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---
:name: cheevx
:md5sum: 16e52f5a970fe326d98bf7b6bca8e538
:category: :subroutine
:arguments:
- jobz:
:type: char
:intent: input
- range:
:type: char
:intent: input
- uplo:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- a:
:type: complex
:intent: input/output
:dims:
- lda
- n
- lda:
:type: integer
:intent: input
- vl:
:type: real
:intent: input
- vu:
:type: real
:intent: input
- il:
:type: integer
:intent: input
- iu:
:type: integer
:intent: input
- abstol:
:type: real
:intent: input
- m:
:type: integer
:intent: output
- w:
:type: real
:intent: output
:dims:
- n
- z:
:type: complex
:intent: output
:dims:
- ldz
- MAX(1,m)
- ldz:
:type: integer
:intent: input
- work:
:type: complex
:intent: output
:dims:
- MAX(1,lwork)
- lwork:
:type: integer
:intent: input
:option: true
:default: "n<=1 ? 1 : 2*n"
- rwork:
:type: real
:intent: workspace
:dims:
- 7*n
- iwork:
:type: integer
:intent: workspace
:dims:
- 5*n
- ifail:
:type: integer
:intent: output
:dims:
- n
- info:
:type: integer
:intent: output
:substitutions:
ldz: "lsame_(&jobz,\"V\") ? MAX(1,n) : 1"
m: "lsame_(&range,\"A\") ? n : lsame_(&range,\"I\") ? iu-il+1 : 0"
:fortran_help: " SUBROUTINE CHEEVX( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, LWORK, RWORK, IWORK, IFAIL, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* CHEEVX computes selected eigenvalues and, optionally, eigenvectors\n\
* of a complex Hermitian matrix A. Eigenvalues and eigenvectors can\n\
* be selected by specifying either a range of values or a range of\n\
* indices for the desired eigenvalues.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* JOBZ (input) CHARACTER*1\n\
* = 'N': Compute eigenvalues only;\n\
* = 'V': Compute eigenvalues and eigenvectors.\n\
*\n\
* RANGE (input) CHARACTER*1\n\
* = 'A': all eigenvalues will be found.\n\
* = 'V': all eigenvalues in the half-open interval (VL,VU]\n\
* will be found.\n\
* = 'I': the IL-th through IU-th eigenvalues will be found.\n\
*\n\
* UPLO (input) CHARACTER*1\n\
* = 'U': Upper triangle of A is stored;\n\
* = 'L': Lower triangle of A is stored.\n\
*\n\
* N (input) INTEGER\n\
* The order of the matrix A. N >= 0.\n\
*\n\
* A (input/output) COMPLEX array, dimension (LDA, N)\n\
* On entry, the Hermitian matrix A. If UPLO = 'U', the\n\
* leading N-by-N upper triangular part of A contains the\n\
* upper triangular part of the matrix A. If UPLO = 'L',\n\
* the leading N-by-N lower triangular part of A contains\n\
* the lower triangular part of the matrix A.\n\
* On exit, the lower triangle (if UPLO='L') or the upper\n\
* triangle (if UPLO='U') of A, including the diagonal, is\n\
* destroyed.\n\
*\n\
* LDA (input) INTEGER\n\
* The leading dimension of the array A. LDA >= max(1,N).\n\
*\n\
* VL (input) REAL\n\
* VU (input) REAL\n\
* If RANGE='V', the lower and upper bounds of the interval to\n\
* be searched for eigenvalues. VL < VU.\n\
* Not referenced if RANGE = 'A' or 'I'.\n\
*\n\
* IL (input) INTEGER\n\
* IU (input) INTEGER\n\
* If RANGE='I', the indices (in ascending order) of the\n\
* smallest and largest eigenvalues to be returned.\n\
* 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.\n\
* Not referenced if RANGE = 'A' or 'V'.\n\
*\n\
* ABSTOL (input) REAL\n\
* The absolute error tolerance for the eigenvalues.\n\
* An approximate eigenvalue is accepted as converged\n\
