.TH "trevc" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME trevc \- trevc: eigenvectors of triangular Schur form, old .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBctrevc\fP (side, howmny, select, n, t, ldt, vl, ldvl, vr, ldvr, mm, m, work, rwork, info)" .br .RI "\fBCTREVC\fP " .ti -1c .RI "subroutine \fBdtrevc\fP (side, howmny, select, n, t, ldt, vl, ldvl, vr, ldvr, mm, m, work, info)" .br .RI "\fBDTREVC\fP " .ti -1c .RI "subroutine \fBstrevc\fP (side, howmny, select, n, t, ldt, vl, ldvl, vr, ldvr, mm, m, work, info)" .br .RI "\fBSTREVC\fP " .ti -1c .RI "subroutine \fBztrevc\fP (side, howmny, select, n, t, ldt, vl, ldvl, vr, ldvr, mm, m, work, rwork, info)" .br .RI "\fBZTREVC\fP " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "subroutine ctrevc (character side, character howmny, logical, dimension( * ) select, integer n, complex, dimension( ldt, * ) t, integer ldt, complex, dimension( ldvl, * ) vl, integer ldvl, complex, dimension( ldvr, * ) vr, integer ldvr, integer mm, integer m, complex, dimension( * ) work, real, dimension( * ) rwork, integer info)" .PP \fBCTREVC\fP .PP \fBPurpose:\fP .RS 4 .PP .nf CTREVC computes some or all of the right and/or left eigenvectors of a complex upper triangular matrix T\&. Matrices of this type are produced by the Schur factorization of a complex general matrix: A = Q*T*Q**H, as computed by CHSEQR\&. The right eigenvector x and the left eigenvector y of T corresponding to an eigenvalue w are defined by: T*x = w*x, (y**H)*T = w*(y**H) where y**H denotes the conjugate transpose of the vector y\&. The eigenvalues are not input to this routine, but are read directly from the diagonal of T\&. This routine returns the matrices X and/or Y of right and left eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an input matrix\&. If Q is the unitary factor that reduces a matrix A to Schur form T, then Q*X and Q*Y are the matrices of right and left eigenvectors of A\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fISIDE\fP .PP .nf SIDE is CHARACTER*1 = 'R': compute right eigenvectors only; = 'L': compute left eigenvectors only; = 'B': compute both right and left eigenvectors\&. .fi .PP .br \fIHOWMNY\fP .PP .nf HOWMNY is CHARACTER*1 = 'A': compute all right and/or left eigenvectors; = 'B': compute all right and/or left eigenvectors, backtransformed using the matrices supplied in VR and/or VL; = 'S': compute selected right and/or left eigenvectors, as indicated by the logical array SELECT\&. .fi .PP .br \fISELECT\fP .PP .nf SELECT is LOGICAL array, dimension (N) If HOWMNY = 'S', SELECT specifies the eigenvectors to be computed\&. The eigenvector corresponding to the j-th eigenvalue is computed if SELECT(j) = \&.TRUE\&.\&. Not referenced if HOWMNY = 'A' or 'B'\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrix T\&. N >= 0\&. .fi .PP .br \fIT\fP .PP .nf T is COMPLEX array, dimension (LDT,N) The upper triangular matrix T\&. T is modified, but restored on exit\&. .fi .PP .br \fILDT\fP .PP .nf LDT is INTEGER The leading dimension of the array T\&. LDT >= max(1,N)\&. .fi .PP .br \fIVL\fP .PP .nf VL is COMPLEX array, dimension (LDVL,MM) On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must contain an N-by-N matrix Q (usually the unitary matrix Q of Schur vectors returned by CHSEQR)\&. On exit, if SIDE = 'L' or 'B', VL contains: if HOWMNY = 'A', the matrix Y of left eigenvectors of T; if HOWMNY = 'B', the matrix Q*Y; if HOWMNY = 'S', the left eigenvectors of T specified by SELECT, stored consecutively in the columns of VL, in the same order as their eigenvalues\&. Not referenced if SIDE = 'R'\&. .fi .PP .br \fILDVL\fP .PP .nf LDVL is INTEGER The leading dimension of the array VL\&. LDVL >= 1, and if SIDE = 'L' or 'B', LDVL >= N\&. .fi .PP .br \fIVR\fP .PP .nf VR is COMPLEX array, dimension (LDVR,MM) On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must contain an N-by-N matrix Q (usually the unitary matrix Q of Schur vectors returned by CHSEQR)\&. On exit, if SIDE = 'R' or 'B', VR contains: if HOWMNY = 'A', the matrix X of right