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---
:name: chpgvd
:md5sum: 64f7065ad380a8ee00723d15be61d9d1
: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: complex
:intent: input/output
:dims:
- ldap
- bp:
:type: complex
:intent: input/output
:dims:
- n*(n+1)/2
- w:
:type: real
:intent: output
:dims:
- n
- z:
:type: complex
:intent: output
:dims:
- ldz
- n
- ldz:
:type: integer
:intent: input
- work:
:type: complex
:intent: workspace
:dims:
- MAX(1,lwork)
- lwork:
:type: integer
:intent: input
:option: true
:default: "n<=1 ? 1 : lsame_(&jobz,\"N\") ? n : lsame_(&jobz,\"V\") ? 2*n : 0"
- rwork:
:type: real
:intent: workspace
:dims:
- MAX(1,lrwork)
- lrwork:
:type: integer
:intent: input
:option: true
:default: "n<=1 ? 1 : lsame_(&jobz,\"N\") ? 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<=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 CHPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* CHPGVD computes all the eigenvalues and, optionally, the eigenvectors\n\
* of a complex generalized Hermitian-definite eigenproblem, of the form\n\
* A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and\n\
* B are assumed to be Hermitian, stored in packed format, and B is also\n\
* positive definite.\n\
* If eigenvectors are 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\
* 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) COMPLEX array, dimension (N*(N+1)/2)\n\
* On entry, the upper or lower triangle of the Hermitian 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) COMPLEX array, dimension (N*(N+1)/2)\n\
* On entry, the upper or lower triangle of the Hermitian 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**H*U or B = L*L**H, 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) COMPLEX 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**H*B*Z = I;\n\
* if ITYPE = 3, Z**H*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) COMPLEX 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 array WORK.\n\
* If N <= 1, LWORK >= 1.\n\
* If JOBZ = 'N' and N > 1, LWORK >= N.\n\
* If JOBZ = 'V' and N > 1, LWORK >= 2*N.\n\
*\n\
* If LWORK = -1, then a workspace query is assumed; the routine\n\
* only calculates the required sizes of the WORK, RWORK and\n\
* IWORK arrays, returns these values as the first entries of\n\
* the WORK, RWORK and IWORK arrays, and no error message\n\
* related to LWORK or LRWORK or LIWORK is issued by XERBLA.\n\
*\n\
* RWORK (workspace) REAL array, dimension (MAX(1,LRWORK))\n\
* On exit, if INFO = 0, RWORK(1) returns the required LRWORK.\n\
*\n\
* LRWORK (input) INTEGER\n\
* The dimension of array RWORK.\n\
* If N <= 1, LRWORK >= 1.\n\
* If JOBZ = 'N' and N > 1, LRWORK >= N.\n\
* If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2.\n\
*\n\
* If LRWORK = -1, then a workspace query is assumed; the\n\
* routine only calculates the required sizes of the WORK, RWORK\n\
* and IWORK arrays, returns these values as the first entries\n\
* of the WORK, RWORK and IWORK arrays, and no error message\n\
* related to LWORK or LRWORK or 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 array IWORK.\n\
* If JOBZ = 'N' or N <= 1, LIWORK >= 1.\n\
* If JOBZ = 'V' and N > 1, LIWORK >= 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, RWORK\n\
* and IWORK arrays, returns these values as the first entries\n\
* of the WORK, RWORK and IWORK arrays, and no error message\n\
* related to LWORK or LRWORK 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: CPPTRF or CHPEVD returned an error code:\n\
* <= N: if INFO = i, CHPEVD failed to converge;\n\
* i off-diagonal elements of an intermediate\n\
* tridiagonal form did not convergeto 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\
* Further Details\n\
* ===============\n\
*\n\
* Based on contributions by\n\
* Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA\n\
*\n\
* =====================================================================\n\
*\n\
* .. Local Scalars ..\n LOGICAL LQUERY, UPPER, WANTZ\n CHARACTER TRANS\n INTEGER J, LIWMIN, LRWMIN, LWMIN, NEIG\n\
* ..\n\
* .. External Functions ..\n LOGICAL LSAME\n EXTERNAL LSAME\n\
* ..\n\
* .. External Subroutines ..\n EXTERNAL CHPEVD, CHPGST, CPPTRF, CTPMV, CTPSV, XERBLA\n\
* ..\n\
* .. Intrinsic Functions ..\n INTRINSIC MAX, REAL\n\
* ..\n"
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