/// <summary>
/// Compute the inverse of a matrix, using the Cholesky factorization of the <c>A</c> matrix,
/// typically returned from <c>Pptrf</c>.
/// The <c>pptrf</c> name comes from LAPACK, and means PositiveDefinitePackedTriangular(Cholesky)Invert.
/// </summary>
/// <param name="layout">The storage order of this matrix</param>
/// <param name="uplo">Whether the passed in matrix stores the upper or lower triangular part of the matrix</param>
/// <param name="n">The order of the matrix</param>
/// <param name="ap">An array with at least n*(n+1)/2 entries, containing a Cholesky factorization
/// of the matrix in the linear equation. The inverse is returned in this array.</param>
public static void Pptri(Layout layout, UpLo uplo, int n, Double[] ap)
{
Contracts.CheckParam((long)n * (n + 1) / 2 <= ap.Length, nameof(ap), "vector had insufficient length");
int retval = PptriInternal(layout, uplo, n, ap);
if (retval == 0)
{
return;
}
switch (-1 - retval)
{
case 0:
throw Contracts.ExceptParam(nameof(layout));
case 1:
throw Contracts.ExceptParam(nameof(uplo));
case 2:
throw Contracts.ExceptParam(nameof(n));
case 3:
throw Contracts.ExceptParam(nameof(ap));
default:
throw Contracts.Except();
}
}
/// <summary>
/// Solves a system of linear equations, using the Cholesky factorization of the <c>A</c> matrix,
/// typically returned from <c>Pptrf</c>.
/// The <c>pptrf</c> name comes from LAPACK, and means PositiveDefinitePackedTriangular(Cholesky)Solve.
/// </summary>
/// <param name="layout">The storage order of this matrix</param>
/// <param name="uplo">Whether the passed in matrix stores the upper or lower triangular part of the matrix</param>
/// <param name="n">The order of the matrix</param>
/// <param name="nrhs">The number of columns in the right hand side matrix</param>
/// <param name="ap">An array with at least n*(n+1)/2 entries, containing a Cholesky factorization
/// of the matrix in the linear equation.</param>
/// <param name="b">The right hand side</param>
/// <param name="ldb">The major index step size (typically for row major order, the number of columns,
/// or something larger)</param>
public static void Pptrs(Layout layout, UpLo uplo, int n, int nrhs, Double[] ap, Double[] b, int ldb)
{
Contracts.CheckParam((long)n * (n + 1) / 2 <= ap.Length, nameof(ap), "vector had insufficient length");
Contracts.CheckParam((long)n * ldb <= b.Length, nameof(b), "vector had insufficient length");
int retval = PptrsInternal(layout, uplo, n, nrhs, ap, b, ldb);
if (retval == 0)
return;
switch (-1 - retval)
{
case 0:
throw Contracts.ExceptParam(nameof(layout));
case 1:
throw Contracts.ExceptParam(nameof(uplo));
case 2:
throw Contracts.ExceptParam(nameof(n));
case 3:
throw Contracts.ExceptParam(nameof(nrhs));
case 4:
throw Contracts.ExceptParam(nameof(ap));
case 5:
throw Contracts.ExceptParam(nameof(b));
case 6:
throw Contracts.ExceptParam(nameof(ldb));
default:
throw Contracts.Except();
}
}
/// <summary>
/// Cholesky factorization of a symmetric positive-definite double matrix, using packed storage.
/// The <c>pptrf</c> name comes from LAPACK, and means PositiveDefinitePackedTriangular(Cholesky)Factorize.
/// </summary>
/// <param name="layout">The storage order of this matrix</param>
/// <param name="uplo">Whether the passed in matrix stores the upper or lower triangular part of the matrix</param>
/// <param name="n">The order of the matrix</param>
/// <param name="ap">An array with at least n*(n+1)/2 entries, containing the packed upper/lower part of the matrix.
