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---
:name: chetrf
:md5sum: f5e1a64640b9b7eecf825c98401cf6ac
:category: :subroutine
:arguments:
- uplo:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- a:
:type: complex
:intent: input/output
:dims:
- lda
- n
- lda:
:type: integer
:intent: input
- ipiv:
:type: integer
:intent: output
:dims:
- n
- work:
:type: complex
:intent: output
:dims:
- MAX(1,lwork)
- lwork:
:type: integer
:intent: input
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE CHETRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* CHETRF computes the factorization of a complex Hermitian matrix A\n\
* using the Bunch-Kaufman diagonal pivoting method. The form of the\n\
* factorization is\n\
*\n\
* A = U*D*U**H or A = L*D*L**H\n\
*\n\
* where U (or L) is a product of permutation and unit upper (lower)\n\
* triangular matrices, and D is Hermitian and block diagonal with \n\
* 1-by-1 and 2-by-2 diagonal blocks.\n\
*\n\
* This is the blocked version of the algorithm, calling Level 3 BLAS.\n\
*\n\n\
* Arguments\n\
* =========\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 leading\n\
* N-by-N upper triangular part of A contains the upper\n\
* triangular part of the matrix A, and the strictly lower\n\
* triangular part of A is not referenced. If UPLO = 'L', the\n\
* leading N-by-N lower triangular part of A contains the lower\n\
* triangular part of the matrix A, and the strictly upper\n\
* triangular part of A is not referenced.\n\
*\n\
* On exit, the block diagonal matrix D and the multipliers used\n\
* to obtain the factor U or L (see below for further details).\n\
*\n\
* LDA (input) INTEGER\n\
* The leading dimension of the array A. LDA >= max(1,N).\n\
*\n\
* IPIV (output) INTEGER array, dimension (N)\n\
* Details of the interchanges and the block structure of D.\n\
* If IPIV(k) > 0, then rows and columns k and IPIV(k) were\n\
* interchanged and D(k,k) is a 1-by-1 diagonal block.\n\
* If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and\n\
* columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)\n\
* is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) =\n\
* IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were\n\
* interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.\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 WORK. LWORK >=1. For best performance\n\
* LWORK >= N*NB, where NB is the block size returned by ILAENV.\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, D(i,i) is exactly zero. The factorization\n\
* has been completed, but the block diagonal matrix D is\n\
* exactly singular, and division by zero will occur if it\n\
* is used to solve a system of equations.\n\
*\n\n\
* Further Details\n\
* ===============\n\
*\n\
* If UPLO = 'U', then A = U*D*U', where\n\
* U = P(n)*U(n)* ... *P(k)U(k)* ...,\n\
* i.e., U is a product of terms P(k)*U(k), where k decreases from n to\n\
* 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1\n\
* and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as\n\
* defined by IPIV(k), and U(k) is a unit upper triangular matrix, such\n\
* that if the diagonal block D(k) is of order s (s = 1 or 2), then\n\
*\n\
* ( I v 0 ) k-s\n\
* U(k) = ( 0 I 0 ) s\n\
* ( 0 0 I ) n-k\n\
* k-s s n-k\n\
*\n\
* If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).\n\
* If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),\n\
* and A(k,k), and v overwrites A(1:k-2,k-1:k).\n\
*\n\
* If UPLO = 'L', then A = L*D*L', where\n\
* L = P(1)*L(1)* ... *P(k)*L(k)* ...,\n\
* i.e., L is a product of terms P(k)*L(k), where k increases from 1 to\n\
* n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1\n\
* and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as\n\
* defined by IPIV(k), and L(k) is a unit lower triangular matrix, such\n\
* that if the diagonal block D(k) is of order s (s = 1 or 2), then\n\
*\n\
* ( I 0 0 ) k-1\n\
* L(k) = ( 0 I 0 ) s\n\
* ( 0 v I ) n-k-s+1\n\
* k-1 s n-k-s+1\n\
*\n\
* If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).\n\
* If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),\n\
* and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).\n\
*\n\
* =====================================================================\n\
*\n\
* .. Local Scalars ..\n LOGICAL LQUERY, UPPER\n INTEGER IINFO, IWS, J, K, KB, LDWORK, LWKOPT, NB, NBMIN\n\
* ..\n\
* .. External Functions ..\n LOGICAL LSAME\n INTEGER ILAENV\n EXTERNAL LSAME, ILAENV\n\
* ..\n\
* .. External Subroutines ..\n EXTERNAL CHETF2, CLAHEF, XERBLA\n\
* ..\n\
* .. Intrinsic Functions ..\n INTRINSIC MAX\n\
* ..\n"
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