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blas2.cpp
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# include <cstdlib>
# include <iostream>
# include <iomanip>
# include <cmath>
# include <complex>
using namespace std;
# include "blas0.hpp"
# include "blas2.hpp"
//****************************************************************************80
void dgemv ( char trans, int m, int n, double alpha, double a[], int lda,
double x[], int incx, double beta, double y[], int incy )
//****************************************************************************80
//
// Purpose:
//
// DGEMV computes y := alpha * A * x + beta * y for general matrix A.
//
// Discussion:
//
// DGEMV performs one of the matrix-vector operations
// y := alpha*A *x + beta*y
// or
// y := alpha*A'*x + beta*y,
// where alpha and beta are scalars, x and y are vectors and A is an
// m by n matrix.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 02 April 2014
//
// Author:
//
// C++ version by John Burkardt
//
// Parameters:
//
// Input, char TRANS, specifies the operation to be performed:
// 'n' or 'N' y := alpha*A *x + beta*y.
// 't' or 'T' y := alpha*A'*x + beta*y.
// 'c' or 'C' y := alpha*A'*x + beta*y.
//
// Input, int M, the number of rows of the matrix A.
// 0 <= M.
//
// Input, int N, the number of columns of the matrix A.
// 0 <= N.
//
// Input, double ALPHA, the scalar multiplier for A * x.
//
// Input, double A[LDA*N]. The M x N subarray contains
// the matrix A.
//
// Input, int LDA, the the first dimension of A as declared
// in the calling routine. max ( 1, M ) <= LDA.
//
// Input, double X[*], an array containing the vector to be
// multiplied by the matrix A.
// If TRANS = 'N' or 'n', then X must contain N entries, stored in INCX
// increments in a space of at least ( 1 + ( N - 1 ) * abs ( INCX ) )
// locations.
// Otherwise, X must contain M entries, store in INCX increments
// in a space of at least ( 1 + ( M - 1 ) * abs ( INCX ) ) locations.
//
// Input, int INCX, the increment for the elements of
// X. INCX must not be zero.
//
// Input, double BETA, the scalar multiplier for Y.
//
// Input/output, double Y[*], an array containing the vector to
// be scaled and incremented by A*X.
// If TRANS = 'N' or 'n', then Y must contain M entries, stored in INCY
// increments in a space of at least ( 1 + ( M - 1 ) * abs ( INCY ) )
// locations.
// Otherwise, Y must contain N entries, store in INCY increments
// in a space of at least ( 1 + ( N - 1 ) * abs ( INCY ) ) locations.
//
// Input, int INCY, the increment for the elements of
// Y. INCY must not be zero.
//
{
int i;
int info;
int ix;
int iy;
int j;
int jx;
int jy;
int kx;
int ky;
int lenx;
int leny;
double temp;
//
// Test the input parameters.
//
info = 0;
if ( ! lsame ( trans, 'N' ) &&
! lsame ( trans, 'T' ) &&
! lsame ( trans, 'C' ) )
{
info = 1;
}
else if ( m < 0 )
{
info = 2;
}
else if ( n < 0 )
{
info = 3;
}
else if ( lda < i4_max ( 1, m ) )
{
info = 6;
}
else if ( incx == 0 )
{
info = 8;
}
else if ( incy == 0 )
{
info = 11;
}
if ( info != 0 )
{
xerbla ( "DGEMV", info );
return;
}
//
// Quick return if possible.
//
if ( ( m == 0 ) ||
( n == 0 ) ||
( ( alpha == 0.0 ) && ( beta == 1.0 ) ) )
{
return;
}
//
// Set LENX and LENY, the lengths of the vectors x and y, and set
// up the start points in X and Y.
//
if ( lsame ( trans, 'N' ) )
{
lenx = n;
leny = m;
}
else
{
lenx = m;
leny = n;
}
if ( 0 < incx )
{
kx = 0;
}
else
{
kx = 0 - ( lenx - 1 ) * incx;
}
if ( 0 < incy )
{
ky = 0;
}
else
{
ky = 0 - ( leny - 1 ) * incy;
}
//
// Start the operations. In this version the elements of A are
// accessed sequentially with one pass through A.
//
// First form y := beta*y.
