.TH "geqrt" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME geqrt \- geqrt: QR factor, with T .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBcgeqrt\fP (m, n, nb, a, lda, t, ldt, work, info)" .br .RI "\fBCGEQRT\fP " .ti -1c .RI "subroutine \fBdgeqrt\fP (m, n, nb, a, lda, t, ldt, work, info)" .br .RI "\fBDGEQRT\fP " .ti -1c .RI "subroutine \fBsgeqrt\fP (m, n, nb, a, lda, t, ldt, work, info)" .br .RI "\fBSGEQRT\fP " .ti -1c .RI "subroutine \fBzgeqrt\fP (m, n, nb, a, lda, t, ldt, work, info)" .br .RI "\fBZGEQRT\fP " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "subroutine cgeqrt (integer m, integer n, integer nb, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldt, * ) t, integer ldt, complex, dimension( * ) work, integer info)" .PP \fBCGEQRT\fP .PP \fBPurpose:\fP .RS 4 .PP .nf CGEQRT computes a blocked QR factorization of a complex M-by-N matrix A using the compact WY representation of Q\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIM\fP .PP .nf M is INTEGER The number of rows of the matrix A\&. M >= 0\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The number of columns of the matrix A\&. N >= 0\&. .fi .PP .br \fINB\fP .PP .nf NB is INTEGER The block size to be used in the blocked QR\&. MIN(M,N) >= NB >= 1\&. .fi .PP .br \fIA\fP .PP .nf A is COMPLEX array, dimension (LDA,N) On entry, the M-by-N matrix A\&. On exit, the elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if M >= N); the elements below the diagonal are the columns of V\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER The leading dimension of the array A\&. LDA >= max(1,M)\&. .fi .PP .br \fIT\fP .PP .nf T is COMPLEX array, dimension (LDT,MIN(M,N)) The upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks\&. See below for further details\&. .fi .PP .br \fILDT\fP .PP .nf LDT is INTEGER The leading dimension of the array T\&. LDT >= NB\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is COMPLEX array, dimension (NB*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 matrix V stores the elementary reflectors H(i) in the i-th column below the diagonal\&. For example, if M=5 and N=3, the matrix V is V = ( 1 ) ( v1 1 ) ( v1 v2 1 ) ( v1 v2 v3 ) ( v1 v2 v3 ) where the vi's represent the vectors which define H(i), which are returned in the matrix A\&. The 1's along the diagonal of V are not stored in A\&. Let K=MIN(M,N)\&. The number of blocks is B = ceiling(K/NB), where each block is of order NB except for the last block, which is of order IB = K - (B-1)*NB\&. For each of the B blocks, a upper triangular block reflector factor is computed: T1, T2, \&.\&.\&., TB\&. The NB-by-NB (and IB-by-IB for the last block) T's are stored in the NB-by-K matrix T as T = (T1 T2 \&.\&.\&. TB)\&. .fi .PP .RE .PP .SS "subroutine dgeqrt (integer m, integer n, integer nb, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldt, * ) t, integer ldt, double precision, dimension( * ) work, integer info)" .PP \fBDGEQRT\fP .PP \fBPurpose:\fP .RS 4 .PP .nf DGEQRT computes a blocked QR factorization of a real M-by-N matrix A using the compact WY representation of Q\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIM\fP .PP .nf M is INTEGER The number of rows of the matrix A\&. M >= 0\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The number of columns of the matrix A\&. N >= 0\&. .fi .PP .br \fINB\fP .PP .nf NB is INTEGER The block size to be used in the blocked QR\&. MIN(M,N) >= NB >= 1\&. .fi .PP .br \fIA\fP .PP .nf A is DOUBLE PRECISION array, dimension (LDA,N) On entry, the M-by-N matrix A\&. On exit, the elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if M >= N); the elements below the diagonal are the columns of V\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER The leading dimension of the array A\&. LDA >= max(1,M)\&. .fi .PP .br \fIT\fP .PP .nf T is DOUBLE PRECISION array, dimension (LDT,MIN(M,N)) The upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks\&. See below for further details\&. .fi .PP .br \fILDT\fP .PP .nf LDT is INTEGER The leading dimension of the array T\&. LDT >= NB\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is DOUBLE PRECISION array, dimension (NB*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 matrix V stores the elementary reflectors H(i) in the i-th column below the diagonal\&. For example, if M=5 and N=3, the matrix V is V = ( 1 ) ( v1 1 ) ( v1 v2 1 ) ( v1 v2 v3 ) ( v1 v2 v3 ) where the vi's represent the vectors which define H(i), which are returned in the matrix A\&. The 1's along the diagonal of V are not stored in A\&. Let K=MIN(M,N)\&. The number of blocks is B = ceiling(K/NB), where each block is of order NB except for the last block, which is of order IB = K - (B-1)*NB\&. For each of the B blocks, a upper triangular block reflector factor is computed: T1, T2, \&.