/**
* Generalized Least Squares via *GELSD.
*
* <p>Note that B must be padded to contain the solution matrix. This occurs when A has fewer rows
* than columns.
*
* <p>For example: in A * X = B, A is (m,n), X is (n,k) and B is (m,k). Now if m < n, since B is
* overwritten to contain the solution (in classical LAPACK style), B needs to be padded to be an
* (n,k) matrix.
*
* <p>Likewise, if m > n, the solution consists only of the first n rows of B.
*
* @param A an (m,n) matrix
* @param B an (max(m,n), k) matrix (well, at least)
*/
public static void gelsd(FloatMatrix A, FloatMatrix B) {
int m = A.rows;
int n = A.columns;
int nrhs = B.columns;
int minmn = min(m, n);
int maxmn = max(m, n);
if (B.rows < maxmn) {
throw new SizeException("Result matrix B must be padded to contain the solution matrix X!");
}
int smlsiz = NativeBlas.ilaenv(9, "DGELSD", "", m, n, nrhs, 0);
int nlvl = max(0, (int) log2(minmn / (smlsiz + 1)) + 1);
// System.err.printf("GELSD\n");
// System.err.printf("m = %d, n = %d, nrhs = %d\n", m, n, nrhs);
// System.err.printf("smlsiz = %d, nlvl = %d\n", smlsiz, nlvl);
// System.err.printf("iwork size = %d\n", 3 * minmn * nlvl + 11 * minmn);
int[] iwork = new int[3 * minmn * nlvl + 11 * minmn];
float[] s = new float[minmn];
int[] rank = new int[1];
int info =
NativeBlas.sgelsd(m, n, nrhs, A.data, 0, m, B.data, 0, B.rows, s, 0, -1, rank, 0, iwork, 0);
if (info == 0) {
return;
} else if (info < 0) {
throw new LapackArgumentException("DGESD", -info);
} else if (info > 0) {
throw new LapackConvergenceException(
"DGESD",
info + " off-diagonal elements of an intermediat bidiagonal form did not converge to 0.");
}
}
/** Compute c <- a*b + beta * c (general matrix matrix multiplication) */
public static FloatMatrix gemm(
float alpha, FloatMatrix a, FloatMatrix b, float beta, FloatMatrix c) {
NativeBlas.sgemm(
'N', 'N', c.rows, c.columns, a.columns, alpha, a.data, 0, a.rows, b.data, 0, b.rows, beta,
c.data, 0, c.rows);
return c;
}
/** Compute c <- a*b + beta * c (general matrix matrix multiplication) */
public static DoubleMatrix gemm(
double alpha, DoubleMatrix a, DoubleMatrix b, double beta, DoubleMatrix c) {
NativeBlas.dgemm(
'N', 'N', c.rows, c.columns, a.columns, alpha, a.data, 0, a.rows, b.data, 0, b.rows, beta,
c.data, 0, c.rows);
return c;
}
/** Compute y <- alpha*op(a)*x + beta * y (general matrix vector multiplication) */
public static FloatMatrix gemv(
float alpha, FloatMatrix a, FloatMatrix x, float beta, FloatMatrix y) {
if (false) {
NativeBlas.sgemv(
'N', a.rows, a.columns, alpha, a.data, 0, a.rows, x.data, 0, 1, beta, y.data, 0, 1);
} else {
if (beta == 0.0f) {
for (int i = 0; i < y.length; i++) y.data[i] = 0.0f;
for (int j = 0; j < a.columns; j++) {
float xj = x.get(j);
if (xj != 0.0f) {
for (int i = 0; i < a.rows; i++) y.data[i] += a.get(i, j) * xj;
}
}
} else {
for (int j = 0; j < a.columns; j++) {
float byj = beta * y.data[j];
float xj = x.get(j);
for (int i = 0; i < a.rows; i++) y.data[j] = a.get(i, j) * xj + byj;
}
}
}
return y;
}
public static int syevr(
char jobz,
char range,
char uplo,
FloatMatrix a,
float vl,
float vu,
int il,
int iu,
float abstol,
FloatMatrix w,
FloatMatrix z,
int[] isuppz) {
int n = a.rows;
int[] m = new int[1];
int info =
NativeBlas.ssyevr(
jobz, range, uplo, n, a.data, 0, a.rows, vl, vu, il, iu, abstol, m, 0, w.data, 0,
z.data, 0, z.rows, isuppz, 0);
checkInfo("SYEVR", info);
return info;
}
public static void ormqr(char side, char trans, FloatMatrix A, FloatMatrix tau, FloatMatrix C) {
int k = tau.length;
int info =
NativeBlas.sormqr(
side, trans, C.rows, C.columns, k, A.data, 0, A.rows, tau.data, 0, C.data, 0, C.rows);
checkInfo("ORMQR", info);
}
/** Compute y <- alpha*op(a)*x + beta * y (general matrix vector multiplication) */
public static DoubleMatrix gemv(
