zspsv - compute the solution to a complex system of linear equations A*X = B, where A is an N-by-N symmetric matrix stored in packed format and X and B are N-by-NRHS matrices
SUBROUTINE ZSPSV(UPLO, N, NRHS, AP, IPIVOT, B, LDB, INFO) CHARACTER*1 UPLO DOUBLE COMPLEX AP(*), B(LDB,*) INTEGER N, NRHS, LDB, INFO INTEGER IPIVOT(*) SUBROUTINE ZSPSV_64(UPLO, N, NRHS, AP, IPIVOT, B, LDB, INFO) CHARACTER*1 UPLO DOUBLE COMPLEX AP(*), B(LDB,*) INTEGER*8 N, NRHS, LDB, INFO INTEGER*8 IPIVOT(*) F95 INTERFACE SUBROUTINE SPSV(UPLO, N, NRHS, AP, IPIVOT, B, LDB, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX(8), DIMENSION(:) :: AP COMPLEX(8), DIMENSION(:,:) :: B INTEGER :: N, NRHS, LDB, INFO INTEGER, DIMENSION(:) :: IPIVOT SUBROUTINE SPSV_64(UPLO, N, NRHS, AP, IPIVOT, B, LDB, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX(8), DIMENSION(:) :: AP COMPLEX(8), DIMENSION(:,:) :: B INTEGER(8) :: N, NRHS, LDB, INFO INTEGER(8), DIMENSION(:) :: IPIVOT C INTERFACE #include <sunperf.h> void zspsv(char uplo, int n, int nrhs, doublecomplex *ap, int *ipivot, doublecomplex *b, int ldb, int *info); void zspsv_64(char uplo, long n, long nrhs, doublecomplex *ap, long *ipivot, doublecomplex *b, long ldb, long *info);
Oracle Solaris Studio Performance Library zspsv(3P) NAME zspsv - compute the solution to a complex system of linear equations A*X = B, where A is an N-by-N symmetric matrix stored in packed format and X and B are N-by-NRHS matrices SYNOPSIS SUBROUTINE ZSPSV(UPLO, N, NRHS, AP, IPIVOT, B, LDB, INFO) CHARACTER*1 UPLO DOUBLE COMPLEX AP(*), B(LDB,*) INTEGER N, NRHS, LDB, INFO INTEGER IPIVOT(*) SUBROUTINE ZSPSV_64(UPLO, N, NRHS, AP, IPIVOT, B, LDB, INFO) CHARACTER*1 UPLO DOUBLE COMPLEX AP(*), B(LDB,*) INTEGER*8 N, NRHS, LDB, INFO INTEGER*8 IPIVOT(*) F95 INTERFACE SUBROUTINE SPSV(UPLO, N, NRHS, AP, IPIVOT, B, LDB, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX(8), DIMENSION(:) :: AP COMPLEX(8), DIMENSION(:,:) :: B INTEGER :: N, NRHS, LDB, INFO INTEGER, DIMENSION(:) :: IPIVOT SUBROUTINE SPSV_64(UPLO, N, NRHS, AP, IPIVOT, B, LDB, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX(8), DIMENSION(:) :: AP COMPLEX(8), DIMENSION(:,:) :: B INTEGER(8) :: N, NRHS, LDB, INFO INTEGER(8), DIMENSION(:) :: IPIVOT C INTERFACE #include <sunperf.h> void zspsv(char uplo, int n, int nrhs, doublecomplex *ap, int *ipivot, doublecomplex *b, int ldb, int *info); void zspsv_64(char uplo, long n, long nrhs, doublecomplex *ap, long *ipivot, doublecomplex *b, long ldb, long *info); PURPOSE zspsv computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N symmetric matrix stored in packed format and X and B are N-by-NRHS matrices. The diagonal pivoting method is used to factor A as A = U * D * U**T, if UPLO = 'U', or A = L * D * L**T, if UPLO = 'L', where U (or L) is a product of permutation and unit upper (lower) tri- angular matrices, D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. The factored form of A is then used to solve the system of equations A * X = B. ARGUMENTS UPLO (input) = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. N (input) The number of linear equations, i.e., the order of the matrix A. N >= 0. NRHS (input) The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. AP (input/output) Double complex array, dimension (N*(N+1)/2) On entry, the upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. See below for further details. On exit, the block diagonal matrix D and the multipliers used to obtain the factor U or L from the factorization A = U*D*U**T or A = L*D*L**T as computed by ZSPTRF, stored as a packed triangular matrix in the same storage format as A. IPIVOT (output) Integer array, dimension (N) Details of the interchanges and the block structure of D, as determined by ZSPTRF. 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. B (input/output) Double complex array, dimension (LDB,NRHS) On entry, the N- by-NRHS right hand side matrix B. On exit, if INFO = 0, the N-by-NRHS solution matrix X. LDB (input) The leading dimension of the array B. LDB >= max(1,N). 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, so the solution could not be computed. FURTHER DETAILS The packed storage scheme is illustrated by the following example when N = 4, UPLO = 'U': Two-dimensional storage of the symmetric matrix A: a11 a12 a13 a14 a22 a23 a24 a33 a34 (aij = aji) a44 Packed storage of the upper triangle of A: AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ] 7 Nov 2015 zspsv(3P)