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---
:name: clahef
:md5sum: 495b64a6cbdc181f0b2a8122b9805ff0
:category: :subroutine
:arguments:
- uplo:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- nb:
:type: integer
:intent: input
- kb:
:type: integer
:intent: output
- a:
:type: complex
:intent: input/output
:dims:
- lda
- n
- lda:
:type: integer
:intent: input
- ipiv:
:type: integer
:intent: output
:dims:
- n
- w:
:type: complex
:intent: workspace
:dims:
- ldw
- MAX(n,nb)
- ldw:
:type: integer
:intent: input
- info:
:type: integer
:intent: output
:substitutions:
ldw: MAX(1,n)
:fortran_help: " SUBROUTINE CLAHEF( UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* CLAHEF computes a partial factorization of a complex Hermitian\n\
* matrix A using the Bunch-Kaufman diagonal pivoting method. The\n\
* partial factorization has the form:\n\
*\n\
* A = ( I U12 ) ( A11 0 ) ( I 0 ) if UPLO = 'U', or:\n\
* ( 0 U22 ) ( 0 D ) ( U12' U22' )\n\
*\n\
* A = ( L11 0 ) ( D 0 ) ( L11' L21' ) if UPLO = 'L'\n\
* ( L21 I ) ( 0 A22 ) ( 0 I )\n\
*\n\
* where the order of D is at most NB. The actual order is returned in\n\
* the argument KB, and is either NB or NB-1, or N if N <= NB.\n\
* Note that U' denotes the conjugate transpose of U.\n\
*\n\
* CLAHEF is an auxiliary routine called by CHETRF. It uses blocked code\n\
* (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or\n\
* A22 (if UPLO = 'L').\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* UPLO (input) CHARACTER*1\n\
* Specifies whether the upper or lower triangular part of the\n\
* Hermitian matrix A is stored:\n\
* = 'U': Upper triangular\n\
* = 'L': Lower triangular\n\
*\n\
* N (input) INTEGER\n\
* The order of the matrix A. N >= 0.\n\
*\n\
* NB (input) INTEGER\n\
* The maximum number of columns of the matrix A that should be\n\
* factored. NB should be at least 2 to allow for 2-by-2 pivot\n\
* blocks.\n\
*\n\
* KB (output) INTEGER\n\
* The number of columns of A that were actually factored.\n\
* KB is either NB-1 or NB, or N if N <= NB.\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\
* On exit, A contains details of the partial factorization.\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 UPLO = 'U', only the last KB elements of IPIV are set;\n\
* if UPLO = 'L', only the first KB elements are set.\n\
*\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\
* W (workspace) COMPLEX array, dimension (LDW,NB)\n\
*\n\
* LDW (input) INTEGER\n\
* The leading dimension of the array W. LDW >= max(1,N).\n\
*\n\
* INFO (output) INTEGER\n\
* = 0: successful exit\n\
* > 0: if INFO = k, D(k,k) is exactly zero. The factorization\n\
* has been completed, but the block diagonal matrix D is\n\
* exactly singular.\n\
*\n\n\
* =====================================================================\n\
*\n"
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