eigenvectors of T; if HOWMNY = 'B', the matrix Q*X; if HOWMNY = 'S', the right eigenvectors of T specified by SELECT, stored consecutively in the columns of VR, in the same order as their eigenvalues\&. Not referenced if SIDE = 'L'\&. .fi .PP .br \fILDVR\fP .PP .nf LDVR is INTEGER The leading dimension of the array VR\&. LDVR >= 1, and if SIDE = 'R' or 'B'; LDVR >= N\&. .fi .PP .br \fIMM\fP .PP .nf MM is INTEGER The number of columns in the arrays VL and/or VR\&. MM >= M\&. .fi .PP .br \fIM\fP .PP .nf M is INTEGER The number of columns in the arrays VL and/or VR actually used to store the eigenvectors\&. If HOWMNY = 'A' or 'B', M is set to N\&. Each selected eigenvector occupies one column\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is COMPLEX array, dimension (2*N) .fi .PP .br \fIRWORK\fP .PP .nf RWORK is REAL array, dimension (N) .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBFurther Details:\fP .RS 4 .PP .nf The algorithm used in this program is basically backward (forward) substitution, with scaling to make the the code robust against possible overflow\&. Each eigenvector is normalized so that the element of largest magnitude has magnitude 1; here the magnitude of a complex number (x,y) is taken to be |x| + |y|\&. .fi .PP .RE .PP .SS "subroutine dtrevc (character side, character howmny, logical, dimension( * ) select, integer n, double precision, dimension( ldt, * ) t, integer ldt, double precision, dimension( ldvl, * ) vl, integer ldvl, double precision, dimension( ldvr, * ) vr, integer ldvr, integer mm, integer m, double precision, dimension( * ) work, integer info)" .PP \fBDTREVC\fP .PP \fBPurpose:\fP .RS 4 .PP .nf DTREVC computes some or all of the right and/or left eigenvectors of a real upper quasi-triangular matrix T\&. Matrices of this type are produced by the Schur factorization of a real general matrix: A = Q*T*Q**T, as computed by DHSEQR\&. The right eigenvector x and the left eigenvector y of T corresponding to an eigenvalue w are defined by: T*x = w*x, (y**H)*T = w*(y**H) where y**H denotes the conjugate transpose of y\&. The eigenvalues are not input to this routine, but are read directly from the diagonal blocks of T\&. This routine returns the matrices X and/or Y of right and left eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an input matrix\&. If Q is the orthogonal factor that reduces a matrix A to Schur form T, then Q*X and Q*Y are the matrices of right and left eigenvectors of A\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fISIDE\fP .PP .nf SIDE is CHARACTER*1 = 'R': compute right eigenvectors only; = 'L': compute left eigenvectors only; = 'B': compute both right and left eigenvectors\&. .fi .PP .br \fIHOWMNY\fP .PP .nf HOWMNY is CHARACTER*1 = 'A': compute all right and/or left eigenvectors; = 'B': compute all right and/or left eigenvectors, backtransformed by the matrices in VR and/or VL; = 'S': compute selected right and/or left eigenvectors, as indicated by the logical array SELECT\&. .fi .PP .br \fISELECT\fP .PP .nf SELECT is LOGICAL array, dimension (N) If HOWMNY = 'S', SELECT specifies the eigenvectors to be computed\&. If w(j) is a real eigenvalue, the corresponding real eigenvector is computed if SELECT(j) is \&.TRUE\&.\&. If w(j) and w(j+1) are the real and imaginary parts of a complex eigenvalue, the corresponding complex eigenvector is computed if either SELECT(j) or SELECT(j+1) is \&.TRUE\&., and on exit SELECT(j) is set to \&.TRUE\&. and SELECT(j+1) is set to \&.FALSE\&.