TESTING/EIG/cdrvst2stg.f(3) Library Functions Manual NAME TESTING/EIG/cdrvst2stg.f SYNOPSIS Functions/Subroutines subroutine cdrvst2stg (nsizes, nn, ntypes, dotype, iseed, thresh, nounit, a, lda, d1, d2, d3, wa1, wa2, wa3, u, ldu, v, tau, z, work, lwork, rwork, lrwork, iwork, liwork, result, info) CDRVST2STG Function/Subroutine Documentation subroutine cdrvst2stg (integer nsizes, integer, dimension( * ) nn, integer ntypes, logical, dimension( * ) dotype, integer, dimension( 4 ) iseed, real thresh, integer nounit, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) d1, real, dimension( * ) d2, real, dimension( * ) d3, real, dimension( * ) wa1, real, dimension( * ) wa2, real, dimension( * ) wa3, complex, dimension( ldu, * ) u, integer ldu, complex, dimension( ldu, * ) v, complex, dimension( * ) tau, complex, dimension( ldu, * ) z, complex, dimension( * ) work, integer lwork, real, dimension( * ) rwork, integer lrwork, integer, dimension( * ) iwork, integer liwork, real, dimension( * ) result, integer info) CDRVST2STG Purpose: CDRVST2STG checks the Hermitian eigenvalue problem drivers. CHEEVD computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, using a divide-and-conquer algorithm. CHEEVX computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix. CHEEVR computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix using the Relatively Robust Representation where it can. CHPEVD computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage, using a divide-and-conquer algorithm. CHPEVX computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage. CHBEVD computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix, using a divide-and-conquer algorithm. CHBEVX computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix. CHEEV computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix. CHPEV computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage. CHBEV computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix. When CDRVST2STG 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 appropriate drivers. For each matrix and each driver routine called, the following tests will be performed: (1) | A - Z D Z' | / ( |A| n ulp ) (2) | I - Z Z' | / ( n ulp ) (3) | D1 - D2 | / ( |D1| ulp ) where Z is the matrix of eigenvectors returned when the eigenvector option is given and D1 and D2 are the eigenvalues returned with and without the eigenvector option. The 'sizes' 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) 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 'clustered' 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 'clustered' 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) Symmetric 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 ) (16) A band matrix with half bandwidth randomly chosen between 0 and N-1, with evenly spaced eigenvalues 1, ..., ULP with random signs. (17) Same as (16), but multiplied by SQRT( overflow threshold ) (18) Same as (16), but multiplied by SQRT( underflow threshold ) NSIZES INTEGER The number of sizes of matrices to use. If it is zero, CDRVST2STG does nothing. It must be at least zero. Not modified. NN 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. Not modified. NTYPES INTEGER The number of elements in DOTYPE. If it is zero, CDRVST2STG 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. . Not modified. DOTYPE 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. Not modified. ISEED 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 CDRVST2STG to continue the same random number sequence. Modified. THRESH 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. Not modified. NOUNIT INTEGER The FORTRAN unit number for printing out error messages (e.g., if a routine returns IINFO not equal to 0.) Not modified. A COMPLEX array, dimension (LDA , max(NN)) Used to hold the matrix whose eigenvalues are to be computed. On exit, A contains the last matrix actually used. Modified. LDA INTEGER The leading dimension of A. It must be at least 1 and at least max( NN ). Not modified. D1 REAL array, dimension (max(NN)) The eigenvalues of A, as computed by CSTEQR simultaneously with Z. On exit, the eigenvalues in D1 correspond with the matrix in A. Modified. D2 REAL array, dimension (max(NN)) The eigenvalues of A, as computed by CSTEQR if Z is not computed. On exit, the eigenvalues in D2 correspond with the matrix in A. Modified. D3 REAL array, dimension (max(NN)) The eigenvalues of A, as computed by SSTERF. On exit, the eigenvalues in D3 correspond with the matrix in A. Modified. WA1 REAL array, dimension WA2 REAL array, dimension WA3 REAL array, dimension U COMPLEX array, dimension (LDU, max(NN)) The unitary matrix computed by CHETRD + CUNGC3. Modified. LDU INTEGER The leading dimension of U, Z, and V. It must be at least 1 and at least max( NN ). Not modified. V COMPLEX array, dimension (LDU, max(NN)) The Housholder vectors computed by CHETRD in reducing A to tridiagonal form. Modified. TAU COMPLEX array, dimension (max(NN)) The Householder factors computed by CHETRD in reducing A to tridiagonal form. Modified. Z COMPLEX array, dimension (LDU, max(NN)) The unitary matrix of eigenvectors computed by CHEEVD, CHEEVX, CHPEVD, CHPEVX, CHBEVD, and CHBEVX. Modified. WORK - COMPLEX array of dimension ( LWORK ) Workspace. Modified. LWORK - INTEGER The number of entries in WORK. This must be at least 2*max( NN(j), 2 )**2. Not modified. RWORK REAL array, dimension (3*max(NN)) Workspace. Modified. LRWORK - INTEGER The number of entries in RWORK. IWORK INTEGER array, dimension (6*max(NN)) Workspace. Modified. LIWORK - INTEGER The number of entries in IWORK. RESULT REAL array, dimension (??) The values computed by the tests described above. The values are currently limited to 1/ulp, to avoid overflow. Modified. INFO INTEGER If 0, then everything ran OK. -1: NSIZES < 0 -2: Some NN(j) < 0 -3: NTYPES < 0 -5: THRESH < 0 -9: LDA < 1 or LDA < NMAX, where NMAX is max( NN(j) ). -16: LDU < 1 or LDU < NMAX. -21: LWORK too small. If SLATMR, SLATMS, CHETRD, SORGC3, CSTEQR, SSTERF, or SORMC2 returns an error code, the absolute value of it is returned. Modified. ----------------------------------------------------------------------- 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 (computed by SLAFTS). 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 'j'. KMODE(j) The MODE value to be passed to the matrix generator for type 'j'. KMAGN(j) The order of magnitude ( O(1), O(overflow^(1/2) ), O(underflow^(1/2) ) Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 334 of file cdrvst2stg.f. Author Generated automatically by Doxygen for LAPACK from the source code. LAPACK Version 3.12.0 TESTING/EIG/cdrvst2stg.f(3)