.TH "unbdb6" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME unbdb6 \- {un,or}bdb6: step in uncsd2by1 .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBcunbdb6\fP (m1, m2, n, x1, incx1, x2, incx2, q1, ldq1, q2, ldq2, work, lwork, info)" .br .RI "\fBCUNBDB6\fP " .ti -1c .RI "subroutine \fBdorbdb6\fP (m1, m2, n, x1, incx1, x2, incx2, q1, ldq1, q2, ldq2, work, lwork, info)" .br .RI "\fBDORBDB6\fP " .ti -1c .RI "subroutine \fBsorbdb6\fP (m1, m2, n, x1, incx1, x2, incx2, q1, ldq1, q2, ldq2, work, lwork, info)" .br .RI "\fBSORBDB6\fP " .ti -1c .RI "subroutine \fBzunbdb6\fP (m1, m2, n, x1, incx1, x2, incx2, q1, ldq1, q2, ldq2, work, lwork, info)" .br .RI "\fBZUNBDB6\fP " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "subroutine cunbdb6 (integer m1, integer m2, integer n, complex, dimension(*) x1, integer incx1, complex, dimension(*) x2, integer incx2, complex, dimension(ldq1,*) q1, integer ldq1, complex, dimension(ldq2,*) q2, integer ldq2, complex, dimension(*) work, integer lwork, integer info)" .PP \fBCUNBDB6\fP .PP \fBPurpose:\fP .RS 4 .PP .nf CUNBDB6 orthogonalizes the column vector X = [ X1 ] [ X2 ] with respect to the columns of Q = [ Q1 ] \&. [ Q2 ] The columns of Q must be orthonormal\&. The orthogonalized vector will be zero if and only if it lies entirely in the range of Q\&. The projection is computed with at most two iterations of the classical Gram-Schmidt algorithm, see * L\&. Giraud, J\&. Langou, M\&. Rozložník\&. 'On the round-off error analysis of the Gram-Schmidt algorithm with reorthogonalization\&.' 2002\&. CERFACS Technical Report No\&. TR/PA/02/33\&. URL: https://www\&.cerfacs\&.fr/algor/reports/2002/TR_PA_02_33\&.pdf .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIM1\fP .PP .nf M1 is INTEGER The dimension of X1 and the number of rows in Q1\&. 0 <= M1\&. .fi .PP .br \fIM2\fP .PP .nf M2 is INTEGER The dimension of X2 and the number of rows in Q2\&. 0 <= M2\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The number of columns in Q1 and Q2\&. 0 <= N\&. .fi .PP .br \fIX1\fP .PP .nf X1 is COMPLEX array, dimension (M1) On entry, the top part of the vector to be orthogonalized\&. On exit, the top part of the projected vector\&. .fi .PP .br \fIINCX1\fP .PP .nf INCX1 is INTEGER Increment for entries of X1\&. .fi .PP .br \fIX2\fP .PP .nf X2 is COMPLEX array, dimension (M2) On entry, the bottom part of the vector to be orthogonalized\&. On exit, the bottom part of the projected vector\&. .fi .PP .br \fIINCX2\fP .PP .nf INCX2 is INTEGER Increment for entries of X2\&. .fi .PP .br \fIQ1\fP .PP .nf Q1 is COMPLEX array, dimension (LDQ1, N) The top part of the orthonormal basis matrix\&. .fi .PP .br \fILDQ1\fP .PP .nf LDQ1 is INTEGER The leading dimension of Q1\&. LDQ1 >= M1\&. .fi .PP .br \fIQ2\fP .PP .nf Q2 is COMPLEX array, dimension (LDQ2, N) The bottom part of the orthonormal basis matrix\&. .fi .PP .br \fILDQ2\fP .PP .nf LDQ2 is INTEGER The leading dimension of Q2\&. LDQ2 >= M2\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is COMPLEX array, dimension (LWORK) .fi .PP .br \fILWORK\fP .PP .nf LWORK is INTEGER The dimension of the array WORK\&. LWORK >= 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 .SS "subroutine dorbdb6 (integer m1, integer m2, integer n, double precision, dimension(*) x1, integer incx1, double precision, dimension(*) x2, integer incx2, double precision, dimension(ldq1,*) q1, integer ldq1, double precision, dimension(ldq2,*) q2, integer ldq2, double precision, dimension(*) work, integer lwork, integer info)" .PP \fBDORBDB6\fP .PP \fBPurpose:\fP .RS 4 .PP .nf DORBDB6 orthogonalizes the column vector X = [ X1 ] [ X2 ] with respect to the columns of Q = [ Q1 ] \&. [ Q2 ] The columns of Q must be orthonormal\&. The orthogonalized vector will be zero if and only if it lies entirely in the range of Q\&. The projection is computed with at most two iterations of the classical Gram-Schmidt algorithm, see * L\&. Giraud, J\&. Langou, M\&. Rozložník\&. 