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LAPACK
3.5.0
LAPACK: Linear Algebra PACKage
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Functions/Subroutines | |
subroutine | sdrvgg (NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH, THRSHN, NOUNIT, A, LDA, B, S, T, S2, T2, Q, LDQ, Z, ALPHR1, ALPHI1, BETA1, ALPHR2, ALPHI2, BETA2, VL, VR, WORK, LWORK, RESULT, INFO) |
SDRVGG More... | |
subroutine sdrvgg | ( | integer | NSIZES, |
integer, dimension( * ) | NN, | ||
integer | NTYPES, | ||
logical, dimension( * ) | DOTYPE, | ||
integer, dimension( 4 ) | ISEED, | ||
real | THRESH, | ||
real | THRSHN, | ||
integer | NOUNIT, | ||
real, dimension( lda, * ) | A, | ||
integer | LDA, | ||
real, dimension( lda, * ) | B, | ||
real, dimension( lda, * ) | S, | ||
real, dimension( lda, * ) | T, | ||
real, dimension( lda, * ) | S2, | ||
real, dimension( lda, * ) | T2, | ||
real, dimension( ldq, * ) | Q, | ||
integer | LDQ, | ||
real, dimension( ldq, * ) | Z, | ||
real, dimension( * ) | ALPHR1, | ||
real, dimension( * ) | ALPHI1, | ||
real, dimension( * ) | BETA1, | ||
real, dimension( * ) | ALPHR2, | ||
real, dimension( * ) | ALPHI2, | ||
real, dimension( * ) | BETA2, | ||
real, dimension( ldq, * ) | VL, | ||
real, dimension( ldq, * ) | VR, | ||
real, dimension( * ) | WORK, | ||
integer | LWORK, | ||
real, dimension( * ) | RESULT, | ||
integer | INFO | ||
) |
SDRVGG
SDRVGG checks the nonsymmetric generalized eigenvalue driver routines. T T T SGEGS 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 (block upper triangular, with 1x1 and 2x2 blocks on the diagonal, the 2x2 blocks corresponding to complex conjugate pairs of generalized eigenvalues), and Q and Z are orthogonal. It also computes the generalized eigenvalues (alpha(1),beta(1)), ..., (alpha(n),beta(n)), where alpha(j)=S(j,j) and beta(j)=P(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 SGEGV 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 SDRVGG 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 SGEGS: T (1) | A - Q S Z | / ( |A| n ulp ) T (2) | B - Q T Z | / ( |B| n ulp ) T (3) | I - QQ | / ( n ulp ) T (4) | I - ZZ | / ( n ulp ) (5) maximum over j of D(j) where: if alpha(j) is real: |alpha(j) - S(j,j)| |beta(j) - T(j,j)| D(j) = ------------------------ + ----------------------- max(|alpha(j)|,|S(j,j)|) max(|beta(j)|,|T(j,j)|) if alpha(j) is complex: | det( s S - w T ) | D(j) = --------------------------------------------------- ulp max( s norm(S), |w| norm(T) )*norm( s S - w T ) and S and T are here the 2 x 2 diagonal blocks of S and T corresponding to the j-th eigenvalue. Results from SGEGV: (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 orthogonal 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, SDRVGG 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, SDRVGG 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 SDRVGG to continue the same random number sequence. |
[in] | 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. |
[in] | THRSHN | THRSHN is REAL 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 REAL 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 REAL 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 REAL array, dimension (LDA, max(NN)) The Schur form matrix computed from A by SGEGS. On exit, S contains the Schur form matrix corresponding to the matrix in A. |
[out] | T | T is REAL array, dimension (LDA, max(NN)) The upper triangular matrix computed from B by SGEGS. |
[out] | S2 | S2 is REAL array, dimension (LDA, max(NN)) The matrix computed from A by SGEGV. This will be the Schur form of some matrix related to A, but will not, in general, be the same as S. |
[out] | T2 | T2 is REAL array, dimension (LDA, max(NN)) The matrix computed from B by SGEGV. 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 REAL array, dimension (LDQ, max(NN)) The (left) orthogonal matrix computed by SGEGS. |
[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 REAL array of dimension( LDQ, max(NN) ) The (right) orthogonal matrix computed by SGEGS. |
[out] | ALPHR1 | ALPHR1 is REAL array, dimension (max(NN)) |
[out] | ALPHI1 | ALPHI1 is REAL array, dimension (max(NN)) |
[out] | BETA1 | BETA1 is REAL array, dimension (max(NN)) The generalized eigenvalues of (A,B) computed by SGEGS. ( ALPHR1(k)+ALPHI1(k)*i ) / BETA1(k) is the k-th generalized eigenvalue of the matrices in A and B. |
[out] | ALPHR2 | ALPHR2 is REAL array, dimension (max(NN)) |
[out] | ALPHI2 | ALPHI2 is REAL array, dimension (max(NN)) |
[out] | BETA2 | BETA2 is REAL array, dimension (max(NN)) The generalized eigenvalues of (A,B) computed by SGEGV. ( ALPHR2(k)+ALPHI2(k)*i ) / BETA2(k) is the k-th generalized eigenvalue of the matrices in A and B. |
[out] | VL | VL is REAL array, dimension (LDQ, max(NN)) The (block lower triangular) left eigenvector matrix for the matrices in A and B. (See STGEVC for the format.) |
[out] | VR | VR is REAL array, dimension (LDQ, max(NN)) The (block upper triangular) right eigenvector matrix for the matrices in A and B. (See STGEVC for the format.) |
[out] | WORK | WORK is REAL array, dimension (LWORK) |
[in] | LWORK | LWORK is INTEGER The number of entries in WORK. This must be at least 2*N + MAX( 6*N, N*(NB+1), (k+1)*(2*k+N+1) ), where "k" is the sum of the blocksize and number-of-shifts for SHGEQZ, and NB is the greatest of the blocksizes for SGEQRF, SORMQR, and SORGQR. (The blocksizes and the number-of-shifts are retrieved through calls to ILAENV.) |
[out] | RESULT | RESULT is REAL array, dimension (15) 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 454 of file sdrvgg.f.