\&.\&., TB\&. The NB-by-NB (and IB-by-IB for the last block) T's are stored in the NB-by-K matrix T as T = (T1 T2 \&.\&.\&. TB)\&. .fi .PP .RE .PP .SS "subroutine sgeqrt (integer m, integer n, integer nb, real, dimension( lda, * ) a, integer lda, real, dimension( ldt, * ) t, integer ldt, real, dimension( * ) work, integer info)" .PP \fBSGEQRT\fP .PP \fBPurpose:\fP .RS 4 .PP .nf SGEQRT computes a blocked QR factorization of a real M-by-N matrix A using the compact WY representation of Q\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIM\fP .PP .nf M is INTEGER The number of rows of the matrix A\&. M >= 0\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The number of columns of the matrix A\&. N >= 0\&. .fi .PP .br \fINB\fP .PP .nf NB is INTEGER The block size to be used in the blocked QR\&. MIN(M,N) >= NB >= 1\&. .fi .PP .br \fIA\fP .PP .nf A is REAL array, dimension (LDA,N) On entry, the M-by-N matrix A\&. On exit, the elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if M >= N); the elements below the diagonal are the columns of V\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER The leading dimension of the array A\&. LDA >= max(1,M)\&. .fi .PP .br \fIT\fP .PP .nf T is REAL array, dimension (LDT,MIN(M,N)) The upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks\&. See below for further details\&. .fi .PP .br \fILDT\fP .PP .nf LDT is INTEGER The leading dimension of the array T\&. LDT >= NB\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is REAL array, dimension (NB*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 matrix V stores the elementary reflectors H(i) in the i-th column below the diagonal\&. For example, if M=5 and N=3, the matrix V is V = ( 1 ) ( v1 1 ) ( v1 v2 1 ) ( v1 v2 v3 ) ( v1 v2 v3 ) where the vi's represent the vectors which define H(i), which are returned in the matrix A\&. The 1's along the diagonal of V are not stored in A\&. Let K=MIN(M,N)\&. The number of blocks is B = ceiling(K/NB), where each block is of order NB except for the last block, which is of order IB = K - (B-1)*NB\&. For each of the B blocks, a upper triangular block reflector factor is computed: T1, T2, \&.\&.\&., TB\&. The NB-by-NB (and IB-by-IB for the last block) T's are stored in the NB-by-K matrix T as T = (T1 T2 \&.\&.\&. TB)\&. .fi .PP .RE .PP .SS "subroutine zgeqrt (integer m, integer n, integer nb, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldt, * ) t, integer ldt, complex*16, dimension( * ) work, integer info)" .PP \fBZGEQRT\fP .PP \fBPurpose:\fP .RS 4 .PP .nf ZGEQRT computes a blocked QR factorization of a complex M-by-N matrix A using the compact WY representation of Q\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIM\fP .PP .nf M is INTEGER The number of rows of the matrix A\&. M >= 0\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The number of columns of the matrix A\&. N >= 0\&. .fi .PP .br \fINB\fP .PP .nf NB is INTEGER The block size to be used in the blocked QR\&. MIN(M,N) >= NB >= 1\&. .fi .PP .br \fIA\fP .PP .nf A is COMPLEX*16 array, dimension (LDA,N) On entry, the M-by-N matrix A\&. On exit, the elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if M >= N); the elements below the diagonal are the columns of V\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER The leading dimension of the array A\&. LDA >= max(1,M)\&. .fi .PP .br \fIT\fP .PP .nf T is COMPLEX*16 array, dimension (LDT,MIN(M,N)) The upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks\&. See below for further details\&. .fi .PP .br \fILDT\fP .PP .nf LDT is INTEGER The leading dimension of the array T\&. LDT >= NB\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is COMPLEX*16 array, dimension (NB*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 matrix V stores the elementary reflectors H(i) in the i-th column below the diagonal\&. For example, if M=5 and N=3, the matrix V is V = ( 1 ) ( v1 1 ) ( v1 v2 1 ) ( v1 v2 v3 ) ( v1 v2 v3 ) where the vi's represent the vectors which define H(i), which are returned in the matrix A\&. The 1's along the diagonal of V are not stored in A\&. Let K=MIN(M,N)\&. The number of blocks is B = ceiling(K/NB), where each block is of order NB except for the last block, which is of order IB = K - (B-1)*NB\&. For each of the B blocks, a upper triangular block reflector factor is computed: T1, T2, \&.\&.\&., TB\&. The NB-by-NB (and IB-by-IB for the last block) T's are stored in the NB-by-K matrix T as T = (T1 T2 \&.\&.\&. TB)\&. .fi .PP .RE .PP .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.