.TH "tplqt" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME tplqt \- tplqt: QR factor .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBctplqt\fP (m, n, l, mb, a, lda, b, ldb, t, ldt, work, info)" .br .RI "\fBCTPLQT\fP " .ti -1c .RI "subroutine \fBdtplqt\fP (m, n, l, mb, a, lda, b, ldb, t, ldt, work, info)" .br .RI "\fBDTPLQT\fP " .ti -1c .RI "subroutine \fBstplqt\fP (m, n, l, mb, a, lda, b, ldb, t, ldt, work, info)" .br .RI "\fBSTPLQT\fP " .ti -1c .RI "subroutine \fBztplqt\fP (m, n, l, mb, a, lda, b, ldb, t, ldt, work, info)" .br .RI "\fBZTPLQT\fP " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "subroutine ctplqt (integer m, integer n, integer l, integer mb, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( ldt, * ) t, integer ldt, complex, dimension( * ) work, integer info)" .PP \fBCTPLQT\fP .PP \fBPurpose:\fP .RS 4 .PP .nf CTPLQT computes a blocked LQ factorization of a complex 'triangular-pentagonal' matrix C, which is composed of a triangular block A and pentagonal block B, using the compact WY representation for Q\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIM\fP .PP .nf M is INTEGER The number of rows of the matrix B, and the order of the triangular matrix A\&. M >= 0\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The number of columns of the matrix B\&. N >= 0\&. .fi .PP .br \fIL\fP .PP .nf L is INTEGER The number of rows of the lower trapezoidal part of B\&. MIN(M,N) >= L >= 0\&. See Further Details\&. .fi .PP .br \fIMB\fP .PP .nf MB is INTEGER The block size to be used in the blocked QR\&. M >= MB >= 1\&. .fi .PP .br \fIA\fP .PP .nf A is COMPLEX array, dimension (LDA,M) On entry, the lower triangular M-by-M matrix A\&. On exit, the elements on and below the diagonal of the array contain the lower triangular matrix L\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER The leading dimension of the array A\&. LDA >= max(1,M)\&. .fi .PP .br \fIB\fP .PP .nf B is COMPLEX array, dimension (LDB,N) On entry, the pentagonal M-by-N matrix B\&. The first N-L columns are rectangular, and the last L columns are lower trapezoidal\&. On exit, B contains the pentagonal matrix V\&. See Further Details\&. .fi .PP .br \fILDB\fP .PP .nf LDB is INTEGER The leading dimension of the array B\&. LDB >= max(1,M)\&. .fi .PP .br \fIT\fP .PP .nf T is COMPLEX array, dimension (LDT,N) The lower triangular block reflectors stored in compact form as a sequence of upper triangular blocks\&. See Further Details\&. .fi .PP .br \fILDT\fP .PP .nf LDT is INTEGER The leading dimension of the array T\&. LDT >= MB\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is COMPLEX array, dimension (MB*M) .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 input matrix C is a M-by-(M+N) matrix C = [ A ] [ B ] where A is an lower triangular M-by-M matrix, and B is M-by-N pentagonal matrix consisting of a M-by-(N-L) rectangular matrix B1 on left of a M-by-L upper trapezoidal matrix B2: [ B ] = [ B1 ] [ B2 ] [ B1 ] <- M-by-(N-L) rectangular [ B2 ] <- M-by-L lower trapezoidal\&. The lower trapezoidal matrix B2 consists of the first L columns of a M-by-M lower triangular matrix, where 0 <= L <= MIN(M,N)\&. If L=0, B is rectangular M-by-N; if M=L=N, B is lower triangular\&. The matrix W stores the elementary reflectors H(i) in the i-th row above the diagonal (of A) in the M-by-(M+N) input matrix C [ C ] = [ A ] [ B ] [ A ] <- lower triangular M-by-M [ B ] <- M-by-N pentagonal so that W can be represented as [ W ] = [ I ] [ V ] [ I ] <- identity, M-by-M [ V ] <- M-by-N, same form as B\&. Thus, all of information needed for W is contained on exit in B, which we call V above\&. Note that V has the same form as B; that is, [ V ] = [ V1 ] [ V2 ] [ V1 ] <- M-by-(N-L) rectangular [ V2 ] <- M-by-L lower trapezoidal\&. The rows of V represent the vectors which define the H(i)'s\&. The number of blocks is B = ceiling(M/MB), where each block is of order MB except for the last block, which is of order IB = M - (M-1)*MB\&. For each of the B blocks, a upper triangular block reflector factor is computed: T1, T2, \&.