# sget22.f - Man Page

TESTING/EIG/sget22.f

## Synopsis

### Functions/Subroutines

subroutine **sget22** (transa, transe, transw, n, a, lda, e, **lde**, wr, wi, work, result)**SGET22**

## Function/Subroutine Documentation

### subroutine sget22 (character transa, character transe, character transw, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( lde, * ) e, integer lde, real, dimension( * ) wr, real, dimension( * ) wi, real, dimension( * ) work, real, dimension( 2 ) result)

**SGET22**

**Purpose:**

SGET22 does an eigenvector check. The basic test is: RESULT(1) = | A E - E W | / ( |A| |E| ulp ) using the 1-norm. It also tests the normalization of E: RESULT(2) = max | m-norm(E(j)) - 1 | / ( n ulp ) j where E(j) is the j-th eigenvector, and m-norm is the max-norm of a vector. If an eigenvector is complex, as determined from WI(j) nonzero, then the max-norm of the vector ( er + i*ei ) is the maximum of |er(1)| + |ei(1)|, ... , |er(n)| + |ei(n)| W is a block diagonal matrix, with a 1 by 1 block for each real eigenvalue and a 2 by 2 block for each complex conjugate pair. If eigenvalues j and j+1 are a complex conjugate pair, so that WR(j) = WR(j+1) = wr and WI(j) = - WI(j+1) = wi, then the 2 by 2 block corresponding to the pair will be: ( wr wi ) ( -wi wr ) Such a block multiplying an n by 2 matrix ( ur ui ) on the right will be the same as multiplying ur + i*ui by wr + i*wi. To handle various schemes for storage of left eigenvectors, there are options to use A-transpose instead of A, E-transpose instead of E, and/or W-transpose instead of W.

**Parameters***TRANSA*TRANSA is CHARACTER*1 Specifies whether or not A is transposed. = 'N': No transpose = 'T': Transpose = 'C': Conjugate transpose (= Transpose)

*TRANSE*TRANSE is CHARACTER*1 Specifies whether or not E is transposed. = 'N': No transpose, eigenvectors are in columns of E = 'T': Transpose, eigenvectors are in rows of E = 'C': Conjugate transpose (= Transpose)

*TRANSW*TRANSW is CHARACTER*1 Specifies whether or not W is transposed. = 'N': No transpose = 'T': Transpose, use -WI(j) instead of WI(j) = 'C': Conjugate transpose, use -WI(j) instead of WI(j)

*N*N is INTEGER The order of the matrix A. N >= 0.

*A*A is REAL array, dimension (LDA,N) The matrix whose eigenvectors are in E.

*LDA*LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).

*E*E is REAL array, dimension (LDE,N) The matrix of eigenvectors. If TRANSE = 'N', the eigenvectors are stored in the columns of E, if TRANSE = 'T' or 'C', the eigenvectors are stored in the rows of E.

*LDE*LDE is INTEGER The leading dimension of the array E. LDE >= max(1,N).

*WR*WR is REAL array, dimension (N)

*WI*WI is REAL array, dimension (N) The real and imaginary parts of the eigenvalues of A. Purely real eigenvalues are indicated by WI(j) = 0. Complex conjugate pairs are indicated by WR(j)=WR(j+1) and WI(j) = - WI(j+1) non-zero; the real part is assumed to be stored in the j-th row/column and the imaginary part in the (j+1)-th row/column.

*WORK*WORK is REAL array, dimension (N*(N+1))

*RESULT*RESULT is REAL array, dimension (2) RESULT(1) = | A E - E W | / ( |A| |E| ulp ) RESULT(2) = max | m-norm(E(j)) - 1 | / ( n ulp ) j

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **166** of file **sget22.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page sget22(3) is an alias of sget22.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK