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---
:name: sspgv
:md5sum: b3c519ead837e7b587434eb8d06cec29
:category: :subroutine
:arguments:
- itype:
:type: integer
:intent: input
- jobz:
:type: char
:intent: input
- uplo:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- ap:
:type: real
:intent: input/output
:dims:
- ldap
- bp:
:type: real
:intent: input/output
:dims:
- n*(n+1)/2
- w:
:type: real
:intent: output
:dims:
- n
- z:
:type: real
:intent: output
:dims:
- ldz
- n
- ldz:
:type: integer
:intent: input
- work:
:type: real
:intent: workspace
:dims:
- 3*n
- 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 SSPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* SSPGV computes all the eigenvalues and, optionally, the eigenvectors\n\
* of a real generalized symmetric-definite eigenproblem, of the form\n\
* A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x.\n\
* Here A and B are assumed to be symmetric, stored in packed format,\n\
* and B is also positive definite.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* ITYPE (input) INTEGER\n\
* Specifies the problem type to be solved:\n\
* = 1: A*x = (lambda)*B*x\n\
* = 2: A*B*x = (lambda)*x\n\
* = 3: B*A*x = (lambda)*x\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 triangles of A and B are stored;\n\
* = 'L': Lower triangles of A and B are stored.\n\
*\n\
* N (input) INTEGER\n\
* The order of the matrices A and B. N >= 0.\n\
*\n\
* AP (input/output) REAL array, dimension\n\
* (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, the contents of AP are destroyed.\n\
*\n\
* BP (input/output) REAL array, dimension (N*(N+1)/2)\n\
* On entry, the upper or lower triangle of the symmetric matrix\n\
* B, packed columnwise in a linear array. The j-th column of B\n\
* is stored in the array BP as follows:\n\
* if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;\n\
* if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.\n\
*\n\
* On exit, the triangular factor U or L from the Cholesky\n\
* factorization B = U**T*U or B = L*L**T, in the same storage\n\
* format as B.\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 matrix Z of\n\
* eigenvectors. The eigenvectors are normalized as follows:\n\
* if ITYPE = 1 or 2, Z**T*B*Z = I;\n\
* if ITYPE = 3, Z**T*inv(B)*Z = 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) REAL array, dimension (3*N)\n\
*\n\
* INFO (output) INTEGER\n\
* = 0: successful exit\n\
* < 0: if INFO = -i, the i-th argument had an illegal value\n\
* > 0: SPPTRF or SSPEV returned an error code:\n\
* <= N: if INFO = i, SSPEV failed to converge;\n\
* i off-diagonal elements of an intermediate\n\
* tridiagonal form did not converge to zero.\n\
* > N: if INFO = n + i, for 1 <= i <= n, then the leading\n\
* minor of order i of B is not positive definite.\n\
* The factorization of B could not be completed and\n\
* no eigenvalues or eigenvectors were computed.\n\
*\n\n\
* =====================================================================\n\
*\n\
* .. Local Scalars ..\n LOGICAL UPPER, WANTZ\n CHARACTER TRANS\n INTEGER J, NEIG\n\
* ..\n\
* .. External Functions ..\n LOGICAL LSAME\n EXTERNAL LSAME\n\
* ..\n\
* .. External Subroutines ..\n EXTERNAL SPPTRF, SSPEV, SSPGST, STPMV, STPSV, XERBLA\n\
* ..\n"
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