\&.\&., TB\&. The MB-by-MB (and IB-by-IB for the last block) T's are stored in the MB-by-N matrix T as T = [T1 T2 \&.\&.\&. TB]\&. .fi .PP .RE .PP .PP Definition at line \fB172\fP of file \fBctplqt\&.f\fP\&. .SS "subroutine dtplqt (integer m, integer n, integer l, integer mb, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( ldt, * ) t, integer ldt, double precision, dimension( * ) work, integer info)" .PP \fBDTPLQT\fP .PP \fBPurpose:\fP .RS 4 .PP .nf DTPLQT computes a blocked LQ factorization of a real 'triangular-pentagonal' matrix C, which is composed of a triangular block A and pentagonal block B, using the compact WY representation for Q\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIM\fP .PP .nf M is INTEGER The number of rows of the matrix B, and the order of the triangular matrix A\&. M >= 0\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The number of columns of the matrix B\&. N >= 0\&. .fi .PP .br \fIL\fP .PP .nf L is INTEGER The number of rows of the lower trapezoidal part of B\&. MIN(M,N) >= L >= 0\&. See Further Details\&. .fi .PP .br \fIMB\fP .PP .nf MB is INTEGER The block size to be used in the blocked QR\&. M >= MB >= 1\&. .fi .PP .br \fIA\fP .PP .nf A is DOUBLE PRECISION array, dimension (LDA,M) On entry, the lower triangular M-by-M matrix A\&. On exit, the elements on and below the diagonal of the array contain the lower triangular matrix L\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER The leading dimension of the array A\&. LDA >= max(1,M)\&. .fi .PP .br \fIB\fP .PP .nf B is DOUBLE PRECISION array, dimension (LDB,N) On entry, the pentagonal M-by-N matrix B\&. The first N-L columns are rectangular, and the last L columns are lower trapezoidal\&. On exit, B contains the pentagonal matrix V\&. See Further Details\&. .fi .PP .br \fILDB\fP .PP .nf LDB is INTEGER The leading dimension of the array B\&. LDB >= max(1,M)\&. .fi .PP .br \fIT\fP .PP .nf T is DOUBLE PRECISION array, dimension (LDT,N) The lower triangular block reflectors stored in compact form as a sequence of upper triangular blocks\&. See Further Details\&. .fi .PP .br \fILDT\fP .PP .nf LDT is INTEGER The leading dimension of the array T\&. LDT >= MB\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is DOUBLE PRECISION array, dimension (MB*M) .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 input matrix C is a M-by-(M+N) matrix C = [ A ] [ B ] where A is an lower triangular M-by-M matrix, and B is M-by-N pentagonal matrix consisting of a M-by-(N-L) rectangular matrix B1 on left of a M-by-L upper trapezoidal matrix B2: [ B ] = [ B1 ] [ B2 ] [ B1 ] <- M-by-(N-L) rectangular [ B2 ] <- M-by-L lower trapezoidal\&. The lower trapezoidal matrix B2 consists of the first L columns of a M-by-M lower triangular matrix, where 0 <= L <= MIN(M,N)\&. If L=0, B is rectangular M-by-N; if M=L=N, B is lower triangular\&. The matrix W stores the elementary reflectors H(i) in the i-th row above the diagonal (of A) in the M-by-(M+N) input matrix C [ C ] = [ A ] [ B ] [ A ] <- lower triangular M-by-M [ B ] <- M-by-N pentagonal so that W can be represented as [ W ] = [ I ] [ V ] [ I ] <- identity, M-by-M [ V ] <- M-by-N, same form as B\&. Thus, all of information needed for W is contained on exit in B, which we call V above\&. Note that V has the same form as B; that is, [ V ] = [ V1 ] [ V2 ] [ V1 ] <- M-by-(N-L) rectangular [ V2 ] <- M-by-L lower trapezoidal\&. The rows of V represent the vectors which define the H(i)'s\&. The number of blocks is B = ceiling(M/MB), where each block is of order MB except for the last block, which is of order IB = M - (M-1)*MB\&. For each of the B blocks, a upper triangular block reflector factor is computed: T1, T2, \&.