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LAPACK
3.5.0
LAPACK: Linear Algebra PACKage
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Functions/Subroutines | |
subroutine | zdrvgg (NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH, THRSHN, NOUNIT, A, LDA, B, S, T, S2, T2, Q, LDQ, Z, ALPHA1, BETA1, ALPHA2, BETA2, VL, VR, WORK, LWORK, RWORK, RESULT, INFO) |
ZDRVGG More... | |
subroutine zdrvgg | ( | integer | NSIZES, |
integer, dimension( * ) | NN, | ||
integer | NTYPES, | ||
logical, dimension( * ) | DOTYPE, | ||
integer, dimension( 4 ) | ISEED, | ||
double precision | THRESH, | ||
double precision | THRSHN, | ||
integer | NOUNIT, | ||
complex*16, dimension( lda, * ) | A, | ||
integer | LDA, | ||
complex*16, dimension( lda, * ) | B, | ||
complex*16, dimension( lda, * ) | S, | ||
complex*16, dimension( lda, * ) | T, | ||
complex*16, dimension( lda, * ) | S2, | ||
complex*16, dimension( lda, * ) | T2, | ||
complex*16, dimension( ldq, * ) | Q, | ||
integer | LDQ, | ||
complex*16, dimension( ldq, * ) | Z, | ||
complex*16, dimension( * ) | ALPHA1, | ||
complex*16, dimension( * ) | BETA1, | ||
complex*16, dimension( * ) | ALPHA2, | ||
complex*16, dimension( * ) | BETA2, | ||
complex*16, dimension( ldq, * ) | VL, | ||
complex*16, dimension( ldq, * ) | VR, | ||
complex*16, dimension( * ) | WORK, | ||
integer | LWORK, | ||
double precision, dimension( * ) | RWORK, | ||
double precision, dimension( * ) | RESULT, | ||
integer | INFO | ||
) |
ZDRVGG
ZDRVGG checks the nonsymmetric generalized eigenvalue driver routines. T T T ZGEGS factors A and B as Q S Z and Q T Z , where means transpose, T is upper triangular, S is in generalized Schur form (upper triangular), and Q and Z are unitary. It also computes the generalized eigenvalues (alpha(1),beta(1)), ..., (alpha(n),beta(n)), where alpha(j)=S(j,j) and beta(j)=T(j,j) -- thus, w(j) = alpha(j)/beta(j) is a root of the generalized eigenvalue problem det( A - w(j) B ) = 0 and m(j) = beta(j)/alpha(j) is a root of the essentially equivalent problem det( m(j) A - B ) = 0 ZGEGV computes the generalized eigenvalues (alpha(1),beta(1)), ..., (alpha(n),beta(n)), the matrix L whose columns contain the generalized left eigenvectors l, and the matrix R whose columns contain the generalized right eigenvectors r for the pair (A,B). When ZDRVGG is called, a number of matrix "sizes" ("n's") and a number of matrix "types" are specified. For each size ("n") and each type of matrix, one matrix will be generated and used to test the nonsymmetric eigenroutines. For each matrix, 7 tests will be performed and compared with the threshhold THRESH: Results from ZGEGS: H (1) | A - Q S Z | / ( |A| n ulp ) H (2) | B - Q T Z | / ( |B| n ulp ) H (3) | I - QQ | / ( n ulp ) H (4) | I - ZZ | / ( n ulp ) (5) maximum over j of D(j) where: |alpha(j) - S(j,j)| |beta(j) - T(j,j)| D(j) = ------------------------ + ----------------------- max(|alpha(j)|,|S(j,j)|) max(|beta(j)|,|T(j,j)|) Results from ZGEGV: (6) max over all left eigenvalue/-vector pairs (beta/alpha,l) of | l**H * (beta A - alpha B) | / ( ulp max( |beta A|, |alpha B| ) ) where l**H is the conjugate tranpose of l. (7) max over all right eigenvalue/-vector pairs (beta/alpha,r) of | (beta A - alpha B) r | / ( ulp max( |beta A|, |alpha B| ) ) Test Matrices ---- -------- The sizes of the test matrices are specified by an array NN(1:NSIZES); the value of each element NN(j) specifies one size. The "types" are specified by a logical array DOTYPE( 1:NTYPES ); if DOTYPE(j) is .TRUE., then matrix type "j" will be generated. Currently, the list of possible types is: (1) ( 0, 0 ) (a pair of zero matrices) (2) ( I, 0 ) (an identity and a zero matrix) (3) ( 0, I ) (an