'On the round-off error analysis of the Gram-Schmidt algorithm with reorthogonalization\&.' 2002\&. CERFACS Technical Report No\&. TR/PA/02/33\&. URL: https://www\&.cerfacs\&.fr/algor/reports/2002/TR_PA_02_33\&.pdf .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIM1\fP .PP .nf M1 is INTEGER The dimension of X1 and the number of rows in Q1\&. 0 <= M1\&. .fi .PP .br \fIM2\fP .PP .nf M2 is INTEGER The dimension of X2 and the number of rows in Q2\&. 0 <= M2\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The number of columns in Q1 and Q2\&. 0 <= N\&. .fi .PP .br \fIX1\fP .PP .nf X1 is DOUBLE PRECISION array, dimension (M1) On entry, the top part of the vector to be orthogonalized\&. On exit, the top part of the projected vector\&. .fi .PP .br \fIINCX1\fP .PP .nf INCX1 is INTEGER Increment for entries of X1\&. .fi .PP .br \fIX2\fP .PP .nf X2 is DOUBLE PRECISION array, dimension (M2) On entry, the bottom part of the vector to be orthogonalized\&. On exit, the bottom part of the projected vector\&. .fi .PP .br \fIINCX2\fP .PP .nf INCX2 is INTEGER Increment for entries of X2\&. .fi .PP .br \fIQ1\fP .PP .nf Q1 is DOUBLE PRECISION array, dimension (LDQ1, N) The top part of the orthonormal basis matrix\&. .fi .PP .br \fILDQ1\fP .PP .nf LDQ1 is INTEGER The leading dimension of Q1\&. LDQ1 >= M1\&. .fi .PP .br \fIQ2\fP .PP .nf Q2 is DOUBLE PRECISION array, dimension (LDQ2, N) The bottom part of the orthonormal basis matrix\&. .fi .PP .br \fILDQ2\fP .PP .nf LDQ2 is INTEGER The leading dimension of Q2\&. LDQ2 >= M2\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is DOUBLE PRECISION array, dimension (LWORK) .fi .PP .br \fILWORK\fP .PP .nf LWORK is INTEGER The dimension of the array WORK\&. LWORK >= 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 .SS "subroutine sorbdb6 (integer m1, integer m2, integer n, real, dimension(*) x1, integer incx1, real, dimension(*) x2, integer incx2, real, dimension(ldq1,*) q1, integer ldq1, real, dimension(ldq2,*) q2, integer ldq2, real, dimension(*) work, integer lwork, integer info)" .PP \fBSORBDB6\fP .PP \fBPurpose:\fP .RS 4 .PP .nf SORBDB6 orthogonalizes the column vector X = [ X1 ] [ X2 ] with respect to the columns of Q = [ Q1 ] \&. [ Q2 ] The columns of Q must be orthonormal\&. The orthogonalized vector will be zero if and only if it lies entirely in the range of Q\&. The projection is computed with at most two iterations of the classical Gram-Schmidt algorithm, see * L\&. Giraud, J\&. Langou, M\&. Rozložník\&. 'On the round-off error analysis of the Gram-Schmidt algorithm with reorthogonalization\&.' 2002\&. CERFACS Technical Report No\&. TR/PA/02/33\&. URL: https://www\&.cerfacs\&.fr/algor/reports/2002/TR_PA_02_33\&.pdf .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIM1\fP .PP .nf M1 is INTEGER The dimension of X1 and the number of rows in Q1\&. 0 <= M1\&. .fi .PP .br \fIM2\fP .PP .nf M2 is INTEGER The dimension of X2 and the number of rows in Q2\&. 0 <= M2\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The number of columns in Q1 and Q2\&. 