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---
:name: ssbevd
:md5sum: 71100f8057bbfe6a4838357d0d1b2105
:category: :subroutine
:arguments:
- jobz:
:type: char
:intent: input
- uplo:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- kd:
:type: integer
:intent: input
- ab:
:type: real
:intent: input/output
:dims:
- ldab
- n
- ldab:
:type: integer
:intent: input
- w:
:type: real
:intent: output
:dims:
- n
- z:
:type: real
:intent: output
:dims:
- ldz
- n
- ldz:
:type: integer
:intent: input
- work:
:type: real
:intent: output
:dims:
- MAX(1,lwork)
- lwork:
:type: integer
:intent: input
:option: true
:default: "n<=0 ? 1 : lsame_(&jobz,\"N\") ? 2*n : lsame_(&jobz,\"V\") ? 1+5*n+2*n*n : 0"
- iwork:
:type: integer
:intent: output
:dims:
- MAX(1,liwork)
- liwork:
:type: integer
:intent: input
:option: true
:default: "(lsame_(&jobz,\"N\")||n<=0) ? 1 : lsame_(&jobz,\"V\") ? 3+5*n : 0"
- info:
:type: integer
:intent: output
:substitutions:
ldz: "lsame_(&jobz,\"V\") ? MAX(1,n) : 1"
:fortran_help: " SUBROUTINE SSBEVD( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK, LWORK, IWORK, LIWORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* SSBEVD computes all the eigenvalues and, optionally, eigenvectors of\n\
* a real symmetric band matrix A. If eigenvectors are desired, it uses\n\
* a divide and conquer algorithm.\n\
*\n\
* The divide and conquer algorithm makes very mild assumptions about\n\
* floating point arithmetic. It will work on machines with a guard\n\
* digit in add/subtract, or on those binary machines without guard\n\
* digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or\n\
* Cray-2. It could conceivably fail on hexadecimal or decimal machines\n\
* without guard digits, but we know of none.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* JOBZ (input) CHARACTER*1\n\
* = 'N': Compute eigenvalues only;\n\
* = 'V': Compute eigenvalues and eigenvectors.\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\
* KD (input) INTEGER\n\
* The number of superdiagonals of the matrix A if UPLO = 'U',\n\
* or the number of subdiagonals if UPLO = 'L'. KD >= 0.\n\
*\n\
* AB (input/output) REAL array, dimension (LDAB, N)\n\
* On entry, the upper or lower triangle of the symmetric band\n\
* matrix A, stored in the first KD+1 rows of the array. The\n\
* j-th column of A is stored in the j-th column of the array AB\n\
* as follows:\n\
* if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;\n\
* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).\n\
*\n\
* On exit, AB is overwritten by values generated during the\n\
* reduction to tridiagonal form. If UPLO = 'U', the first\n\
* superdiagonal and the diagonal of the tridiagonal matrix T\n\
* are returned in rows KD and KD+1 of AB, and if UPLO = 'L',\n\
* the diagonal and first subdiagonal of T are returned in the\n\
* first two rows of AB.\n\
*\n\
* LDAB (input) INTEGER\n\
* The leading dimension of the array AB. LDAB >= KD + 1.\n\
*\n\
* W (output) REAL array, dimension (N)\n\
* If INFO = 0, the eigenvalues in ascending order.\n\
*\n\
* Z (output) REAL array, dimension (LDZ, N)\n\
* If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal\n\
* eigenvectors of the matrix A, with the i-th column of Z\n\
* holding the eigenvector associated with W(i).\n\
* If JOBZ = 'N', then Z is not referenced.\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) REAL array,\n\
* dimension (LWORK)\n\
* On exit, if INFO = 0, WORK(1) returns the optimal LWORK.\n\
*\n\
* LWORK (input) INTEGER\n\
* The dimension of the array WORK.\n\
* IF N <= 1, LWORK must be at least 1.\n\
* If JOBZ = 'N' and N > 2, LWORK must be at least 2*N.\n\
* If JOBZ = 'V' and N > 2, LWORK must be at least\n\
* ( 1 + 5*N + 2*N**2 ).\n\
*\n\
* If LWORK = -1, then a workspace query is assumed; the routine\n\
* only calculates the optimal sizes of the WORK and IWORK\n\
* arrays, returns these values as the first entries of the WORK\n\
* and IWORK arrays, and no error message related to LWORK or\n\
* LIWORK is issued by XERBLA.\n\
*\n\
* IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))\n\
* On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.\n\
*\n\
* LIWORK (input) INTEGER\n\
* The dimension of the array LIWORK.\n\
* If JOBZ = 'N' or N <= 1, LIWORK must be at least 1.\n\
* If JOBZ = 'V' and N > 2, LIWORK must be at least 3 + 5*N.\n\
*\n\
* If LIWORK = -1, then a workspace query is assumed; the\n\
* routine only calculates the optimal sizes of the WORK and\n\
* IWORK arrays, returns these values as the first entries of\n\
* the WORK and IWORK arrays, and no error message related to\n\
* LWORK or LIWORK is issued by XERBLA.\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, the algorithm failed to converge; i\n\
* off-diagonal elements of an intermediate tridiagonal\n\
* form did not converge to zero.\n\
*\n\n\
* =====================================================================\n\
*\n"
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