double alpha, DoubleMatrix a, DoubleMatrix x, double beta, DoubleMatrix y) {
if (false) {
NativeBlas.dgemv(
'N', a.rows, a.columns, alpha, a.data, 0, a.rows, x.data, 0, 1, beta, y.data, 0, 1);
} else {
if (beta == 0.0) {
for (int i = 0; i < y.length; i++) y.data[i] = 0.0;
for (int j = 0; j < a.columns; j++) {
double xj = x.get(j);
if (xj != 0.0) {
for (int i = 0; i < a.rows; i++) y.data[i] += a.get(i, j) * xj;
}
}
} else {
for (int j = 0; j < a.columns; j++) {
double byj = beta * y.data[j];
double xj = x.get(j);
for (int i = 0; i < a.rows; i++) y.data[j] = a.get(i, j) * xj + byj;
}
}
}
return y;
}
public static int syevd(char jobz, char uplo, FloatMatrix A, FloatMatrix w) {
int n = A.rows;
int info = NativeBlas.ssyevd(jobz, uplo, n, A.data, 0, A.rows, w.data, 0);
if (info > 0) throw new LapackConvergenceException("SYEVD", "Not all eigenvalues converged.");
return info;
}
public static void posv(char uplo, FloatMatrix A, FloatMatrix B) {
int n = A.rows;
int nrhs = B.columns;
int info = NativeBlas.sposv(uplo, n, nrhs, A.data, 0, A.rows, B.data, 0, B.rows);
checkInfo("DPOSV", info);
if (info > 0)
throw new LapackArgumentException(
"DPOSV", "Leading minor of order i of A is not positive definite.");
}
/** ************************************************************************* LAPACK */
public static FloatMatrix gesv(FloatMatrix a, int[] ipiv, FloatMatrix b) {
int info = NativeBlas.sgesv(a.rows, b.columns, a.data, 0, a.rows, ipiv, 0, b.data, 0, b.rows);
checkInfo("DGESV", info);
if (info > 0)
throw new LapackException(
"DGESV", "Linear equation cannot be solved because the matrix was singular.");
return b;
}
public static int syev(char jobz, char uplo, FloatMatrix a, FloatMatrix w) {
int info = NativeBlas.ssyev(jobz, uplo, a.rows, a.data, 0, a.rows, w.data, 0);
if (info > 0)
throw new LapackConvergenceException(
"SYEV",
"Eigenvalues could not be computed " + info + " off-diagonal elements did not converge");
return info;
}
public static ComplexFloatMatrix gemm(
ComplexFloat alpha,
ComplexFloatMatrix a,
ComplexFloatMatrix b,
ComplexFloat beta,
ComplexFloatMatrix c) {
NativeBlas.cgemm(
'N', 'N', c.rows, c.columns, a.columns, alpha, a.data, 0, a.rows, b.data, 0, b.rows, beta,
c.data, 0, c.rows);
return c;
}
public static FloatMatrix sysv(char uplo, FloatMatrix a, int[] ipiv, FloatMatrix b) {
int info =
NativeBlas.ssysv(uplo, a.rows, b.columns, a.data, 0, a.rows, ipiv, 0, b.data, 0, b.rows);
checkInfo("SYSV", info);
if (info > 0)
throw new LapackSingularityException(
"SYV", "Linear equation cannot be solved because the matrix was singular.");
return b;
}
public static int geev(
char jobvl,
char jobvr,
FloatMatrix A,
FloatMatrix WR,
FloatMatrix WI,
FloatMatrix VL,
FloatMatrix VR) {
int info =
NativeBlas.sgeev(
jobvl, jobvr, A.rows, A.data, 0, A.rows, WR.data, 0, WI.data, 0, VL.data, 0, VL.rows,
VR.data, 0, VR.rows);
if (info > 0)
throw new LapackConvergenceException(
"DGEEV", "First " + info + " eigenvalues have not converged.");
return info;
}
public static int sygvd(
int itype, char jobz, char uplo, FloatMatrix A, FloatMatrix B, FloatMatrix W) {
int info =
NativeBlas.ssygvd(
itype, jobz, uplo, A.rows, A.data, 0, A.rows, B.data, 0, B.rows, W.data, 0);
if (info == 0) return 0;
else {
if (info < 0) throw new LapackArgumentException("DSYGVD", -info);
if (info <= A.rows && jobz == 'N')
throw new LapackConvergenceException(
"DSYGVD", info + " off-diagonal elements did not converge to 0.");
if (info <= A.rows && jobz == 'V')
throw new LapackException(
"DSYGVD",
"Failed to compute an eigenvalue while working on a sub-matrix " + info + ".");
else
throw new LapackException(
"DSYGVD",
"The leading minor of order " + (info - A.rows) + " of B is not positive definite.");
}
}
public static int sygvx(
int itype,
char jobz,
char range,
char uplo,
FloatMatrix A,
