unbdb5 - {un,or}bdb5: step in uncsd2by1

Generated automatically by Doxygen for LAPACK from the source code. Version 3.12.0 Sun Jul 20 2025 01:40:05 unbdb5(3)

subroutinecunbdb5(integerm1,integerm2,integern,complex,dimension(*)x1,integerincx1,complex,dimension(*)x2,integerincx2,complex,dimension(ldq1,*)q1,integerldq1,complex,dimension(ldq2,*)q2,integerldq2,complex,dimension(*)work,integerlwork,integerinfo)CUNBDB5Purpose: CUNBDB5 orthogonalizes the column vector X = [ X1 ] [ X2 ] with respect to the columns of Q = [ Q1 ] . [ Q2 ] The columns of Q must be orthonormal. If the projection is zero according to Kahan's 'twice is enough' criterion, then some other vector from the orthogonal complement is returned. This vector is chosen in an arbitrary but deterministic way. ParametersM1 M1 is INTEGER The dimension of X1 and the number of rows in Q1. 0 <= M1. M2 M2 is INTEGER The dimension of X2 and the number of rows in Q2. 0 <= M2. N N is INTEGER The number of columns in Q1 and Q2. 0 <= N. X1 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. INCX1 INCX1 is INTEGER Increment for entries of X1. X2 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. INCX2 INCX2 is INTEGER Increment for entries of X2. Q1 Q1 is COMPLEX array, dimension (LDQ1, N) The top part of the orthonormal basis matrix. LDQ1 LDQ1 is INTEGER The leading dimension of Q1. LDQ1 >= M1. Q2 Q2 is COMPLEX array, dimension (LDQ2, N) The bottom part of the orthonormal basis matrix. LDQ2 LDQ2 is INTEGER The leading dimension of Q2. LDQ2 >= M2. WORK WORK is COMPLEX array, dimension (LWORK) LWORK LWORK is INTEGER The dimension of the array WORK. LWORK >= N. INFO INFO is INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. subroutinedorbdb5(integerm1,integerm2,integern,doubleprecision,dimension(*)x1,integerincx1,doubleprecision,dimension(*)x2,integerincx2,doubleprecision,dimension(ldq1,*)q1,integerldq1,doubleprecision,dimension(ldq2,*)q2,integerldq2,doubleprecision,dimension(*)work,integerlwork,integerinfo)DORBDB5Purpose: DORBDB5 orthogonalizes the column vector X = [ X1 ] [ X2 ] with respect to the columns of Q = [ Q1 ] . [ Q2 ] The columns of Q must be orthonormal. If the projection is zero according to Kahan's 'twice is enough' criterion, then some other vector from the orthogonal complement is returned. This vector is chosen in an arbitrary but deterministic way. ParametersM1 M1 is INTEGER The dimension of X1 and the number of rows in Q1. 0 <= M1. M2 M2 is INTEGER The dimension of X2 and the number of rows in Q2. 0 <= M2. N N is INTEGER The number of columns in Q1 and Q2. 0 <= N. X1 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. INCX1 INCX1 is INTEGER Increment for entries of X1. X2 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. INCX2 INCX2 is INTEGER Increment for entries of X2. Q1 Q1 is DOUBLE PRECISION array, dimension (LDQ1, N) The top part of the orthonormal basis matrix. LDQ1 LDQ1 is INTEGER The leading dimension of Q1. LDQ1 >= M1. Q2 Q2 is DOUBLE PRECISION array, dimension (LDQ2, N) The bottom part of the orthonormal basis matrix. LDQ2 LDQ2 is INTEGER The leading dimension of Q2. LDQ2 >= M2. WORK WORK is DOUBLE PRECISION array, dimension (LWORK) LWORK LWORK is INTEGER The dimension of the array WORK. LWORK >= N. INFO INFO is INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. subroutinesorbdb5(integerm1,integerm2,integern,real,dimension(*)x1,integerincx1,real,dimension(*)x2,integerincx2,real,dimension(ldq1,*)q1,integerldq1,real,dimension(ldq2,*)q2,integerldq2,real,dimension(*)work,integerlwork,integerinfo)SORBDB5Purpose: