cpftrf - itive definite matrix A, the block version of the algorithm
SUBROUTINE CPFTRF(TRANSR, UPLO, N, A, INFO) CHARACTER*1 TRANSR, UPLO INTEGER N, INFO COMPLEX A(0:*) SUBROUTINE CPFTRF_64(TRANSR, UPLO, N, A, INFO) CHARACTER*1 TRANSR, UPLO INTEGER*8 N, INFO COMPLEX A(0:*) F95 INTERFACE SUBROUTINE PFTRF(TRANSR, UPLO, N, A, INFO) INTEGER :: N, INFO CHARACTER(LEN=1) :: TRANSR, UPLO COMPLEX, DIMENSION(:) :: A SUBROUTINE PFTRF_64(TRANSR, UPLO, N, A, INFO) INTEGER(8) :: N, INFO CHARACTER(LEN=1) :: TRANSR, UPLO COMPLEX, DIMENSION(:) :: A C INTERFACE #include <sunperf.h> void cpftrf (char transr, char uplo, int n, floatcomplex *a, int *info); void cpftrf_64 (char transr, char uplo, long n, floatcomplex *a, long *info);
Oracle Solaris Studio Performance Library cpftrf(3P) NAME cpftrf - compute the Cholesky factorization of a complex Hermitian pos- itive definite matrix A, the block version of the algorithm SYNOPSIS SUBROUTINE CPFTRF(TRANSR, UPLO, N, A, INFO) CHARACTER*1 TRANSR, UPLO INTEGER N, INFO COMPLEX A(0:*) SUBROUTINE CPFTRF_64(TRANSR, UPLO, N, A, INFO) CHARACTER*1 TRANSR, UPLO INTEGER*8 N, INFO COMPLEX A(0:*) F95 INTERFACE SUBROUTINE PFTRF(TRANSR, UPLO, N, A, INFO) INTEGER :: N, INFO CHARACTER(LEN=1) :: TRANSR, UPLO COMPLEX, DIMENSION(:) :: A SUBROUTINE PFTRF_64(TRANSR, UPLO, N, A, INFO) INTEGER(8) :: N, INFO CHARACTER(LEN=1) :: TRANSR, UPLO COMPLEX, DIMENSION(:) :: A C INTERFACE #include <sunperf.h> void cpftrf (char transr, char uplo, int n, floatcomplex *a, int *info); void cpftrf_64 (char transr, char uplo, long n, floatcomplex *a, long *info); PURPOSE cpftrf computes the Cholesky factorization of a complex Hermitian posi- tive definite matrix A. The factorization has the form A=U**H * U, if UPLO = 'U', or A=L* L**H, if UPLO = 'L', where U is an upper triangular matrix and L is lower triangular. This is the block version of the algorithm, calling Level 3 BLAS. ARGUMENTS TRANSR (input) TRANSR is CHARACTER*1 = 'N': The Normal TRANSR of RFP A is stored; = 'C': The Conjugate-transpose TRANSR of RFP A is stored. UPLO (input) UPLO is CHARACTER*1 = 'U': Upper triangle of RFP A is stored; = 'L': Lower triangle of RFP A is stored. N (input) N is INTEGER The order of the matrix A. N >= 0. A (input/output) A is COMPLEX array, dimension ( N*(N+1)/2 ); On entry, the Hermitian matrix A in RFP format. RFP format is described by TRANSR, UPLO, and N as follows: If TRANSR = 'N' then RFP A is (0:N,0:k-1) when N is even; k=N/2. RFP A is (0:N-1,0:k) when N is odd; k=N/2. IF TRANSR = 'C' then RFP is the Conjugate-transpose of RFP A as defined when TRANSR = 'N'. The contents of RFP A are defined by UPLO as follows: If UPLO = 'U' the RFP A contains the nt elements of upper packed A. If UPLO = 'L' the RFP A contains the elements of lower packed A. The LDA of RFP A is (N+1)/2 when TRANSR = is odd. See the Note below for more details. On exit, if INFO = 0, the factor U or L from the Cholesky factorization RFP A=U**H*U or RFP A=L*L**H. INFO (output) INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value; > 0: if INFO = i, the leading minor of order i is not posi- tive definite, and the factorization could not be completed. FURTHER NOTES ON RFP FORMAT We first consider Standard Packed Format when N is even. We give an example where N = 6. AP is Upper AP is Lower 00 01 02 03 04 05 00 11 12 13 14 15 10 11 22 23 24 25 20 21 22 33 34 35 30 31 32 33 44 45 40 41 42 43 44 55 50 51 52 53 54 55 Let TRANSR = 'N'. RFP holds AP as follows: For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last three columns of AP upper. The lower triangle A(4:6,0:2) consists of conjugate-transpose of the first three columns of AP upper. For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first three columns of AP lower. The upper triangle A(0:2,0:2) consists of conjugate-transpose of the last three columns of AP lower. To denote conjugate we place -- above the element. This covers the case N even and TRANSR = 'N'. RFP A RFP A -- -- -- 03 04 05 33 43 53 -- -- 13 14 15 00 44 54 -- 23 24 25 10 11 55 33 34 35 20 21 22 -- 00 44 45 30 31 32 -- -- 01 11 55 40 41 42 -- -- -- 02 12 22 50 51 52 Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate- transpose of RFP A above. One therefore gets: RFP A RFP A -- -- -- -- -- -- -- -- -- -- 03 13 23 33 00 01 02 33 00 10 20 30 40 50 -- -- -- -- -- -- -- -- -- -- 04 14 24 34 44 11 12 43 44 11 21 31 41 51 -- -- -- -- -- -- -- -- -- -- 05 15 25 35 45 55 22 53 54 55 22 32 42 52 We next consider Standard Packed Format when N is odd. We give an example where N = 5. AP is Upper AP is Lower 00 01 02 03 04 00 11 12 13 14 10 11 22 23 24 20 21 22 33 34 30 31 32 33 44 40 41 42 43 44 Let TRANSR = 'N'. RFP holds AP as follows: For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last three columns of AP upper. The lower triangle A(3:4,0:1) consists of conjugate-transpose of the first two columns of AP upper. For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first three columns of AP lower. The upper triangle A(0:1,1:2) consists of conjugate-transpose of the last two columns of AP lower. To denote conjugate we place -- above the element. This covers the case N odd and TRANSR = 'N'. RFP A RFP A -- -- 02 03 04 00 33 43 -- 12 13 14 10 11 44 22 23 24 20 21 22 -- 00 33 34 30 31 32 -- -- 01 11 44 40 41 42 Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate- transpose of RFP A above. One therefore gets: RFP A RFP A -- -- -- -- -- -- -- -- -- 02 12 22 00 01 00 10 20 30 40 50 -- -- -- -- -- -- -- -- -- 03 13 23 33 11 33 11 21 31 41 51 -- -- -- -- -- -- -- -- -- 04 14 24 34 44 43 44 22 32 42 52 7 Nov 2015 cpftrf(3P)