FloatMatrix B,
float vl,
float vu,
int il,
int iu,
float abstol,
int[] m,
FloatMatrix W,
FloatMatrix Z) {
int[] iwork = new int[1];
int[] ifail = new int[1];
int info =
NativeBlas.ssygvx(
itype, jobz, range, uplo, A.rows, A.data, 0, A.rows, B.data, 0, B.rows, vl, vu, il, iu,
abstol, m, 0, W.data, 0, Z.data, 0, Z.rows, iwork, 0, ifail, 0);
if (info == 0) {
return 0;
} else {
if (info < 0) {
throw new LapackArgumentException("DSYGVX", -info);
}
if (info <= A.rows) {
throw new LapackConvergenceException("DSYGVX", info + " eigenvectors failed to converge");
} else {
throw new LapackException(
"DSYGVX",
"The leading minor order " + (info - A.rows) + " of B is not postivie definite.");
}
}
}
public static int syevx(
char jobz,
char range,
char uplo,
FloatMatrix a,
float vl,
float vu,
int il,
int iu,
float abstol,
FloatMatrix w,
FloatMatrix z) {
int n = a.rows;
int[] iwork = new int[5 * n];
int[] ifail = new int[n];
int[] m = new int[1];
int info;
info =
NativeBlas.ssyevx(
jobz, range, uplo, n, a.data, 0, a.rows, vl, vu, il, iu, abstol, m, 0, w.data, 0,
z.data, 0, z.rows, iwork, 0, ifail, 0);
if (info > 0) {
StringBuilder msg = new StringBuilder();
msg.append("Not all eigenvalues converged. Non-converging eigenvalues were: ");
for (int i = 0; i < info; i++) {
if (i > 0) msg.append(", ");
msg.append(ifail[i]);
}
msg.append(".");
throw new LapackConvergenceException("SYEVX", msg.toString());
}
return info;
}
public static void geqrf(FloatMatrix A, FloatMatrix tau) {
int info = NativeBlas.sgeqrf(A.rows, A.columns, A.data, 0, A.rows, tau.data, 0);
checkInfo("GEQRF", info);
}
public static ComplexFloatMatrix axpy(
ComplexFloat da, ComplexFloatMatrix dx, ComplexFloatMatrix dy) {
NativeBlas.caxpy(dx.length, da, dx.data, 0, 1, dy.data, 0, 1);
return dy;
}
public static ComplexDoubleMatrix copy(ComplexDoubleMatrix x, ComplexDoubleMatrix y) {
NativeBlas.zcopy(x.length, x.data, 0, 1, y.data, 0, 1);
return y;
}
/** Compute x <- alpha * x (scale a matrix) */
public static DoubleMatrix scal(double alpha, DoubleMatrix x) {
NativeBlas.dscal(x.length, alpha, x.data, 0, 1);
return x;
}
/** Compute || x ||_2 (2-norm) */
public static float nrm2(FloatMatrix x) {
return NativeBlas.snrm2(x.length, x.data, 0, 1);
}
public static float asum(ComplexFloatMatrix x) {
return NativeBlas.scasum(x.length, x.data, 0, 1);
}
public static ComplexDoubleMatrix scal(ComplexDouble alpha, ComplexDoubleMatrix x) {
NativeBlas.zscal(x.length, alpha, x.data, 0, 1);
return x;
}
/**
* Compute index of element with largest absolute value (complex version).
*
* @param x matrix
* @return index of element with largest absolute value.
*/
public static int iamax(ComplexFloatMatrix x) {
return NativeBlas.icamax(x.length, x.data, 0, 1) - 1;
}
/** Compute A <- alpha * x * y^T + A (general rank-1 update) */
public static FloatMatrix ger(float alpha, FloatMatrix x, FloatMatrix y, FloatMatrix a) {
NativeBlas.sger(a.rows, a.columns, alpha, x.data, 0, 1, y.data, 0, 1, a.data, 0, a.rows);
return a;
}
public static ComplexFloatMatrix copy(ComplexFloatMatrix x, ComplexFloatMatrix y) {
NativeBlas.ccopy(x.length, x.data, 0, 1, y.data, 0, 1);
return y;
}
/** Compute x^T * y (dot product) */
public static ComplexFloat dotu(ComplexFloatMatrix x, ComplexFloatMatrix y) {
return NativeBlas.cdotu(x.length, x.data, 0, 1, y.data, 0, 1);
}
public static ComplexDoubleMatrix axpy(
ComplexDouble da, ComplexDoubleMatrix dx, ComplexDoubleMatrix dy) {
NativeBlas.zaxpy(dx.length, da, dx.data, 0, 1, dy.data, 0, 1);
return dy;
}
/** Compute A <- alpha * x * y^H + A (general rank-1 update) */
public static ComplexFloatMatrix gerc(
ComplexFloat alpha, ComplexFloatMatrix x, ComplexFloatMatrix y, ComplexFloatMatrix a) {
NativeBlas.cgerc(a.rows, a.columns, alpha, x.data, 0, 1, y.data, 0, 1, a.data, 0, a.rows);
return a;
}
