zgbtrf - n band matrix A using partial pivoting with row interchanges
SUBROUTINE ZGBTRF(M, N, KL, KU, A, LDA, IPIVOT, INFO) DOUBLE COMPLEX A(LDA,N) INTEGER M, N, KL, KU, LDA, INFO INTEGER IPIVOT(MIN(M,N)) SUBROUTINE ZGBTRF_64(M, N, KL, KU, A, LDA, IPIVOT, INFO) DOUBLE COMPLEX A(LDA,N) INTEGER*8 M, N, KL, KU, LDA, INFO INTEGER*8 IPIVOT(MIN(M,N)) F95 INTERFACE SUBROUTINE GBTRF(M, N, KL, KU, A, LDA, IPIVOT, INFO) COMPLEX(8), DIMENSION(:,:) :: A INTEGER :: M, N, KL, KU, LDA, INFO INTEGER, DIMENSION(:) :: IPIVOT SUBROUTINE GBTRF_64(M, N, KL, KU, A, LDA, IPIVOT, INFO) COMPLEX(8), DIMENSION(:,:) :: A INTEGER(8) :: M, N, KL, KU, LDA, INFO INTEGER(8), DIMENSION(:) :: IPIVOT C INTERFACE #include <sunperf.h> void zgbtrf(int m, int n, int kl, int ku, doublecomplex *a, int lda, int *ipivot, int *info); void zgbtrf_64(long m, long n, long kl, long ku, doublecomplex *a, long lda, long *ipivot, long *info);
Oracle Solaris Studio Performance Library zgbtrf(3P) NAME zgbtrf - compute an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges SYNOPSIS SUBROUTINE ZGBTRF(M, N, KL, KU, A, LDA, IPIVOT, INFO) DOUBLE COMPLEX A(LDA,N) INTEGER M, N, KL, KU, LDA, INFO INTEGER IPIVOT(MIN(M,N)) SUBROUTINE ZGBTRF_64(M, N, KL, KU, A, LDA, IPIVOT, INFO) DOUBLE COMPLEX A(LDA,N) INTEGER*8 M, N, KL, KU, LDA, INFO INTEGER*8 IPIVOT(MIN(M,N)) F95 INTERFACE SUBROUTINE GBTRF(M, N, KL, KU, A, LDA, IPIVOT, INFO) COMPLEX(8), DIMENSION(:,:) :: A INTEGER :: M, N, KL, KU, LDA, INFO INTEGER, DIMENSION(:) :: IPIVOT SUBROUTINE GBTRF_64(M, N, KL, KU, A, LDA, IPIVOT, INFO) COMPLEX(8), DIMENSION(:,:) :: A INTEGER(8) :: M, N, KL, KU, LDA, INFO INTEGER(8), DIMENSION(:) :: IPIVOT C INTERFACE #include <sunperf.h> void zgbtrf(int m, int n, int kl, int ku, doublecomplex *a, int lda, int *ipivot, int *info); void zgbtrf_64(long m, long n, long kl, long ku, doublecomplex *a, long lda, long *ipivot, long *info); PURPOSE zgbtrf computes an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges. This is the blocked version of the algorithm, calling Level 3 BLAS. ARGUMENTS M (input) Integer The number of rows of the matrix A. M >= 0. N (input) Integer The number of columns of the matrix A. N >= 0. KL (input) Integer The number of subdiagonals within the band of A. KL >= 0. KU (input) Integer The number of superdiagonals within the band of A. KU >= 0. A (input/output) Double complex array of dimension (LDA,N). On entry, the matrix A in band storage, in rows KL+1 to 2*KL+KU+1; rows 1 to KL of the array need not be set. The j- th column of A is stored in the j-th column of the array A as follows: A(KL+KU+1+I-J,J) = A(I,J) for MAX(1,J-KU)<=I<=MIN(M,J+KL) On exit, details of the factorization: U is stored as an upper triangular band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and the multipliers used during the fac- torization are stored in rows KL+KU+2 to 2*KL+KU+1. See below for further details. LDA (input) Integer The leading dimension of the array A. LDA >= 2*KL+KU+1. IPIVOT (output) Integer array of dimension MIN(M,N) The pivot indices; for 1 <= I <= min(M,N), row I of the matrix was interchanged with row IPIVOT(I). INFO (output) Integer = 0: successful exit; < 0: if INFO = -I, the I-th argument had an illegal value; > 0: if INFO = +I, U(I,I) is exactly zero. The factorization has been completed, but the factor U is exactly singular, and division by zero will occur if it is used to solve a system of equations. FURTHER DETAILS The band storage scheme is illustrated by the following example, when M = N = 6, KL = 2, KU = 1: On entry: On exit: * * * + + + * * * u14 u25 u36 * * + + + + * * u13 u24 u35 u46 * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56 a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66 a21 a32 a43 a54 a65 * m21 m32 m43 m54 m65 * a31 a42 a53 a64 * * m31 m42 m53 m64 * * Array elements marked * are not used by the routine; elements marked + need not be set on entry, but are required by the routine to store ele- ments of U because of fill-in resulting from the row interchanges. 7 Nov 2015 zgbtrf(3P)