//
if ( beta != 1.0 )
{
if ( incy == 1 )
{
if ( beta == 0.0 )
{
for ( i = 0; i < leny; i++ )
{
y[i] = 0.0;
}
}
else
{
for ( i = 0; i < leny; i++ )
{
y[i] = beta * y[i];
}
}
}
else
{
iy = ky;
if ( beta == 0.0 )
{
for ( i = 0; i < leny; i++ )
{
y[iy] = 0.0;
iy = iy + incy;
}
}
else
{
for ( i = 0; i < leny; i++ )
{
y[iy] = beta * y[iy];
iy = iy + incy;
}
}
}
}
if ( alpha == 0.0 )
{
return;
}
//
// Form y := alpha*A*x + y.
//
if ( lsame ( trans, 'N' ) )
{
jx = kx;
if ( incy == 1 )
{
for ( j = 0; j < n; j++ )
{
if ( x[jx] != 0.0 )
{
temp = alpha * x[jx];
for ( i = 0; i < m; i++ )
{
y[i] = y[i] + temp * a[i+j*lda];
}
}
jx = jx + incx;
}
}
else
{
for ( j = 0; j < n; j++ )
{
if ( x[jx] != 0.0 )
{
temp = alpha * x[jx];
iy = ky;
for ( i = 0; i < m; i++ )
{
y[iy] = y[iy] + temp * a[i+j*lda];
iy = iy + incy;
}
}
jx = jx + incx;
}
}
}
/*
Form y := alpha*A'*x + y.
*/
else
{
jy = ky;
if ( incx == 1 )
{
for ( j = 0; j < n; j++ )
{
temp = 0.0;
for ( i = 0; i < m; i++ )
{
temp = temp + a[i+j*lda] * x[i];
}
y[jy] = y[jy] + alpha * temp;
jy = jy + incy;
}
}
else
{
for ( j = 0; j < n; j++ )
{
temp = 0.0;
ix = kx;
for ( i = 0; i < m; i++ )
{
temp = temp + a[i+j*lda] * x[ix];
ix = ix + incx;
}
y[jy] = y[jy] + alpha * temp;
jy = jy + incy;
}
}
}
return;
}
//****************************************************************************80
void dger ( int m, int n, double alpha, double x[], int incx, double y[],
int incy, double a[], int lda )
//****************************************************************************80
//
// Purpose:
//
// DGER computes A := alpha*x*y' + A.
//
// Discussion:
//
// DGER performs the rank 1 operation
//
// A := alpha*x*y' + A,
//
// where alpha is a scalar, x is an m element vector, y is an n element
// vector and A is an m by n matrix.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 04 April 2014
//
// Author:
//
// Original FORTRAN77 version by Jack Dongarra, Jeremy Du Croz,
// Sven Hammarling, Richard Hanson.
// This C++ version by John Burkardt.
//
// Parameters:
//
// Input, int M, the number of rows of the matrix A.
// 0 <= M.
//
// Input, int N, the number of columns of the matrix A.
// 0 <= N.
//
// Input, double ALPHA, the scalar multiplier.
//
// Input, double X[1+(M-1)*abs(INCX)], the first vector.
//
// Input, int INCX, the increment for elements of X.
// INCX must not be zero.
//
// Input, double Y[1+(N-1)*abs(INCY)], the second vector.
//
// Input, int INCY, the increment for elements of Y.
// INCY must not be zero.
//
// Input/output, double A[LDA*N]. On entry, the leading M by N
// part of the array contains the matrix of coefficients. On exit, A is
// overwritten by the updated matrix.
//
// Input, int LDA, the first dimension of A as declared
// in the calling program. max ( 1, M ) <= LDA.
//
{
int i;
int info;
int ix;
int j;
int jy;
int kx;
double temp;
//
// Test the input parameters.
//
info = 0;
if ( m < 0 )
{
info = 1;
}
else if ( n < 0 )
{
info = 2;
}
else if ( incx == 0 )
{
info = 5;
}
else if ( incy == 0 )
{
info = 7;
}
else if ( lda < i4_max ( 1, m ) )
{
info = 9;
}
if ( info != 0 )
{
xerbla ( "DGER", info );
return;
}
//
// Quick return if possible.