identity and a zero matrix) (4) ( I, I ) (a pair of identity matrices) t t (5) ( J , J ) (a pair of transposed Jordan blocks) t ( I 0 ) (6) ( X, Y ) where X = ( J 0 ) and Y = ( t ) ( 0 I ) ( 0 J ) and I is a k x k identity and J a (k+1)x(k+1) Jordan block; k=(N-1)/2 (7) ( D, I ) where D is diag( 0, 1,..., N-1 ) (a diagonal matrix with those diagonal entries.) (8) ( I, D ) (9) ( big*D, small*I ) where "big" is near overflow and small=1/big (10) ( small*D, big*I ) (11) ( big*I, small*D ) (12) ( small*I, big*D ) (13) ( big*D, big*I ) (14) ( small*D, small*I ) (15) ( D1, D2 ) where D1 is diag( 0, 0, 1, ..., N-3, 0 ) and D2 is diag( 0, N-3, N-4,..., 1, 0, 0 ) t t (16) Q ( J , J ) Z where Q and Z are random unitary matrices. (17) Q ( T1, T2 ) Z where T1 and T2 are upper triangular matrices with random O(1) entries above the diagonal and diagonal entries diag(T1) = ( 0, 0, 1, ..., N-3, 0 ) and diag(T2) = ( 0, N-3, N-4,..., 1, 0, 0 ) (18) Q ( T1, T2 ) Z diag(T1) = ( 0, 0, 1, 1, s, ..., s, 0 ) diag(T2) = ( 0, 1, 0, 1,..., 1, 0 ) s = machine precision. (19) Q ( T1, T2 ) Z diag(T1)=( 0,0,1,1, 1-d, ..., 1-(N-5)*d=s, 0 ) diag(T2) = ( 0, 1, 0, 1, ..., 1, 0 ) N-5 (20) Q ( T1, T2 ) Z diag(T1)=( 0, 0, 1, 1, a, ..., a =s, 0 ) diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 ) (21) Q ( T1, T2 ) Z diag(T1)=( 0, 0, 1, r1, r2, ..., r(N-4), 0 ) diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 ) where r1,..., r(N-4) are random. (22) Q ( big*T1, small*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 ) diag(T2) = ( 0, 1, ..., 1, 0, 0 ) (23) Q ( small*T1, big*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 ) diag(T2) = ( 0, 1, ..., 1, 0, 0 ) (24) Q ( small*T1, small*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 ) diag(T2) = ( 0, 1, ..., 1, 0, 0 ) (25) Q ( big*T1, big*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 ) diag(T2) = ( 0, 1, ..., 1, 0, 0 ) (26) Q ( T1, T2 ) Z where T1 and T2 are random upper-triangular matrices.
[in] | NSIZES | NSIZES is INTEGER The number of sizes of matrices to use. If it is zero, ZDRVGG does nothing. It must be at least zero. |
[in] | NN | NN is INTEGER array, dimension (NSIZES) An array containing the sizes to be used for the matrices. Zero values will be skipped. The values must be at least zero. |
[in] | NTYPES | NTYPES is INTEGER The number of elements in DOTYPE. If it is zero, ZDRVGG does nothing. It must be at least zero. If it is MAXTYP+1 and NSIZES is 1, then an additional type, MAXTYP+1 is defined, which is to use whatever matrix is in A. This is only useful if DOTYPE(1:MAXTYP) is .FALSE. and DOTYPE(MAXTYP+1) is .TRUE. . |
[in] | DOTYPE | DOTYPE is LOGICAL array, dimension (NTYPES) If DOTYPE(j) is .TRUE., then for each size in NN a matrix of that size and of type j will be generated. If NTYPES is smaller than the maximum number of types defined (PARAMETER MAXTYP), then types NTYPES+1 through MAXTYP will not be generated. If NTYPES is larger than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES) will be ignored. |
[in,out] | ISEED | ISEED is INTEGER array, dimension (4) On entry ISEED specifies the seed of the random number generator. The array elements should be between 0 and 4095; if not they will be reduced mod 4096. Also, ISEED(4) must be odd. The random number generator uses a linear congruential sequence limited to small integers, and so should produce machine independent random numbers. The values of ISEED are changed on exit, and can be used in the next call to ZDRVGG to continue the same random number sequence. |
[in] | THRESH | THRESH is DOUBLE PRECISION 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. |
