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---
:name: sspevd
:md5sum: 83441e80c70bbab2f5bee13cf131faa6
:category: :subroutine
:arguments:
- jobz:
:type: char
:intent: input
- uplo:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- ap:
:type: real
:intent: input/output
:dims:
- ldap
- 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<=1 ? 1 : lsame_(&jobz,\"N\") ? 2*n : lsame_(&jobz,\"V\") ? 1+6*n+n*n : 2"
- iwork:
:type: integer
:intent: output
:dims:
- MAX(1,liwork)
- liwork:
:type: integer
:intent: input
:option: true
:default: "(lsame_(&jobz,\"N\")||n<=1) ? 1 : lsame_(&jobz,\"V\") ? 3+5*n : 0"
- info:
:type: integer
:intent: output
:substitutions:
ldz: "lsame_(&jobz,\"V\") ? MAX(1,n) : 1"
n: ((int)sqrtf(ldap*8+1.0f)-1)/2
:fortran_help: " SUBROUTINE SSPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, IWORK, LIWORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* SSPEVD computes all the eigenvalues and, optionally, eigenvectors\n\
* of a real symmetric matrix A in packed storage. If eigenvectors are\n\
* desired, it uses 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\
* AP (input/output) REAL array, dimension (N*(N+1)/2)\n\
* On entry, the upper or lower triangle of the symmetric matrix\n\
* A, packed columnwise in a linear array. The j-th column of A\n\
* is stored in the array AP as follows:\n\
* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;\n\
* if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.\n\
*\n\
* On exit, AP is overwritten by values generated during the\n\
* reduction to tridiagonal form. If UPLO = 'U', the diagonal\n\
* and first superdiagonal of the tridiagonal matrix T overwrite\n\
* the corresponding elements of A, and if UPLO = 'L', the\n\
* diagonal and first subdiagonal of T overwrite the\n\
* corresponding elements of A.\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, dimension (MAX(1,LWORK))\n\
* On exit, if INFO = 0, WORK(1) returns the required 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 > 1, LWORK must be at least 2*N.\n\
* If JOBZ = 'V' and N > 1, LWORK must be at least\n\
* 1 + 6*N + N**2.\n\
*\n\
* If LWORK = -1, then a workspace query is assumed; the routine\n\
* only calculates the required 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 required LIWORK.\n\
*\n\
* LIWORK (input) INTEGER\n\
* The dimension of the array IWORK.\n\
* If JOBZ = 'N' or N <= 1, LIWORK must be at least 1.\n\
* If JOBZ = 'V' and N > 1, 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 required 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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