0 <= N\&. .fi .PP .br \fIX1\fP .PP .nf X1 is REAL array, dimension (M1) On entry, the top part of the vector to be orthogonalized\&. On exit, the top part of the projected vector\&. .fi .PP .br \fIINCX1\fP .PP .nf INCX1 is INTEGER Increment for entries of X1\&. .fi .PP .br \fIX2\fP .PP .nf X2 is REAL array, dimension (M2) On entry, the bottom part of the vector to be orthogonalized\&. On exit, the bottom part of the projected vector\&. .fi .PP .br \fIINCX2\fP .PP .nf INCX2 is INTEGER Increment for entries of X2\&. .fi .PP .br \fIQ1\fP .PP .nf Q1 is REAL array, dimension (LDQ1, N) The top part of the orthonormal basis matrix\&. .fi .PP .br \fILDQ1\fP .PP .nf LDQ1 is INTEGER The leading dimension of Q1\&. LDQ1 >= M1\&. .fi .PP .br \fIQ2\fP .PP .nf Q2 is REAL array, dimension (LDQ2, N) The bottom part of the orthonormal basis matrix\&. .fi .PP .br \fILDQ2\fP .PP .nf LDQ2 is INTEGER The leading dimension of Q2\&. LDQ2 >= M2\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is REAL array, dimension (LWORK) .fi .PP .br \fILWORK\fP .PP .nf LWORK is INTEGER The dimension of the array WORK\&. LWORK >= 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 .SS "subroutine zunbdb6 (integer m1, integer m2, integer n, complex*16, dimension(*) x1, integer incx1, complex*16, dimension(*) x2, integer incx2, complex*16, dimension(ldq1,*) q1, integer ldq1, complex*16, dimension(ldq2,*) q2, integer ldq2, complex*16, dimension(*) work, integer lwork, integer info)" .PP \fBZUNBDB6\fP .PP \fBPurpose:\fP .RS 4 .PP .nf ZUNBDB6 orthogonalizes the column vector X = [ X1 ] [ X2 ] with respect to the columns of Q = [ Q1 ] \&. [ Q2 ] The columns of Q must be orthonormal\&. The orthogonalized vector will be zero if and only if it lies entirely in the range of Q\&. The projection is computed with at most two iterations of the classical Gram-Schmidt algorithm, see * L\&. Giraud, J\&. Langou, M\&. Rozložník\&. 'On the round-off error analysis of the Gram-Schmidt algorithm with reorthogonalization\&.' 2002\&. CERFACS Technical Report No\&. TR/PA/02/33\&. URL: https://www\&.cerfacs\&.fr/algor/reports/2002/TR_PA_02_33\&.pdf .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIM1\fP .PP .nf M1 is INTEGER The dimension of X1 and the number of rows in Q1\&. 0 <= M1\&. .fi .PP .br \fIM2\fP .PP .nf M2 is INTEGER The dimension of X2 and the number of rows in Q2\&. 0 <= M2\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The number of columns in Q1 and Q2\&. 0 <= N\&. .fi .PP .br \fIX1\fP .PP .nf X1 is COMPLEX*16 array, dimension (M1) On entry, the top part of the vector to be orthogonalized\&. On exit, the top part of the projected vector\&. .fi .PP .br \fIINCX1\fP .PP .nf INCX1 is INTEGER Increment for entries of X1\&. .fi .PP .br \fIX2\fP .PP .nf X2 is COMPLEX*16 array, dimension (M2) On entry, the bottom part of the vector to be orthogonalized\&. On exit, the bottom part of the projected vector\&. .fi .PP .br \fIINCX2\fP .PP .nf INCX2 is INTEGER Increment for entries of X2\&. .fi .PP .br \fIQ1\fP .PP .nf Q1 is COMPLEX*16 array, dimension (LDQ1, N) The top part of the orthonormal basis matrix\&. .fi .PP .br \fILDQ1\fP .PP .nf LDQ1 is INTEGER The leading dimension of Q1\&. LDQ1 >= M1\&. .fi .PP .br \fIQ2\fP .PP .nf Q2 is COMPLEX*16 array, dimension (LDQ2, N) The bottom part of the orthonormal basis matrix\&. .fi .PP .br \fILDQ2\fP .PP .nf LDQ2 is INTEGER The leading dimension of Q2\&. LDQ2 >= M2\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is COMPLEX*16 array, dimension (LWORK) .fi .PP .br \fILWORK\fP .PP .nf LWORK is INTEGER The dimension of the array WORK\&. LWORK >= 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 .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.