cspsv - 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 CSPSV(UPLO, N, NRHS, AP, IPIVOT, B, LDB, INFO) CHARACTER*1 UPLO COMPLEX AP(*), B(LDB,*) INTEGER N, NRHS, LDB, INFO INTEGER IPIVOT(*) SUBROUTINE CSPSV_64(UPLO, N, NRHS, AP, IPIVOT, B, LDB, INFO) CHARACTER*1 UPLO 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, DIMENSION(:) :: AP COMPLEX, 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, DIMENSION(:) :: AP COMPLEX, DIMENSION(:,:) :: B INTEGER(8) :: N, NRHS, LDB, INFO INTEGER(8), DIMENSION(:) :: IPIVOT C INTERFACE #include <sunperf.h> void cspsv(char uplo, int n, int nrhs, complex *ap, int *ipivot, com- plex *b, int ldb, int *info); void cspsv_64(char uplo, long n, long nrhs, complex *ap, long *ipivot, complex *b, long ldb, long *info);
Oracle Solaris Studio Performance Library cspsv(3P)
NAME
cspsv - 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 CSPSV(UPLO, N, NRHS, AP, IPIVOT, B, LDB, INFO)
CHARACTER*1 UPLO
COMPLEX AP(*), B(LDB,*)
INTEGER N, NRHS, LDB, INFO
INTEGER IPIVOT(*)
SUBROUTINE CSPSV_64(UPLO, N, NRHS, AP, IPIVOT, B, LDB, INFO)
CHARACTER*1 UPLO
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, DIMENSION(:) :: AP
COMPLEX, 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, DIMENSION(:) :: AP
COMPLEX, DIMENSION(:,:) :: B
INTEGER(8) :: N, NRHS, LDB, INFO
INTEGER(8), DIMENSION(:) :: IPIVOT
C INTERFACE
#include <sunperf.h>
void cspsv(char uplo, int n, int nrhs, complex *ap, int *ipivot, com-
plex *b, int ldb, int *info);
void cspsv_64(char uplo, long n, long nrhs, complex *ap, long *ipivot,
complex *b, long ldb, long *info);
PURPOSE
cspsv 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)
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 CSPTRF, 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 CSPTRF. 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)
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 cspsv(3P)