dsytd2 - reduce a real symmetric matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation
SUBROUTINE DSYTD2(UPLO, N, A, LDA, D, E, TAU, INFO) CHARACTER*1 UPLO INTEGER N, LDA, INFO DOUBLE PRECISION A(LDA,*), D(*), E(*), TAU(*) SUBROUTINE DSYTD2_64(UPLO, N, A, LDA, D, E, TAU, INFO) CHARACTER*1 UPLO INTEGER*8 N, LDA, INFO DOUBLE PRECISION A(LDA,*), D(*), E(*), TAU(*) F95 INTERFACE SUBROUTINE SYTD2(UPLO, N, A, LDA, D, E, TAU, INFO) CHARACTER(LEN=1) :: UPLO INTEGER :: N, LDA, INFO REAL(8), DIMENSION(:) :: D, E, TAU REAL(8), DIMENSION(:,:) :: A SUBROUTINE SYTD2_64(UPLO, N, A, LDA, D, E, TAU, INFO) CHARACTER(LEN=1) :: UPLO INTEGER(8) :: N, LDA, INFO REAL(8), DIMENSION(:) :: D, E, TAU REAL(8), DIMENSION(:,:) :: A C INTERFACE #include <sunperf.h> void dsytd2(char uplo, int n, double *a, int lda, double *d, double *e, double *tau, int *info); void dsytd2_64(char uplo, long n, double *a, long lda, double *d, dou- ble *e, double *tau, long *info);
Oracle Solaris Studio Performance Library dsytd2(3P) NAME dsytd2 - reduce a real symmetric matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation SYNOPSIS SUBROUTINE DSYTD2(UPLO, N, A, LDA, D, E, TAU, INFO) CHARACTER*1 UPLO INTEGER N, LDA, INFO DOUBLE PRECISION A(LDA,*), D(*), E(*), TAU(*) SUBROUTINE DSYTD2_64(UPLO, N, A, LDA, D, E, TAU, INFO) CHARACTER*1 UPLO INTEGER*8 N, LDA, INFO DOUBLE PRECISION A(LDA,*), D(*), E(*), TAU(*) F95 INTERFACE SUBROUTINE SYTD2(UPLO, N, A, LDA, D, E, TAU, INFO) CHARACTER(LEN=1) :: UPLO INTEGER :: N, LDA, INFO REAL(8), DIMENSION(:) :: D, E, TAU REAL(8), DIMENSION(:,:) :: A SUBROUTINE SYTD2_64(UPLO, N, A, LDA, D, E, TAU, INFO) CHARACTER(LEN=1) :: UPLO INTEGER(8) :: N, LDA, INFO REAL(8), DIMENSION(:) :: D, E, TAU REAL(8), DIMENSION(:,:) :: A C INTERFACE #include <sunperf.h> void dsytd2(char uplo, int n, double *a, int lda, double *d, double *e, double *tau, int *info); void dsytd2_64(char uplo, long n, double *a, long lda, double *d, dou- ble *e, double *tau, long *info); PURPOSE dsytd2 reduces a real symmetric matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation: Q' * A * Q = T. ARGUMENTS UPLO (input) Specifies whether the upper or lower triangular part of the symmetric matrix A is stored: = 'U': Upper triangular = 'L': Lower triangular N (input) The order of the matrix A. N >= 0. A (input) On entry, the symmetric matrix A. If UPLO = 'U', the leading n-by-n upper triangular part of A contains the upper triangu- lar part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n- by-n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if UPLO = 'U', the diagonal and first superdiagonal of A are overwritten by the corre- sponding elements of the tridiagonal matrix T, and the ele- ments above the first superdiagonal, with the array TAU, rep- resent the orthogonal matrix Q as a product of elementary reflectors; if UPLO = 'L', the diagonal and first subdiagonal of A are over- written by the corresponding elements of the tridiagonal matrix T, and the elements below the first subdi- agonal, with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors. See Further Details. LDA (input) The leading dimension of the array A. LDA >= max(1,N). D (output) The diagonal elements of the tridiagonal matrix T: D(i) = A(i,i). E (output) The off-diagonal elements of the tridiagonal matrix T: E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'. TAU (output) The scalar factors of the elementary reflectors (see Further Details). INFO (output) = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value. FURTHER DETAILS If UPLO = 'U', the matrix Q is represented as a product of elementary reflectors Q = H(n-1) . . . H(2) H(1). Each H(i) has the form H(i) = I - tau * v * v' where tau is a real scalar, and v is a real vector with v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in A(1:i-1,i+1), and tau in TAU(i). If UPLO = 'L', the matrix Q is represented as a product of elementary reflectors Q = H(1) H(2) . . . H(n-1). Each H(i) has the form H(i) = I - tau * v * v' where tau is a real scalar, and v is a real vector with v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i), and tau in TAU(i). The contents of A on exit are illustrated by the following examples with n = 5: if UPLO = 'U': if UPLO = 'L': ( d e v2 v3 v4 ) ( d ) ( d e v3 v4 ) ( e d ) ( d e v4 ) ( v1 e d ) ( d e ) ( v1 v2 e d ) ( d ) ( v1 v2 v3 e d ) where d and e denote diagonal and off-diagonal elements of T, and vi denotes an element of the vector defining H(i). 7 Nov 2015 dsytd2(3P)