/// The triangular factorization is stored in this passed in matrix, when it returns. (U^T U or L L^T depending
/// on whether this was upper or lower.)</param>
public static void Pptrf(Layout layout, UpLo uplo, int n, Double[] ap)
{
Contracts.CheckParam((long)n * (n + 1) / 2 <= ap.Length, nameof(ap), "vector had insufficient length");
int retval = PptrfInternal(layout, uplo, n, ap);
if (retval == 0)
{
return;
}
switch (-1 - retval)
{
case 0:
throw Contracts.ExceptParam(nameof(layout));
case 1:
throw Contracts.ExceptParam(nameof(uplo));
case 2:
throw Contracts.ExceptParam(nameof(n));
case 3:
throw Contracts.ExceptParam(nameof(ap));
default:
throw Contracts.ExceptParam(nameof(ap), "Input matrix was not positive-definite. Try using a larger L2 regularization weight.");
}
}
private static void ArgumentCheck(UpLo uplo, int n, int nrhs, object A, int lda, object B, int ldb)
{
if (n < 0)
{
throw new ArgumentException("n must be at least zero.", "n");
}
if (nrhs < 0)
{
throw new ArgumentException("nrhs must be at least zero.", "nrhs");
}
if (A == null)
{
throw new ArgumentNullException("A", "A cannot be null.");
}
if (lda < n || lda < 1)
{
throw new ArgumentException("lda must be at least max(1,n)");
}
if (B == null)
{
throw new ArgumentNullException("B", "B cannot be null.");
}
if (ldb < n || ldb < 1)
{
throw new ArgumentException("ldb must be at least max(1,n)", "ldb");
}
}
internal static void Compute( Order order, Side side, UpLo uplo, Transpose transA, Diag diag, int m,int n, double alpha, double[] A, int lda, double[] B, int ldb ){
if ( transA == Transpose.ConjTrans ) {
transA = Transpose.Trans;
}
ArgumentCheck(side, m, n, A, lda, B, ldb);
dna_blas_dtrsm(order, side, uplo, transA, diag, m, n, alpha, A, lda, B, ldb);
}
private static void ArgumentCheck(UpLo uplo, int n, object A, int lda){
if (n<0)
throw new ArgumentException("n must be at least zero.", "n");
if (A==null)
throw new ArgumentNullException("A","A cannot be null.");
if (lda<n || lda<1)
throw new ArgumentException("lda must be at least max(1,n)", "lda");
}
internal static void Compute(Order order, Side side, UpLo uplo, Transpose transA, Diag diag, int m, int n, double alpha, double[] A, int lda, double[] B, int ldb)
{
if (transA == Transpose.ConjTrans)
{
transA = Transpose.Trans;
}
ArgumentCheck(side, m, n, A, lda, B, ldb);
dna_blas_dtrsm(order, side, uplo, transA, diag, m, n, alpha, A, lda, B, ldb);
}
private static void ArgumentCheck(UpLo uplo, int n, int nrhs, object A, int lda, object B, int ldb){
if (n<0)
throw new ArgumentException("n must be at least zero.", "n");
if (nrhs<0)
throw new ArgumentException("nrhs must be at least zero.", "nrhs");
if (A==null)
throw new ArgumentNullException("A","A cannot be null.");
if (lda<n || lda<1)
throw new ArgumentException("lda must be at least max(1,n)");
if (B==null)
throw new ArgumentNullException("B","B cannot be null.");
if (ldb<n || ldb<1)
throw new ArgumentException("ldb must be at least max(1,n)", "ldb");
}
private static void ArgumentCheck(UpLo uplo, int n, object A, int lda)
{
if (n < 0)
{
throw new ArgumentException("n must be at least zero.", "n");
}
if (A == null)
{
throw new ArgumentNullException("A", "A cannot be null.");
}
if (lda < n || lda < 1)
{
throw new ArgumentException("lda must be at least max(1,n)", "lda");
}
}
internal static void Compute(Order order, Side side, UpLo uplo, Transpose transA, Diag diag, int m, int n, Complex alpha, Complex[] A, int lda, Complex[] B, int ldb)