[in] | THRSHN | THRSHN is DOUBLE PRECISION Threshhold for reporting eigenvector normalization error. If the normalization of any eigenvector differs from 1 by more than THRSHN*ulp, then a special error message will be printed. (This is handled separately from the other tests, since only a compiler or programming error should cause an error message, at least if THRSHN is at least 5--10.) |
[in] | NOUNIT | NOUNIT is INTEGER The FORTRAN unit number for printing out error messages (e.g., if a routine returns IINFO not equal to 0.) |
[in,out] | A | A is COMPLEX*16 array, dimension (LDA, max(NN)) Used to hold the original A matrix. Used as input only if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and DOTYPE(MAXTYP+1)=.TRUE. |
[in] | LDA | LDA is INTEGER The leading dimension of A, B, S, T, S2, and T2. It must be at least 1 and at least max( NN ). |
[in,out] | B | B is COMPLEX*16 array, dimension (LDA, max(NN)) Used to hold the original B matrix. Used as input only if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and DOTYPE(MAXTYP+1)=.TRUE. |
[out] | S | S is COMPLEX*16 array, dimension (LDA, max(NN)) The upper triangular matrix computed from A by ZGEGS. |
[out] | T | T is COMPLEX*16 array, dimension (LDA, max(NN)) The upper triangular matrix computed from B by ZGEGS. |
[out] | S2 | S2 is COMPLEX*16 array, dimension (LDA, max(NN)) The matrix computed from A by ZGEGV. This will be the Schur (upper triangular) form of some matrix related to A, but will not, in general, be the same as S. |
[out] | T2 | T2 is COMPLEX*16 array, dimension (LDA, max(NN)) The matrix computed from B by ZGEGV. This will be the Schur form of some matrix related to B, but will not, in general, be the same as T. |
[out] | Q | Q is COMPLEX*16 array, dimension (LDQ, max(NN)) The (left) unitary matrix computed by ZGEGS. |
[in] | LDQ | LDQ is INTEGER The leading dimension of Q, Z, VL, and VR. It must be at least 1 and at least max( NN ). |
[out] | Z | Z is COMPLEX*16 array, dimension (LDQ, max(NN)) The (right) unitary matrix computed by ZGEGS. |
[out] | ALPHA1 | ALPHA1 is COMPLEX*16 array, dimension (max(NN)) |
[out] | BETA1 | BETA1 is COMPLEX*16 array, dimension (max(NN)) The generalized eigenvalues of (A,B) computed by ZGEGS. ALPHA1(k) / BETA1(k) is the k-th generalized eigenvalue of the matrices in A and B. |
[out] | ALPHA2 | ALPHA2 is COMPLEX*16 array, dimension (max(NN)) |
[out] | BETA2 | BETA2 is COMPLEX*16 array, dimension (max(NN)) The generalized eigenvalues of (A,B) computed by ZGEGV. ALPHA2(k) / BETA2(k) is the k-th generalized eigenvalue of the matrices in A and B. |
[out] | VL | VL is COMPLEX*16 array, dimension (LDQ, max(NN)) The (lower triangular) left eigenvector matrix for the matrices in A and B. |
[out] | VR | VR is COMPLEX*16 array, dimension (LDQ, max(NN)) The (upper triangular) right eigenvector matrix for the matrices in A and B. |
[out] | WORK | WORK is COMPLEX*16 array, dimension (LWORK) |
[in] | LWORK | LWORK is INTEGER The number of entries in WORK. This must be at least MAX( 2*N, N*(NB+1), (k+1)*(2*k+N+1) ), where "k" is the sum of the blocksize and number-of-shifts for ZHGEQZ, and NB is the greatest of the blocksizes for ZGEQRF, ZUNMQR, and ZUNGQR. (The blocksizes and the number-of-shifts are retrieved through calls to ILAENV.) |
[out] | RWORK | RWORK is DOUBLE PRECISION array, dimension (8*N) |
[out] | RESULT | RESULT is DOUBLE PRECISION array, dimension (7) The values computed by the tests described above. The values are currently limited to 1/ulp, to avoid overflow. |
[out] | INFO | INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value. > 0: A routine returned an error code. INFO is the absolute value of the INFO value returned. |
Definition at line 420 of file zdrvgg.f.