tplqt - tplqt: QR factor

Generated automatically by Doxygen for LAPACK from the source code. Version 3.12.0 Thu Aug 7 2025 17:26:25 tplqt(3)

subroutinectplqt(integerm,integern,integerl,integermb,complex,dimension(lda,*)a,integerlda,complex,dimension(ldb,*)b,integerldb,complex,dimension(ldt,*)t,integerldt,complex,dimension(*)work,integerinfo)CTPLQTPurpose: 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. ParametersM M is INTEGER The number of rows of the matrix B, and the order of the triangular matrix A. M >= 0. N N is INTEGER The number of columns of the matrix B. N >= 0. L L is INTEGER The number of rows of the lower trapezoidal part of B. MIN(M,N) >= L >= 0. See Further Details. MB MB is INTEGER The block size to be used in the blocked QR. M >= MB >= 1. A 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. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). B 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. LDB LDB is INTEGER The leading dimension of the array B. LDB >= max(1,M). T 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. LDT LDT is INTEGER The leading dimension of the array T. LDT >= MB. WORK WORK is COMPLEX array, dimension (MB*M) 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. FurtherDetails: 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]. subroutinedtplqt(integerm,integern,integerl,integermb,doubleprecision,dimension(lda,*)a,integerlda,doubleprecision,dimension(ldb,*)b,integerldb,doubleprecision,dimension(ldt,*)t,integerldt,doubleprecision,dimension(*)work,integerinfo)DTPLQTPurpose: 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. ParametersM M is INTEGER The number of rows of the matrix B, and the order of the triangular matrix A. M >= 0. N N is INTEGER The number of columns of the matrix B. N >= 0. L L is INTEGER The number of rows of the lower trapezoidal part of B. MIN(M,N) >= L >= 0. See Further Details. MB MB is INTEGER The block size to be used in the blocked QR. M >= MB >= 1. A 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. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). B 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. LDB LDB is INTEGER The leading dimension of the array B. LDB >= max(1,M). T 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. LDT LDT is INTEGER The leading dimension of the array T. LDT >= MB. WORK WORK is DOUBLE PRECISION array, dimension (MB*M) 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. FurtherDetails: 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]. subroutinestplqt(integerm,integern,integerl,integermb,real,dimension(lda,*)a,integerlda,real,dimension(ldb,*)b,integerldb,real,dimension(ldt,*)t,integerldt,real,dimension(*)work,integerinfo)STPLQTPurpose: 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. ParametersM M is INTEGER The number of rows of the matrix B, and the order of the triangular matrix A. M >= 0. N N is INTEGER The number of columns of the matrix B. N >= 0. L L is INTEGER The number of rows of the lower trapezoidal part of B. MIN(M,N) >= L >= 0. See Further Details. MB MB is INTEGER The block size to be used in the blocked QR. M >= MB >= 1. A 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. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). B 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. LDB LDB is INTEGER The leading dimension of the array B. LDB >= max(1,M). T 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. LDT LDT is INTEGER The leading dimension of the array T. LDT >= MB. WORK WORK is REAL array, dimension (MB*M) 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. FurtherDetails: 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]. subroutineztplqt(integerm,integern,integerl,integermb,complex*16,dimension(lda,*)a,integerlda,complex*16,dimension(ldb,*)b,integerldb,complex*16,dimension(ldt,*)t,integerldt,complex*16,dimension(*)work,integerinfo)ZTPLQTPurpose: 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. ParametersM M is INTEGER The number of rows of the matrix B, and the order of the triangular matrix A. M >= 0. N N is INTEGER The number of columns of the matrix B. N >= 0. L L is INTEGER The number of rows of the lower trapezoidal part of B. MIN(M,N) >= L >= 0. See Further Details. MB MB is INTEGER The block size to be used in the blocked QR. M >= MB >= 1. A 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. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). B 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. LDB LDB is INTEGER The leading dimension of the array B. LDB >= max(1,M). T 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. LDT LDT is INTEGER The leading dimension of the array T. LDT >= MB. WORK WORK is COMPLEX*16 array, dimension (MB*M) 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. FurtherDetails: 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].

tplqt - tplqt: QR factor

Functions subroutine ctplqt (m, n, l, mb, a, lda, b, ldb, t, ldt, work, info) CTPLQT subroutine dtplqt (m, n, l, mb, a, lda, b, ldb, t, ldt, work, info) DTPLQT subroutine stplqt (m, n, l, mb, a, lda, b, ldb, t, ldt, work, info) STPLQT subroutine ztplqt (m, n, l, mb, a, lda, b, ldb, t, ldt, work, info) ZTPLQT