\&.\&., TB\&. The MB-by-MB (and IB-by-IB for the last block) T's are stored in the MB-by-N matrix T as T = [T1 T2 \&.\&.\&. TB]\&. .fi .PP .RE .PP .PP Definition at line \fB187\fP of file \fBdtplqt\&.f\fP\&. .SS "subroutine stplqt (integer m, integer n, integer l, integer mb, real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, real, dimension( ldt, * ) t, integer ldt, real, dimension( * ) work, integer info)" .PP \fBSTPLQT\fP .PP \fBPurpose:\fP .RS 4 .PP .nf STPLQT computes a blocked LQ factorization of a real 'triangular-pentagonal' matrix C, which is composed of a triangular block A and pentagonal block B, using the compact WY representation for Q\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIM\fP .PP .nf M is INTEGER The number of rows of the matrix B, and the order of the triangular matrix A\&. M >= 0\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The number of columns of the matrix B\&. N >= 0\&. .fi .PP .br \fIL\fP .PP .nf L is INTEGER The number of rows of the lower trapezoidal part of B\&. MIN(M,N) >= L >= 0\&. See Further Details\&. .fi .PP .br \fIMB\fP .PP .nf MB is INTEGER The block size to be used in the blocked QR\&. M >= MB >= 1\&. .fi .PP .br \fIA\fP .PP .nf A is REAL array, dimension (LDA,M) On entry, the lower triangular M-by-M matrix A\&. On exit, the elements on and below the diagonal of the array contain the lower triangular matrix L\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER The leading dimension of the array A\&. LDA >= max(1,M)\&. .fi .PP .br \fIB\fP .PP .nf B is REAL array, dimension (LDB,N) On entry, the pentagonal M-by-N matrix B\&. The first N-L columns are rectangular, and the last L columns are lower trapezoidal\&. On exit, B contains the pentagonal matrix V\&. See Further Details\&. .fi .PP .br \fILDB\fP .PP .nf LDB is INTEGER The leading dimension of the array B\&. LDB >= max(1,M)\&. .fi .PP .br \fIT\fP .PP .nf T is REAL array, dimension (LDT,N) The lower triangular block reflectors stored in compact form as a sequence of upper triangular blocks\&. See Further Details\&. .fi .PP .br \fILDT\fP .PP .nf LDT is INTEGER The leading dimension of the array T\&. LDT >= MB\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is REAL array, dimension (MB*M) .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 input matrix C is a M-by-(M+N) matrix C = [ A ] [ B ] where A is an lower triangular M-by-M matrix, and B is M-by-N pentagonal matrix consisting of a M-by-(N-L) rectangular matrix B1 on left of a M-by-L upper trapezoidal matrix B2: [ B ] = [ B1 ] [ B2 ] [ B1 ] <- M-by-(N-L) rectangular [ B2 ] <- M-by-L lower trapezoidal\&. The lower trapezoidal matrix B2 consists of the first L columns of a M-by-M lower triangular matrix, where 0 <= L <= MIN(M,N)\&. If L=0, B is rectangular M-by-N; if M=L=N, B is lower triangular\&. The matrix W stores the elementary reflectors H(i) in the i-th row above the diagonal (of A) in the M-by-(M+N) input matrix C [ C ] = [ A ] [ B ] [ A ] <- lower triangular M-by-M [ B ] <- M-by-N pentagonal so that W can be represented as [ W ] = [ I ] [ V ] [ I ] <- identity, M-by-M [ V ] <- M-by-N, same form as B\&. Thus, all of information needed for W is contained on exit in B, which we call V above\&. Note that V has the same form as B; that is, [ V ] = [ V1 ] [ V2 ] [ V1 ] <- M-by-(N-L) rectangular [ V2 ] <- M-by-L lower trapezoidal\&. The rows of V represent the vectors which define the H(i)'s\&. The number of blocks is B = ceiling(M/MB), where each block is of order MB except for the last block, which is of order IB = M - (M-1)*MB\&. For each of the B blocks, a upper triangular block reflector factor is computed: T1, T2, \&.\&.\&., TB\&. The MB-by-MB (and IB-by-IB for the last block) T's are stored in the MB-by-N matrix T as T = [T1 T2 \&.