# cget23.f - Man Page

TESTING/EIG/cget23.f

## Synopsis

### Functions/Subroutines

subroutine **cget23** (comp, isrt, balanc, jtype, thresh, iseed, nounit, n, a, lda, h, w, w1, vl, ldvl, vr, ldvr, lre, ldlre, rcondv, rcndv1, rcdvin, rconde, rcnde1, rcdein, scale, scale1, result, work, lwork, rwork, info)**CGET23**

## Function/Subroutine Documentation

### subroutine cget23 (logical comp, integer isrt, character balanc, integer jtype, real thresh, integer, dimension( 4 ) iseed, integer nounit, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( lda, * ) h, complex, dimension( * ) w, complex, dimension( * ) w1, complex, dimension( ldvl, * ) vl, integer ldvl, complex, dimension( ldvr, * ) vr, integer ldvr, complex, dimension( ldlre, * ) lre, integer ldlre, real, dimension( * ) rcondv, real, dimension( * ) rcndv1, real, dimension( * ) rcdvin, real, dimension( * ) rconde, real, dimension( * ) rcnde1, real, dimension( * ) rcdein, real, dimension( * ) scale, real, dimension( * ) scale1, real, dimension( 11 ) result, complex, dimension( * ) work, integer lwork, real, dimension( * ) rwork, integer info)

**CGET23**

**Purpose:**

CGET23 checks the nonsymmetric eigenvalue problem driver CGEEVX. If COMP = .FALSE., the first 8 of the following tests will be performed on the input matrix A, and also test 9 if LWORK is sufficiently large. if COMP is .TRUE. all 11 tests will be performed. (1) | A * VR - VR * W | / ( n |A| ulp ) Here VR is the matrix of unit right eigenvectors. W is a diagonal matrix with diagonal entries W(j). (2) | A**H * VL - VL * W**H | / ( n |A| ulp ) Here VL is the matrix of unit left eigenvectors, A**H is the conjugate transpose of A, and W is as above. (3) | |VR(i)| - 1 | / ulp and largest component real VR(i) denotes the i-th column of VR. (4) | |VL(i)| - 1 | / ulp and largest component real VL(i) denotes the i-th column of VL. (5) 0 if W(full) = W(partial), 1/ulp otherwise W(full) denotes the eigenvalues computed when VR, VL, RCONDV and RCONDE are also computed, and W(partial) denotes the eigenvalues computed when only some of VR, VL, RCONDV, and RCONDE are computed. (6) 0 if VR(full) = VR(partial), 1/ulp otherwise VR(full) denotes the right eigenvectors computed when VL, RCONDV and RCONDE are computed, and VR(partial) denotes the result when only some of VL and RCONDV are computed. (7) 0 if VL(full) = VL(partial), 1/ulp otherwise VL(full) denotes the left eigenvectors computed when VR, RCONDV and RCONDE are computed, and VL(partial) denotes the result when only some of VR and RCONDV are computed. (8) 0 if SCALE, ILO, IHI, ABNRM (full) = SCALE, ILO, IHI, ABNRM (partial) 1/ulp otherwise SCALE, ILO, IHI and ABNRM describe how the matrix is balanced. (full) is when VR, VL, RCONDE and RCONDV are also computed, and (partial) is when some are not computed. (9) 0 if RCONDV(full) = RCONDV(partial), 1/ulp otherwise RCONDV(full) denotes the reciprocal condition numbers of the right eigenvectors computed when VR, VL and RCONDE are also computed. RCONDV(partial) denotes the reciprocal condition numbers when only some of VR, VL and RCONDE are computed. (10) |RCONDV - RCDVIN| / cond(RCONDV) RCONDV is the reciprocal right eigenvector condition number computed by CGEEVX and RCDVIN (the precomputed true value) is supplied as input. cond(RCONDV) is the condition number of RCONDV, and takes errors in computing RCONDV into account, so that the resulting quantity should be O(ULP). cond(RCONDV) is essentially given by norm(A)/RCONDE. (11) |RCONDE - RCDEIN| / cond(RCONDE) RCONDE is the reciprocal eigenvalue condition number computed by CGEEVX and RCDEIN (the precomputed true value) is supplied as input. cond(RCONDE) is the condition number of RCONDE, and takes errors in computing RCONDE into account, so that the resulting quantity should be O(ULP). cond(RCONDE) is essentially given by norm(A)/RCONDV.

