# sget23.f - Man Page

TESTING/EIG/sget23.f

## Synopsis

### Functions/Subroutines

subroutine **sget23** (comp, balanc, jtype, thresh, iseed, nounit, n, a, lda, h, wr, wi, wr1, wi1, vl, ldvl, vr, ldvr, lre, ldlre, rcondv, rcndv1, rcdvin, rconde, rcnde1, rcdein, scale, scale1, result, work, lwork, iwork, info)**SGET23**

## Function/Subroutine Documentation

### subroutine sget23 (logical comp, character balanc, integer jtype, real thresh, integer, dimension( 4 ) iseed, integer nounit, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( lda, * ) h, real, dimension( * ) wr, real, dimension( * ) wi, real, dimension( * ) wr1, real, dimension( * ) wi1, real, dimension( ldvl, * ) vl, integer ldvl, real, dimension( ldvr, * ) vr, integer ldvr, real, 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, real, dimension( * ) work, integer lwork, integer, dimension( * ) iwork, integer info)

**SGET23**

**Purpose:**

SGET23 checks the nonsymmetric eigenvalue problem driver SGEEVX. 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 block diagonal matrix, with a 1x1 block for each real eigenvalue and a 2x2 block for each complex conjugate pair. If eigenvalues j and j+1 are a complex conjugate pair, so WR(j) = WR(j+1) = wr and WI(j) = - WI(j+1) = wi, then the 2 x 2 block corresponding to the pair will be: ( wr wi ) ( -wi wr ) Such a block multiplying an n x 2 matrix ( ur ui ) on the right will be the same as multiplying ur + i*ui by wr + i*wi. (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 SGEEVX 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 SGEEVX 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

*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 REAL 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 REAL array, dimension (LDA,N) Another copy of the test matrix A, modified by SGEEVX.

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

*WI*WI is REAL array, dimension (N) The real and imaginary parts of the eigenvalues of A. On exit, WR + WI*i are the eigenvalues of the matrix in A.

*WR1*WR1 is REAL array, dimension (N)

*WI1*WI1 is REAL array, dimension (N) Like WR, WI, these arrays contain the eigenvalues of A, but those computed when SGEEVX only computes a partial eigendecomposition, i.e. not the eigenvalues and left and right eigenvectors.

*VL*VL is REAL 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 REAL 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 REAL 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 REAL array, dimension (LWORK)

*LWORK*LWORK is INTEGER The number of entries in WORK. This must be at least 3*N, and 6*N+N**2 if tests 9, 10 or 11 are to be performed.

*IWORK*IWORK is INTEGER array, dimension (2*N)

*INFO*INFO is INTEGER If 0, successful exit. If <0, input parameter -INFO had an incorrect value. If >0, SGEEVX 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 **373** of file **sget23.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page sget23(3) is an alias of sget23.f(3).

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