\&.\&. TB]\&. .fi .PP .RE .PP .PP Definition at line \fB187\fP of file \fBstplqt\&.f\fP\&. .SS "subroutine ztplqt (integer m, integer n, integer l, integer mb, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( ldt, * ) t, integer ldt, complex*16, dimension( * ) work, integer info)" .PP \fBZTPLQT\fP .PP \fBPurpose:\fP .RS 4 .PP .nf ZTPLQT computes a blocked LQ factorization of a complex 'triangular-pentagonal' matrix C, which is composed of a triangular block A and pentagonal block B, using the compact WY representation for Q\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIM\fP .PP .nf M is INTEGER The number of rows of the matrix B, and the order of the triangular matrix A\&. M >= 0\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The number of columns of the matrix B\&. N >= 0\&. .fi .PP .br \fIL\fP .PP .nf L is INTEGER The number of rows of the lower trapezoidal part of B\&. MIN(M,N) >= L >= 0\&. See Further Details\&. .fi .PP .br \fIMB\fP .PP .nf MB is INTEGER The block size to be used in the blocked QR\&. M >= MB >= 1\&. .fi .PP .br \fIA\fP .PP .nf A is COMPLEX*16 array, dimension (LDA,M) On entry, the lower triangular M-by-M matrix A\&. On exit, the elements on and below the diagonal of the array contain the lower triangular matrix L\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER The leading dimension of the array A\&. LDA >= max(1,M)\&. .fi .PP .br \fIB\fP .PP .nf B is COMPLEX*16 array, dimension (LDB,N) On entry, the pentagonal M-by-N matrix B\&. The first N-L columns are rectangular, and the last L columns are lower trapezoidal\&. On exit, B contains the pentagonal matrix V\&. See Further Details\&. .fi .PP .br \fILDB\fP .PP .nf LDB is INTEGER The leading dimension of the array B\&. LDB >= max(1,M)\&. .fi .PP .br \fIT\fP .PP .nf T is COMPLEX*16 array, dimension (LDT,N) The lower triangular block reflectors stored in compact form as a sequence of upper triangular blocks\&. See Further Details\&. .fi .PP .br \fILDT\fP .PP .nf LDT is INTEGER The leading dimension of the array T\&. LDT >= MB\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is COMPLEX*16 array, dimension (MB*M) .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 input matrix C is a M-by-(M+N) matrix C = [ A ] [ B ] where A is an lower triangular M-by-M matrix, and B is M-by-N pentagonal matrix consisting of a M-by-(N-L) rectangular matrix B1 on left of a M-by-L upper trapezoidal matrix B2: [ B ] = [ B1 ] [ B2 ] [ B1 ] <- M-by-(N-L) rectangular [ B2 ] <- M-by-L lower trapezoidal\&. The lower trapezoidal matrix B2 consists of the first L columns of a M-by-M lower triangular matrix, where 0 <= L <= MIN(M,N)\&. If L=0, B is rectangular M-by-N; if M=L=N, B is lower triangular\&. The matrix W stores the elementary reflectors H(i) in the i-th row above the diagonal (of A) in the M-by-(M+N) input matrix C [ C ] = [ A ] [ B ] [ A ] <- lower triangular M-by-M [ B ] <- M-by-N pentagonal so that W can be represented as [ W ] = [ I ] [ V ] [ I ] <- identity, M-by-M [ V ] <- M-by-N, same form as B\&. Thus, all of information needed for W is contained on exit in B, which we call V above\&. Note that V has the same form as B; that is, [ V ] = [ V1 ] [ V2 ] [ V1 ] <- M-by-(N-L) rectangular [ V2 ] <- M-by-L lower trapezoidal\&. The rows of V represent the vectors which define the H(i)'s\&. The number of blocks is B = ceiling(M/MB), where each block is of order MB except for the last block, which is of order IB = M - (M-1)*MB\&. For each of the B blocks, a upper triangular block reflector factor is computed: T1, T2, \&.\&.\&., TB\&. The MB-by-MB (and IB-by-IB for the last block) T's are stored in the MB-by-N matrix T as T = [T1 T2 \&.\&.\&. TB]\&. .fi .PP .RE .PP .PP Definition at line \fB187\fP of file \fBztplqt\&.f\fP\&. .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.