**Parameters***COMP*COMP is LOGICAL COMP describes which input tests to perform: = .FALSE. if the computed condition numbers are not to be tested against RCDVIN and RCDEIN = .TRUE. if they are to be compared

*ISRT*ISRT is INTEGER If COMP = .TRUE., ISRT indicates in how the eigenvalues corresponding to values in RCDVIN and RCDEIN are ordered: = 0 means the eigenvalues are sorted by increasing real part = 1 means the eigenvalues are sorted by increasing imaginary part If COMP = .FALSE., ISRT is not referenced.

*BALANC*BALANC is CHARACTER Describes the balancing option to be tested. = 'N' for no permuting or diagonal scaling = 'P' for permuting but no diagonal scaling = 'S' for no permuting but diagonal scaling = 'B' for permuting and diagonal scaling

*JTYPE*JTYPE is INTEGER Type of input matrix. Used to label output if error occurs.

*THRESH*THRESH is REAL A test will count as 'failed' if the 'error', computed as described above, exceeds THRESH. Note that the error is scaled to be O(1), so THRESH should be a reasonably small multiple of 1, e.g., 10 or 100. In particular, it should not depend on the precision (single vs. double) or the size of the matrix. It must be at least zero.

*ISEED*ISEED is INTEGER array, dimension (4) If COMP = .FALSE., the random number generator seed used to produce matrix. If COMP = .TRUE., ISEED(1) = the number of the example. Used to label output if error occurs.

*NOUNIT*NOUNIT is INTEGER The FORTRAN unit number for printing out error messages (e.g., if a routine returns INFO not equal to 0.)

*N*N is INTEGER The dimension of A. N must be at least 0.

*A*A is COMPLEX array, dimension (LDA,N) Used to hold the matrix whose eigenvalues are to be computed.

*LDA*LDA is INTEGER The leading dimension of A, and H. LDA must be at least 1 and at least N.

*H*H is COMPLEX array, dimension (LDA,N) Another copy of the test matrix A, modified by CGEEVX.

*W*W is COMPLEX array, dimension (N) Contains the eigenvalues of A.

*W1*W1 is COMPLEX array, dimension (N) Like W, this array contains the eigenvalues of A, but those computed when CGEEVX only computes a partial eigendecomposition, i.e. not the eigenvalues and left and right eigenvectors.

*VL*VL is COMPLEX array, dimension (LDVL,N) VL holds the computed left eigenvectors.

*LDVL*LDVL is INTEGER Leading dimension of VL. Must be at least max(1,N).

*VR*VR is COMPLEX array, dimension (LDVR,N) VR holds the computed right eigenvectors.

*LDVR*LDVR is INTEGER Leading dimension of VR. Must be at least max(1,N).

*LRE*LRE is COMPLEX array, dimension (LDLRE,N) LRE holds the computed right or left eigenvectors.

*LDLRE*LDLRE is INTEGER Leading dimension of LRE. Must be at least max(1,N).

*RCONDV*RCONDV is REAL array, dimension (N) RCONDV holds the computed reciprocal condition numbers for eigenvectors.

*RCNDV1*RCNDV1 is REAL array, dimension (N) RCNDV1 holds more computed reciprocal condition numbers for eigenvectors.

*RCDVIN*RCDVIN is REAL array, dimension (N) When COMP = .TRUE. RCDVIN holds the precomputed reciprocal condition numbers for eigenvectors to be compared with RCONDV.

*RCONDE*RCONDE is REAL array, dimension (N) RCONDE holds the computed reciprocal condition numbers for eigenvalues.

*RCNDE1*RCNDE1 is REAL array, dimension (N) RCNDE1 holds more computed reciprocal condition numbers for eigenvalues.

*RCDEIN*RCDEIN is REAL array, dimension (N) When COMP = .TRUE. RCDEIN holds the precomputed reciprocal condition numbers for eigenvalues to be compared with RCONDE.

*SCALE*SCALE is REAL array, dimension (N) Holds information describing balancing of matrix.

*SCALE1*SCALE1 is REAL array, dimension (N) Holds information describing balancing of matrix.

*RESULT*RESULT is REAL array, dimension (11) The values computed by the 11 tests described above. The values are currently limited to 1/ulp, to avoid overflow.

*WORK*WORK is COMPLEX array, dimension (LWORK)

*LWORK*LWORK is INTEGER The number of entries in WORK. This must be at least 2*N, and 2*N+N**2 if tests 9, 10 or 11 are to be performed.

*RWORK*RWORK is REAL array, dimension (2*N)

*INFO*INFO is INTEGER If 0, successful exit. If <0, input parameter -INFO had an incorrect value. If >0, CGEEVX returned an error code, the absolute value of which is returned.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **363** of file **cget23.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page cget23(3) is an alias of cget23.f(3).

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