zhetrf - compute the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method
SUBROUTINE ZHETRF(UPLO, N, A, LDA, IPIVOT, WORK, LDWORK, INFO) CHARACTER*1 UPLO DOUBLE COMPLEX A(LDA,*), WORK(*) INTEGER N, LDA, LDWORK, INFO INTEGER IPIVOT(*) SUBROUTINE ZHETRF_64(UPLO, N, A, LDA, IPIVOT, WORK, LDWORK, INFO) CHARACTER*1 UPLO DOUBLE COMPLEX A(LDA,*), WORK(*) INTEGER*8 N, LDA, LDWORK, INFO INTEGER*8 IPIVOT(*) F95 INTERFACE SUBROUTINE HETRF(UPLO, N, A, LDA, IPIVOT, WORK, LDWORK, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: A INTEGER :: N, LDA, LDWORK, INFO INTEGER, DIMENSION(:) :: IPIVOT SUBROUTINE HETRF_64(UPLO, N, A, LDA, IPIVOT, WORK, LDWORK, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: A INTEGER(8) :: N, LDA, LDWORK, INFO INTEGER(8), DIMENSION(:) :: IPIVOT C INTERFACE #include <sunperf.h> void zhetrf(char uplo, int n, doublecomplex *a, int lda, int *ipivot, int *info); void zhetrf_64(char uplo, long n, doublecomplex *a, long lda, long *ipivot, long *info);
Oracle Solaris Studio Performance Library zhetrf(3P) NAME zhetrf - compute the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method SYNOPSIS SUBROUTINE ZHETRF(UPLO, N, A, LDA, IPIVOT, WORK, LDWORK, INFO) CHARACTER*1 UPLO DOUBLE COMPLEX A(LDA,*), WORK(*) INTEGER N, LDA, LDWORK, INFO INTEGER IPIVOT(*) SUBROUTINE ZHETRF_64(UPLO, N, A, LDA, IPIVOT, WORK, LDWORK, INFO) CHARACTER*1 UPLO DOUBLE COMPLEX A(LDA,*), WORK(*) INTEGER*8 N, LDA, LDWORK, INFO INTEGER*8 IPIVOT(*) F95 INTERFACE SUBROUTINE HETRF(UPLO, N, A, LDA, IPIVOT, WORK, LDWORK, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: A INTEGER :: N, LDA, LDWORK, INFO INTEGER, DIMENSION(:) :: IPIVOT SUBROUTINE HETRF_64(UPLO, N, A, LDA, IPIVOT, WORK, LDWORK, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: A INTEGER(8) :: N, LDA, LDWORK, INFO INTEGER(8), DIMENSION(:) :: IPIVOT C INTERFACE #include <sunperf.h> void zhetrf(char uplo, int n, doublecomplex *a, int lda, int *ipivot, int *info); void zhetrf_64(char uplo, long n, doublecomplex *a, long lda, long *ipivot, long *info); PURPOSE zhetrf computes the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method. The form of the factoriza- tion is A = U*D*U**H or A = L*D*L**H where U (or L) is a product of permutation and unit upper (lower) tri- angular matrices, and D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. This is the blocked version of the algorithm, calling Level 3 BLAS. ARGUMENTS UPLO (input) = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. N (input) The order of the matrix A. N >= 0. A (input/output) On entry, the Hermitian matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangu- lar 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. On exit, the block diagonal matrix D and the multipliers used to obtain the factor U or L (see below for further details). LDA (input) The leading dimension of the array A. LDA >= max(1,N). IPIVOT (output) Details of the interchanges and the block structure of D. If IPIVOT(k) > 0, then rows and columns k and IPIVOT(k) were interchanged and D(k,k) is a 1-by-1 diagonal block. If UPLO = 'U' and IPIVOT(k) = IPIVOT(k-1) < 0, then rows and columns k-1 and -IPIVOT(k) were interchanged and D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L' and IPIVOT(k) = IPIVOT(k+1) < 0, then rows and columns k+1 and -IPIVOT(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. WORK (workspace) On exit, if INFO = 0, WORK(1) returns the optimal LDWORK. LDWORK (input) The length of WORK. LDWORK >=1. For best performance LDWORK >= N*NB, where NB is the block size returned by ILAENV. INFO (output) = 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. FURTHER DETAILS 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 IPIVOT(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 ( I v 0 ) k-s U(k) = ( 0 I 0 ) s ( 0 0 I ) n-k k-s s n-k 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 IPIVOT(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 ( 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 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). 7 Nov 2015 zhetrf(3P)