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 invalid input: '<' n; i++) rather than (FORTRAN style) for (i = 1; i invalid input: '<'= 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."
    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[invalid input: '&#32'][invalid input: '&#32'] and adds the product to the corresponding portion of a vector y[invalid input: '&#32'] --- a portion of y[invalid input: '&#32'] is replaced by the corresponding portion of ax[invalid input: '&#32'][j] + y[invalid input: '&#32'].
    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[invalid input: '&#32'] and adds the product to the corresponding portion of a column of a matrix x[invalid input: '&#32'][invalid input: '&#32'] --- a portion of column j of x[invalid input: '&#32'][invalid input: '&#32'] is replaced by the corresponding portion of ay[invalid input: '&#32'] + x[invalid input: '&#32'][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[invalid input: '&#32'] = da*dx[invalid input: '&#32'] + dy[invalid input: '&#32'].
    static void
    dcopy_j(int n, double[] dx, int incx, double[] dy, int incy)
    This method copies the vector dx[invalid input: '&#32'] to the vector dy[invalid input: '&#32'].
    static void
    dcopyp_j(int nrow, double[] x, double[] y, int begin)
    This method copies a portion of vector x[invalid input: '&#32'] to the corresponding portion of vector y[invalid input: '&#32'].
    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[invalid input: '&#32'] 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[invalid input: '&#32'].
    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 Details

    • Blas

      public Blas()

  • Method Details

    • 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 - [invalid input: '&#32'][invalid input: '&#32'] 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 - [invalid input: '&#32'][invalid input: '&#32'] 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 - [invalid input: '&#32'][invalid input: '&#32'] The matrix
      incx - The subscript increment for x[invalid input: '&#32'][invalid input: '&#32']
      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 - [invalid input: '&#32'][invalid input: '&#32'] 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[invalid input: '&#32'][invalid input: '&#32']
      x - [invalid input: '&#32'][invalid input: '&#32'] 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 - [invalid input: '&#32'][invalid input: '&#32'] 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 - [invalid input: '&#32'][invalid input: '&#32'] 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[invalid input: '&#32'][invalid input: '&#32'] and adds the product to the corresponding portion of a vector y[invalid input: '&#32'] --- a portion of y[invalid input: '&#32'] is replaced by the corresponding portion of ax[invalid input: '&#32'][j] + y[invalid input: '&#32']. 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 - [invalid input: '&#32'][invalid input: '&#32'] The matrix
      y - [invalid input: '&#32'] 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 - [invalid input: '&#32'][invalid input: '&#32'] The matrix
      y - [invalid input: '&#32'] 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[invalid input: '&#32'] and adds the product to the corresponding portion of a column of a matrix x[invalid input: '&#32'][invalid input: '&#32'] --- a portion of column j of x[invalid input: '&#32'][invalid input: '&#32'] is replaced by the corresponding portion of ay[invalid input: '&#32'] + x[invalid input: '&#32'][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 - [invalid input: '&#32'] The vector
      x - [invalid input: '&#32'][invalid input: '&#32'] 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[invalid input: '&#32'] = da*dx[invalid input: '&#32'] + dy[invalid input: '&#32']. 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[invalid input: '&#32'] and dx[invalid input: '&#32']
      da - The constant
      dx - [invalid input: '&#32'] This vector will be multiplied by the constant da
      incx - The subscript increment for dx[invalid input: '&#32']
      dy - [invalid input: '&#32'] This vector will be added to da*dx[invalid input: '&#32']
      incy - The subscript increment for dy[invalid input: '&#32']

    • dcopy_j

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

      This method copies the vector dx[invalid input: '&#32'] to the vector dy[invalid input: '&#32']. 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[invalid input: '&#32'] and dy[invalid input: '&#32']
      dx - [invalid input: '&#32'] vector
      incx - The subscript increment for dx[invalid input: '&#32']
      dy - [invalid input: '&#32'] vector
      incy - The subscript increment for dy[invalid input: '&#32']

    • dcopyp_j

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

      This method copies a portion of vector x[invalid input: '&#32'] to the corresponding portion of vector y[invalid input: '&#32']. 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 - [invalid input: '&#32'] vector
      y - [invalid input: '&#32'] 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[invalid input: '&#32'] and dy[invalid input: '&#32']
      dx - [invalid input: '&#32'] vector
      incx - The subscript increment for dx[invalid input: '&#32']
      dy - [invalid input: '&#32'] vector
      incy - The subscript increment for dy[invalid input: '&#32']

    • 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[invalid input: '&#32'] 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[invalid input: '&#32']
      x - [invalid input: '&#32'] vector
      incx - The subscript increment for x[invalid input: '&#32']

    • 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[invalid input: '&#32']. 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 - [invalid input: '&#32'] 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[invalid input: '&#32']
      da - The constant
      dx - [invalid input: '&#32'] This vector will be multiplied by the constant da
      incx - The subscript increment for dx[invalid input: '&#32']

    • 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 - [invalid input: '&#32'] 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[invalid input: '&#32'] and dy[invalid input: '&#32']
      dx - [invalid input: '&#32'] vector
      incx - The subscript increment for dx[invalid input: '&#32']
      dy - [invalid input: '&#32'] vector
      incy - The subscript increment for dy[invalid input: '&#32']

    • 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 - [invalid input: '&#32'] vector
      incx - The subscript increment for x[invalid input: '&#32']

    • 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 - [invalid input: '&#32'][invalid input: '&#32'] The left matrix
      b - [invalid input: '&#32'][invalid input: '&#32'] The right matrix
      c - [invalid input: '&#32'][invalid input: '&#32'] 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 - [invalid input: '&#32'][invalid input: '&#32'] matrix
      at - [invalid input: '&#32'][invalid input: '&#32'] 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 - [invalid input: '&#32'][invalid input: '&#32'] The matrix
      b - [invalid input: '&#32'] The vector
      c - [invalid input: '&#32'] 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