\&. Not referenced if HOWMNY = 'A' or 'B'\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrix T\&. N >= 0\&. .fi .PP .br \fIT\fP .PP .nf T is DOUBLE PRECISION array, dimension (LDT,N) The upper quasi-triangular matrix T in Schur canonical form\&. .fi .PP .br \fILDT\fP .PP .nf LDT is INTEGER The leading dimension of the array T\&. LDT >= max(1,N)\&. .fi .PP .br \fIVL\fP .PP .nf VL is DOUBLE PRECISION array, dimension (LDVL,MM) On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must contain an N-by-N matrix Q (usually the orthogonal matrix Q of Schur vectors returned by DHSEQR)\&. On exit, if SIDE = 'L' or 'B', VL contains: if HOWMNY = 'A', the matrix Y of left eigenvectors of T; if HOWMNY = 'B', the matrix Q*Y; if HOWMNY = 'S', the left eigenvectors of T specified by SELECT, stored consecutively in the columns of VL, in the same order as their eigenvalues\&. A complex eigenvector corresponding to a complex eigenvalue is stored in two consecutive columns, the first holding the real part, and the second the imaginary part\&. Not referenced if SIDE = 'R'\&. .fi .PP .br \fILDVL\fP .PP .nf LDVL is INTEGER The leading dimension of the array VL\&. LDVL >= 1, and if SIDE = 'L' or 'B', LDVL >= N\&. .fi .PP .br \fIVR\fP .PP .nf VR is DOUBLE PRECISION array, dimension (LDVR,MM) On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must contain an N-by-N matrix Q (usually the orthogonal matrix Q of Schur vectors returned by DHSEQR)\&. On exit, if SIDE = 'R' or 'B', VR contains: if HOWMNY = 'A', the matrix X of right eigenvectors of T; if HOWMNY = 'B', the matrix Q*X; if HOWMNY = 'S', the right eigenvectors of T specified by SELECT, stored consecutively in the columns of VR, in the same order as their eigenvalues\&. A complex eigenvector corresponding to a complex eigenvalue is stored in two consecutive columns, the first holding the real part and the second the imaginary part\&. Not referenced if SIDE = 'L'\&. .fi .PP .br \fILDVR\fP .PP .nf LDVR is INTEGER The leading dimension of the array VR\&. LDVR >= 1, and if SIDE = 'R' or 'B', LDVR >= N\&. .fi .PP .br \fIMM\fP .PP .nf MM is INTEGER The number of columns in the arrays VL and/or VR\&. MM >= M\&. .fi .PP .br \fIM\fP .PP .nf M is INTEGER The number of columns in the arrays VL and/or VR actually used to store the eigenvectors\&. If HOWMNY = 'A' or 'B', M is set to N\&. Each selected real eigenvector occupies one column and each selected complex eigenvector occupies two columns\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is DOUBLE PRECISION array, dimension (3*N) .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBFurther Details:\fP .RS 4 .PP .nf The algorithm used in this program is basically backward (forward) substitution, with scaling to make the the code robust against possible overflow\&. Each eigenvector is normalized so that the element of largest magnitude has magnitude 1; here the magnitude of a complex number (x,y) is taken to be |x| + |y|\&. .fi .PP .RE .PP .SS "subroutine strevc (character side, character howmny, logical, dimension( * ) select, integer n, real, dimension( ldt, * ) t, integer ldt, real, dimension( ldvl, * ) vl, integer ldvl, real, dimension( ldvr, * ) vr, integer ldvr, integer mm, integer m, real, dimension( * ) work, integer info)" .PP \fBSTREVC\fP .PP \fBPurpose:\fP .RS 4 .PP .nf STREVC computes some or all of the right and/or left eigenvectors of a real upper quasi-triangular matrix T\&. Matrices of this type are produced by the Schur factorization of a real general matrix: A = Q*T*Q**T, as computed by SHSEQR\&. The right eigenvector x and the left eigenvector y of T corresponding to an eigenvalue w are defined by: T*x = w*x, (y**H)*T = w*(y**H) where y**H denotes the conjugate transpose of y\&. The eigenvalues are not input to this routine, but are read directly from the diagonal blocks of T\&. This routine returns the matrices X and/or Y of right and left eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an input matrix\&. If Q is the orthogonal factor that reduces a matrix A to Schur form T, then Q*X and Q*Y are the matrices of right and left eigenvectors of A\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fISIDE\fP .PP .nf SIDE is CHARACTER*1 = 'R': compute right eigenvectors only; = 'L': compute left eigenvectors only; = 'B': compute both right and left eigenvectors\&. .fi .PP .br \fIHOWMNY\fP .PP .nf HOWMNY is CHARACTER*1 = 'A': compute all right and/or left eigenvectors; = 'B': compute all right and/or left eigenvectors, backtransformed by the matrices in VR and/or VL; = 'S': compute selected right and/or left eigenvectors, as indicated by the logical array SELECT\&. .fi .PP .br \fISELECT\fP .PP .nf SELECT is LOGICAL array, dimension (N) If HOWMNY = 'S', SELECT specifies the eigenvectors to be computed\&. If w(j) is a real eigenvalue, the corresponding real eigenvector is computed if SELECT(j) is \&.TRUE\&.