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LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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| subroutine cchkhb | ( | integer | nsizes, |
| integer, dimension( * ) | nn, | ||
| integer | nwdths, | ||
| integer, dimension( * ) | kk, | ||
| integer | ntypes, | ||
| logical, dimension( * ) | dotype, | ||
| integer, dimension( 4 ) | iseed, | ||
| real | thresh, | ||
| integer | nounit, | ||
| complex, dimension( lda, * ) | a, | ||
| integer | lda, | ||
| real, dimension( * ) | sd, | ||
| real, dimension( * ) | se, | ||
| complex, dimension( ldu, * ) | u, | ||
| integer | ldu, | ||
| complex, dimension( * ) | work, | ||
| integer | lwork, | ||
| real, dimension( * ) | rwork, | ||
| real, dimension( * ) | result, | ||
| integer | info ) |
CCHKHB
!> !> CCHKHB tests the reduction of a Hermitian band matrix to tridiagonal !> from, used with the Hermitian eigenvalue problem. !> !> CHBTRD factors a Hermitian band matrix A as U S U* , where * means !> conjugate transpose, S is symmetric tridiagonal, and U is unitary. !> CHBTRD can use either just the lower or just the upper triangle !> of A; CCHKHB checks both cases. !> !> When CCHKHB is called, a number of matrix (), a number !> of bandwidths (), and a number of matrix are !> specified. For each size (), each bandwidth () less than or !> equal to , and each type of matrix, one matrix will be generated !> and used to test the hermitian banded reduction routine. For each !> matrix, a number of tests will be performed: !> !> (1) | A - V S V* | / ( |A| n ulp ) computed by CHBTRD with !> UPLO='U' !> !> (2) | I - UU* | / ( n ulp ) !> !> (3) | A - V S V* | / ( |A| n ulp ) computed by CHBTRD with !> UPLO='L' !> !> (4) | I - UU* | / ( n ulp ) !> !> The are specified by an array NN(1:NSIZES); the value of !> each element NN(j) specifies one size. !> The are specified by a logical array DOTYPE( 1:NTYPES ); !> if DOTYPE(j) is .TRUE., then matrix type will be generated. !> Currently, the list of possible types is: !> !> (1) The zero matrix. !> (2) The identity matrix. !> !> (3) A diagonal matrix with evenly spaced entries !> 1, ..., ULP and random signs. !> (ULP = (first number larger than 1) - 1 ) !> (4) A diagonal matrix with geometrically spaced entries !> 1, ..., ULP and random signs. !> (5) A diagonal matrix with entries 1, ULP, ..., ULP !> and random signs. !> !> (6) Same as (4), but multiplied by SQRT( overflow threshold ) !> (7) Same as (4), but multiplied by SQRT( underflow threshold ) !> !> (8) A matrix of the form U* D U, where U is unitary and !> D has evenly spaced entries 1, ..., ULP with random signs !> on the diagonal. !> !> (9) A matrix of the form U* D U, where U is unitary and !> D has geometrically spaced entries 1, ..., ULP with random !> signs on the diagonal. !> !> (10) A matrix of the form U* D U, where U is unitary and !> D has entries 1, ULP,..., ULP with random !> signs on the diagonal. !> !> (11) Same as (8), but multiplied by SQRT( overflow threshold ) !> (12) Same as (8), but multiplied by SQRT( underflow threshold ) !> !> (13) Hermitian matrix with random entries chosen from (-1,1). !> (14) Same as (13), but multiplied by SQRT( overflow threshold ) !> (15) Same as (13), but multiplied by SQRT( underflow threshold ) !>
| [in] | NSIZES | !> NSIZES is INTEGER !> The number of sizes of matrices to use. If it is zero, !> CCHKHB 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] | NWDTHS | !> NWDTHS is INTEGER !> The number of bandwidths to use. If it is zero, !> CCHKHB does nothing. It must be at least zero. !> |
| [in] | KK | !> KK is INTEGER array, dimension (NWDTHS) !> An array containing the bandwidths to be used for the band !> matrices. The values must be at least zero. !> |
| [in] | NTYPES | !> NTYPES is INTEGER !> The number of elements in DOTYPE. If it is zero, CCHKHB !> 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 CCHKHB to continue the same random number !> sequence. !> |
| [in] | THRESH | !> THRESH is REAL !> A test will count as if the , 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] | 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 array, dimension !> (LDA, max(NN)) !> Used to hold the matrix whose eigenvalues are to be !> computed. !> |
| [in] | LDA | !> LDA is INTEGER !> The leading dimension of A. It must be at least 2 (not 1!) !> and at least max( KK )+1. !> |
| [out] | SD | !> SD is REAL array, dimension (max(NN)) !> Used to hold the diagonal of the tridiagonal matrix computed !> by CHBTRD. !> |
| [out] | SE | !> SE is REAL array, dimension (max(NN)) !> Used to hold the off-diagonal of the tridiagonal matrix !> computed by CHBTRD. !> |
| [out] | U | !> U is COMPLEX array, dimension (LDU, max(NN)) !> Used to hold the unitary matrix computed by CHBTRD. !> |
| [in] | LDU | !> LDU is INTEGER !> The leading dimension of U. It must be at least 1 !> and at least max( NN ). !> |
| [out] | WORK | !> WORK is COMPLEX array, dimension (LWORK) !> |
| [in] | LWORK | !> LWORK is INTEGER !> The number of entries in WORK. This must be at least !> max( LDA+1, max(NN)+1 )*max(NN). !> |
| [out] | RWORK | !> RWORK is REAL array !> |
| [out] | RESULT | !> RESULT is REAL array, dimension (4) !> The values computed by the tests described above. !> The values are currently limited to 1/ulp, to avoid !> overflow. !> |
| [out] | INFO | !> INFO is INTEGER !> If 0, then everything ran OK. !> !>----------------------------------------------------------------------- !> !> Some Local Variables and Parameters: !> ---- ----- --------- --- ---------- !> ZERO, ONE Real 0 and 1. !> MAXTYP The number of types defined. !> NTEST The number of tests performed, or which can !> be performed so far, for the current matrix. !> NTESTT The total number of tests performed so far. !> NMAX Largest value in NN. !> NMATS The number of matrices generated so far. !> NERRS The number of tests which have exceeded THRESH !> so far. !> COND, IMODE Values to be passed to the matrix generators. !> ANORM Norm of A; passed to matrix generators. !> !> OVFL, UNFL Overflow and underflow thresholds. !> ULP, ULPINV Finest relative precision and its inverse. !> RTOVFL, RTUNFL Square roots of the previous 2 values. !> The following four arrays decode JTYPE: !> KTYPE(j) The general type (1-10) for type . !> KMODE(j) The MODE value to be passed to the matrix !> generator for type . !> KMAGN(j) The order of magnitude ( O(1), !> O(overflow^(1/2) ), O(underflow^(1/2) ) !> |
Definition at line 295 of file cchkhb.f.
1.11.0