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- CHETRF - compute the factorization of a complex Hermitian matrix A using
- the Bunch-Kaufman diagonal pivoting method
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- SUBROUTINE CHETRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
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- CHARACTER UPLO
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- INTEGER INFO, LDA, LWORK, N
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- INTEGER IPIV( * )
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- COMPLEX A( LDA, * ), WORK( * )
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- IIIIMMMMPPPPLLLLEEEEMMMMEEEENNNNTTTTAAAATTTTIIIIOOOONNNN
- These routines are part of the SCSL Scientific Library and can be loaded
- using either the -lscs or the -lscs_mp option. The -lscs_mp option
- directs the linker to use the multi-processor version of the library.
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- When linking to SCSL with -lscs or -lscs_mp, the default integer size is
- 4 bytes (32 bits). Another version of SCSL is available in which integers
- are 8 bytes (64 bits). This version allows the user access to larger
- memory sizes and helps when porting legacy Cray codes. It can be loaded
- by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
- only one of the two versions; 4-byte integer and 8-byte integer library
- calls cannot be mixed.
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- PPPPUUUURRRRPPPPOOOOSSSSEEEE
- CHETRF computes the factorization of a complex Hermitian matrix A using
- the Bunch-Kaufman diagonal pivoting method. The form of the factorization
- is
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- A = U*D*U**H or A = L*D*L**H
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- where U (or L) is a product of permutation and unit upper (lower)
- triangular matrices, and D is Hermitian and block diagonal with 1-by-1
- and 2-by-2 diagonal blocks.
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- This is the blocked version of the algorithm, calling Level 3 BLAS.
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- UPLO (input) CHARACTER*1
- = 'U': Upper triangle of A is stored;
- = 'L': Lower triangle of A is stored.
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- N (input) INTEGER
- The order of the matrix A. N >= 0.
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- A (input/output) COMPLEX array, dimension (LDA,N)
- On entry, the Hermitian matrix A. If UPLO = 'U', the leading N-
- by-N upper triangular part of A contains the upper triangular
- part of the matrix A, and the strictly lower triangular part of A
- is not referenced. If UPLO = 'L', the leading N-by-N lower
- triangular part of A contains the lower triangular part of the
- matrix A, and the strictly upper triangular part of A is not
- referenced.
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- On exit, the block diagonal matrix D and the multipliers used to
- obtain the factor U or L (see below for further details).
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- LDA (input) INTEGER
- The leading dimension of the array A. LDA >= max(1,N).
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- IPIV (output) INTEGER array, dimension (N)
- Details of the interchanges and the block structure of D. If
- IPIV(k) > 0, then rows and columns k and IPIV(k) were
- interchanged and D(k,k) is a 1-by-1 diagonal block. If UPLO =
- 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and columns k-1 and
- -IPIV(k) were interchanged and D(k-1:k,k-1:k) is a 2-by-2
- diagonal block. If UPLO = 'L' and IPIV(k) = IPIV(k+1) < 0, then
- rows and columns k+1 and -IPIV(k) were interchanged and
- D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
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- WORK (workspace/output) COMPLEX array, dimension (LWORK)
- On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
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- LWORK (input) INTEGER
- The length of WORK. LWORK >=1. For best performance LWORK >=
- N*NB, where NB is the block size returned by ILAENV.
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- INFO (output) INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
- > 0: if INFO = i, D(i,i) is exactly zero. The factorization has
- been completed, but the block diagonal matrix D is exactly
- singular, and division by zero will occur if it is used to solve
- a system of equations.
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- FFFFUUUURRRRTTTTHHHHEEEERRRR DDDDEEEETTTTAAAAIIIILLLLSSSS
- If UPLO = 'U', then A = U*D*U', where
- U = P(n)*U(n)* ... *P(k)U(k)* ...,
- i.e., U is a product of terms P(k)*U(k), where k decreases from n to 1 in
- steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 and 2-by-2
- diagonal blocks D(k). P(k) is a permutation matrix as defined by
- IPIV(k), and U(k) is a unit upper triangular matrix, such that if the
- diagonal block D(k) is of order s (s = 1 or 2), then
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- ( I v 0 ) k-s
- U(k) = ( 0 I 0 ) s
- ( 0 0 I ) n-k
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- k-s s n-k
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- If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k). If s = 2,
- the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k), and A(k,k),
- and v overwrites A(1:k-2,k-1:k).
-
- If UPLO = 'L', then A = L*D*L', where
- L = P(1)*L(1)* ... *P(k)*L(k)* ...,
- i.e., L is a product of terms P(k)*L(k), where k increases from 1 to n in
- steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 and 2-by-2
- diagonal blocks D(k). P(k) is a permutation matrix as defined by
- IPIV(k), and L(k) is a unit lower triangular matrix, such that if the
- diagonal block D(k) is of order s (s = 1 or 2), then
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- ( I 0 0 ) k-1
- L(k) = ( 0 I 0 ) s
- ( 0 v I ) n-k-s+1
- k-1 s n-k-s+1
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- If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k). If s = 2,
- the lower triangle of D(k) overwrites A(k,k), A(k+1,k), and A(k+1,k+1),
- and v overwrites A(k+2:n,k:k+1).
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- SSSSEEEEEEEE AAAALLLLSSSSOOOO
- INTRO_LAPACK(3S), INTRO_SCSL(3S)
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- This man page is available only online.
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