//
if ( m == 0 || n == 0 || alpha == 0.0 )
{
return;
}
//
// Start the operations. In this version the elements of A are
// accessed sequentially with one pass through A.
//
if ( 0 < incy )
{
jy = 0;
}
else
{
jy = 0 - ( n - 1 ) * incy;
}
if ( incx == 1 )
{
for ( j = 0; j < n; j++ )
{
if ( y[jy] != 0.0 )
{
temp = alpha * y[jy];
for ( i = 0; i < m; i++ )
{
a[i+j*lda] = a[i+j*lda] + x[i] * temp;
}
}
jy = jy + incy;
}
}
else
{
if ( 0 < incx )
{
kx = 0;
}
else
{
kx = 0 - ( m - 1 ) * incx;
}
for ( j = 0; j < n; j++ )
{
if ( y[jy] != 0.0 )
{
temp = alpha * y[jy];
ix = kx;
for ( i = 0; i < m; i++ )
{
a[i+j*lda] = a[i+j*lda] + x[ix] * temp;
ix = ix + incx;
}
}
jy = jy + incy;
}
}
return;
}
//****************************************************************************80
void dtrmv ( char uplo, char trans, char diag, int n, double a[], int lda,
double x[], int incx )
//****************************************************************************80
//
// Purpose:
//
// DTRMV computes x: = A*x or x = A'*x for a triangular matrix A.
//
// Discussion:
//
// DTRMV performs one of the matrix-vector operations
//
// x := A*x, or x := A'*x,
//
// where x is an n element vector and A is an n by n unit, or non-unit,
// upper or lower triangular matrix.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 04 April 2014
//
// Author:
//
// This C++ version by John Burkardt.
//
// Parameters:
//
// Input, char UPLO, specifies whether the matrix is an upper or
// lower triangular matrix as follows:
// 'u' or 'U': A is an upper triangular matrix.
// 'l' or 'L': A is a lower triangular matrix.
//
// Input, char TRANS, specifies the operation to be performed as
// follows:
// 'n' or 'N': x := A*x.
// 't' or 'T': x := A'*x.
// 'c' or 'C': x := A'*x.
//
// Input, char DIAG, specifies whether or not A is unit
// triangular as follows:
// 'u' or 'U': A is assumed to be unit triangular.
// 'n' or 'N': A is not assumed to be unit triangular.
//
// Input, int N, the order of the matrix A.
// 0 <= N.
//
// Input, double A[LDA*N].
// Before entry with UPLO = 'u' or 'U', the leading n by n
// upper triangular part of the array A must contain the upper
// triangular matrix and the strictly lower triangular part of
// A is not referenced.
// Before entry with UPLO = 'l' or 'L', the leading n by n
// lower triangular part of the array A must contain the lower
// triangular matrix and the strictly upper triangular part of
// A is not referenced.
// Note that when DIAG = 'u' or 'U', the diagonal elements of
// A are not referenced either, but are assumed to be unity.
//
// Input, int LDA, the first dimension of A as declared
// in the calling program. max ( 1, N ) <= LDA.
//
// Input/output, double X[1+(N-1)*abs( INCX)].
// Before entry, the incremented array X must contain the n
// element vector x. On exit, X is overwritten with the
// tranformed vector x.
//
// Input, int INCX, the increment for the elements of
// X. INCX must not be zero.
//
{
int i;
int info;
int ix;
int j;
int jx;
int kx;
bool nounit;
double temp;
//
// Test the input parameters.
//
info = 0;
if ( ! lsame ( uplo, 'U' ) && ! lsame ( uplo, 'L' ) )
{
info = 1;
}
else if ( ! lsame ( trans, 'N' ) && ! lsame ( trans, 'T' ) &&
! lsame ( trans, 'C' ) )
{
info = 2;
}
else if ( ! lsame ( diag, 'U' ) && ! lsame ( diag, 'N' ) )
{
info = 3;
}
else if ( n < 0 )
{
info = 4;
}
else if ( lda < i4_max ( 1, n ) )
{
info = 6;
}
else if ( incx == 0 )
{
info = 8;
}
if ( info != 0 )
{
xerbla ( "DTRMV", info );
return;
}
//
// Quick return if possible.
