MQL5のドキュメンテーション: MatrixInfo / 行列とベクトルのメソッド

MatrixInfo

The method analyzes the matrix contents, determines its structural type (symmetric, Hermitian, triangular, banded, and so on), and fills the MqlMatrixInfo structure.

bool matrix::MatrixInfo(
MqlMatrixInfo& info // matrix info
);

Parameters

info

[out] An object of the MqlMatrixInfo type where matrix information is placed.

Return Value

Returns true if the matrix is initialized and has a nonzero size. Otherwise, false is returned.

Note

The MqlMatrixInfo structure object contains more information than individual matrix classification methods can provide (IsSymmetric, IsHermitian, IsUpperTriangular, and so on).

MqlMatrixInfo Structure

struct MqlMatrixInfo
{
ushort version, // 5940
char signature[2], // "GE", "SY", "HE", "TR", ...
ENUM_BLAS_TYPE matrix_class, // BLASTYPE_GE, BLASTYPE_SY, BLASTYPE_HE etc must match signature
ENUM_DATATYPE data_type, // TYPE_MATRIXD, TYPE_MATRIXF, TYPE_MATRIXCD, TYPE_MATRIXCF
uint flags, // MATRIX_UPPER, MATRIX_LOWER, MATRIX_UNITDIAG, ...
ulong rows, // rows of matrix
ulong cols, // cols of matrix
long lower_bandwidth, // kl: number of potentially non-zero subdiagonals
long upper_bandwidth, // ku: number of potentially non-zero superdiagonals
ulong data_size, // size of following payload in bytes
};

Information from the MqlMatrixInfo structure is used when writing a matrix to a file (the Write method will be added later) and when reading a matrix from a file.

ENUM_BLAS_TYPE

An enumeration containing the type of the recognized matrix.

ID	Description
BLASTYPE_GE	'GE': general matrix
BLASTYPE_BD	'BD': bidiagonal matrix
BLASTYPE_DI	'DI': diagonal matrix
BLASTYPE_GB	'GB': general band matrix
BLASTYPE_GT	'GT': general tridiagonal matrix
BLASTYPE_HB	'HB': Hermitian band matrix
BLASTYPE_HE	'HE': Hermitian matrix
BLASTYPE_HT	'HT': Hermitian tridiagonal matrix
BLASTYPE_HS	'HS': Hessenberg matrix
BLASTYPE_SB	'SB': symmetric band matrix
BLASTYPE_ST	'ST': symmetric tridiagonal matrix
BLASTYPE_SY	'SY': symmetric matrix
BLASTYPE_TB	'TB': triangular band matrix
BLASTYPE_TR	'TR': triangular matrix
BLASTYPE_TZ	'TZ': trapezoidal matrix
BLASTYPE_VE	'VE': vector (not used yet)

The enumeration item names correspond to the abbreviations used in LAPACK to denote various matrix classes. The HT type is an exception: Hermitian tridiagonal. HT is not present in standard LAPACK terminology and is introduced by analogy with ST (symmetric tridiagonal) to denote a Hermitian tridiagonal matrix, which also allows the corresponding matrix to be stored compactly.

MqlMatrixInfo::flags

Flags that refine the recognized matrix type.

ID	Value	Description
MATRIX_UPPER	0x0001	upper part above main diagonal
MATRIX_LOWER	0x0002	lower part below main diagonal
MATRIX_UNITDIAG	0x0004	main diagonal contains ones (1) only
MATRIX_DIAGSCALAR	0x0008	main diagonal contains the same values
MATRIX_QUASI_TRIANGULAR	0x0010	possible quasi-triangular matrix
MATRIX_TRIANGLE_RIGHT_ALIGNED	0x0020	upper triangular part aligned to right bound of wide matrix
MATRIX_TRIANGLE_BOTTOM_ALIGNED	0x0040	lower triangular part aligned to bottom bound of tall matrix

The listed flags (except MATRIX_QUASI_TRIANGULAR) allow matrices to be stored more compactly.

Example

ulong n=10;
matrix matrix_a=matrix::Random(n,n);
vectorc vector_ev;
matrix matrix_t,matrix_z;
MqlMatrixInfo info;

matrix_a.EigenSolverSchur(EIGSCHUR_V,vector_ev,matrix_t,matrix_z);
matrix_t.MatrixInfo(info);
PrintFormat("%d, %c%c, %s, %s, 0x%04x, rows=%I64u, cols=%I64u, lower_bandwidth=%I64d, upper_bandwidth=%I64d",info.version,info.signature[0],info.signature[1],EnumToString(info.matrix_class),
EnumToString(info.data_type),info.flags,info.rows,info.cols,
info.lower_bandwidth,info.upper_bandwidth);
string flags="";
if((info.flags&MATRIX_UPPER)==MATRIX_UPPER)
flags+=" MATRIX_UPPER";
if((info.flags&MATRIX_LOWER)==MATRIX_LOWER)
flags+=" MATRIX_LOWER";
if((info.flags&MATRIX_UNITDIAG)==MATRIX_UNITDIAG)
flags+=" MATRIX_UNITDIAG";
if((info.flags&MATRIX_DIAGSCALAR)==MATRIX_DIAGSCALAR)
flags+=" MATRIX_DIAGSCALAR";
if((info.flags&MATRIX_QUASI_TRIANGULAR)==MATRIX_QUASI_TRIANGULAR)
flags+=" MATRIX_QUASI_TRIANGULAR";
if((info.flags&MATRIX_TRIANGLE_RIGHT_ALIGNED)==MATRIX_TRIANGLE_RIGHT_ALIGNED)
flags+=" MATRIX_TRIANGLE_RIGHT_ALIGNED";
if((info.flags&MATRIX_TRIANGLE_BOTTOM_ALIGNED)==MATRIX_TRIANGLE_BOTTOM_ALIGNED)
flags+=" MATRIX_TRIANGLE_BOTTOM_ALIGNED";
Print("info.flags :",flags);

/*
5940, HS, BLASTYPE_HS, TYPE_MATRIX, 0x0011, rows=10, cols=10, lower_bandwidth=1, upper_bandwidth=-1
info.flags : MATRIX_UPPER MATRIX_QUASI_TRIANGULAR
*/

行列の分類

IsSymmetric