* when it is determined to lie in an interval [a,b]\n\
* of width less than or equal to\n\
*\n\
* ABSTOL + EPS * max( |a|,|b| ) ,\n\
*\n\
* where EPS is the machine precision. If ABSTOL is less than\n\
* or equal to zero, then EPS*|T| will be used in its place,\n\
* where |T| is the 1-norm of the tridiagonal matrix obtained\n\
* by reducing A to tridiagonal form.\n\
*\n\
* Eigenvalues will be computed most accurately when ABSTOL is\n\
* set to twice the underflow threshold 2*SLAMCH('S'), not zero.\n\
* If this routine returns with INFO>0, indicating that some\n\
* eigenvectors did not converge, try setting ABSTOL to\n\
* 2*SLAMCH('S').\n\
*\n\
* See \"Computing Small Singular Values of Bidiagonal Matrices\n\
* with Guaranteed High Relative Accuracy,\" by Demmel and\n\
* Kahan, LAPACK Working Note #3.\n\
*\n\
* M (output) INTEGER\n\
* The total number of eigenvalues found. 0 <= M <= N.\n\
* If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.\n\
*\n\
* W (output) REAL array, dimension (N)\n\
* On normal exit, the first M elements contain the selected\n\
* eigenvalues in ascending order.\n\
*\n\
* Z (output) COMPLEX array, dimension (LDZ, max(1,M))\n\
* If JOBZ = 'V', then if INFO = 0, the first M columns of Z\n\
* contain the orthonormal eigenvectors of the matrix A\n\
* corresponding to the selected eigenvalues, with the i-th\n\
* column of Z holding the eigenvector associated with W(i).\n\
* If an eigenvector fails to converge, then that column of Z\n\
* contains the latest approximation to the eigenvector, and the\n\
* index of the eigenvector is returned in IFAIL.\n\
* If JOBZ = 'N', then Z is not referenced.\n\
* Note: the user must ensure that at least max(1,M) columns are\n\
* supplied in the array Z; if RANGE = 'V', the exact value of M\n\
* is not known in advance and an upper bound must be used.\n\
*\n\
* LDZ (input) INTEGER\n\
* The leading dimension of the array Z. LDZ >= 1, and if\n\
* JOBZ = 'V', LDZ >= max(1,N).\n\
*\n\
* WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))\n\
* On exit, if INFO = 0, WORK(1) returns the optimal LWORK.\n\
*\n\
* LWORK (input) INTEGER\n\
* The length of the array WORK. LWORK >= 1, when N <= 1;\n\
* otherwise 2*N.\n\
* For optimal efficiency, LWORK >= (NB+1)*N,\n\
* where NB is the max of the blocksize for CHETRD and for\n\
* CUNMTR as returned by ILAENV.\n\
*\n\
* If LWORK = -1, then a workspace query is assumed; the routine\n\
* only calculates the optimal size of the WORK array, returns\n\
* this value as the first entry of the WORK array, and no error\n\
* message related to LWORK is issued by XERBLA.\n\
*\n\
* RWORK (workspace) REAL array, dimension (7*N)\n\
*\n\
* IWORK (workspace) INTEGER array, dimension (5*N)\n\
*\n\
* IFAIL (output) INTEGER array, dimension (N)\n\
* If JOBZ = 'V', then if INFO = 0, the first M elements of\n\
* IFAIL are zero. If INFO > 0, then IFAIL contains the\n\
* indices of the eigenvectors that failed to converge.\n\
* If JOBZ = 'N', then IFAIL is not referenced.\n\
*\n\
* INFO (output) INTEGER\n\
* = 0: successful exit\n\
* < 0: if INFO = -i, the i-th argument had an illegal value\n\
* > 0: if INFO = i, then i eigenvectors failed to converge.\n\
* Their indices are stored in array IFAIL.\n\
*\n\n\
* =====================================================================\n\
*\n"
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