Contents
zspsv - compute the solution to a complex system of linear
equations A * X = B,
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);
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) triangular matrices, D is symmetric and block diago-
nal 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.
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 sym-
metric 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 mul-
tipliers used to obtain the factor U or L from the
factorization A = U*D*U**T or A = L*D*L**T as com-
puted by CSPTRF, stored as a packed triangular
matrix in the same storage format as A.
IPIVOT (output)
Integer array, dimension (N) Details of the inter-
changes 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 inter-
changed 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 ille-
gal 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.
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 ]