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MatrixGLM

MatrixGLM [/Z] matrixA, matrixB, waveD​

The MatrixGLM operation solves the general Gauss-Markov Linear Model problem (GLM) which minimizes the 2-norm of a vector y

min⁡∥y∥2 subject to d=Ax+By.\displaystyle \min \|y\|_{2} \quad \text { subject to } \quad d=A x+B y .

A is matrixA (an NxM wave), B is matrixB (an NxP wave), and d is provided by waveD which is a 1D wave of N rows. The vectors x and y are the results of the calculation; they are stored in output waves Mat_X and Mat_Y in the current data folder.

Flags​

/DSTX=xWaveSpecify the destination of the x-wave. If you don't use this flag, the operation saves the x-wave in Mat_x in the current data folder.
The /FREE flag was added in Igor Pro 10.00.
/DSTY=yWaveSpecify the destination of the y-wave. If you don't use this flag, the operation saves the y-wave in Mat_y in the current data folder.
The /FREE flag was added in Igor Pro 10.00.
/FREECreates all specified destination waves as free waves. This flag does not affect output waves that are created by default without a user-specified destination.
/FREE is allowed only in functions and only if the destination wave, as specified by /DSTX and /DSTY, is a simple name or wave reference structure field.
See Free Waves for more discussion.
The /FREE flag was added in Igor Pro 10.00.
/ZIn the event of an error, MatrixGLM will not return the error to Igor, which would cause procedure execute to abort. Your code should use the V_flag output variable to detect and handle errors.

Details​

All input waves must have the same numeric type. Supported types are single-precision and double-precision floating point, both real and complex. The output waves Mat_X and Mat_Y have the same numeric type as the input.

The LAPACK algorithm assumes that M <= N <= M+P and

rank⁡(A)=M,rank⁡(AB)=N.\displaystyle \begin{array}{l} \operatorname{rank}(A)=M, \\ \\ \operatorname{rank}(A B)=N . \end{array}

Under these assumptions there is a unique solution x and a minimal 2-norm solution y, which are obtained using a generalized QR factorization of A and B. If the operation completes successfully the variable V_Flag is set to zero. Otherwise it contains a LAPACK error code.

Output Variables​

V_flagSet to 0 if MatrixGLM succeeds or to a LAPACK error code.

See Also​

Matrix Math Operations for more about Igor's matrix routines and for background references with details about the LAPACK libraries.