SORBDB5 orthogonalizes the column vector X = [ X1 ] [ X2 ] with respect to the columns of Q = [ Q1 ] . [ Q2 ] The columns of Q must be orthonormal. If the projection is zero according to Kahan's 'twice is enough' criterion, then some other vector from the orthogonal complement is returned. This vector is chosen in an arbitrary but deterministic way. ParametersM1 M1 is INTEGER The dimension of X1 and the number of rows in Q1. 0 <= M1. M2 M2 is INTEGER The dimension of X2 and the number of rows in Q2. 0 <= M2. N N is INTEGER The number of columns in Q1 and Q2. 0 <= N. X1 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. INCX1 INCX1 is INTEGER Increment for entries of X1. X2 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. INCX2 INCX2 is INTEGER Increment for entries of X2. Q1 Q1 is REAL array, dimension (LDQ1, N) The top part of the orthonormal basis matrix. LDQ1 LDQ1 is INTEGER The leading dimension of Q1. LDQ1 >= M1. Q2 Q2 is REAL array, dimension (LDQ2, N) The bottom part of the orthonormal basis matrix. LDQ2 LDQ2 is INTEGER The leading dimension of Q2. LDQ2 >= M2. WORK WORK is REAL array, dimension (LWORK) LWORK LWORK is INTEGER The dimension of the array WORK. LWORK >= N. INFO INFO is INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. subroutinezunbdb5(integerm1,integerm2,integern,complex*16,dimension(*)x1,integerincx1,complex*16,dimension(*)x2,integerincx2,complex*16,dimension(ldq1,*)q1,integerldq1,complex*16,dimension(ldq2,*)q2,integerldq2,complex*16,dimension(*)work,integerlwork,integerinfo)ZUNBDB5Purpose: ZUNBDB5 orthogonalizes the column vector X = [ X1 ] [ X2 ] with respect to the columns of Q = [ Q1 ] . [ Q2 ] The columns of Q must be orthonormal. If the projection is zero according to Kahan's 'twice is enough' criterion, then some other vector from the orthogonal complement is returned. This vector is chosen in an arbitrary but deterministic way. ParametersM1 M1 is INTEGER The dimension of X1 and the number of rows in Q1. 0 <= M1. M2 M2 is INTEGER The dimension of X2 and the number of rows in Q2. 0 <= M2. N N is INTEGER The number of columns in Q1 and Q2. 0 <= N. X1 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. INCX1 INCX1 is INTEGER Increment for entries of X1. X2 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. INCX2 INCX2 is INTEGER Increment for entries of X2. Q1 Q1 is COMPLEX*16 array, dimension (LDQ1, N) The top part of the orthonormal basis matrix. LDQ1 LDQ1 is INTEGER The leading dimension of Q1. LDQ1 >= M1. Q2 Q2 is COMPLEX*16 array, dimension (LDQ2, N) The bottom part of the orthonormal basis matrix. LDQ2 LDQ2 is INTEGER The leading dimension of Q2. LDQ2 >= M2. WORK WORK is COMPLEX*16 array, dimension (LWORK) LWORK LWORK is INTEGER The dimension of the array WORK. LWORK >= N. INFO INFO is INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.

unbdb5 - {un,or}bdb5: step in uncsd2by1

Functions subroutine cunbdb5 (m1, m2, n, x1, incx1, x2, incx2, q1, ldq1, q2, ldq2, work, lwork, info) CUNBDB5 subroutine dorbdb5 (m1, m2, n, x1, incx1, x2, incx2, q1, ldq1, q2, ldq2, work, lwork, info) DORBDB5 subroutine sorbdb5 (m1, m2, n, x1, incx1, x2, incx2, q1, ldq1, q2, ldq2, work, lwork, info) SORBDB5 subroutine zunbdb5 (m1, m2, n, x1, incx1, x2, incx2, q1, ldq1, q2, ldq2, work, lwork, info) ZUNBDB5