//
if ( n == 0 )
{
return;
}
nounit = lsame ( diag, 'N' );
//
// Set up the start point in X if the increment is not unity. This
// will be ( N - 1 ) * INCX too small for descending loops.
//
if ( incx <= 0 )
{
kx = 0 - ( n - 1 ) * incx;
}
else if ( incx != 1 )
{
kx = 0;
}
//
// Start the operations. In this version the elements of A are
// accessed sequentially with one pass through A.
//
if ( lsame ( trans, 'N' ) )
{
//
// Form x := A*x.
//
if ( lsame ( uplo, 'U' ) )
{
if ( incx == 1 )
{
for ( j = 0; j < n; j++ )
{
if ( x[j] != 0.0 )
{
temp = x[j];
for ( i = 0; i < j; i++ )
{
x[i] = x[i] + temp * a[i+j*lda];
}
if ( nounit )
{
x[j] = x[j] * a[j+j*lda];
}
}
}
}
else
{
jx = kx;
for ( j = 0; j < n; j++ )
{
if ( x[jx] != 0.0 )
{
temp = x[jx];
ix = kx;
for ( i = 0; i < j; i++ )
{
x[ix] = x[ix] + temp * a[i+j*lda];
ix = ix + incx;
}
if ( nounit )
{
x[jx] = x[jx] * a[j+j*lda];
}
}
jx = jx + incx;
}
}
}
else
{
if ( incx == 1 )
{
for ( j = n - 1; 0 <= j; j-- )
{
if ( x[j] != 0.0 )
{
temp = x[j];
for ( i = n - 1; j < i; i-- )
{
x[i] = x[i] + temp * a[i+j*lda];
}
if ( nounit )
{
x[j] = x[j] * a[j+j*lda];
}
}
}
}
else
{
kx = kx + ( n - 1 ) * incx;
jx = kx;
for ( j = n - 1; 0 <= j; j-- )
{
if ( x[jx] != 0.0 )
{
temp = x[jx];
ix = kx;
for ( i = n - 1; j < i; i-- )
{
x[ix] = x[ix] + temp * a[i+j*lda];
ix = ix - incx;
}
if ( nounit )
{
x[jx] = x[jx] * a[j+j*lda];
}
}
jx = jx - incx;
}
}
}
}
//
// Form x := A'*x.
//
else
{
if ( lsame ( uplo, 'U' ) )
{
if ( incx == 1 )
{
for ( j = n - 1; 0 <= j; j-- )
{
temp = x[j];
if ( nounit )
{
temp = temp * a[j+j*lda];
}
for ( i = j - 1; 0 <= i; i-- )
{
temp = temp + a[i+j*lda] * x[i];
}
x[j] = temp;
}
}
else
{
jx = kx + ( n - 1 ) * incx;
for ( j = n - 1; 0 <= j; j-- )
{
temp = x[jx];
ix = jx;
if ( nounit )
{
temp = temp * a[j+j*lda];
}
for ( i = j - 1; 0 <= i; i-- )
{
ix = ix - incx;
temp = temp + a[i+j*lda] * x[ix];
}
x[jx] = temp;
jx = jx - incx;
}
}
}
else
{
if ( incx == 1 )
{
for ( j = 0; j < n; j++ )
{
temp = x[j];
if ( nounit )
{
temp = temp * a[j+j*lda];
}
for ( i = j + 1; i < n; i++ )
{
temp = temp + a[i+j*lda] * x[i];
}
x[j] = temp;
}
}
else
{
jx = kx;
for ( j = 0; j < n; j++ )
{
temp = x[jx];
ix = jx;
if ( nounit )
{
temp = temp * a[j+j*lda];
}
for ( i = j + 1; i < n; i++ )
{
ix = ix + incx;
temp = temp + a[i+j*lda] * x[ix];
}
x[jx] = temp;
jx = jx + incx;
}
}
}
}
return;
}
//****************************************************************************80
void sgemv ( char trans, int m, int n, float alpha, float a[], int lda,
float x[], int incx, float beta, float y[], int incy )
//****************************************************************************80
//
// Purpose:
//
// SGEMV computes y := alpha * A * x + beta * y for general matrix A.