{
ArgumentCheck(side, m, n, A, lda, B, ldb);
dna_blas_ztrsm(order, side, uplo, transA, diag, m, n, ref alpha, A, lda, B, ldb);
}
private static extern int dna_lapack_cbdsqr( UpLo uplo, int n, int ncvt, int nru, int ncc, [In,Out]float[] d, [In,Out]float[] e, [In,Out]ComplexFloat[] vt, int ldvt, [In,Out]ComplexFloat[] u, int ldu, [In,Out]ComplexFloat[] c, int ldc );
private static extern int dna_lapack_dpotri(UpLo uplo, int n, [In, Out] double[] A, int lda);
internal static int Compute(UpLo uplo, int n, Complex[] A, int lda)
{
ArgumentCheck(uplo, n, A, lda);
return(dna_lapack_zpotri(uplo, n, A, lda));
}
private static extern int dna_lapack_dpotrs(UpLo uplo, int n, int nrsh, [In, Out] double[] A, int lda, [In, Out] double[] B, int ldb);
private static extern int dna_lapack_dpotrs( UpLo uplo, int n, int nrsh, [In,Out]double[] A, int lda, [In,Out]double[] B, int ldb );
private static extern void dna_blas_dtrsm( Order order, Side side, UpLo uplo, Transpose transA, Diag diag, int m,int n, double alpha, [In]double[] A, int lda, [In,Out]double[] B, int ldb );
internal static int Compute(UpLo uplo, int n, ComplexFloat[] A, int lda, float anorm, out float rcond)
{
ArgumentCheck(uplo, n, A, lda);
rcond = 0;
return(dna_lapack_cpocon(uplo, n, A, lda, anorm, out rcond));
}
private static extern int dna_lapack_zbdsqr(UpLo uplo, int n, int ncvt, int nru, int ncc, [In, Out] double[] d, [In, Out] double[] e, [In, Out] Complex[] vt, int ldvt, [In, Out] Complex[] u, int ldu, [In, Out] Complex[] c, int ldc);
private static extern int dna_lapack_cbdsqr(UpLo uplo, int n, int ncvt, int nru, int ncc, [In, Out] float[] d, [In, Out] float[] e, [In, Out] ComplexFloat[] vt, int ldvt, [In, Out] ComplexFloat[] u, int ldu, [In, Out] ComplexFloat[] c, int ldc);
private static extern int dna_lapack_cpotrf(UpLo uplo, int n, [In, Out] ComplexFloat[] A, int lda);
internal static int Compute(UpLo uplo, int n, double[] A, int lda)
{
ArgumentCheck(uplo, n, A, lda);
return(dna_lapack_dpotrf(uplo, n, A, lda));
}
private static extern int dna_lapack_zpotri( UpLo uplo, int n, [In,Out]Complex[] A, int lda );
private static extern int dna_lapack_dpotri( UpLo uplo, int n, [In,Out]double[] A, int lda );
private static extern void dna_blas_dtrsm(Order order, Side side, UpLo uplo, Transpose transA, Diag diag, int m, int n, double alpha, [In] double[] A, int lda, [In, Out] double[] B, int ldb);
internal static int Compute( UpLo uplo, int n, double[] A, int lda ){
ArgumentCheck(uplo, n, A, lda);
return dna_lapack_dpotrf(uplo, n, A, lda);
}
internal static int Compute(UpLo uplo, int n, Complex[] A, int lda, double anorm, out double rcond)
{
ArgumentCheck(uplo, n, A, lda);
rcond = 0;
return(dna_lapack_zpocon(uplo, n, A, lda, anorm, out rcond));
}
private static extern int dna_lapack_zpotrs( UpLo uplo, int n, int nrsh, [In,Out]Complex[] A, int lda, [In,Out]Complex[] B, int ldb );
private static extern int dna_lapack_cpocon(UpLo uplo, int n, [In, Out] ComplexFloat[] A, int lda, float anorm, out float rcond);
private static extern int dna_lapack_spotri( UpLo uplo, int n, [In,Out]float[] A, int lda );
private static extern int dna_lapack_zpocon(UpLo uplo, int n, [In, Out] Complex[] A, int lda, double anorm, out double rcond);
public static extern int PptrfInternal(Layout layout, UpLo uplo, int n, Double[] ap);