\&. If w(j) and w(j+1) are the real and imaginary parts of a complex eigenvalue, the corresponding complex eigenvector is computed if either SELECT(j) or SELECT(j+1) is \&.TRUE\&., and on exit SELECT(j) is set to \&.TRUE\&. and SELECT(j+1) is set to \&.FALSE\&.\&. Not referenced if HOWMNY = 'A' or 'B'\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrix T\&. N >= 0\&. .fi .PP .br \fIT\fP .PP .nf T is REAL array, dimension (LDT,N) The upper quasi-triangular matrix T in Schur canonical form\&. .fi .PP .br \fILDT\fP .PP .nf LDT is INTEGER The leading dimension of the array T\&. LDT >= max(1,N)\&. .fi .PP .br \fIVL\fP .PP .nf VL is REAL array, dimension (LDVL,MM) On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must contain an N-by-N matrix Q (usually the orthogonal matrix Q of Schur vectors returned by SHSEQR)\&. On exit, if SIDE = 'L' or 'B', VL contains: if HOWMNY = 'A', the matrix Y of left eigenvectors of T; if HOWMNY = 'B', the matrix Q*Y; if HOWMNY = 'S', the left eigenvectors of T specified by SELECT, stored consecutively in the columns of VL, in the same order as their eigenvalues\&. A complex eigenvector corresponding to a complex eigenvalue is stored in two consecutive columns, the first holding the real part, and the second the imaginary part\&. Not referenced if SIDE = 'R'\&. .fi .PP .br \fILDVL\fP .PP .nf LDVL is INTEGER The leading dimension of the array VL\&. LDVL >= 1, and if SIDE = 'L' or 'B', LDVL >= N\&. .fi .PP .br \fIVR\fP .PP .nf VR is REAL array, dimension (LDVR,MM) On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must contain an N-by-N matrix Q (usually the orthogonal matrix Q of Schur vectors returned by SHSEQR)\&. On exit, if SIDE = 'R' or 'B', VR contains: if HOWMNY = 'A', the matrix X of right eigenvectors of T; if HOWMNY = 'B', the matrix Q*X; if HOWMNY = 'S', the right eigenvectors of T specified by SELECT, stored consecutively in the columns of VR, in the same order as their eigenvalues\&. A complex eigenvector corresponding to a complex eigenvalue is stored in two consecutive columns, the first holding the real part and the second the imaginary part\&. Not referenced if SIDE = 'L'\&. .fi .PP .br \fILDVR\fP .PP .nf LDVR is INTEGER The leading dimension of the array VR\&. LDVR >= 1, and if SIDE = 'R' or 'B', LDVR >= N\&. .fi .PP .br \fIMM\fP .PP .nf MM is INTEGER The number of columns in the arrays VL and/or VR\&. MM >= M\&. .fi .PP .br \fIM\fP .PP .nf M is INTEGER The number of columns in the arrays VL and/or VR actually used to store the eigenvectors\&. If HOWMNY = 'A' or 'B', M is set to N\&. Each selected real eigenvector occupies one column and each selected complex eigenvector occupies two columns\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is REAL array, dimension (3*N) .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBFurther Details:\fP .RS 4 .PP .nf The algorithm used in this program is basically backward (forward) substitution, with scaling to make the the code robust against possible overflow\&. Each eigenvector is normalized so that the element of largest magnitude has magnitude 1; here the magnitude of a complex number (x,y) is taken to be |x| + |y|\&. .fi .PP .RE .PP .SS "subroutine ztrevc (character side, character howmny, logical, dimension( * ) select, integer n, complex*16, dimension( ldt, * ) t, integer ldt, complex*16, dimension( ldvl, * ) vl, integer ldvl, complex*16, dimension( ldvr, * ) vr, integer ldvr, integer mm, integer m, complex*16, dimension( * ) work, double precision, dimension( * ) rwork, integer info)" .PP \fBZTREVC\fP .PP \fBPurpose:\fP .RS 4 .PP .nf ZTREVC computes some or all of the right and/or left eigenvectors of a complex upper triangular matrix T\&. Matrices of this type are produced by the Schur factorization of a complex general matrix: A = Q*T*Q**H, as computed by ZHSEQR\&. The right eigenvector x and the left eigenvector y of T corresponding to an eigenvalue w are defined by: T*x = w*x, (y**H)*T = w*(y**H) where y**H denotes the conjugate transpose of the vector y\&. The eigenvalues are not input to this routine, but are read directly from the diagonal of T\&. This routine returns the matrices X and/or Y of right and left eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an input matrix\&. If Q is the unitary factor that reduces a matrix A to Schur form T, then Q*X and Q*Y are the matrices of right and left eigenvectors of A\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fISIDE\fP .PP .nf SIDE is CHARACTER*1 = 'R': compute right eigenvectors only; = 'L': compute left eigenvectors only; = 'B': compute both right and left eigenvectors\&. .fi .PP .br \fIHOWMNY\fP .PP .nf HOWMNY is CHARACTER*1 = 'A': compute all right and/or left eigenvectors; = 'B': compute all right and/or left eigenvectors, backtransformed using the matrices supplied in VR and/or VL; = 'S': compute selected right and/or left eigenvectors, as indicated by the logical array SELECT\&. .fi .PP .br \fISELECT\fP .PP .nf SELECT is LOGICAL array, dimension (N) If HOWMNY = 'S', SELECT specifies the eigenvectors to be computed\&. The eigenvector corresponding to the j-th eigenvalue is computed if SELECT(j) = \&.TRUE\&.\&. Not referenced if HOWMNY = 'A' or 'B'\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrix T\&. N >= 0\&. .fi .PP .br \fIT\fP .PP .nf T is COMPLEX*16 array, dimension (LDT,N) The upper triangular matrix T\&. T is modified, but restored on exit\&. .fi .PP .br \fILDT\fP .PP .nf LDT is INTEGER The leading dimension of the array T\&. LDT >= max(1,N)\&. .fi .PP .br \fIVL\fP .PP .nf VL is COMPLEX*16 array, dimension (LDVL,MM) On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must contain an N-by-N matrix Q (usually the unitary matrix Q of Schur vectors returned by ZHSEQR)\&. On exit, if SIDE = 'L' or 'B', VL contains: if HOWMNY = 'A', the matrix Y of left eigenvectors of T; if HOWMNY = 'B', the matrix Q*Y; if HOWMNY = 'S', the left eigenvectors of T specified by SELECT, stored consecutively in the columns of VL, in the same order as their eigenvalues\&. Not referenced if SIDE = 'R'\&. .fi .PP .br \fILDVL\fP .PP .nf LDVL is INTEGER The leading dimension of the array VL\&. LDVL >= 1, and if SIDE = 'L' or 'B', LDVL >= N\&. .fi .PP .br \fIVR\fP .PP .nf VR is COMPLEX*16 array, dimension (LDVR,MM) On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must contain an N-by-N matrix Q (usually the unitary matrix Q of Schur vectors returned by ZHSEQR)\&. On exit, if SIDE = 'R' or 'B', VR contains: if HOWMNY = 'A', the matrix X of right eigenvectors of T; if HOWMNY = 'B', the matrix Q*X; if HOWMNY = 'S', the right eigenvectors of T specified by SELECT, stored consecutively in the columns of VR, in the same order as their eigenvalues\&. Not referenced if SIDE = 'L'\&. .fi .PP .br \fILDVR\fP .PP .nf LDVR is INTEGER The leading dimension of the array VR\&. LDVR >= 1, and if SIDE = 'R' or 'B'; LDVR >= N\&. .fi .PP .br \fIMM\fP .PP .nf MM is INTEGER The number of columns in the arrays VL and/or VR\&. MM >= M\&. .fi .PP .br \fIM\fP .PP .nf M is INTEGER The number of columns in the arrays VL and/or VR actually used to store the eigenvectors\&. If HOWMNY = 'A' or 'B', M is set to N\&. Each selected eigenvector occupies one column\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is COMPLEX*16 array, dimension (2*N) .fi .PP .br \fIRWORK\fP .PP .nf RWORK is DOUBLE PRECISION array, dimension (N) .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBFurther Details:\fP .RS 4 .PP .nf The algorithm used in this program is basically backward (forward) substitution, with scaling to make the the code robust against possible overflow\&. Each eigenvector is normalized so that the element of largest magnitude has magnitude 1; here the magnitude of a complex number (x,y) is taken to be |x| + |y|\&. .fi .PP .RE .PP .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.