Blas_f77
extends java.lang.Object

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

  1. isamax_f77
  2. daxpy_f77
  3. ddot_f77
  4. dscal_f77
  5. dswap_f77
  6. dnrm2_f77
  7. dcopy_f77
  8. drotg_f77
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_f77
  2. colaxpy_f77
  3. colvaxpy_f77
  4. colvraxpy_f77
  5. coldot_f77
  6. colvdot_f77
  7. colscal_f77
  8. dscalp_f77
  9. colswap_f77
  10. colnrm2_f77
  11. dnrm2p_f77
  12. dcopyp_f77
  13. colrot_f77
  14. sign_f77

IMPORTANT: The "_f77" suffixes indicate that these routines use FORTRAN style indexing. For example, you will see for (i = 1; i <= n; i++) rather than for (i = 0; i < n; i++) To use the "_f77" routines you will have to declare your vectors and matrices to be one element larger (e.g., v[101] rather than v[100], and a[101][101] rather than a[100][100]), and you will have to fill elements 1 through n rather than elements 0 through n - 1. Versions of these programs that use C/Java style indexing will soon be available. They will end with the suffix "_j".

This class was translated by a statistician from FORTRAN versions of the LINPACK blas. It is NOT an official translation. It wastes memory by failing to use the first elements of vectors. 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 steve@ws13.fpl.fs.fed.us.


Constructor Summary
Blas_f77()
           
 
Method Summary
static void colaxpy_f77(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_f77(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_f77(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_f77(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_f77(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_f77(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_f77(int n, double[][] x, int j1, int j2)
           This method interchanges two columns of a matrix.
static void colvaxpy_f77(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_f77(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_f77(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_f77(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_f77(int n, double[] dx, int incx, double[] dy, int incy)
           This method copies the vector dx[ ] to the vector dy[ ].
static void dcopyp_f77(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_f77(int n, double[] dx, int incx, double[] dy, int incy)
           This method calculates the dot product of two vectors.
static double dnrm2_f77(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_f77(int nrow, double[] x, int begin)
           This method calculates the Euclidean norm of a portion of a vector x[ ].
static void drotg_f77(double[] rotvec)
           This method constructs a Givens plane rotation.
static void dscal_f77(int n, double da, double[] dx, int incx)
           This method scales a vector by a constant.
static void dscalp_f77(int nrow, double a, double[] x, int begin)
           This method scales a portion of a vector by a constant.
static void dswap_f77(int n, double[] dx, int incx, double[] dy, int incy)
           This method interchanges two vectors.
static int isamax_f77(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_f77(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_f77(double[][] a, double[][] at, int n, int p)
           This method obtains the transpose of an n x p matrix.
static void matvec_f77(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_f77(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_f77

public Blas_f77()
Method Detail

isamax_f77

public static int isamax_f77(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. Translated by Steve Verrill, March 10, 1998.

Parameters:
n - The number of elements to be checked
incx - The subscript increment for x[ ]

colisamax_f77

public static int colisamax_f77(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
incx - The subscript increment for x[ ][ ]
begin - The starting row
j - The id of the column

daxpy_f77

public static void daxpy_f77(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, February 25, 1997.

Parameters:
n - The order of the vectors dy[ ] and dx[ ]
da - The constant
incx - The subscript increment for dx[ ]
incy - The subscript increment for dy[ ]

ddot_f77

public static double ddot_f77(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, February 25, 1997.

Parameters:
n - The order of the vectors dx[ ] and dy[ ]
incx - The subscript increment for dx[ ]
incy - The subscript increment for dy[ ]

dscal_f77

public static void dscal_f77(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, February 25, 1997.

Parameters:
n - The order of the vector dx[ ]
da - The constant
incx - The subscript increment for dx[ ]

dswap_f77

public static void dswap_f77(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, February 25, 1997.

Parameters:
n - The order of the vectors dx[ ] and dy[ ]
incx - The subscript increment for dx[ ]
incy - The subscript increment for dy[ ]

dnrm2_f77

public static double dnrm2_f77(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, February 25, 1997.

Parameters:
n - The order of the vector x[ ]
incx - The subscript increment for x[ ]

dcopy_f77

public static void dcopy_f77(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[ ]
incx - The subscript increment for dx[ ]
incy - The subscript increment for dy[ ]

drotg_f77

public static void drotg_f77(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.


colaxpy_f77

public static void colaxpy_f77(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
begin - The starting row
j1 - The id of col1
j2 - The id of col2

colvaxpy_f77

public static void colvaxpy_f77(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
begin - The starting row
j - The id of the column of the x matrix

colvraxpy_f77

public static void colvraxpy_f77(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
begin - The starting row
j - The id of the column of the x matrix

coldot_f77

public static double coldot_f77(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
begin - The starting row
j1 - The id of the first column
j2 - The id of the second column

colvdot_f77

public static double colvdot_f77(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
begin - The starting row
j - The id of the column of the matrix

colscal_f77

public static void colscal_f77(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
begin - The starting row
j - The id of the column

dscalp_f77

public static void dscalp_f77(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
begin - The starting row

colswap_f77

public static void colswap_f77(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
j1 - The id of the first column
j2 - The id of the second column

colnrm2_f77

public static double colnrm2_f77(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
begin - The starting row
j - The id of the column

dnrm2p_f77

public static double dnrm2p_f77(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
begin - The starting row

dcopyp_f77

public static void dcopyp_f77(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
begin - The starting row

colrot_f77

public static void colrot_f77(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[ ][ ]
j1 - The id of the first column
j2 - The id of the second column
c - "cos"
s - "sin"

sign_f77

public static double sign_f77(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

matmat_f77

public static void matmat_f77(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:
n - n
p - p
r - r

mattran_f77

public static void mattran_f77(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:
n - n
p - p

matvec_f77

public static void matvec_f77(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:
n - n
p - p