private static extern int dna_lapack_cpotrf( UpLo uplo, int n, [In,Out]ComplexFloat[] A, int lda );
private static extern int dna_lapack_spotri(UpLo uplo, int n, [In, Out] float[] A, int lda);
internal static int Compute( UpLo uplo, int n, ComplexFloat[] A, int lda, float anorm, out float rcond){
ArgumentCheck(uplo, n, A, lda);
rcond = 0;
return dna_lapack_cpocon(uplo, n, A, lda, anorm, out rcond);
}
private static extern int dna_lapack_zpotri(UpLo uplo, int n, [In, Out] Complex[] A, int lda);
internal static int Compute( UpLo uplo, int n, Complex[] A, int lda, double anorm, out double rcond){
ArgumentCheck(uplo, n, A, lda);
rcond = 0;
return dna_lapack_zpocon(uplo, n, A, lda, anorm, out rcond);
}
private static extern int dna_lapack_zbdsqr( UpLo uplo, int n, int ncvt, int nru, int ncc, [In,Out]double[] d, [In,Out]double[] e, [In,Out]Complex[] vt, int ldvt, [In,Out]Complex[] u, int ldu, [In,Out]Complex[] c, int ldc );
private static extern int dna_lapack_cpocon(UpLo uplo, int n, [In,Out]ComplexFloat[] A, int lda, float anorm, out float rcond);
private static extern void dna_blas_strsm(Order order, Side side, UpLo uplo, Transpose transA, Diag diag, int m, int n, float alpha, [In] float[] A, int lda, [In, Out] float[] B, int ldb);
private static extern int dna_lapack_zpocon(UpLo uplo, int n, [In,Out]Complex[] A, int lda, double anorm, out double rcond);
private static extern void dna_blas_ztrsm(Order order, Side side, UpLo uplo, Transpose transA, Diag diag, int m, int n, ref Complex alpha, [In] Complex[] A, int lda, [In, Out] Complex[] B, int ldb);
private static extern int PptriInternal(Layout layout, UpLo uplo, int n, Double[] ap);
private static extern void dna_blas_strsm( Order order, Side side, UpLo uplo, Transpose transA, Diag diag, int m,int n, float alpha, [In]float[] A, int lda, [In,Out]float[] B, int ldb );
private static extern int dna_lapack_spotrs( UpLo uplo, int n, int nrsh, [In,Out]float[] A, int lda, [In,Out]float[] B, int ldb );
private static extern void dna_blas_ztrsm( Order order, Side side, UpLo uplo, Transpose transA, Diag diag, int m,int n, ref Complex alpha, [In]Complex[] A, int lda, [In,Out]Complex[] B, int ldb );
internal static int Compute(UpLo uplo, int n, int nrhs, Complex[] A, int lda, Complex[] B, int ldb)
{
ArgumentCheck(uplo, n, nrhs, A, lda, B, ldb);
return(dna_lapack_zpotrs(uplo, n, nrhs, A, lda, B, ldb));
}
internal static void Compute( Order order, Side side, UpLo uplo, Transpose transA, Diag diag, int m,int n, Complex alpha, Complex[] A, int lda, Complex[] B, int ldb ){
ArgumentCheck(side, m, n, A, lda, B, ldb);
dna_blas_ztrsm(order, side, uplo, transA, diag, m, n, ref alpha, A, lda, B, ldb);
}
private static extern int dna_lapack_spotrs(UpLo uplo, int n, int nrsh, [In, Out] float[] A, int lda, [In, Out] float[] B, int ldb);
private static extern int PptrsInternal(Layout layout, UpLo uplo, int n, int nrhs, Double[] ap, Double[] b, int ldb);
internal static int Compute( UpLo uplo, int n, Complex[] A, int lda ){
ArgumentCheck(uplo, n, A, lda);
return dna_lapack_zpotri(uplo, n, A, lda);
}
private static extern int dna_lapack_zpotrs(UpLo uplo, int n, int nrsh, [In, Out] Complex[] A, int lda, [In, Out] Complex[] B, int ldb);
internal static int Compute( UpLo uplo, int n, int nrhs, Complex[] A, int lda, Complex[] B, int ldb ){
ArgumentCheck(uplo, n, nrhs, A, lda, B, ldb);
return dna_lapack_zpotrs(uplo, n, nrhs, A, lda, B, ldb);
}
