zhbtrd - reduce a complex Hermitian band matrix A to real symmetric tridiagonal form T by a unitary similarity transformation
SUBROUTINE ZHBTRD(VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, WORK, INFO) CHARACTER*1 VECT, UPLO DOUBLE COMPLEX AB(LDAB,*), Q(LDQ,*), WORK(*) INTEGER N, KD, LDAB, LDQ, INFO DOUBLE PRECISION D(*), E(*) SUBROUTINE ZHBTRD_64(VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, WORK, INFO) CHARACTER*1 VECT, UPLO DOUBLE COMPLEX AB(LDAB,*), Q(LDQ,*), WORK(*) INTEGER*8 N, KD, LDAB, LDQ, INFO DOUBLE PRECISION D(*), E(*) F95 INTERFACE SUBROUTINE HBTRD(VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, WORK, INFO) CHARACTER(LEN=1) :: VECT, UPLO COMPLEX(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: AB, Q INTEGER :: N, KD, LDAB, LDQ, INFO REAL(8), DIMENSION(:) :: D, E SUBROUTINE HBTRD_64(VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, WORK, INFO) CHARACTER(LEN=1) :: VECT, UPLO COMPLEX(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: AB, Q INTEGER(8) :: N, KD, LDAB, LDQ, INFO REAL(8), DIMENSION(:) :: D, E C INTERFACE #include <sunperf.h> void zhbtrd(char vect, char uplo, int n, int kd, doublecomplex *ab, int ldab, double *d, double *e, doublecomplex *q, int ldq, int *info); void zhbtrd_64(char vect, char uplo, long n, long kd, doublecomplex *ab, long ldab, double *d, double *e, doublecomplex *q, long ldq, long *info);
Oracle Solaris Studio Performance Library zhbtrd(3P) NAME zhbtrd - reduce a complex Hermitian band matrix A to real symmetric tridiagonal form T by a unitary similarity transformation SYNOPSIS SUBROUTINE ZHBTRD(VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, WORK, INFO) CHARACTER*1 VECT, UPLO DOUBLE COMPLEX AB(LDAB,*), Q(LDQ,*), WORK(*) INTEGER N, KD, LDAB, LDQ, INFO DOUBLE PRECISION D(*), E(*) SUBROUTINE ZHBTRD_64(VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, WORK, INFO) CHARACTER*1 VECT, UPLO DOUBLE COMPLEX AB(LDAB,*), Q(LDQ,*), WORK(*) INTEGER*8 N, KD, LDAB, LDQ, INFO DOUBLE PRECISION D(*), E(*) F95 INTERFACE SUBROUTINE HBTRD(VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, WORK, INFO) CHARACTER(LEN=1) :: VECT, UPLO COMPLEX(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: AB, Q INTEGER :: N, KD, LDAB, LDQ, INFO REAL(8), DIMENSION(:) :: D, E SUBROUTINE HBTRD_64(VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, WORK, INFO) CHARACTER(LEN=1) :: VECT, UPLO COMPLEX(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: AB, Q INTEGER(8) :: N, KD, LDAB, LDQ, INFO REAL(8), DIMENSION(:) :: D, E C INTERFACE #include <sunperf.h> void zhbtrd(char vect, char uplo, int n, int kd, doublecomplex *ab, int ldab, double *d, double *e, doublecomplex *q, int ldq, int *info); void zhbtrd_64(char vect, char uplo, long n, long kd, doublecomplex *ab, long ldab, double *d, double *e, doublecomplex *q, long ldq, long *info); PURPOSE zhbtrd reduces a complex Hermitian band matrix A to real symmetric tridiagonal form T by a unitary similarity transformation: Q**H * A * Q = T. ARGUMENTS VECT (input) = 'N': do not form Q; = 'V': form Q; = 'U': update a matrix X, by forming X*Q. UPLO (input) = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. N (input) The order of the matrix A. N >= 0. KD (input) The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0. AB (input/output) On entry, the upper or lower triangle of the Hermitian band matrix A, stored in the first KD+1 rows of the array. The j- th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). On exit, the diagonal elements of AB are overwritten by the diagonal elements of the tridiagonal matrix T; if KD > 0, the elements on the first superdiagonal (if UPLO = 'U') or the first subdiagonal (if UPLO = 'L') are overwritten by the off-diagonal elements of T; the rest of AB is overwritten by values generated during the reduction. LDAB (input) The leading dimension of the array AB. LDAB >= KD+1. D (output) The diagonal elements of the tridiagonal matrix T. E (output) The off-diagonal elements of the tridiagonal matrix T: E(i) = T(i,i+1) if UPLO = 'U'; E(i) = T(i+1,i) if UPLO = 'L'. Q (input/output) On entry, if VECT = 'U', then Q must contain an N-by-N matrix X; if VECT = 'N' or 'V', then Q need not be set. On exit: if VECT = 'V', Q contains the N-by-N unitary matrix Q; if VECT = 'U', Q contains the product X*Q; if VECT = 'N', the array Q is not referenced. LDQ (input) The leading dimension of the array Q. LDQ >= 1, and LDQ >= N if VECT = 'V' or 'U'. WORK (workspace) dimension(N) INFO (output) = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value FURTHER DETAILS Modified by Linda Kaufman, Bell Labs. 7 Nov 2015 zhbtrd(3P)