//
// Discussion:
//
// SGEMV performs one of the matrix-vector operations
// y := alpha*A *x + beta*y
// or
// y := alpha*A'*x + beta*y,
// where alpha and beta are scalars, x and y are vectors and A is an
// m by n matrix.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 02 April 2014
//
// Author:
//
// C++ version by John Burkardt
//
// Parameters:
//
// Input, char TRANS, specifies the operation to be performed:
// 'n' or 'N' y := alpha*A *x + beta*y.
// 't' or 'T' y := alpha*A'*x + beta*y.
// 'c' or 'C' y := alpha*A'*x + beta*y.
//
// Input, int M, the number of rows of the matrix A.
// 0 <= M.
//
// Input, int N, the number of columns of the matrix A.
// 0 <= N.
//
// Input, float ALPHA, the scalar multiplier for A * x.
//
// Input, float A[LDA*N]. The M x N subarray contains
// the matrix A.
//
// Input, int LDA, the the first dimension of A as declared
// in the calling routine. max ( 1, M ) <= LDA.
//
// Input, float X[*], an array containing the vector to be
// multiplied by the matrix A.
// If TRANS = 'N' or 'n', then X must contain N entries, stored in INCX
// increments in a space of at least ( 1 + ( N - 1 ) * abs ( INCX ) )
// locations.
// Otherwise, X must contain M entries, store in INCX increments
// in a space of at least ( 1 + ( M - 1 ) * abs ( INCX ) ) locations.
//
// Input, int INCX, the increment for the elements of
// X. INCX must not be zero.
//
// Input, float BETA, the scalar multiplier for Y.
//
// Input/output, float Y[*], an array containing the vector to
// be scaled and incremented by A*X.
// If TRANS = 'N' or 'n', then Y must contain M entries, stored in INCY
// increments in a space of at least ( 1 + ( M - 1 ) * abs ( INCY ) )
// locations.
// Otherwise, Y must contain N entries, store in INCY increments
// in a space of at least ( 1 + ( N - 1 ) * abs ( INCY ) ) locations.
//
// Input, int INCY, the increment for the elements of
// Y. INCY must not be zero.
//
{
int i;
int info;
int ix;
int iy;
int j;
int jx;
int jy;
int kx;
int ky;
int lenx;
int leny;
float temp;
//
// Test the input parameters.
//
info = 0;
if ( ! lsame ( trans, 'N' ) &&
! lsame ( trans, 'T' ) &&
! lsame ( trans, 'C' ) )
{
info = 1;
}
else if ( m < 0 )
{
info = 2;
}
else if ( n < 0 )
{
info = 3;
}
else if ( lda < i4_max ( 1, m ) )
{
info = 6;
}
else if ( incx == 0 )
{
info = 8;
}
else if ( incy == 0 )
{
info = 11;
}
if ( info != 0 )
{
xerbla ( "SGEMV", info );
return;
}
//
// Quick return if possible.
//
if ( ( m == 0 ) ||
( n == 0 ) ||
( ( alpha == 0.0 ) && ( beta == 1.0 ) ) )
{
return;
}
//
// Set LENX and LENY, the lengths of the vectors x and y, and set
// up the start points in X and Y.
//
if ( lsame ( trans, 'N' ) )
{
lenx = n;
leny = m;
}
else
{
lenx = m;
leny = n;
}
if ( 0 < incx )
{
kx = 0;
}
else
{
kx = 0 - ( lenx - 1 ) * incx;
}
if ( 0 < incy )
{
ky = 0;
}
else
{
ky = 0 - ( leny - 1 ) * incy;
}
//
// Start the operations. In this version the elements of A are
// accessed sequentially with one pass through A.
//
// First form y := beta*y.
//
if ( beta != 1.0 )
{
if ( incy == 1 )
{
if ( beta == 0.0 )
{
for ( i = 0; i < leny; i++ )
{
y[i] = 0.0;
}
}
else
{
for ( i = 0; i < leny; i++ )
{
y[i] = beta * y[i];
}
}
}
else
{
iy = ky;
if ( beta == 0.0 )
{
for ( i = 0; i < leny; i++ )
{
y[iy] = 0.0;
iy = iy + incy;
}
}
else
{
for ( i = 0; i < leny; i++ )
{